Answer Happy

2. [30 points) A commuter bus system with headway H (hrs) has a demand rate such that N/2 trips head into the Central Business District (CBD) at this time, and N/2 trips head out from the CBD at the same time. The streets form a dense square gnid in the rectangular service area (dimensions 2L by W. see figure below) 1 of 3 UNIVERSITY OF MASSACHUSETTS, AMHERST CEE 410/510.SPRING 2022 CBD W We look for a set of bus lines with headway H and the location of their stops Bus lines travel perpendicularly to the main arterial with stop spacing << LW, and then along it without making any stops. The bus line spacing is also. The walking speed is much less than the the speed of the bus (r <<»). The lost time per stop ist. (a) Write a formula for the travel time, T. of the worst case passenger, assuming that he knows the service schedule, so he does not have to spend time waiting for the next dis- patch (b) Write a formula for the total number of bus-miles operated in order to transport the passengers (c) Write a formula for the total number of bus-hours operated in order to transport the passengers (d) If the cost per bus-hour operated is (s/bus-hour), write a mathematical program that gives the optimal spacing # by minimizing the fare Frequired to avoid subsidies while achieving a total time service standard T, for the worst passenger (e) Assume L = 3 miles: W = 7 miles; N = 1000 passengers/dispatch: x = 15 miles/hour Uw = 3 miles/hour, c = 30$/hour; and t = 0.01 hours, and a total time service standard T. equal to 1 hr. What is the optimal spacing that minimizes the fare. F. per passenger? (1) "Repeat part (v) if we allow the stop spacing to be different from the line spacing S.