Control Strategies for an Idealized Public Transportation System

TLDR

In a simplified public transport model, vehicles load passengers at a single service point, travel along a route, and return, with successive trip times modeled as independent identically distributed random variables with a known distribution. The study aims to minimize the average passenger wait time by optimizing vehicle dispatch decisions. The authors formulate the dispatch‑or‑hold decision as a dynamic programming problem for m vehicles, and analyze the optimal policies for one and two vehicles. They find that with one vehicle the optimal rule is to hold if the return time is less than roughly half the mean trip time, while with two vehicles and low trip‑time variability the optimal policy keeps dispatches nearly evenly spaced, with spacing variation proportional to the 4/3 power of the coefficient of variation.

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).