The Real–Time Stop–Skipping Problem

Abstract

As a departure from previous studies on the stop–skipping control problem, this study investigates the possibility of implementing a stop–skipping policy for operations control in a real–time manner. Stop–skipping is investigated for a service disruption of varying length, occurring in the middle of a route, as a means of responding to the disruption more rapidly. Based on a preliminary analysis that shows that a basic stop–skipping policy may not be appropriate for real–time application, a policy alternative is constructed such that the control vehicle can still drop off passengers at stops in the skipping segment. The stop–skipping strategy is formulated separately for both policies as a nonlinear integer programming problem. The problem formulation includes assumptions of random distributions of passenger boardings and alightings, specifically with the binomial distribution and Poisson distribution representing the passenger alighting and boarding processes, respectively. The problem solution uses an exhaustive search method by taking advantage of the relatively small scale of the problem. A simulation study is conducted to examine how the performance of the two stop–skipping policies changes with the passenger distribution pattern, the service disruption location, the disruption length, as well as the vehicle travel time variability on the route. These simulation results suggest that both policies are not very sensitive to the travel time variability individually, when compared to other major factors. However, the travel time variability could contribute significantly to the difference in performance of the two policies because it affects the performance of the two policies in opposite ways. For both normal and downtown–oriented passenger distribution patterns, both policies perform similarly in term of total passenger waiting time reduction for a majority of cases. However, a significant difference in the performance of the two policies can still be seen for a large percentage of cases under varying circumstances. These results suggest that the downtown–oriented passenger distribution pattern may present the most desirable condition for the policy alternative. For the reverse–direction passenger distribution pattern, the policy alternative rarely outperforms the basic policy due to the inherent dynamics of the policy itself.