uppose in a simple network with one OD pair and 10,000 daily person trips, there
ID: 1713828 • Letter: U
Question
uppose in a simple network with one OD pair and 10,000 daily person trips, there are two modes (i.e., cars and buses) available to travelers. The travel cost per person trip of each mode can be calculated by using Equation (3.1), given the cost components of each mode as shown in Table 3-1. The mode split ratio of each mode can be determined by a logit model as shown in Equation (3.2). If the toll charge for each car trip is increased from 3 dollars to 4 dollars, find out the change in the total amount of toll revenue collected from car trips on the daily basis. Here, we assume that each car carries 1.1 persons on average Table 3-1: Cost components of bus and car trips Mode Ialk (walkingTit (waitingFare (Fare Toll (Toll for Tin (in vehicle travel time, min)door to a bus for a busa car trip, S) time at the door or at auser, S) bus stop, min) time from the stop, min 3 (before) and 4 (after) ar 30 45 10 0.07 us 0.04 0.05 0.2 (coefficients in The travel cost function of a person trip carried by a mode (Equation 3.1) The mode split model for the person trips by car: exp(-Cea exp(-Car) + exp(-C,Lr) car (Equation 3.2) The mode split model for the person trips by bus exp(-Cb) (Equation 3.3)Explanation / Answer
Case-1 : Before toll for car trip is increased
Ccar = 0.04 x 30 + 0.05 x 0 + 0.07 x 5 + 0.2 x 0 + 0.1 x 3 = 1.85
Cbus = 0.04 x 45 + 0.05 x 5 + 0.07 x 10 + 0.2 x 5 + 0.1 x 0 = 3.75
Pcar = exp(-1.85) / (exp(-1.85) + exp(-3.75)) = 0.87
Pbus = exp(-3.75) / (exp(-1.85) + exp(-3.75)) = 0.13
Total number of daily person trips by car = 10000 x Pcar = 10000 x 0.87 = 8700
Number of daily car trips = 8700/1.1 = 7909
Total toll revenue from daily car trips = $ (7909 x 3) = $ 23727
Case-2 : After toll for car trip is increased
Ccar = 0.04 x 30 + 0.05 x 0 + 0.07 x 5 + 0.2 x 0 + 0.1 x 4 = 1.95
Cbus = 0.04 x 45 + 0.05 x 5 + 0.07 x 10 + 0.2 x 5 + 0.1 x 0 = 3.75
Pcar = exp(-1.95) / (exp(-1.95) + exp(-3.75)) = 0.858
Pbus = exp(-3.75) / (exp(-1.95) + exp(-3.75)) = 0.142
Total number of daily person trips by car = 10000 x Pcar = 10000 x 0.858 = 8580
Number of daily car trips = 8580/1.1 = 7800
Total toll revenue from daily car trips = $ (7800 x 4) = $ 31200
Therefore, toll revenue increases in the 2nd case.
Change in toll revenue from daily car trips = $ 31200 - $ 23727 = $ 7473
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