The Holding Problem with Real–Time Information Available

Holding is one of the most commonly used real–time control strategies in transit operations. Given a transit network and its operations plan, the holding problem is to decide at a given time at a control station, which vehicle is to be held and for how long, such that the total passenger cost along the route is minimized over a time period. Previous research on the holding problem has always assumed no real–time information available. Such an assumption not only poses great difficulties in solving the problem, but also limits practical applications in a real–time, dynamic operations environment. In this paper we formulate the holding problem as a deterministic quadratic program in a rolling horizon scheme, and develop an efficient solution algorithm to solve it. Using headway data collected by an automated system, we tested the algorithm and evaluated the impact of the resulting holding policies. Important and interesting properties of the holding solution, obtained from both theoretical and computational analyses, are presented.