A Probabilistic Model of Bus Route Performance

Abstract

This paper addresses the problem of describing bus route performance as a first step toward developing strategies for improving service reliability. Previous work in the area has consisted of costly simulation models or analytical treatments of highly simplified problems. An alternative approach is proposed here based on the idea of numerically calculating probability distributions of the time each bus arrives to and departs from each stop. A set of recursive relationships is developed, together with a reasonable set of assumptions, which allows the efficient calculation of all the necessary distributions. An important feature of the model is that it incorporates the effect of the trajectory of one bus on that of the following bus, thereby modeling the well known phenomenon of bus bunching. Numerical experiments demonstrate that the model performs quite well in this respect. It is expected that the methodology will be extremely cost effective, and without the statistical problems associated with interpreting the outputs of a simulation model.

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