Modeling schedule recovery processes in transit operations for bus arrival time prediction

Many existing algorithms for bus arrival time prediction assume that buses travel at free-flow speed in the absence of congestion. As a result, delay incurred at one stop would propagate to downstream stops at the same magnitude. In reality, skilled bus operators often constantly adjust their speeds to keep their bus on schedule. This paper formulates a Markov chain model for bus arrival time prediction that explicitly captures the behavior of bus operators in actively pursuing schedule recovery. The model exhibits some desirable properties in capturing the schedule recovery process. It guarantees provision of the schedule information if the probability of recovering from the current schedule deviation is sufficiently high. The proposed model can be embedded into a transit arrival time estimation model for transit information systems that use both real-time and schedule information. It also has the potential to be used as a decision support tool to determine when dynamic or static information should be used.