Control Strategies for an Idealized Public Transportation System

E. E. Osuna and G. F. Newell
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E. E. Osuna: Ministry of Public Works of Venezuela, Caracas, Venezuela
G. F. Newell: University of California, Berkeley

Transportation Science, 1972, vol. 6, issue 1, 52-72

Abstract: Vehicles load passengers at a single service point and, after traversing some route, return for another trip. The travel times of successive trips are independent identically distributed random variables with a known distribution function. After a vehicle returns to the service point, one has the option of holding it, or dispatching it immediately. Passengers arrive at a uniform rate and the objective is to minimize the average wait per passenger. The problem of determining the optimal strategy (dispatch or hold) for a system of m vehicles is formulated as a dynamic programming problem. It is analyzed in detail for m = 1 and m = 2. For m = 1, the optimal strategy will hold a vehicle if it returns within less than about half the mean trip time. For m = 2, and for a small coefficient of variation of trip time C ( T ), the optimal strategy will control the vehicles so as to retain nearly equally spaced dispatch times, within a range of time proportional to C 4/3 ( T ).

Date: 1972
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