Holding strategies in a bus-route model

A major source of delays in public transportation is the clustering instability, which causes late buses to become progressively later while the buses trailing it become progressively earlier. In this paper, we study this instability and how to neutralize it using the common practices of holding and schedule slack. Starting with an on-time route, we delay one or more buses at a single stop, and determine how these delays grow over time. We compare the effects of two different types of holding on the stability of the system, and briefly investigate how our results change with the use of timepoints.