A Study of the Economics of ITNS in Cities



Economicsof theIntelligent Transportation Network SystemITNSJ. E. AndersonJune 2019A Study of the Economics of ITNS in CitiesJ. E. AndersonIntroductionThe purpose of this paper is to provide a generic examination of the economics of HCPRT networks of various sizes in cities of various total populations and population densities. To do so realistically, it is necessary to consider the variation in density from the Central Business District (CBD) outward. In the CBD, the population of interest is not the resident population, but the daytime population, which is generally considerably higher. Edwin S. Mills of Princeton University showed that a density distribution decreasing exponentially from the center is a good approximation of the density of many cities, so this model will be used. The PRT system for each city is modeled as a series of five square grid networks of increasing size. Each consists of mutually perpendicular lines with a station at the midpoint of each line segment that outlines a square. We assume a line spacing of half a mile, hence the stations on each line are half a mile apart and no point in the network area is farther than a quarter mile from a station. In the CBD it is likely that lines will be spaced closer together, perhaps averaging a quarter mile apart. In such cases, the modal split will be substantially higher than calculated in this paper, but of course at higher cost. While in any city the line spacing will be constrained by the street pattern and other factors so it can’t be expected to be uniform, the main factors that determine the mode split and hence the economics are the distances to stations rather than the specific topology of the layout. Next, it is necessary to model the variation of the number of vehicle trips per person per day as the network grows. This is done based on available data on this quantity. Then comes the difficult problem of estimating the modal split to the PRT system. We use the data summarized in the attached file “Ridership.doc” and develop a model that shows the mode split growing modestly as the network grows. Using these models, system characteristics needed for study of the economics and costs are calculated for nine cities in nine separate files “System Economics (i).xls, i=1…9.” All are U. S. cities, and a wide range of city sizes and densities has been selected. The results show, as expected, that the after-tax profit increases markedly as the network grows. Studies such as this are no substitute for detailed economic studies based on specific layouts of lines and stations but are useful to obtain a broad appreciation for the economics of PRT networks.Population Density ModelMathematically, Mills assumed(1)in which D is the density at the center (the core density), e is the base of the natural logarithm, r is the radius from the center, and (Gamma) is a constant.The population within a radius R of the center of the city is .(2)In which is the angle in radians that subtends the city. For example, if there are no natural barriers so that the city expands in all directions or 360o. If the city is located on a large body of water, such as Chicago or Milwaukee, The population of the whole city, P, is found by setting . Thus, (3)so equation (2) can be written in the form(4)Data in the file “PopulationStatistics.xls” gives the total population of cities and the population density within a stated land area. But, with the exponential model, the populated area has an infinite radius, so the population density would be zero. Thus, the figures for population density in the data file must be assumed to correspond to a finite area(5) which has a finite radius Rf. Let us assume that(6)so, from equation (4) from which(7)This equation can be solved by trial and error. The solution is Hence, from equation (5), and (8)Thus, the constant is a function only of the area of the city and the angle . Combining equations (4) and (6), the population within any radius is (11)in which, from equations (8), (12)So, with , Af , and given for a specific city, the population within a given radius R can be found from equation (11). From equations (3) and (6), the core population density is (13)Model of the PRT SystemThe PRT system will be assumed to be a square network with given line spacing and stations spaced midway between the intersections between the north-south and east-west lines. The network will be described by giving its side s. Its area is then An = s2. To determine the population within a network of a given area, we will assume that the radius to be substituted into equation (11) is (14)Internal Trips per Person per DayBy “internal trips” is meant the trips with both the origin and destination within the area of the PRT network. The number of vehicle trips per person per day in an average U.S. city varies from about 3 in the CBD to 6 or more in the suburbs. To be conservative, I assume that the average number of internal trips per person per day in the core is only 2, and that when the PRT network area measures 10 miles by 10 miles, the average number of internal trips per person per day is 4. This quantity is logically a function of the network area An. It is necessary to express the variation by means of a reasonable function. A straight line between the core and an area of 100 sq-mi could be assumed, but a curve of continuous slope is more likely. Thus, I assume the following cosine function:(15)in which An is the area of the network. It may be noted that cos (0) = 1 and so the result varies smoothly from 2 when An = 0 to 4 when An = 100 sq-mi.Mode SplitFor a person starting a trip near a specific station of a PRT system, the number of opportunities to use the system increases in proportion to the number of stations. But the same is true for persons starting their trips at any of the stations. Consequently, considering all possible trip makers, the likelihood or probability of using the PRT system ought to increase as the square of the number of stations. The number of stations in a square PRT network is given by the formula(16)in which L is the line spacing and An as before, is the network area. A reasonable line spacing is half a mile, which places everyone within a quarter mile of a station. So, as the area An increases from 4 to 100 in the examples to be calculated, the number of stations increases from 40 to 840 and the square of the number of stations increases by (840/40)2 = 441. Certainly, the mode split (a quantity between 0 and 1) will saturate long before this much of an increase occurs. With 40 stations in the smallest network we will consider, in a well-configured network, there are many opportunities to travel on the PRT system. Consider also that the data provided in the file “Ridership.doc” shows that in reasonable sized networks PRT mode splits up to 30% to 50% are likely. Suppose we make the drastic assumption that the mode split increases only as the square root of the number of stations. In the above case that would be a ratio of , which is still a lot. With these considerations in mind, consider a possible mode split variation to be (17)in which case, the mode split in the smallest network is only 8.7%. Perhaps this is too conservative? What are the alternatives in the CBD? For internal trips the alternative may be a taxi, an auto, or perhaps a bus, none of which are very attractive. All bog down in traffic, so the average speed of these modes in the CBD is usually markedly reduced over the average speed in a wider area. For these reasons, it seems likely that the mode split to PRT will not be so low in the CBD. A more moderate variation could be the following:(18)which, for 40 stations gives 16.8% and for the 100 sq-mi network with 840 stations 36%. This is the formula used in the calculations.Average Trip LengthIf the probability of taking a trip were not to depend on the length of the trip within a city, it has been shown that the average trip length is two-thirds the square root of the area. In actual cities, data show average trip lengths of about half the square root of the area. Thus, in the calculations, it will be assumed that(19)CalculationsIn each of nine files “System Economics(i).xls, i = 1,…, 9” factors for the three parameters close to those for a specific city are calculated. The cities and the parameters that represent them are given in Table 1 along with values of core density calculated from equation (13). The cities with average densities over 5000 persons per sq-mi were selected from the file “PopulationStatistics.xls” to represent a wide variety of populations and densities, some restrained in expansion by a large body of water, and others not so restrained. Of the two remaining cities, in the 1990 census Atlanta had a density of 2990 persons per sq-mi and Phoenix 2342 persons per sq-mi, so these are examples of large, low-density cities. Table 1. Parametric Data for Cities AnalyzedFile CityP(Rf)AfDsq-midegreespeople/sq-mi1Los Angeles3,485,002469.318062,4182Chicago2,783,427227.2180102,9753Detroit1,027,767138.718062,2844Minneapolis368,15954.936056,3675St. Louis396,47061.918053,8296Syracuse163,85325.136054,8717St. Paul272,29052.836062,4188Atlanta394,082131.836025,1329Phoenix983,406419.936019,686Consider the first page of each of the System-Economics files. The first 19 quantities are common to the example and can be changed at will. The first item under “System Number” defines the size of the five square networks with sides appropriate to the specific city. The fifth item is the population served per sq-mi. Note how it falls as the network grows. The quantity “Average person-trips per peak-hour per station” is needed to determine the average station size. Only in the largest cities do the quantities shown require more than a one- or two-berth station, but to be conservative about potential ridership, three-berth stations are assumed in all cases. Farther down the list, “Vehicles per mile” is included to see how close the network is to saturation. Since we can handle up to about 140 vehicles per mile, the values shown are not a problem. It is significant that the network handles almost a third of the traffic of the city without approaching close to saturation. Why is this so? Because we have postulated guideways every half mile in the north-south and east-west directions capable of handling the traffic of three freeway lanes. If that were possible with freeways, there would be little congestion. Attempts to funnel substantial portions of the traffic of a city down one corridor, is a reason the flow requirements there are high.“Average Time Headway” is next. Since we can accommodate average values down to about two thirds of a second, the values shown are not a problem. Since the “brick-wall” headway for our HCPRT system is under two seconds, we encroach on standard railroad practice in only a few of the cases calculated, but only after planners and officials have had time to witness the performance of smaller systems. The quantity “Percentage of guideway length required for off-line station guideways” is included because critics often markedly exaggerate this quantity. The quantity “Passenger-miles per year per lane-mile” is included because this is the basic economic indicator of ridership. Note that when it is greater than about one million the system becomes profitable.Cost DataThe capital and operating cost data given in the files “System Economics(i).xls” are obtained from the detailed spreadsheet file “Select Systems P&L (2).xls,” which are summarized in the file “CostSummary.xls.” The data there were calculated for a series of five systems having total guideway length 21, 78, 156, 210, 420 miles, for which the number of vehicles and stations are listed in the first of the two “CostSummary.xls” data sheets. All costs are lumped into three categories: Vehicles, Stations, and Guideways. The vehicle costs are complete including all propulsion and control costs. Guideway costs include power supply and distribution, communications, posts, foundations, erection, adjustment, and landscaping. Wayside capital costs that generally vary with the number of vehicles are included in the unit vehicle cost, and the rest of the wayside costs are assumed proportional to the system length and thus are included in the values of guideway cost per mile. Thus, all capital costs associated with building and operating a PRT system are included in the costs tabulated. This includes site engineering, insurance, central facilities, storage facilities, maintenance facilities, R&D, marketing, training, and, of course, profit. The second sheet in “CostSummary.xls” contains annual costs with and without depreciation. These annual costs include all costs required to operate and maintain the system. Straight-line depreciation is assumed over 5 years for wayside equipment, 10 years for vehicles, and 20 years for stations, guideways, and buildings for maintenance, storage, central control, and administration.Cost Reduction due to LearningData accumulated by industrial engineers shows that the cost of an item of production decreases as the production quantity increases according to the equation(20)in which is the cost at some starting production quantity , and k is a positive constant, usually found by identifying the reduction in cost if the production quantity doubles. Thus, let , be the cost at double production, and take the natural logarithm of equation (20). The result is .(21)Based on information given in industrial engineering texts, for common components such as guideways and stations in which case k = 0.0740; and for higher tech components such as vehicles and control systems in which case k = 0.1520. Using these values, the costs per vehicle, station, and guideway are tabulated in the first sheet of “CostSummary.xls” under the headings 5% and 10%, corresponding to k = 0.740 and 0.152, respectively. Under the heading 0%, Cost per Vehicle and Cost per Guideway-Mile decrease somewhat due to economics not related to reduction in component costs as production increases. In the lower set of numbers, the total costs with and without industrial learning are tabulated, and below them, for reference, the corresponding system costs per nominal guideway mile, i.e., not counting extra guideway for off-line stations for passengers and storage. So we see that the total system cost per mile varies from $6.6 million to $4.1 million.The second sheet in the file “CostSummary.xls” shows the annual costs for operations and maintenance per vehicle, per station, and per mile of guideway with and without depreciation. Again, all costs are lumped into these quantities. Addition of depreciation provides the total cost for capital and operation and is the basis for calculating “Break-Even Fare.” Comparing “Break-Even Fare” with a fare that can reasonably be charged determines the level of profit that can be produced by construction and operation of the system. In the spreadsheets “System Economics(i).xls” the number of miles of guideway, vehicles, and stations differs from the data in the file “CostSummary.xls,” therefore it was necessary to curve-fit the data. For the case of no “Learning,” I drew a straight line between the points for the 21-mile system and the 420-mile system. Examination of the data shows that for the three intermediate points, the results used in the spreadsheets “System Economics(i).xls” for no “Learning” are conservative. For the case “With Learning” the above-computed factors k are applied to the data for the 21-mile system. Thus, the cost per vehicle is$because the costs were estimated based on a production quantity of 400 vehicles. The cost per station is$because the costs were estimated based on a production quantity of 24 stations. Finally, the cost per mile of guideway is$because the costs were estimated based on a production quantity of 12 miles of guideway. Summary of Costs and EconomicsThe second and third sheets in the files “System Economics(i).xls” contain cost tabulations with and without learning for cases for which there is a profit after all costs. For example, in the smaller, lower-density cities 4 to 9, a 4 sq-mi network would require a subsidy. In each set of tabulations, the first nine rows are calculated directly from the file “CostSummary.xls” as indicated above. The remaining 13 rows summarize the acquisition cost and the annual support cost for operations and maintenance for each case. It is of particular interest to note that the difference in profit and payback period with and without learning are small, and the profit potential becomes very large as each system grows. The after-tax profit and payback period calculated with learning for the nine systems are summarized in Table 2. As can be expected, the smallest city considered, Syracuse, New York, exhibits the longest payback periods.Table 2. After-Tax Profit and Payback Period 1Los Angeles4 sq-mi16 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K111,129394,991869,2531,620,7922,524,989Net Profit/yr, $K99739,842194,975617,8691,332,670Pay Back Period111 yrs9.9 yrs4.5 yrs2.6 yrs1.9 yrs2Chicago4 sq-mi16 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K116,169416,133911,8891,609,1642,587,975Net Profit/yr, $K3,63159,545251,748725,8791,455,114Pay Back Period32 yrs7.9 yrs3.6 yrs2.3 yrs1.8 yrs3Detroit4 sq-mi16 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K109,249376,179797,1961,403,8652,116,463Net Profit/yr, $K6223,106103,318295,381574,470Pay Back Period1,76516.37.74.83.74Minneapolis9 sq-mi16 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K215,998357,614740,7741,262,9611,888,891Net Profit/yr, $K1,2407,56736,983104,123192,520Pay Back Period17447.120.012.19.85St. Louis9 sq-mi16 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K216,098358,163743,2591,269,7491,900,003Net Profit/yr, $K1.3058,02839,766112,840210,089Pay Back Period16644.618.711.39.06Syracuse36 sq-mi49 sq-mi64 sq-mi81 sq-mi100 sq-miCapital Cost, $K713,198940,0361,197,7971,484,0261,793,747Net Profit/yr, $K3,75111,94724,32038,01449,222Pay Back Period19078.749.339.036.47St. Paul16 sq-mi25 sq-mi36 sq-mi49 sq-mi64 sq-miCapital Cost, $K352,334522,809725,588962,4581,222,976Net Profit/yr, $K1,8248,51020,34238,72866,134Pay Back Period19361.435.724.918.68Atlanta16 sq-mi25 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K349,805522,603727,8971,247,8571,879,190Net Profit/yr, $K2657,87422,82984,942177,303Pay Back Period132066.331.914.710.69Phoenix16 sq-mi25 sq-mi36 sq-mi64 sq-mi100 sq-miCapital Cost, $K352,508529,159742,1931,298,1401,981,210Net Profit/yr, $K2,00213,97338,570149,941342,359Pay Back Period17637.919.28.75.8Referenced FilesRidership.docPopulationStatistics.xlsSystem Economics(i).xls, i = 1, 2, 3, 4, 5, 6, 7, 8, 9CostSummary.xlsEconomics of the Intelligent Transportation Network SystemJ. E. AndersonIntroductionThis paper describes the calculations needed to determine the break-even fare and other useful values of an ITNS operating system. The calculations are based on the Microsoft Excel program included at the end of this paper. If the reader has that program installed and has the accompanying Excel file, he or she will be able to change any parameter and instantly see the effects on all the other parameters upon which that parameter depends. In the calculation process, other useful quantities are calculated. In this paper, I will go through the calculations line by line. Note that in the attached program I have numbered every row, and at the top I label column C, where the calculations are made.This kind of analysis can be considered a template for the detailed analysis of a specific application, in which The system would be laid out in a specific setting, Specific ridership analyses would be performed using the latest techniques,Simulations will be performed to determine specific wait times and ride times that will be fed back into the ridership analyses, the number of loading berths required in each station, and the adequacy of the line layout and station locations.Costing will be done based on up-to-date data obtained by the team that will build the system, andThe specific way the system will be financed will be considered.Application The application is defined by giving the Transit Service Area (row 4) and the separation between lines or guideways (row 5). In a specific application, in laying out the lines and stations the line length and service area will be determined. In the attached spread sheet, I have assumed a 2.5 mi by 2.5 mi square network shaped as follows:I take these lines to be a half mile apart north-south and east-west and that there is a station at the midpoint between each pair of guideways. In this case the network spans 2.5 miles both north-south and east-west, and there is a station every half mile. I assume that the Transit Service Area (TSA) is the area from which trips are drawn, and since the maximum distance most people will walk to a bus station is about 0.25 mile, I assume that the TSA extends three miles north-south and east-west. Thus, in the above network, the service area is 9 square miles and there are 2.5/0.5 + 1 or 6 lines going north-south and 6 going east-west. In the notation used in the spread sheet, TSA = C4 and the separation between lines is C5. Thus, the number of lines going either north-south or east-west is C4C5. The total length of lines (guideways) isC6=2C6-C5C4C5The number of stations per mile is C7, and the total number of stations is C8 = C7*C6. Ridership.C10 is the expected number of weekdays of travel per year, if travel on weekends and holidays is somewhat less. In conventional transit studies, this number is usually taken to be 299, which looks better than about 300, because people do not ride conventional transit as often as on the 110 weekend days and holidays. Based on data from Public Transportation and Land Use Policy, by Boris S. Pushkarev and Jeffrey M. Zupan, the more the service concept of a transit system permits travel at any time of day or night with very short wait times the more travel there will be on weekends and holidays. I set C10 = 340.C11, C12, C13: C11 is the number of people per square mile and C12 is the number of trips per person per day, called mobility. Table 6-1 in my textbook Transit Systems Theory gives 1974 data on mobility in 21 cities in the United States, with values from 1.65 in the New York City Area to 3.18 in Oklahoma City, i.e. the more auto-oriented the city, the higher the mobility, and mobility has increased substantially during the 40 years since 1974. I thus feel justified in assuming a mobility of 4 vehicle-trips per person per day. C13 is the mode split to ITNS, i.e. the fraction of all vehicle trips that will be taken by ITNS. Because of its short to zero wait and nonstop private-party trips, studies have shown that the mode split to ITNS may be higher than 30%.The ridership per day per square mile, C14, is the product of these three numbers. C14=C11×C12×C13C15 is the ratio of off-peak freight trips that can be taken in passenger vehicles to the number of passenger trips. Based on the paper “Programmed Module Urban Transport Systems in National Perspective for Canada” by Norman D. Lea and Dr. Derek Scrafton (Personal Rapid Transit: A selection of papers on a promising new mode of public transportation, edited by J. Edward Anderson, Jack L. Dais, William L. Garrard and Alain L. Kornhauser, University of Minnesota 1972) Norman Lea reported that there may be as much as 80% of the freight of a city that could profitably be carried in vehicles of the size of ITNS vehicles. A problem for freight movement is that someone needs to be available to load the vehicle, and someone needs to be available at the destination end to receive it. I set C15 = 0.50. C16, the total number of trips per year per square mile, isC16=C14*C101+C15C17 is the ratio of daily to peak-hour trips. Pushkarev and Zupan (op. cit.) show that for the most demand-responsive mode of travel, C17 would be 12.2. For the least demand-responsive mode (commuter rail) this number for travel into Manhattan is only 4.2. Since service via ITNS is close to that on the most demand-responsive system, I take C17 = 10. Then the number of passenger-trips per peak-hour per square-mile isC18=C14/C17.PerformanceC20. The number of passenger-trips per peak-hour is C20 = C18 * C4.C21 is the average trip length. From Transit Systems Theory, page 82, if travel were completely uniform the average trip length is 2/3 times the square root of the service area. I assume that the average trip length is 80% of this value. Thus, I take C21 to beC21=0.8(0.667)C3A reasonable value for average speed in an urban system is about 25 mph, so C22 = 25.C23 is the average vehicle occupancy. In 1990 the Twin Cities Area Metropolitan Council did a very comprehensive traffic survey that produced the value of 1.2 for the daily average auto occupancy in the Twin Cities Area and 1.08 for the peak-period average auto occupancy. I will assume that a fare will be charged per vehicle rather than per person to encourage group riding and to simplify fare collection. I assume C23 = 1.35.C24 is the fraction of operating vehicles that will be empty because demand is in general not the same in both directions between any pair of stations. Based on extensive computer simulation of many application networks, I let 25% of the operating vehicles be empty, i.e., C24 = 0.25.The maintenance float is the number of vehicles that must be added to account for vehicles that must be serviced during the busiest hours. I let the maintenance float C25 = 3% of the fleet, even though calculations I have made show that it may be as low as 2%. The number of people riding the system at any one time is the flow of people into the system per hour multiplied by the average trip time in hours, where the average trip time is the average trip length divided by the average speed. This number divided by the average number of people per vehicle including empty vehicles is the number of operating vehicle needed. The average number of people per vehicle counting empties is the average number of people in each occupied vehicle multiplied by the fraction of vehicles that are occupied. Thus, the number of operating vehicles needed is given by the expressionC20*C21C22C23*(1-C24)Since this number is generally not an integer, we make use of the Excel function INT, which strips off from a decimal number every number after the decimal point. Thus, we take for the number of vehicles in operation the quantityINTC20*C21C23*C22*(1-C24)+1The maintenance float, C26, is the small fraction C25 of this number rounded up to the next integer. ThusC26=INTC25*INTC20*C21C22*C23*(1-C24)+1+1 C27=C26+ INTC20*C21C22*C23*(1-C24)+1where C27 is the total number of vehicles in the System. C28 is number of vehicle-miles per year, which is the number of vehicle-miles per year per square mile times multiplied by the TSA and the average trip length. ThusC28=C16*C4*C21The total number of operating vehicles per mile is simplyC29=C27-C26C6The total number of vehicles per mile of guideway isC30=C27C6Headway can be measured in terms of either distance or time. The average headway distance is the average nose-to-nose distance between vehicles, i.e., 1/C29 in miles per vehicle, orC31=5280C29feetThe headway in seconds is the headway in feet divided by the average speed in feet/second. ThusC32=C31C2288/60System CostC35 is the cost of the guideway, posts and foundations per mile. This includes guideway covers, power rails installed inside the guideway, and the communication line. I derived the number I used from three sources:Our Chicago PRT Design study estimated in 1992 with the numbers multiplied by 1.8 to account for inflation, realizing that it is difficult to find good numbers for inflation of a specific product like steel guideways.The 60-ft guideway that I designed and had built in 2002 and exhibited in the 2003 Minnesota State Fair. I talked to the supplier about the cost of fabricating guideways for a half-mile test system. He said they could do it for about $2 per pound. Our guideway weighs about 140 lb/ft, so I guessed that at today’s costs it would be about $400/ ft, or $2,100,000 per mile. Subsequent cost-estimation work.C36 is the cost of one station plus the cost of the bypass guideway used with each station. I give the latter cost asC35×4.88×C22+1005280where 4.88×C22+100 is the length of the bypass guideway in feet and C22 is the speed into the station in miles per hour. ThusC36=$486,000+ C35×4.88×C22+1005280C37 is the estimated cost of one vehicle in lots of 1000 plus the cost of a piece of guideway needed to store it away from a station. Here I take into account that it will be necessary to build storage sidings for about 75% of the vehicles that will be storied at night away from stations. The remaining 25% will be stored at night at stations waiting for passengers. ThusC37=$80,000+ C35*9×0.75ft5280C38 is the cost per mile of control and communication equipment, which I took from our Chicago PRT Design Study increased by a factor of 1.8 even though much of this equipment is cheaper today. Thus C38 = $300,000.C39 is the capital cost of the maintenance facilities required for the project divided by the number of miles of guideway, C4. The cost I used is from the Chicago Study updated for inflation and is given byC39=$1,500,000+$3,360,000C263001C6in which C26 is the Maintenance Float. The maintenance-facility cost calculated for the Chicago Study was for a fleet of 300 vehicles.C40, the construction-management cost per mile, was taken from the Chicago Study, where Stone & Webster estimated that it would be 4.3% of the fixed-facility costs. ThusC40=0.043*C35+C36*C7+C38+C39C41 is overhead, which includes fees, taxes, and all other expenses needed to support the business. In this case I took C41 = 40% of all the fixed-facility costs plus the vehicle costs. In the present example, the system cost is about $384M, 40% of which is about $154M, of which $30M could be used to pay back the $30M cost of the demonstration. If the investor in the demonstration wants his money back in 4 years at a compound interest of 4.5% per year, then he would want $30×1.0454 or $35.8M, which would be 9.3% of the system cost.C42 is the sum of all costs per mile of system. ThusC42=1+C41C35+C36*C7+C38+C39+C37*C30+C40C43 is C42×C6, the total system cost.C44 = 0.045 is the interest on the debt, assuming bond financing of the system.C45 = 30 years is the time required to pay the debtC46 is the annual payment on the debt per mile of guideway. C46=C43*C441-11+C44C45/C6.C47 = $0.33 is the Operating & Maintenance cost per vehicle-mile, which I took from the Chicago study updated for inflation. Note that compared with average costs per mile of small automobiles obtained from FHWA data, it is a little lower than the average, which it should be because the vehicle is simpler and it operates in the most benign environment possible – on smooth rails, no chuck holes or curbs to negotiate, and in the shade of the sun.C48 is the first-year O&M Cost, which is C47 times the number of vehicle-miles per year, C28.C49. As a matter of interest to engineering economists I show here the annual O&M costs a percentage of the total capital costs, C49 = C48/C43.C50. This is the total annual cost per mile of guideway, C50 = C46+C48/C6.C51. Also as a matter of interest I show here the sum of the annual costs per vehicle-mile, which can be compared with auto costs. ThusC51=C50*C6C28RevenueI assume the fare per vehicle trip is C53 = $2, the cost of freight movement per mile is C54 = $1, and the charge for advertising per vehicle trip is C55 = $0.50. I believe these values are reasonable for ITNS. I assume, based on a recommendation from our Chicago PRT study, that the passenger fare will be charged per vehicle rather than per passenger and that the revenue for advertising is charged per vehicle-trip rather than per passenger-trip. This is easier to implement and encourages group riding by choice.C56, revenue per year. The revenue from all three sources per vehicle trip isC53 + C55 + C54 * C21 * C15I assume C23 = 1.35 is the average number of passengers per vehicle. Thus, the revenue per passenger-trip isC53 + C55 + C54 * C21 * C15C23To get C56, the revenue per year, we must multiply this quantity by the number of passenger trips per year, which is C56 = C14 * C4 * C10. ThusRevenue per year=C56=C53+C55+C54*C21*C14C23*C56C57 gives the first-year O&M cost divided by the revenue per year, a number that is roughly 3 for conventional transit system, which do not remotely cover the annual O&M cost with fares, and conventional transit is not suited to moving freight. ThusC57=C48C56C59 = C57/C43 is the annual revenue as a fraction of system cost.The Break-Even FareC60 is the break-even fare, i.e., the annual cost divided by the annual number of trips. ThusBreak-Even Fare=C60=C50*C6C16*C4Here is the Excel spreadsheet showing the formulae:Economics of ITNS Operating System.ABCApplication: A Square Network4Transit Service Area, sq mi9=1+A4Separation between lines, mi0.5=1+A5Guideway Length, mi=2*(SQRT(C4)-C5)*SQRT(C4)/C5=1+A6Stations/mi2=1+A7Total Number of Stations=C6*C7=1+A8Ridership=1+A9Peak Days/year340=1+A10People/sq mi4000=1+A11Trips/person/day4=1+A12Mode split to ITNS0.3=1+A13Passenger-Trips / Day/sq mi=C11*C12*C13=1+A14Off-Peak Light-Freight trips/passenger-trips0.5=1+A15Total Trips/ yr/ sq mi=C14*C10*(1+C15)=1+A16Peak-hrs/Day10=1+A17Passenger-Trips/ pk hr/sq mi=C14/C17=1+A18Performance=1+A19Passenger Trips/pk hr=C18*C4=1+A20Ave Trip Length, mi=0.8*(2/3)*SQRT(C4)=1+A21Average speed, mph25=1+A22People/occupied vehicle1.35=1+A23Fraction of Vehicles empty0.25=1+A24Percent of operating vehicle fleet in maintenance0.03=1+A25Maintenance float, vehicles=INT(C25*(INT(C20*C21)/C22/C23/(1-C24))+1)+1=1+A26Total number of vehicles in the System=C26+INT((C20*C21/C22/C23)*(1+C24))+1=1+A27Vehicle-miles/year=C16*C4*C21=1+A28Number of operating vehicles/mi=(C27-C26)/C6=1+A29Total number of vehicles /mi=C27/C6=1+A30Average headway, ft=5280/C29=1+A31Average headway, sec=C31/(C22*(88/60))=1+A32System Cost=1+A33Cost of Demonstration30000000=1+A34Operating Cost/mi of guideway, posts & foundations5530000=1+A35Cost of one station including bypass guideway=486000+C35*(4.88*C22+100)/5280=1+A36Cost of one vehicle including storage guideway=80000+C35*9*0.75/5180=1+A37Cost of Control & Communication/mi300000=1+A38Cost of Maintenance Facility/mi=(1500000+3360000*C26/300)/C6=1+A39Construction Management Cost/mi=0.043*(C35+C36*C7+C38+C39)=1+A40Overhead, Fees and Taxes0.4=1+A41System Cost/mi=(1+C41)*(C35+C36*C7+C37*C30+C38+C39+C40)=1+A42Cost Of Operating System + Demonstration=C42*C6+C34=1+A43Interest on Bonded Debt0.045=1+A44Time Horizon, years30=1+A45Annual Payment on Bonded Debt/mi=C43*C44/(1-1/(1+C44)^C45)/C6=1+A46O&M Cost/vehicle-mile0.33=1+A47First year annual O&M cost (reduced with learning)=C47*C28=1+A48Annual O&M as fraction of capital cost=C48/C43=1+A49First-Year Total Annual Cost/guideway-mile=C46+C48/C6=1+A50First-Year Total Annual Cost/vehicle-mile=C50*C6/C28=1+A51Revenue=1+A52Fare per vehicle trip2=1+A53Fare per mile for freight1=1+A54Advertizing revenue/vehicle-trip0.5=1+A55Passenger trips per year=C14*C4*C10=1+A56Revenue/year=(C53+C55+C54*C21*C15)/C23*C56=1+A57Annual O&M Cost as % of Annual Revenue=C48/C57=1+A58Annual Revenue/System Cost=C57/C43=1+A59Break-Even Fare=C50*C6/C16/C4Here are the results:Economics of ITNS Operating System.ABCApplication: A Square Network4Transit Service Area, sq mi9.05Separation between lines, mi0.56Guideway Length, mi30.007Stations/mi2.008Total Number of Stations609Ridership10Peak Days/year34011People/sq mi4,00012Trips/person/day413Mode split to ITNS30%14Passenger-Trips / Day/sq mi4,80015Off-Peak Light-Freight trips/passenger-trips0.5016Total Trips/ yr/ sq mi2,448,00017Peak-hrs/Day1018Passenger-Trips/ pk hr/sq mi48019Performance20Passenger Trips/pk hr4,32021Ave Trip Length, mi1.6022Average speed, mph2523People/occupied vehicle1.3524Fraction of Vehicles empty0.2525Percent of operating vehicle fleet in maintenance0.0326Maintenance float, vehicles1027Total number of vehicles in the System26728Vehicle-miles/year35,251,20029Number of operating vehicles/mi8.5730Total number of vehicles /mi8.9031Average headway, ft61632Average headway, sec16.833System Cost34Cost of Demonstration$30,000,00035Operating Cost/mi of guideway, posts & foundations$5,530,00036Cost of one station including bypass guideway$718,51137Cost of one vehicle including storage guideway$87,20638Cost of Control & Communication/mi$300,00039Cost of Maintenance Facility/mi$53,73340Construction Management Cost/mi$314,79341Overhead, Fees and Taxes40%42System Cost/mi$11,776,35643Cost Of Operating System + Demonstration$383,290,67344Interest on Bonded Debt4.50%45Time Horizon, years3046Annual Payment on Bonded Debt/mi$784,36047O&M Cost/vehicle-mile$0.3348First year annual O&M cost (reduced with learning)$11,632,89649Annual O&M as fraction of capital cost3.04%50First-Year Total Annual Cost/guideway-mile$1,172,12351First-Year Total Annual Cost/vehicle-mile$1.0052Revenue53Fare per vehicle trip$2.0054Fare per mile for freight$1.0055Advertizing revenue/vehicle-trip$0.5056Passenger trips per year14,688,00057Revenue/year$35,904,00058Annual O&M Cost as % of Annual Revenue32.4%59Annual Revenue/System Cost9.4%60Break-Even Fare$1.60Economics of ITNS NetworksJ. E. AndersonSummaryThe characteristics of the version of High-Capacity PRT I call an Intelligent Transportation Network Systems or ITNS have been described in a series of papers that can be made available. The problem addressed in this paper is this: If an ITNS network were to be expanded in successive stages in a city of a given population and population growth rate, without going into a detailed and expensive planning study, estimate the return on investment (ROI) to an investment group that provides the funds needed to build and test ITNS full scale in sufficient detail to create an on-going market. The ROI will depend on at least the following system parameters:The current population of the city.The projected population growth rate.The average number of trips per person per day, called the Mobility.The fraction of trips (mode split) in the area served by ITNS as it grows.The ratio of daily travel to peak-period travel.The ratio of yearly travel to daily travel.The average trip length on ITNS as it expands.The average speed on ITNS as it expands.The fraction of moving vehicles that are empty.The size of the maintenance float.And the following economic parameters:The rate at which the capital investment is amortized – the interest rate.The number of years over which the capital investment is amortized.Industrial learning factors that estimate how costs will decrease as production increases.The initial guideway cost per mile taking into account cost reduction with production.The initial station cost taking into account cost reduction with production.The initial vehicle cost taking into account cost reduction with production.The passenger fare.The goods-movement fare.The fraction of goods-movement trips to passenger trips.The advertising revenue.The expected profit on capita costs.The expected profit on operating costs.The rate at which the system can be expanded.The body of this paper derives first the system parameters, based on work documented in my textbook Transit Systems Theory, and then explains all the economic parameters used. The results are presented in an accompanying Excel Spread Sheet of the same name.IntroductionThe annual cost of a transit system is the annual cost of debt service plus the annual cost of operations and maintenance. The total annual revenue is derived from passenger service, goods movement, which is not practical on conventional transit, and from focused advertizing, which will be higher than normal because the system knows the destination of each passenger group and can advertise via a TV set in each vehicle. The break-even fare per passenger-mile is the annual cost divide by the annual number of passenger-miles. The purpose of this paper is to estimate the potential internal rate of return of an investment in the test facility that makes the expansion of a PRT system over a city possible and the internal rate of return to a city that would, by itself, invest in the test facility that makes expansion of the PRT system possible. We begin by estimating ridership and then costs. The results are calculated in an Excel spreadsheet in which the reader can vary 36 parameters that define the ITNS system.Annual Passenger-MilesThe annual number of passenger-miles attracted to a PRT system is the product of the following factors:The average trip length.The number of vehicle trips each urban resident takes each day.The population density.The area covered by the PRT systemThe mode split to PRT.The ratio of the number of yearly trips to daily trips.Several studies have been performed of goods movement on PRT systems, the first of which I am aware was done by N. D. Lea & Associates of Toronto for the Canadian government in the late 1960s. The general consensus of these studies is that the number of possible goods-movement trips in an urban area in units that could be carried in a PRT vehicle is roughly equal to the number of vehicle trips taken by passengers, and that once established the number of goods movement trips will not be as sensitive to the trip charge as will be the case with passenger trips. This fraction may be quite small in a starter system in which there are few stations, but as understanding of the potential for economical goods movements grows as the system grows, the fraction of the total number of vehicle trips for goods will increase. Many of such trips will be taken for package delivery and other high-value items that can easily be transported in passenger vehicles in off-peak hours. As the potential of goods movement increases, vehicles design just for freight movement will be introduced. The potential for advertising revenue has not, to my knowledge, been studied. The value of focused advertising that will be possible on a PRT system will be higher than the usual form of advertising. So we need to include a modest estimate of this revenue.Means of computing each of the parameters in the above list and probable values are discussed in the following paragraphs.The Average Trip Length of city bus trips is typically about 2.5 to 4 mi and for auto trips in urban areas in the USA ranges from about 6 to 10 mi. For ITNS the average trip length in a built-out system covering a large area can be expected to be in between these numbers – say in the range of 4 to 6 mi. Thus, an average trip length of Ltrip = 5 mi in a built-out system is reasonable. The average trip length for smaller start up systems will be less. On pages 82-87 of my textbook Transit Systems Theory I calculate the average trip length under the assumption that trips will be taken in an urban area independent of the length of the trip. Since PRT trips will be relatively non-stressful this is more likely than trips either by auto or conventional transit, but if the fare charged is proportional to trip length, which it should be, shorter trips will be favored over longer trips, which is exhibited from available data on transit trips vs. auto trips. In developing a model of travel in a developing PRT network, we can start with the geometry of travel in PRT networks of various sizes. I calculated in my textbook Transit Systems Theory that the average trip length in a simple square loop with one station on each of the four sides is 2A1/2, where A is the area of the square loop. In an interconnected network of three of such squares east-west and north-south, the average trip length is 1.44A1/2 where A is the area of the whole network consisting of nine squares. In an interconnected network of five of such squares east-west and north-south and having a total of 25 square, the average trip length is 1.21A1/2 where A is the area of the whole network. If this process is carried to the limit of a very large network, the average trip length is 2/3rds of A1/2. The best fit to these points is the following equation, which allows calculation of Ltrip for any size network. Thus, we will estimate the average trip length from the following formula: Ltrip=0.625*A1/22.3e-x/1.836+2/3 (1)where x=A1/2/Lsq and Lsq is the spacing between guideways. Note that for A1/2 = 12 mi and Lsq = 0.5 mi, equation (1) gives Ltrip = 5 mi. When x = 1, equation (1) gives Ltrip = 0.625 mi.The average number of trips per person per day. Data collected in the USA showed that the total number of vehicle trips in urban areas per person per day, called mobility, has ranged from 1.65 in the area around New York City to 3.18 in Oklahoma City. In suburbs mobility is often as high as 10 trips per person per day. The results also show, as can be expected, that ease of travel increases mobility. So, let us assume a mobility of tpppd = 4 trips per person per day.Population density. Almanac data shows a wide range of population densities in cities. The inner city of Minneapolis has a density of about 7000 people per square-mile and within the city limits of Chicago the density is about 13,000 people per square-mile. The density of the Winnipeg area varies from more than 5000 people per square-mile near the central business district to lower values farther out. The reported average is 3534 people per square-mile, but in the area covered by the guideway and in future years the density will be higher. Generally, the population density of cities falls off exponentially from the center. Appendix B shows that the population up to a specific radius R can be represented by the following equation PR=PRf0.951-1+γRe-γR (2) in whichγ=4.744φ2Af=4.7442π2Af=8.41Af1/2 Ninety five percent of the population of a city, P(Rf), falls within an area Af. In the aboveexample P(Rf)/Af = 3534 people per square mile. Using the notation of the next paragraph, R in equation (2) will be taken as one half the square root of the area within radius R.The area covered by the guideway. For the convenience of analysis of any configuration, assume the guideways are spaced Lsq apart and cover a square area L on the side, so that the total service area covered is A=L+Lsq2. Then the total length of guideways is Lsys=2LLLsq+1=2A1/2Lsq-1A1/2. (3)Solving this quadratic equation for A we getA=Lsq21+1+2LsysLsq2 (4)We thus estimate the system length in terms of the area covered and the line spacing, and the area covered in terms of the system length and the line spacing, both of which are needed.The mode split. The fraction of passenger-vehicle trips that would be taken by ITNS is called the “mode split” to ITNS. The studies described in Appendix A show that a factor of 0.3 is reasonable for a system in which all stations in the built-up area of a city are within a quarter mile of any point in the network. This implies that we will use the values Lsq = 0.5 mile. This mode split is far higher than achieved by conventional transit in auto-oriented cities, which are no match for the auto. The mode split for small starter systems will be less, but for curiosity and professional interest the ridership on the first few operating sections of ITNS will draw many people from a wider area. Let’s assume then that for the first operating section of guideway length Lmin the effective mode split is msmin = 10% of the total number of trips generated near each station by people living or working within the area, and that the mode split, ms, will increase linearly up to msmax = 30% on a built-out system. In general ms=msmin+msmax-msminLsys-LminLmax-Lmin (5)in which Lsys is the length of the system at a particular state and Lmax is the system length at which ms = msmax. We will assume that ms will not increase above msmax and will not be less than msmin.The ratio of yearly ridership to week-day ridership. In conventional transit, the ratio of yearly to daily travel is usually assumed to be about 300. Data collected by planners shows that the ratio of daily travel to peak-hour travel is as low as 3 for commuter rail systems and increases to around 12 for taxis and walking, implying that with more personalized service travel is distributed more uniformly throughout the day. For a similar reason, it can be expected that there will be more travel on weekends and holidays with ITNS, a demand-responsive system, than with conventional transit. Thus, for ITNS we estimate the ratio of yearly to weekday travel at DpYr = 340.To determine the peak-hour demand, which determines the number of vehicles needed, we need the ratio of daily travel to peak-hour travel. Based on Pushkarev and Zupan we take this ratio to be DaypPkHr = 10. ThenPeak-hr Demand = Trips/person/day * Pop. Density * Area covered * ms/DaypPkHr (6)Daily average vehicle occupancy. Daily average auto occupancy is about 1.2 people, and the peak-period average is less than 1.1. To encourage higher vehicle occupancy than common in the auto system we have concluded that it is best to charge a fare per vehicle rather than per person. Thus, we anticipate that the average occupancy of PRT vehicles will be higher than in automobile, but how much higher will be a guess until data from daily operations is obtained. In the attached spread sheet I assume 1.5 people per vehicle, but the reader will be able to vary that number.System Capital and Operating CostsFor purposes in this paper, we lump the capital costs into four parts: guideway cost, station cost, vehicle cost, and maintenance cost. The wayside control and power system costs will be lumped into guideway cost and station costs, and everything in a vehicle including control will be included in the vehicle cost. Maintenance costs will include central control and administration costs. An allowance for extra guideway for storage of vehicles in off-peak hours will be included in the vehicle costs. From many simulations, we have found that during the non-busy hours, about 25% of the vehicles will lie in stations and the rest in storage stations.Thus, the total system cost is the sum ofGuideway cost per unit length multiplied by the guideway length not including storage length and station off-line guideway.The cost per station plus the cost of the by-pass guideway for one station multiplied by the number of stations in the system.The cost per vehicle plus the cost of storage guideway per vehicle multiplied by the number of vehicles in the system.Cost of maintenance and administration.Consider the guideway length required for vehicle storage: Assume 75% of the vehicles, each 9 ft long, must be stored off the main guideway, and that each storage siding holds 100 vehicles. ThenStorage guideway length = 0.75 * NumVeh * (9 ft + transition length /100), ftTransition length per storage off line = 2×4VH2J1/3=2×4×30ftsec×23sec= 160 ftStorage guideway length = 7.95 * NumVeh, ftVehicle Cost = (Cost/Veh + Cost/ft gdwy * 7.95ft) * NumVehOff-line station guideway length = 2Ltrans+LberthNberths+1 Ltrans=4VH2Jc1/3=4V10ft2g/41/3=3.41 Vft/sec,ftAssume the average station has four berths each 10 ft long. ThenOff-line station guideway length = 6.83Vft/sec+100, ftStation cost = [Cost of one station + Gdwy Cost/ft * (6.83Vft/sec+100)]*NumStationsMaintenance cost = Cost per 300 vehicles * NumVeh/300To annualize the costs, we use the well-known formula for an annual paymentp=Pi1-11+in (7)in whichp is the annual cost, i.e., the annual payment on a bonded debt,P is the capital cost,i is the interest rate, i.e., the time cost of money, andn is the life time of the system.We must take into account that the cost of manufactured items reduces as quantity increases. This is called “industrial learning” and is defined by how much the unit cost reduces as production is increased. From experience (discussed in industrial-engineering textbooks) the following formula is obtained: CnC0=P0Pnkin which P0 is the initial production rate with cost C0, and Pn is a larger production rate with a lower cost Cn. Thus k=lnCnC0lnP0Pn (8)For common products such as our guideways, stations, and maintenance facilities data shows that when production doubles, costs reduce by about 5%. In the case of high-tech components such as our vehicles, when production doubles costs reduce by about 10%. Thus, in the former case k=ln0.95ln0.5=0.074and in the latter casek=ln0.9ln0.5=0.152These factors are used in the accompanying spreadsheet.The Number of Vehicles in the SystemThe number N of vehicles in a transit system is N=No+Ne+Nm (9)in whichNo is the required number of occupied vehicles needed to meet the peak demand if there isan average of pv people per vehicle;Ne is the number of empty vehicles in circulation during the peak-demand period as a resultof non-uniform demand; andNm is the size of the maintenance float, i.e., the number of extra vehicles required to accountfor the possibility of rush-period breakdowns.The number of occupied vehicles is simply the number of people riding at any one time divided by pv. The number of people riding at any one time is the peak-period flow in people per unit of time multiplied by the average trip time, which is the average trip length Ltrip estimated in equation (1) divided by the average speed, AveSpd, and divided by the average number of people in occupied vehicles. Thus No=MaxDemand×Ltrippv×AveSpd (10)in which MaxDemand is the maximum flow of people per unit of peak-period time, Ltrip is the average trip length, and pv is the average number of people in each vehicle. The unit of time can be taken as an hour or sometimes a smaller interval of time. The smaller that interval is taken, the larger will be No. The consequence of using a longer time interval will be longer wait times. Assume AveSpd increases linearly from 25 mph for the smallest system to 35 mph to the largest, i.e., AveSpd=MinSpd+MaxSpd-MinSpd×Lsys-LminLmax-Lmin (11)By running many PRT simulations I have found that the number of empty vehicles will vary from about 0.6 to 0.8, with the higher number occurring when the demand is more nearly uniform. The number of vehicles in the maintenance float is Nm=No+NeMTTRMTBF(12)in which MTTR is the mean time to repair and MTBF is the mean time between failures.With the reliability that has been built into our PRT system the maintenance float will be less than 2% of the total fleet.Profit per YearAn investor advances the capital necessary to build and operate the test system in exchange for 1) a fraction Prfcap of the capital cost needed to build each operating system and 2) a fraction Prfop of the net revenue from operations. The revenue produced by ITNS will come from three sources: passenger trips, freight trips mostly taking place during off-peak periods, and focused advertising. The latter two sources combined can easily match passenger revenues, and thus the fee should be based on this larger revenue. RevenuePerYr=PassengerFare×PassMiPerYr+GoodsFare× GoodsMiPerYr+Ads-AnnualDebt Service-Annual O&M costin whichPassMiPerYr=Ltrip×tpppd×ms×dp×A×DpYr We need to estimate a reasonable rate of construction of ITNS and for it estimate the internal rate of return (IRR).How soon and how fast can ITNS be built?Operation of the first small system can begin in the fourth year from the date the initial investment is made. Expansion will first increase slowly in the initial city and then as decision leaders understand that ITNS can turn a profit it will expand more and more quickly. In the Excel spreadsheet, I assume a conservative rate of expansion. Discussion of the Excel SpreadsheetThe spreadsheet prints out on one legal-size piece of paper. The 36 parameters that can be varied are listed in three columns of 12 parameters each at the top of the spreadsheet. Data is calculated for the first 52 years of operation. The third column shows the estimated number of miles of guideway built in each of 22 years until the system covers a 12 mile by 12-mile area. These numbers can of course be varied any way the reader desires. The fourth column shows the number of miles of guideway in operation in each year and the fifth column gives the area covered. There is no restriction on the shape of that area. In the sixth column, the population within the area of the network is shown. It increases according to equation (2) and it is assumed that the city population grows at a rate given by the fifth item in the first column of data at the top of the spreadsheet. Next the trip length is calculated according to equation (1). Next the mode split to the PRT system is calculated according to equation (5). Trips per day is the product of trips per person per day, the population served, and the mode split. Trips per year is the product of trips per day and the ratio of yearly travel to weekday travel, the latter of which is given by the second quantity in the second column of data at the top of the spreadsheet. Passenger-miles per year is then calculated by multiplying the previous column by the average trip length. The next column follows by dividing the previous column by the average number of people per vehicle, which is given by the second term in the first column of input data. The next column is the number of goods trips per year. The fraction of goods trips in the first year of operation is given as the last item in the third column of input data. It is then increased from year to year by the same percentage that the population served is increased. Next the total vehicle-miles per year is the sum of the passenger-miles per year and the goods trips multiplied by the average goods-trip length. Trips per peak-hour is trips per day divided by 10. Next the average speed is increased linearly from about 20 mph to 30 mph according to equation (11). Next the number of occupied vehicles is calculated from equation (10). Next the total number of vehicles is found taking into account the empty fraction, which is the sixth item in the second column of input data. The total number included the maintenance float, given equation (12). Vehicles-per-mile-in-operation is then the total number of vehicles minus the maintenance float and divided by the number of miles of guideway in operation. The cost of the fixed facilities purchased each year is calculated as discussed on pages 4 and 5 of this document and is reduced as a result of learning according to equation (8). The cost of vehicles is similarly calculated. The yearly payment on the debt incurred as a result of purchasing more and more of the system each year is the sum of the previous two columns multiplied by the annualizer, equation (7). The debt in any year is the sum of the debts in all previous years. By the 34th year, the debt incurred in the first year is paid off, so it is subtracted from the total. In this way, subtracting the debts paid off, the entire loan is paid off in the 55th year. The annual O&M cost per vehicle-mile is taken from the Chicago study multiplied by an inflation factor of 1.6 and then by the total vehicle-miles per year. I then calculate the break-even fare (BEF) as the sum of the debt payment and the O&M cost divided by the total number of vehicle-miles per year. The next column is the annual difference between the revenue from fares and advertising and the annual O&M cost, indicating a surplus in operating revenue in every year. The next column is the net yearly revenue, in which from the values in the previous column the annual debt payment is subtracted. Hence in the example given, there is a deficit in total costs in the first six years of operation, following which the surplus grows rapidly. The first three items in this column are the investments that made the test program possible. Thus, from this column the Internal Rate of Return to a city that would pay the investment cost plus the cost of installing the system is calculated. In the next column, the profit on the system cost to an independent investor who provided the $30,000,000 needed to enable construction of operating systems is calculated based on the profit rate given as the seventh time in the third column of input data. The next column gives the profit on the net revenue after the capital and O&M expenses are paid. Note that this revenue is negative for the first six years of operation. While the profit on system cost is likely higher (depending of course on the profit rates) it ends when the full system is completely constructed, but the operating profit continues. The next to the last column shows the investment of $30,000,000 then the sum of the two profit streams, and ends with calculation of the IRR to the investor. The final column gives the system cost per mile. Note that it decreases because of industrial learning but increases because the total number of vehicles increases as the system is expanded.Next StepsAny city interested in ITNS will want to perform such calculations using a guideway system that starts and expands according to its specific needs. This process requires detailed line and station layout, detailed simulation, ridership analysis, cost analysis and financial analysis. Based on my experience, hundreds of runs of a simulation program will be needed to settle on all the parameters. No city is likely to do this until our performance and costs are proven from our test track experience, and likely for some not until the first operating system has shown positive experience.Appendix APRT Ridership StudiesThe most significant justification for working to introduce a totally new kind of public transport is that it is expected, based on its service characteristics, to be able to attract many more riders than are attracted to conventional transit. A number of studies have been performed to estimate PRT ridership. Here are the most important:Paper by Francis P. D. Navin, “Time Costs in Personal Rapid Transit,” Personal Rapid Transit II, University of Minnesota, 1974. The author was then Assistant Professor of Civil Engineering, University of British Columbia. He found that observed behavior of conventional-transit riders agrees with the results of analytical ridership models if the model considers total trip time as a disutility of the following form, in which the “C” symbols are dimensionless coefficients:Ride time + Cwalk Walk time + Cwait Wait time + Ctransfer Transfer timeThe larger the disutility the fewer the transit riders. By regression analysis on transit data from several cities, he found the coefficients shown in Table 1. These coefficients show, for example, that in calculating ridership one minute of walk time has the same disutility as 1.65 to 2.08 minutes of ride time, etc.Table 1. Perceived time coefficients for a ridership model.LowHighCwalk1.652.08Cwait4.156.34Ctransfer6.6210.0By applying a model that treated time in this way, he found that for a PRT system in which the walk was three minutes, the wait and transfer times were zero and the travel speed was 40 mph, for data for Minneapolis the fraction of total trips that would be attracted to PRT (the mode split to PRT) was over 50%, and that the mode split to PRT increased with the travel distance.The Aerospace Corporation. Irving, J. H., Bernstein, H., Olson, C. L., and Buyan, J. 1978. Fundamentals of Personal Rapid Transit, Lexington Books, D. C. Heath and Company, Lexington, MA (). This book records the work of The Aerospace Corporation on personal rapid transit. It contains a chapter on Ridership that describes a so-called “Monte Carlo” Mode Split Model. The term “Monte Carlo” means that the origin and destination of a trip are selected at random from a distribution and other attributes of the traveler are also selected at random from their distributions. For this trip the walk time, wait time, and ride time for PRT are calculated; the fare is taken into account; a value of time is taken into account so that the times become costs; and similar quantities are computed for the auto trip, provided an auto is available. The trip is assigned to the mode for which, considering actual and perceived costs, the cost is less. The process is repeated until it converges to a steady value. By applying such a model to traffic in Los Angeles, the Aerospace Corporation PRT group settled on a mode split to PRT of 34% in their economic analysis.Indianapolis. In 1979-1980 a study sponsored jointly by the State of Indiana and the Urban Mass Transportation Administration was performed for automated transit systems for downtown Indianapolis. Vehicles designed for 100, 60, 40, 20, 12, and 3 passengers were included and networks suitable for each vehicle size were laid out. Ridership estimates were developed by the consultant, Barton Aschman Associates, for each system. The 3-passenger-vehicle system used in the study was a PRT system developed by DEMAG+MBB in Germany called Cabintaxi. For this system the layout had 12.2 miles of guideway and 46 stations. The guideway covered an area two miles in the east-west direction and one mile in the north-south direction. The consultant estimated that the ridership on the PRT system would be about 100,000 passenger-trips per day, sufficient to pay all of the costs out of revenues.Swedish Studies. The Swedish Transport and Communications Research Board sponsored a series of studies of PRT in Swedish cities that resulted in 1998 in the report “PRT—a Suitable Transport System for Urban Areas in Sweden?” The conclusion of the report is that in Gothenburg an area-wide PRT system would attract 23% of all transport passengers, and 40% of the trips to and from the city center. A Mode-Split Model. In 1974-5 Dr. Anderson worked at the Colorado Regional Transport District on a large study of transit alternatives. His main task was to monitor and help direct the ridership studies, and in so doing, he became thoroughly familiar with the methods used and he worked with two top ridership professionals, James McLynn and Gordon Schultz. The method used is based on a so-called “logit model.” Using the coefficients used by transit professionals, he developed such a model for a generic square city. The key factors are walk time, wait time, transfer time, and ride time as discussed by Professor Navin in #1 above. With these factors appropriate to a grid bus system, he got mode splits to bus of about one percent. Substituting times appropriate to PRT, the mode split increases to the neighborhood of 30%. This result is consistent with the results presented above and makes logical sense because of the value people generally place on their travel time.A Ridership study for Downtown Minneapolis. In 2001 SRF Consulting Group, Inc. of Minneapolis performed a ridership study of a PRT system in Downtown Minneapolis. The results of the study are reported in the paper “PRT Forecasts for Downtown Minneapolis.” The PRT system had 11.3 miles of guideway, 33 stations, and 650 vehicles. With a fare of $1 and an average waiting time of 30 seconds the study estimated ridership as 73,400 trips per day. The system was estimated to cost about $95 million. On that basis, taking into account all costs (capital and operation) the breakeven fare on this system is about 60 cents per trip, which is easily recoverable from fares, not counting goods movement and advertising revenue. So the system will actually generate net revenue, which is unheard of with conventional transit. Appendix BPopulation Density ModelE. S. Mills found that the density of the population in cities closely follows the exponential function Population Density=De-γr (B-1)in which D is the density at the center (the core density), e is the base of the natural logarithm, r is the radius from the center, and γ (Gamma) is a constant.The population within a radius R of the center of the city is PopulationR=0RDe-γrφrdr=φDγ21-1+γRe-γR (B-2) in which φ is the angle in radians that subtends the city. For example, if there are no natural barriers so that the city expands in all directions φ=2π or 360o. If the city is located on a large body of water φ=π. The population of the whole city, P, is found by setting R=∞. Thus, P=φDγ2 (B-3)so equation (B-2) can be written in the form PR=P1-1+γRe-γR (B-4)Unfortunately, the populated area in the exponential model has an infinite radius, giving a population density of zero, but the value for population density must be assumed to correspond to a finite areaAf=φ2Rf2 (B-5) which has a finite radius Rf. Let us assume thatPRf=0.95P (B-6)Then equation (B-4) gives0.95=1-1+γRfe-γRfOr 201+γRf=eγRf(B-7)This equation can be solved by trial and error. The solution is γRf=4.7439. Hence, from equation (B-5), Rf=2Afφ and γ=4.7439Rf (B-8)Thus, the constant γ is a function only of the area of the city and the angle φ. Combining equations (B-4) and (B-6), the population within any radius is PR=PRf0.951-1+γRe-γR (B-9) in which, from equations (8),γ=4.7439φ2Af (B-10) So, with PRf, Af and φ given for a specific city, the population within a given radius R can be found from equation (B-9). From equations (B-3) and (B-6), the core population density isD=γ2φPRf0.95=11.84PRfAf (B-11)The PRT system is assumed to be a square network with given line spacing and stations spaced midway between the intersections between the north-south and east-west lines. The network will be described by giving its side A1/2. Its area is A. To determine the population within a network of a given area, the radius to be substituted into equation (B-9) is given by equation (B-8). Economic ViabilityConsider the following equation:Cost per Trip=AmortizationFactorCapital Cost+Yearly Operating CostTrips per YearWhereAmortizationFactor=Cost of Capital+Expected ReturnYearly Operating Cost ≈3%×Capital CostWith a markedly low Federal Reserve Interest Rate, the Cost of Capital to borrow money has been in recent years very low.The “Expected Return” must be greater than that obtained with other uses of capital.PRT Ridership StudiesThe most significant justification for working to introduce a totally new kind of public transport is that it is expected, based on its service characteristics, to be able to attract many more riders than are attracted to conventional transit. Several studies have been performed to estimate PRT ridership. Here are the most important:1. Paper by Francis P. D. Navin, “Time Costs in Personal Rapid Transit,” Personal Rapid Transit II, University of Minnesota, 1974. The author was then Assistant Professor of Civil Engineering, University of British Columbia. He found that observed behavior of conventional-transit riders agrees with the results of analytical ridership models if the model considers total trip time as a disutility of the following form, in which the “C” symbols are dimensionless coefficients:Ride time + Cwalk Walk time + Cwait Wait time + Ctransfer Transfer timeThe larger the disutility the fewer the transit riders. By regression analysis on transit data from several cities, he found the coefficients shown in Table 1. These coefficients show, for example, that in calculating ridership one minute of walk time has the same disutility as 1.65 to 2.08 minutes of ride time, etc.Table 1. Perceived time coefficients for a ridership model.LowHighCwalk1.652.08Cwait4.156.34Ctransfer6.6210.0By applying a model that treated time in this way, he found that for a PRT system in which the walk was three minutes, the wait and transfer times were zero and the travel speed was 40 mph, for data for Minneapolis the fraction of total trips that would be attracted to PRT (the mode split to PRT) was over 50%, and that the mode split to PRT increased with the travel distance.2. The Aerospace Corporation. Irving, J. H., Bernstein, H., Olson, C. L., and Buyan, J. 1978. Fundamentals of Personal Rapid Transit, Lexington Books, D. C. Heath and Company, Lexington, MA (). This book records the work of The Aerospace Corporation on personal rapid transit. It contains a chapter on Ridership that describes a so-called “Monte Carlo” Mode Split Model. The term “Monte Carlo” means that the origin and destination of a trip are selected at random from a distribution and other attributes of the traveler are also selected at random from their distributions. For this trip the walk time, wait time, and ride time for PRT are calculated; the fare is taken into account; a value of time is taken into account so that the times become costs; and similar quantities are computed for the auto trip, provided an auto is available. The trip is assigned to the mode for which, considering actual and perceived costs, the cost is less. The process is repeated until it converges to a steady value. By applying such a model to traffic in Los Angeles, the Aerospace Corporation PRT group settled on a mode split to PRT of 34% in their economic analysis.3. Indianapolis. In 1979-1980 a study sponsored jointly by the State of Indiana and the Urban Mass Transportation Administration was performed for automated transit systems for downtown Indianapolis. Vehicles designed for 100, 60, 40, 20, 12, and 3 passengers were included and networks suitable for each vehicle size were laid out. Ridership estimates were developed by the consultant, Barton Aschman Associates, for each system. The 3-passenger-vehicle system used in the study was a PRT system developed by DEMAG+MBB in Germany called Cabintaxi. For this system the layout had 12.2 miles of guideway and 46 stations. The guideway covered an area two miles in the east-west direction and one mile in the north-south direction. The consultant estimated that the ridership on the PRT system would be about 100,000 passenger-trips per day, sufficient to pay all of the costs out of revenues.4. Swedish Studies. The Swedish Transport and Communications Research Board sponsored a series of studies of PRT in Swedish cities that resulted in 1998 in the report “PRT—a Suitable Transport System for Urban Areas in Sweden?” The conclusion of the report is that in Gothenburg an area-wide PRT system would attract 23% of all transport passengers, and 40% of the trips to and from the city center. 5. A Mode-Split Model. In 1974-5 Dr. Anderson worked at the Colorado Regional Transport District on a large study of transit alternatives. His main task was to monitor and help direct the ridership studies, and in so doing, he became thoroughly familiar with the methods used and he worked with two top ridership professionals, James McLynn and Gordon Schultz. The method used is based on a so-called “logit model.” Using the coefficients used by transit professionals, he developed such a model for a generic square city. The key factors are walk time, wait time, transfer time, and ride time as discussed by Professor Navin in #1 above. With these factors appropriate to a grid bus system, he got mode splits to bus of about one percent. Substituting times appropriate to PRT, the mode split increases to the neighborhood of 30%. This result is consistent with the results presented above and makes logical sense because of the value people generally place on their travel time.6. A Ridership study for Downtown Minneapolis. In 2001 SRF Consulting Group, Inc. of Minneapolis performed a ridership study of a PRT system in Downtown Minneapolis. The results of the study are reported in the paper “PRT Forecasts for Downtown Minneapolis.” The PRT system had 11.3 miles of guideway, 33 stations, and 650 vehicles. With a fare of $1 and an average waiting time of 30 seconds the study estimated ridership as 73,400 trips per day. The system was estimated to cost about $95 million. On that basis, taking into account all costs (capital and operation) the breakeven fare on this system is about 60 cents per trip, which is easily recoverable from fares, not counting goods movement and advertising revenue. So the system will actually generate net revenue, which is unheard of with conventional transit. Estimates of Profits and IRR from the ITNS IndustryJ. E. AndersonBreak-Even Fare per Passenger-km of Travel(1)(2)Reasonable ranges of values of the parameters in the above equations in urban areas are discussed in the following paragraphs.The Annual Cost for capital amortization plus operation and maintenance is roughly 10% of the total capital cost, assuming that the system is built using borrowed money.The Average Trip Length of city bus trips is typically about 4 to 6 km and for auto trips in urban areas in the USA is 10 to 16 km. For an ITNS system the average trip length can be expected to be in between these numbers – say in the range of 6 to 10 km. Thus an average trip length of 8 km in a built-out system is reasonable.Data collected in the USA shows that the total number of vehicle trips in urban areas per person per day, called mobility, ranges from 1.65 in the area around New York City to 3.18 in Oklahoma City. In suburbs mobility is often as high as 10 trips per person per day. The results also show, as can be expected, that ease of travel increases mobility. So let us assume a mobility of 4 trips per person per day. For conventional transit, the ratio of yearly to daily travel is usually assumed to be about 300. Data collected by planners shows that the ratio of daily travel to peak-hour travel is as low as 3 for commuter rail systems and increases to around 12 for taxis and walking, implying that with more personalized service travel is distributed more uniformly throughout the day. For a similar reason, it can be expected that there will be more travel on weekends and holidays with a ITNS, a demand-responsive system, than with conventional transit. Thus for ITNS we estimate the ratio of yearly to weekday travel at 340.The population density of cities varies widely, from a low in the USA of about 2000 people per square mile (772 people per square km) to a high of around 100,000 people per square mile (40,000 people per square km). For purposes of discussion let us assume a city population of 6000 people per square mile (2317 people per square km.)The fraction of vehicle trips that would be taken by ITNS is called the “mode split.” A number of studies show that a factor of 0.30 is reasonable for a system in which all stations are within 400 meters of any point in the network. This is far higher than achieved by conventional transit, which is no match for the auto.Now let us assume a square grid of ITNS guideways spaced 0.8 km apart in the north-south and east-west directions, i.e. a square grid that with stations at the midpoints of the squares, places every point within 400 meters of a station. The area of one of these squares is 0.64 square km. There is a length of 3.2 km of guideway around one of these squares, but each is shared with an adjacent square, so we count 1.6 km of guideway for each square.Then, from equation (2) and using the above average parameters,The ITNS system cost is estimated with profit to the suppliers to average about US$7,500.000 per km. Then, equation (1) becomesProfit per Square Kilometer per YearAssuming the above average factors, the number of ITNS trips per year in each of the squares of side 0.8 km is 1780(340) = 605,200 and the number of passenger-km of travel per year is 4,841,600. The break-even cost of construction and operation would with the above numbers be $0.248(4,841,600) = $1,200,700 for each of the squares. (At the beginning of this section we assumed that this cost was $1,200,000.) Adding say a 20% fee to the investor would yield $240,000 for each one of the 0.64 km2 squares or $375,000 per square km of system. However, the revenue produced by the ITNS system will come from three sources: passenger trips, freight trips mostly taking place during off-peak periods, and focused advertising. The later two sources could easily match passenger revenues, and thus the fee should be based on this larger revenue. Suppose we modestly increase the fee by 50% to $375,000(1.5) = $562,500. Then, based on the operation of ITNS systems covering an area A, the annual profit from revenue on an initial investment of $15,000,000 would be $562,500A.If the system is sold to another party, there would be a one-time return on the capital cost with a fee of say 20% of the capital cost of $7,500,000 per km, or $1,500,000 per km. As calculated above, assuming a square grid of guideways spaced 0.8 km apart, there would be 1.6/0.64 = 2.5 km of guideway per square km, so the one-time profit would be 2.5($1,500,000)A = $3,750,000A. In the following paragraph we estimate a reasonable rate of construction of ITNS systems and for it estimate the internal rate of return (IRR).If the company finances the construction of systems both the annual profit on revenue and the one-time profit on construction are available.How soon and how fast can ITNS systems be built?Operation of the first small system can begin in the fifth year from the date the initial investment is made. Expansion will increase slowly for the first few years as consultants begin to become aware that there is a transit system that can turn a profit and later as Transportation Professors seriously begin including ITNS in their courses. After about the tenth year, the business will begin to expand more rapidly as cities around the world become aware that there is a much more efficient solution to their transportation problems. With an effective marketing program it is possible that the business may expand more rapidly.The Cash Flow and Internal Rate of Return on InvestmentIn the following Excel spreadsheet, the cash requirement in the first three years is taken from page 5 of the companion document “Summary of Plan for Testing Personal Rapid Transit.” The meaning of each column is as follows:ColumnData in Column1Beginning of the year for which data is given.2km of guideway in operation at the beginning of each year.3Proposed investment at the beginning of each year.4Cumulative km guideway in operation.5Yearly return on revenue.6One-time return on construction of the system.7Total return.8Cash flow.Internal Rate of Return on InvestmentkmCum kmReturnOne-TimeTotalYearGdwyInvestmentGdwyper yearReturnReturnCash Flow1-$8,520,000-$8,520,0002-$5,498,000-$5,498,0003-$960,000-$960,0004$0555$1,125,000$7,500,000$8,625,000$8,625,00061015$2,250,000$15,000,000$17,250,000$17,250,00071530$3,375,000$22,500,000$25,875,000$25,875,00082555$5,625,000$37,500,000$43,125,000$43,125,00093590$7,875,000$52,500,000$60,375,000$60,375,0001050140$11,250,000$75,000,000$86,250,000$86,250,0001175215$16,875,000$112,500,000$129,375,000$129,375,00012150365$33,750,000$225,000,000$258,750,000$258,750,00013300665$67,500,000$450,000,000$517,500,000$517,500,000145001165$112,500,000$750,000,000$862,500,000$862,500,000157501915$168,750,000$1,125,000,000$1,293,750,000$1,293,750,000161000?2915$225,000,000$1,500,000,000$1,725,000,000$1,725,000,000-$14,978,000AnnualOne-Time?IRR =67%Profit per km:$225,000Profit per km:$1,500,000'This program COSTPPM.BAS calculates the cost per passenger-mile of ITNS 'Systems that was used to prepare Figure 22 of the paper ' “High-Capacity Personal Rapid Transit: Rationale, Attributes, Status, ' Economics, and Benefits”DEFDBL A-ZDIM I AS INTEGERDIM CPPMi(1 TO 7) AS DOUBLESystemCostPerMi = 12000000 'system cost per mileAnnualizationFactor = .1 'ratio of total annual to capital costTripsPPPDay = 4 'trips per person per dayTripsPYrPDay = 340 'ratio of yearly to daily ridershipAveTripLength = 5 'average trip length in milesLineSpacing = .5 'spacing between lines in a square grid 'network in milesMiLinePerSquare = 2 * LineSpacing 'miles of line per squareCostPerSquarePerYr = SystemCostPerMi * AnnualizationFactor * MiLinePerSquareCLSPRINTPRINT " Cost per Passenger-Mile vs. Population Density and Mode Split"PRINT " Density ModeSplit = 10%, 30%, 50%, 70%"FOR I = 2 TO 10 PopDensity = 1000 * I PopPerSquare = PopDensity * LineSpacing ^ 2 TripsPerYrPerSq = TripsPYrPDay * TripsPPPDay * PopPerSquare FOR II = 1 TO 7 STEP 2 ModeSplit = II / 10 ITNSTripsPerYear = TripsPerYrPerSq * ModeSplit PassMiPerYr = ITNSTripsPerYear * AveTripLength CPPMi(II) = CostPerSquarePerYr / PassMiPerYr NEXT II PRINT " "; PRINT USING "#####"; PopDensity; PRINT SPC(11); PRINT USING "####.###"; CPPMi(1); CPPMi(3); CPPMi(5); CPPMi(7) SLEEPNEXT ICost per Passenger-Mile vs. Population Density and Mode Split Density Mode Split = 10%, 30%, 50%, 70% 2000 3.529 1.176 0.706 0.504 3000 2.353 0.784 0.471 0.336 4000 1.765 0.588 0.353 0.252 5000 1.412 0.471 0.282 0.202 6000 1.176 0.392 0.235 0.168 7000 1.008 0.336 0.202 0.144 8000 0.882 0.294 0.176 0.126 9000 0.784 0.261 0.157 0.112 10000 0.706 0.235 0.141 0.101 -114300800100Figure 22 in the paper “High-Capacity Personal Rapid Transit: Rationale, Attributes, Status, Economics, and Benefits”'This program (MODESPLT.BAS) is a Monte Carlo Mode Split Model'============================================================================DECLARE SUB AdvanceToNode ()DECLARE SUB AdvanceToStation ()DECLARE SUB Arrow (X!, Y!, s!)DECLARE SUB ArrowMatrix ()DECLARE SUB ChangeValues ()DECLARE SUB DisplayValues ()DECLARE SUB ExplanationM ()DECLARE SUB ExplanationP ()DECLARE SUB Grid ()DECLARE SUB ModeSplitScale ()DECLARE SUB Pause ()DECLARE SUB PlotCircle ()DECLARE SUB PrintValues ()DECLARE SUB StationLocation ()DECLARE SUB Test ()DECLARE SUB UnitChange ()DECLARE FUNCTION Odd (K)DECLARE FUNCTION Even (K)DIM X(1 TO 2), Y(1 TO 2), Xstation(1 TO 2), Ystation(1 TO 2), Xg(1 TO 2), Yg(1 TO 2)DIM A(2, 2, 1 TO 4) AS INTEGERDIM Trips, N.Trips, N.Watch AS INTEGERCOMMON SHARED X, Y, Xd, Yd, RideDistPRT, LineSpacing, AveSpeedPRT, AveSpeedAuto, WalkSpeedCOMMON SHARED WalktoRide, WaittoRide, WaitTimePRT, WaitTimeAuto, WalkDistAuto, TimeCostCOMMON SHARED CostPRT, CostAuto, ParkCost, Scale, CentsperMinute, LogitCoefCOMMON SHARED Scr, X0, Y0, Xmax, N, M, dA, Flag AS INTEGER'============================================================================CLSSCREEN 9COLOR 7, 8PRINT : PRINTPRINT " *****************************************************************"PRINT " * This is a Monte Carlo Modal-Spit Model designed to estimate *"PRINT " * the mode split between a PRT System and an auto system. *"PRINT " * *"PRINT " * Developed by J. E. Anderson *"PRINT " *****************************************************************"PRINTDO PRINT " It is best to view the model at least once to see how it works. " PRINT " Then, for an explanation of the theory behind the model, press Y." PRINT INPUT " To continue with no explanation press N. ", Expl$ Expl$ = UCASE$(Expl$)LOOP UNTIL Expl$ = "Y" OR Expl$ = "N"IF Expl$ = "Y" THEN PRINT INPUT " Do you want the explanation on the monitor or on the printer? M/P ", MP$ MP$ = UCASE$(MP$) IF MP$ = "M" THEN ExplanationM ELSEIF MP$ = "P" THEN ExplanationP END IFEND IFCONST KmpMi = 5.28 * .3048 'kilometers per mileDO PRINT INPUT " Do you want to use English Units or Metric Units? E/M ", U$ U$ = UCASE$(U$)LOOP UNTIL U$ = "E" OR U$ = "M"IF U$ = "E" THEN Ldist$ = "mi" Spd$ = "mph"ELSE Ldist$ = "km" Spd$ = "kph"END IF'------DO PRINT INPUT " Do you want to load the original data set or a new set? O/N ", Dat$ Dat$ = UCASE$(Dat$)LOOP UNTIL Dat$ = "O" OR Dat$ = "N"IF Dat$ = "O" THEN File$ = "MODESPLT"ELSE INPUT " Enter the name of the file you want to load: ", File$END IF'------OPEN File$ + ".DAT" FOR INPUT AS #1 INPUT #1, Unit$, Scr, X0, Y0, Scale, M, dA, Xmax, LineSpacing, N, AveSpeedPRT INPUT #1, AveSpeedAuto, WalkSpeed, WalktoRide, WaittoRide, WalkDistAuto INPUT #1, WaitTimePRT, WaitTimeAuto, TimeCost, CostPRT, CostAuto, ParkCost, LogitCoefCLOSE #1IF ABS(N / 2 - INT(N / 2)) < .1 THEN N = N + 1 PRINT PRINT " You used an even value of N. N must be odd," PRINT " therefore your value has been increased by one." PRINT " Press any key to continue." PauseEND IFUnitChangeDisplayValuesDO PRINT " If you want to change a value, enter " INPUT " the number of that value, otherwise enter zero: ", NoofValue PRINT ChangeValuesLOOP UNTIL NoofValue = 0IF Flag = 1 THEN DisplayValues DO INPUT " Do you want to store these new values? Y/N ", Sto$ Sto$ = UCASE$(Sto$) LOOP UNTIL Sto$ = "Y" OR Sto$ = "N"END IFIF Sto$ = "Y" THEN DO PRINT PRINT " You must give a name of up to eight characters long for the name of" PRINT " the file of new values. The first character must be a letter, the" PRINT " rest may be numbers or underlines. Do not include a DOS extension." INPUT " Enter the name here: ", File$ File$ = UCASE$(File$) IF File$ = "MODESPLT" THEN PRINT DO PRINT " You have selected the name of the original data file. If you use it" INPUT " you will overwrite that data. Do you want to do that? Y/N ", Dat$ Dat$ = UCASE$(Dat$) LOOP UNTIL Dat$ = "Y" OR Dat$ = "N" ELSEIF File$ = "NETECON" THEN PRINT PRINT " You cannot use this name, please pick another." Dat$ = "N" END IF LOOP WHILE Dat$ = "N" OPEN File$ + ".DAT" FOR OUTPUT AS #1 WRITE #1, Unit$, Scr, X0, Y0, Scale, M, dA, Xmax, LineSpacing, N, AveSpeedPRT WRITE #1, AveSpeedAuto, WalkSpeed, WalktoRide, WaittoRide, WalkDistAuto WRITE #1, WaitTimePRT, WaitTimeAuto, TimeCost, CostPRT, CostAuto, ParkCost, LogitCoef CLOSE #1END IFPRINTDO INPUT " Do you want to print the input and output values on the printer? Y/N ", Prin$ 'Prin$ = "N" Prin$ = UCASE$(Prin$)LOOP UNTIL Prin$ = "Y" OR Prin$ = "N"IF Prin$ = "Y" THEN PrintValuesParkCost = ParkCost * 100 'convert to cents per tripCentsperMinute = TimeCost / .6 'convert from $/hr to cents/minuteAveSpeedPRT = AveSpeedPRT / 60 'convert to minutesAveSpeedAuto = AveSpeedAuto / 60WalkSpeed = WalkSpeed / 60WaitTimePRT = WaitTimePRT / 60WaitTimeAuto = WaitTimeAuto / 60K = INT(M / N) 'spacing between grid lines in graphicsM = K * N 'M must be an integeral multiple of KArrowMatrix 'arrow-direction matrix'----------------------------------------------------------------------------PRINTPRINT " The Monte Carlo calculates a large number of cases."PRINT " A good number to start with is 1000."INPUT " How many trips do you want to calculate? ", N.Trips'N.Trips = 2000PRINTPRINT " The program allows you to watch the progress of the number"PRINT " of trips you specify. Five to ten is a good range."INPUT " How many trips do you want to watch? ", N.Watch'N.Watch = 0PRINTPRINT " Press any key to start and to advance each trip watched."PRINTPRINT " The dots that appear and advance from left to right are the"PRINT " cumulative average mode split in % on the indicated scale."PauseCLSRANDOMIZE TIMERGridModeSplitScale'-------DO 'each cycle calculates one trip WalkDistPRT = 0 'initialize distances RideDistPRT = 0 FOR I = 1 TO 2 '1 = origin, 2 = destination X(I) = (N + 1) * RND(1) - .5 'random selection of origin and destination Y(I) = (N + 1) * RND(1) - .5 'Plot the origin and destination, removing it for the next trip: IF Trips < N.Watch THEN CIRCLE (Xg(I), Yg(I)), I + 2, 0 Xg(I) = X0 + Scale * K * X(I) Yg(I) = Y0 - K * Y(I) IF Trips < N.Watch THEN CIRCLE (Xg(I), Yg(I)), I + 2, 15 Xline = INT(X(I)) 'determine line to left of O & D IF Xline = -1 THEN Xline = 0 ELSEIF Xline = N THEN Xline = N - 1 END IF Yline = INT(Y(I)) 'determine line below O & D IF Yline = -1 THEN Yline = 0 ELSEIF Yline = N THEN Yline = N - 1 END IF Xlocal = X(I) - Xline 'coordinates within a grid square Ylocal = Y(I) - Yline StationLocation 'locates nearest station within grid square WalkDistPRT = WalkDistPRT + ABS(Xlocal - Xs) + ABS(Ylocal - Ys) Xstation(I) = Xline + Xs 'locates the station of O & D in network Ystation(I) = Yline + Ys NEXT I X = Xstation(1): Y = Ystation(1) 'origin and running position Xd = Xstation(2): Yd = Ystation(2) 'destination station '---Plot the destination station Xdg = X0 + Scale * K * Xd Ydg = Y0 - K * Yd IF Trips < N.Watch THEN CIRCLE (Xdg, Ydg), 8, 11 IF X <> Xd AND Y <> Yd THEN 'don't count trip if O & D station same DO 'trip-progression loop IF Trips < N.Watch THEN PlotCircle 'plot trip progress Pause END IF AdvanceToNode 'advance to next node IF Trips < N.Watch THEN PlotCircle AdvanceToStation 'advance to next station LOOP WHILE Flag = 0 IF Trips < N.Watch THEN PlotCircle WalkDistPRT = WalkDistPRT * LineSpacing 'grid spacing previously unity WalkTimePRT = WalkDistPRT / WalkSpeed RideDistPRT = RideDistPRT * LineSpacing RideTimePRT = RideDistPRT / AveSpeedPRT TimePRT = WalktoRide * WalkTimePRT + WaittoRide * WaitTimePRT + RideTimePRT WalkTimeAuto = WalkDistAuto / WalkSpeed RideDistAuto = (ABS(X(1) - X(2)) + ABS(Y(1) - Y(2))) * LineSpacing RideTimeAuto = RideDistAuto / AveSpeedAuto TimeAuto = WalktoRide * WalkTimeAuto + WaittoRide * WaitTimeAuto + RideTimeAuto DisUtilityPRT = CentsperMinute * TimePRT + CostPRT * RideDistPRT DisUtilityAuto = CentsperMinute * TimeAuto + CostAuto * RideDistAuto + ParkCost DeltaDisUtility = (DisUtilityPRT - DisUtilityAuto) / LogitCoef ModeSplitPRT = 1 / (1 + EXP(DeltaDisUtility)) SumSplit = SumSplit + ModeSplitPRT Trips = Trips + 1 MeanSplitPRT = SumSplit / Trips AvePRTTripLength = AvePRTTripLength + RideDistPRT AveAutoTripLength = AveAutoTripLength + RideDistAuto END IF PSET (Xmax * Trips / N.Trips, Y0 + 20 - MeanSplitPRT * Y0) 'plot mode split 'remove markers and start with new trip IF Trips <= N.Watch THEN CIRCLE (Xg(1), Yg(1)), 3, 0 CIRCLE (Xg(2), Yg(2)), 4, 0 CIRCLE (Xdg, Ydg), 8, 0 END IFLOOP UNTIL Trips >= N.TripsAvePRTTripLength = AvePRTTripLength / TripsAveAutoTripLength = AveAutoTripLength / TripsCircuity = AvePRTTripLength / AveAutoTripLengthIF Prin$ = "N" THEN PRINT PRINT "The Mode Split to PRT is"; PRINT USING "###.##"; 100 * MeanSplitPRT; : PRINT " percent." PRINT "Average Auto Trip Length: "; PRINT USING "##.##"; AveAutoTripLength; : PRINT " "; Ldist$ PRINT "PRT Trip Circuity: "; PRINT USING "#.##"; CircuityELSE LPRINT LPRINT "The Mode Split to PRT is"; LPRINT USING "###.#"; 100 * MeanSplitPRT; : LPRINT " percent." LPRINT "Average Auto Trip Length: "; LPRINT USING "##.##"; AveAutoTripLength; : LPRINT " "; Ldist$ LPRINT "PRT Trip Circuity: "; LPRINT USING "#.##"; CircuityEND IFPRINT "Press any key to quit."SLEEPSUB AdvanceToNode IF Odd(X) = 1 THEN Y = Y + .5 ELSEIF Even(X) = 1 THEN Y = Y - .5 ELSEIF Odd(Y) = 1 THEN X = X - .5 ELSEIF Even(Y) = 1 THEN X = X + .5 END IF RideDistPRT = RideDistPRT + .5END SUBSUB AdvanceToStation IF Odd(X) = 1 THEN IF Even(Y) = 1 THEN IF ABS(X - N) < .01 THEN Y = Y + .5 Test ELSEIF Xd - X > Yd - Y THEN X = X + .5 Test ELSEIF Xd - X < Yd - Y THEN IF Yd - Y = 1 AND Xd > X THEN X = X + .5 ELSE Y = Y + .5 Test END IF ELSEIF Odd(Y) = 1 THEN IF ABS(Y - N) < .01 THEN X = X - .5 Test ELSEIF Xd - X < Y - Yd THEN IF X - Xd = 1 AND Yd > Y THEN Y = Y + .5 ELSE X = X - .5 Test ELSEIF Xd - X > Y - Yd THEN Y = Y + .5 Test END IF END IF ELSEIF Even(X) = 1 THEN IF Odd(Y) = 1 THEN IF X < .01 THEN Y = Y - .5 Test ELSEIF Xd - X > Yd - Y THEN IF Y - Yd = 1 AND Xd < X THEN X = X - .5 ELSE Y = Y - .5 Test ELSEIF Xd - X < Yd - Y THEN X = X - .5 Test END IF ELSEIF Even(Y) = 1 THEN IF Y < .01 THEN X = X + .5 Test ELSEIF Xd - X > Y - Yd THEN IF Xd - X = 1 AND Yd < Y THEN Y = Y - .5 ELSE X = X + .5 Test ELSEIF Xd - X < Y - Yd THEN Y = Y - .5 Test END IF END IF END IF RideDistPRT = RideDistPRT + .5END SUBSUB Arrow (X, Y, s) SHARED A() AS INTEGER LINE (X, Y)-(X + A(0, 0, s) * dA, Y + A(0, 1, s) * dA), 10 LINE (X, Y)-(X + A(1, 0, s) * dA, Y + A(1, 1, s) * dA), 10END SUBSUB ArrowMatrix 'of coefficients used to graph arrow heads SHARED A() AS INTEGER A(0, 0, 1) = -1: A(0, 0, 3) = -1 A(1, 1, 1) = -1: A(1, 1, 3) = 1 A(1, 0, 1) = -1: A(1, 0, 3) = 1 A(0, 1, 1) = 1: A(0, 1, 3) = 1 A(0, 0, 2) = 1: A(0, 0, 4) = 1 A(1, 1, 2) = 1: A(1, 1, 4) = -1 A(1, 0, 2) = 1: A(1, 0, 4) = -1 A(0, 1, 2) = -1: A(0, 1, 4) = -1END SUBSUB ChangeValues SHARED Ldist$, Spd$, NoofValue IF NoofValue > 0 THEN Flag = 1 SELECT CASE NoofValue CASE 1 PRINT " 1. Line spacing, "; Ldist$; INPUT ".................................... ", LineSpacing CASE 2 INPUT " 2. The network width is N * LineSpacing. N is ......... ", N CASE 3 PRINT " 3. The average riding speed by PRT, "; Spd$; INPUT "................ ", AveSpeedPRT CASE 4 PRINT " 4. The average riding speed by auto, "; Spd$; INPUT "............... ", AveSpeedAuto CASE 5 PRINT " 5. The average walking speed, "; Spd$; INPUT "...................... ", WalkSpeed CASE 6 INPUT " 6. The average waiting time by PRT, sec ............... ", WaitTimePRT CASE 7 INPUT " 7. The average waiting time by auto, sec .............. ", WaitTimeAuto CASE 8 PRINT " 8. The average auto-walk distance at both ends, "; Ldist$; INPUT "..... ", WalkDistAuto CASE 9 INPUT " 9. Ratio of perceived walk time to ride time........... ", WalktoRide CASE 10 INPUT " 10. Ratio of perceived wait time to ride time........... ", WaittoRide CASE 11 INPUT " 11. The perceived cost of time, $ per hour.............. ", TimeCost CASE 12 PRINT " 12. The fare on PRT, cents per "; Ldist$; INPUT " of trip distance...... ", CostPRT CASE 13 PRINT " 13. Perceived auto cost, cents per "; Ldist$; INPUT " of trip distance.. ", CostAuto CASE 14 INPUT " 14. Auto parking cost, $ per trip ...................... ", ParkCost CASE 15 INPUT " 15. Normalizing logit-model factor, cents .............. ", LogitCoef CASE 16 INPUT " 16. Screen number. HERC = 3, EGA = 9, VGA = 12 ......... ", Scr CASE 17 INPUT " 17. Origin of x-coordinate, pixels...................... ", X0 CASE 18 INPUT " 18. Origin of y-coordinate, pixels...................... ", Y0 CASE 19 INPUT " 19. Ratio of x-scale to y-scale......................... ", Scale CASE 20 INPUT " 20. Height of the grid on the screen, pixels............ ", M CASE 21 INPUT " 21. Arrow length used in plotting network, pixels....... ", dA CASE 22 INPUT " 22. Width of screen, pixels............................. ", Xmax END SELECT PRINTEND SUBSUB DisplayValues SHARED Ldist$, Spd$ PRINT PRINT SPC(6); " The following values describe the system analyzed." PRINT SPC(6); " Write down the numbers of the values you want to change." PRINT PRINT SPC(6); " 1. Line spacing, "; Ldist$; ".................................... "; LineSpacing PRINT SPC(6); " 2. The network width is N * LineSpacing. N is ......... "; N PRINT PRINT SPC(6); " 3. The average riding speed by PRT, "; Spd$; "................ "; AveSpeedPRT PRINT SPC(6); " 4. The average riding speed by auto, "; Spd$; "............... "; AveSpeedAuto PRINT SPC(6); " 5. The average walking speed, "; Spd$; "...................... "; WalkSpeed PRINT SPC(6); " 6. The average waiting time by PRT, sec ............... "; WaitTimePRT PRINT SPC(6); " 7. The average waiting time by auto, sec .............. "; WaitTimeAuto PRINT SPC(6); " 8. The average auto-walk distance at both ends, "; Ldist$; "..... "; WalkDistAuto PRINT SPC(6); " 9. Ratio of perceived walk time to ride time............"; WalktoRide PRINT SPC(6); "10. Ratio of perceived wait time to ride time........... "; WaittoRide PRINT SPC(6); "11. The cost of time, dollars per hour.................. "; TimeCost PRINT SPC(6); "12. The fare on PRT, cents per "; Ldist$; " of trip distance...... "; CostPRT PRINT SPC(6); "13. Perceived auto cost, cents per "; Ldist$; " of trip distance.. "; CostAuto PRINT SPC(6); "14. Auto parking cost, $ per trip ...................... "; ParkCost PRINT SPC(6); "15. Normalizing logit-model factor, cents .............. "; LogitCoef PRINT PRINT SPC(6); "Press any key to continue" PRINT Pause PRINT SPC(6); "Graphic Screen Parameters, distances in pixels: " PRINT SPC(6); "16. Screen number. HERC = 3, EGA = 9, VGA = 12 ......... "; Scr PRINT SPC(6); "17. Origin of x-coordinate ............................. "; X0 PRINT SPC(6); "18. Origin of y-coordinate ............................. "; Y0 PRINT SPC(6); "19. Ratio of x-scale to y-scale......................... "; Scale PRINT SPC(6); "20. Height of the grid on the screen.................... "; M PRINT SPC(6); "21. Arrow length used in plotting network............... "; dA PRINT SPC(6); "22. Width of screen..................................... "; Xmax PRINTEND SUBFUNCTION Even (U) IF ABS(INT(U / 2) - U / 2) < .01 THEN Even = 1 ELSE Even = 0END FUNCTIONSUB ExplanationM PRINT PRINT " ************************************************************************" PRINT " The Monte Carlo Modal-Split Model" PRINT " ************************************************************************" PRINT PRINT " The model determines the modal choice between auto and PRT in a" PRINT " square city which has a north-south and east-west grid of streets for" PRINT " two-way auto travel, upon which is superimposed a one-way grid of PRT" PRINT " lines of specified spacing. The number of such one-way line spacings" PRINT " is specified as an odd integer, N. The transit service area is taken" PRINT " as the area of the grid plus a strip half a line spacing wide outside" PRINT " the grid." PRINT PRINT " The model picks a trip by defining a randomly chosen origin and" PRINT " a randomly chosen destination, each within the transit service area." PRINT " For this trip, the walk distance and ride distance by PRT are found as" PRINT " the vehicle follows the shortest path to its destination. Then, the" PRINT " walk time and ride time in minutes are found from the equations" PRINT PRINT " WalkTimePRT = 60 * WalkDistPRT / WalkSpeed " PRINT " RideTimePRT = 60 * RideDistPRT / AveSpeedPRT " PRINT PRINT " **Press any key to continue**" Pause PRINT PRINT " The weighted trip time by PRT is then" PRINT PRINT " TimePRT = WalktoRide * WalkTimePRT + " PRINT " WaittoRide * WaitTimePRT + RideTimePRT" PRINT PRINT " where the wait time for PRT is one of the input parameters." PRINT PRINT " Regression analysis on modal-split data shows that travel behavior" PRINT " can be explained only if it is assumed that people perceive walking time" PRINT " to advance more slowly than riding time by a ratio denoted by 'WalktoRide.'" PRINT " The term 'WaittoRide' has the corresponding meaning for waiting time." PRINT " Frank Navin, in a paper in the volume 'Personal Rapid Transit II,' " PRINT " discusses this phenomonon and presents data he obtained that shows that" PRINT " these factors are between two and six, depending on various factors." PRINT PRINT " **Press any key to continue**" Pause PRINT PRINT " The corresponding terms for the auto are:" PRINT PRINT " WalkTimeAuto = 60 * WalkDistAuto / WalkSpeed " PRINT " RideDistAuto = ABS(X(1) - X(2)) + ABS(Y(1) - Y(2))" PRINT PRINT " in which X(1), Y(1) are the coordinates of the trip origin and" PRINT " X(2), Y(2) are the coordinates of the trip destination." PRINT PRINT " RideTimeAuto = 60 * RideDistAuto / AveSpeedAuto " PRINT PRINT " The weighted trip time by Auto is then" PRINT PRINT " TimeAuto = WalktoRide * WalkTimeAuto +" PRINT " WaittoRide * WaitTimeAuto + RideTimeAuto" PRINT PRINT " **Press any key to continue**" Pause PRINT PRINT " Now, disutility functions in terms of cost are found from the equations" PRINT PRINT " DisUtilityPRT = CentsperMinute * TimePRT + CostPRT * RideDistPRT" PRINT " DisUtilityAuto = CentsperMinute * TimeAuto + CostAuto * RideDistAuto" PRINT " + ParkingCost" PRINT " DeltaDisUtility = (DisUtilityPRT - DisUtilityAuto) / LogitCoef" PRINT PRINT " in which 'CentsperMinute' is the cost of time in cents per minute," PRINT " CostPRT is the cost in cents per mi or km to travel by PRT, " PRINT " CostAuto is the perceived cost in cents per mi or km to travel by auto," PRINT " and LogitCoef defines the change in disutility required to change the " PRINT " mode split from 0.5 to 1/(1 + e) = 0.27 or 1/(1 + 1/e) = 0.73." PRINT PRINT " Using the standard logit mode-split model, the mode split to PRT" PRINT " corresponding to this difference in disutility is " PRINT PRINT " ModeSplitPRT = 1 / [1 + EXP(DeltaDisUtility)]" PRINT PRINT " **Press any key to continue**" Pause PRINT PRINT " For each run, we then compute " PRINT PRINT " SumSplit = SumSplit + ModeSplitPRT" PRINT " Trips = Trips + 1" PRINT PRINT " from which the accumulated mean mode split is" PRINT PRINT " Mean mode split to PRT = SumSplit / Trips." PRINT PRINT " This value is plotted as a dot superimposed on the image of the PRT grid." PRINT " The sequence of such dots shows how many trip samples are needed before" PRINT " the average converges." PRINT PRINT " Circuity, shown at the end of the run, is the ratio of the " PRINT " average PRT-trip distance to the average auto-trip distance." PRINT " ************************************************************************" PRINTEND SUBSUB ExplanationP LPRINT CHR$(27); "M" WIDTH LPRINT 100 LPRINT SPC(12); "****************************************************************************" LPRINT SPC(12); " The Monte Carlo Modal-Split Model" LPRINT SPC(12); "****************************************************************************" LPRINT LPRINT SPC(12); " Developed by J. E. Anderson" LPRINT LPRINT SPC(12); " The model determines the modal choice between auto and PRT in a square" LPRINT SPC(12); "city which has a north-south and east-west grid of streets for two-way auto" LPRINT SPC(12); "travel, upon which is superimposed a one-way grid of PRT lines of specified" LPRINT SPC(12); "spacing. The number of such one-way line spacings is specified as an odd" LPRINT SPC(12); "integer, N. The transit service area is taken as the area of the grid plus" LPRINT SPC(12); "a strip half a line spacing wide outside the grid." LPRINT LPRINT SPC(12); " The model picks a trip by defining a randomly chosen origin and a ran-" LPRINT SPC(12); "domly chosen destination, each within the transit service area. For this" LPRINT SPC(12); "trip, the walk distance and ride distance by PRT are found as the vehicle" LPRINT SPC(12); "follows the shortest path to its destination. Then, the walk time and ride" LPRINT SPC(12); "time in minutes are found from the equations" LPRINT LPRINT SPC(12); " WalkTimePRT = 60 * WalkDistPRT / WalkSpeed" LPRINT SPC(12); " RideTimePRT = 60 * RideDistPRT / AveSpeedPRT " LPRINT LPRINT SPC(12); "The weighted trip time by PRT is then" LPRINT LPRINT SPC(12); " TimePRT = WalktoRide * WalkTimePRT + " LPRINT SPC(12); " WaittoRide * WaitTimePRT + RideTimePRT" LPRINT LPRINT SPC(12); "where the wait time for PRT is one of the input parameters." LPRINT LPRINT SPC(12); " Regression analysis on modal-split data shows that travel behavior can" LPRINT SPC(12); "be explained only if it is assumed that people perceive walking time to" LPRINT SPC(12); "advance more slowly than riding time by a ratio denoted by 'WalktoRide.' The" LPRINT SPC(12); "term 'WaittoRide' has the corresponding meaning for waiting time. Frank" LPRINT SPC(12); "Navin, in a paper in the volume 'Personal Rapid Transit II,' discusses this" LPRINT SPC(12); "phenomonon and presents data he obtained that shows that these factors are" LPRINT SPC(12); "between two and six, depending on various factors." LPRINT LPRINT SPC(12); "The corresponding terms for the auto are:" LPRINT LPRINT SPC(12); " WalkTimeAuto = 60 * WalkDistAuto / WalkSpeed " LPRINT SPC(12); " RideDistAuto = ABS(X(1) - X(2)) + ABS(Y(1) - Y(2))" LPRINT LPRINT SPC(12); "in which X(1), Y(1) are the coordinates of the trip origin and" LPRINT SPC(12); " X(2), Y(2) are the coordinates of the trip destination." LPRINT LPRINT SPC(12); " RideTimeAuto = 60 * RideDistAuto / AveSpeedAuto " LPRINT LPRINT SPC(12); "The weighted trip time by Auto is then" LPRINT LPRINT SPC(12); " TimeAuto = WalktoRide * WalkTimeAuto +" LPRINT SPC(12); " WaittoRide * WaitTimeAuto + RideTimeAuto" FOR I = 1 TO 14: LPRINT : NEXT I LPRINT SPC(12); "Now, disutility functions in terms of cost are found from the equations" LPRINT LPRINT SPC(12); " DisUtilityPRT = CentsperMinute * TimePRT + CostPRT * RideDistPRT" LPRINT SPC(12); " DisUtilityAuto = CentsperMinute * TimeAuto + CostAuto * RideDistAuto" LPRINT SPC(12); " + ParkingCost" LPRINT SPC(12); " DeltaDisUtility = (DisUtilityPRT - DisUtilityAuto) / LogitCoef" LPRINT LPRINT SPC(12); "in which 'CentsperMinute' is the cost of time in cents per minute, CostPRT" LPRINT SPC(12); "is the cost in cents per mi or km to travel by PRT, CostAuto is the" LPRINT SPC(12); "perceived cost in cents per mi or km to travel by auto, and LogitCoef" LPRINT SPC(12); "defines the change in disutility required to change the mode split from 0.5" LPRINT SPC(12); "1/(1 + e) = 0.27 or 1/(1 + 1/e) = 0.73." LPRINT LPRINT SPC(12); " Using the standard logit mode-split model, the mode split to PRT" LPRINT SPC(12); "corresponding to this difference in disutility is " LPRINT LPRINT SPC(12); " ModeSplitPRT = 1 / [1 + EXP(DeltaDisUtility)]" LPRINT LPRINT SPC(12); "For each run, we then compute " LPRINT LPRINT SPC(12); " SumSplit = SumSplit + ModeSplitPRT" LPRINT SPC(12); " Trips = Trips + 1" LPRINT LPRINT SPC(12); "from which the accumulated mean mode split is" LPRINT LPRINT SPC(12); " Mean mode split to PRT = SumSplit / Trips." LPRINT LPRINT SPC(12); "This value is plotted as a dot superimposed on the image of the PRT grid." LPRINT SPC(12); "The sequence of such dots shows how many trip samples are needed before" LPRINT SPC(12); "the average converges." LPRINT LPRINT SPC(12); " Circuity, shown at the end of the run, is the ratio of the " LPRINT SPC(12); "average PRT-trip distance to the average auto-trip distance." LPRINTEND SUBSUB Grid SHARED K L1 = 1: L2 = 4 FOR I = 0 TO M STEP K LINE (X0 + Scale * I, Y0)-(X0 + Scale * I, Y0 - M), 10 LINE (X0, Y0 - I)-(X0 + Scale * M, Y0 - I), 10 FOR J = 0 TO M - 1 STEP K xah = X0 + Scale * I yah = Y0 - J - .5 * K CALL Arrow(xah, yah, L2) xah = X0 + Scale * (J + .5 * K) yah = Y0 - I CALL Arrow(xah, yah, L1) NEXT J IF L1 = 1 THEN L1 = 2 ELSEIF L1 = 2 THEN L1 = 1 END IF IF L2 = 4 THEN L2 = 3 ELSEIF L2 = 3 THEN L2 = 4 END IF NEXT IEND SUBSUB ModeSplitScale FOR I = 0 TO 1.1 STEP .1 Y = Y0 + 20 - Y0 * I LINE (20, Y)-(26, Y), 10 LINE (Xmax - 4, Y)-(Xmax + 2, Y), 10 NEXT I LINE (34, 17)-(34, 23), 10 CIRCLE (42, 20), 5, 10 CIRCLE (55, 20), 5, 10 CIRCLE (42, Y0 + 20), 5, 10 LINE (Xmax - 36, 17)-(Xmax - 36, 23), 10 CIRCLE (Xmax - 28, 20), 5, 10 CIRCLE (Xmax - 15, 20), 5, 10 CIRCLE (Xmax - 28, Y0 + 20), 5, 10END SUBFUNCTION Odd (U) IF ABS(INT((U + 1) / 2) - (U + 1) / 2) < .01 THEN Odd = 1 ELSE Odd = 0END FUNCTIONSUB Pause DO: LOOP WHILE INKEY$ = ""END SUBSUB PlotCircle STATIC SHARED Xg, Yg, K CIRCLE (Xg, Yg), 6, 0 Xg = X0 + Scale * K * X Yg = Y0 - K * Y CIRCLE (Xg, Yg), 6, 14END SUBSUB PrintValues SHARED Ldist$, Spd$ LPRINT LPRINT " The following values describe the system analyzed." LPRINT LPRINT " 1. Line spacing, "; Ldist$; ".................................... "; LineSpacing LPRINT " 2. The network width is N * LineSpacing. N is ......... "; N LPRINT " 3. The average riding speed by PRT, "; Spd$; "................ "; AveSpeedPRT LPRINT " 4. The average riding speed by auto, "; Spd$; "............... "; AveSpeedAuto LPRINT " 5. The average walking speed, "; Spd$; "...................... "; WalkSpeed LPRINT " 6. The average waiting time by PRT, sec ............... "; WaitTimePRT LPRINT " 7. The average waiting time by auto, sec .............. "; WaitTimeAuto LPRINT " 8. The average auto-walk distance at both ends, "; Ldist$; "..... "; WalkDistAuto LPRINT " 9. Ratio of perceived walk time to ride time............"; WalktoRide LPRINT "10. Ratio of perceived wait time to ride time........... "; WaittoRide LPRINT "11. The cost of time, dollars per hour.................. "; TimeCost LPRINT "12. The fare on PRT, cents per "; Ldist$; " of trip distance...... "; CostPRT LPRINT "13. Perceived auto cost, cents per "; Ldist$; " of trip distance.. "; CostAuto LPRINT "14. Auto parking cost, $ per trip ...................... "; ParkCost LPRINT "15. Normalizing logit-model factor, cents .............. "; LogitCoefEND SUBSUB StationLocation SHARED Xlocal, Ylocal, Xs, Ys IF Ylocal <= Xlocal THEN IF Ylocal <= 1 - Xlocal THEN Xs = .5: Ys = 0 ELSE Xs = 1: Ys = .5 END IF ELSE IF Ylocal <= 1 - Xlocal THEN Xs = 0: Ys = .5 ELSE Xs = .5: Ys = 1 END IF END IFEND SUBSUB Test IF ABS(X - Xd) < .01 AND ABS(Y - Yd) < .01 THEN Flag = 1 ELSE Flag = 0END SUBSUB UnitChange SHARED Unit$, U$ IF Unit$ = "E" AND U$ = "M" THEN LineSpacing = LineSpacing * KmpMi AveSpeedPRT = AveSpeedPRT * KmpMi AveSpeedAuto = AveSpeedAuto * KmpMi WalkSpeed = WalkSpeed * KmpMi WalkDistAuto = WalkDistAuto * KmpMi ELSEIF Unit$ = "M" AND U$ = "E" THEN LineSpacing = LineSpacing / KmpMi AveSpeedPRT = AveSpeedPRT / KmpMi AveSpeedAuto = AveSpeedAuto / KmpMi WalkSpeed = WalkSpeed / KmpMi WalkDistAuto = WalkDistAuto / KmpMi END IFEND SUB ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download