Synchronized scheduling and random delays in urban transit

As a case study, some work is presented which was conducted for the Toronto Transit Commission (TTC) on the ‘blending’ of headways. This involves synchronizing service on a main common portion of a bus route, taking account of the inter-arrival times of other vehicles merging into that major portion from branches on minor arterial roads. Such a synchronized schedule generally requires at least one more vehicle per route. However, the highly stochastic nature of peak-direction travel may yield inter-arrival times for blended headways which are no less random, than when each branch is scheduled as a distinct, independent route. In this paper, an empirical study is described of the inter-arrival distributions. Several TTC routes were first scheduled with blending and then later rescheduled to operate without blending. An operational way is developed to distinguish the effects due to blending from those resulting because the schedule must be changed when blending is implemented. Addition or removal of blending may also change the type of headway distribution. When this results in the summarized on-street data crossing certain parameter boundaries, the level of passenger service may become qualitatively different. The before-and-after experiments thus suggest conditions when the practice of blending is effective on the street. Several examples are also given of how client presentations could have been streamlined by using some technical results from stochastic models, but why this would not have helped the relationship with the client. This paper concludes with estimating the net benefits of this project.