Minimum Cost Schedules for a Public Transportation Route---I. Theory

V. F. Hurdle
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V. F. Hurdle: University of California, Berkeley, California

Transportation Science, 1973, vol. 7, issue 2, 109-137

Abstract: A fleet of vehicles carries passengers in one direction on a public transit route, then returns empty to the dispatch point after a round trip travel time T . The arrival rate of passengers is a known, deterministic, continuous, function of time and the objective is to devise a schedule that minimizes the total cost for passenger waiting time and vehicle operation. It is shown that the optimal dispatch rate at any time t is either equal to the arrival rate at t + kT where k is some integer (not necessarily positive) or proportional to the square root of the average of the passenger arrival rates at t - mT , t - ( m - 1) T , ..., t , ..., t + nT where m and n are nonnegative integers (sometimes both zero). Furthermore, the optimal dispatch rate, expressed as a function of time, can be discontinuous only at t q + jT and at t d , where t q is a time when a queue of waiting passengers forms, t d is a time when a queue disappears, and j is an integer.

Date: 1973
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