Bus Bridging Disruption in Rail Services With Frustrated and Impatient Passengers

Urban rail networks play an important role in urban transportation. An unexpected disruption in a rail network can cause a significant degradation in the level of service. When a disruption occurs, it is crucial to provide quick and efficient substitution of services via alternative transportation modes, including bridging disconnected railway stations using bus services. The amount of disruptions, surprisingly, is high; for example, there are more than 15 000 disruptions in six months in Melbourne, Australia. The provision of bus bridging services calls for proper planning and designing of a temporary bus bridging network considering limited bus and driver resources, and prevailing urban traffic conditions. Among a number of tasks concerning bus bridging, the demand modeling of affected train passengers is a prerequisite for a satisfactory bus bridging practice. This paper explores this demand modeling problem based on the theory of compound Poisson processes and formulates it as a bulk queuing problem involving balking and reneging. The problem is carefully studied, with a series of analytical results delivered. Large-scale Monte Carlo simulations were designed and implemented to demonstrate a range of mathematical conclusions.