A model of the vicious cycle of a bus line

• We present a model for analyzing vicious and virtuous cycles of a bus line.
• The model formalizes passengers’ decisions to use a bus depending on waiting time.
• The fraction of passengers using a bus line converges to one of several equilibria.
• We present the conditions of emergence of a vicious or virtuous cycle.

It has been frequently noted that in a non-regulated environment the development of public transport service is self-adjusting: Faced with decreasing demand, operators will tend to reduce service to cut costs, resulting in a decrease in the level-of-service, which then triggers a further drop in demand. The opposite may also occur: high demand will induce the operator to increase supply, e.g. through an increase in frequency, which results in a higher level-of-service and a subsequent increase in passenger numbers, triggering another round of service improvements. This paper adds to the literature by presenting an analytic model for analyzing these phenomena that we call vicious and virtuous cycles. Based on field data regarding passengers’ variation in willingness-to-wait for a public transport service, we investigate the dynamics of the line service and show how the emergence of a vicious or virtuous cycle depends on the total number of potential passengers, the share of captive riders, and bus capacity. The paper ends with a discussion of the implications of the findings for the planning of public transport services.