Analytical characterization of multi-state effective discharge rates for bus-only lane conversion scheduling problem

An accurate quantification of traffic flow characteristics with and without bus-only lane is important for determining transit priority strategies. Examinations of real-world vehicle trajectory data, like those from the NGSIM dataset, found that an effective discharge rate may be discounted when merging or lane-changing behaviors are observed. To deal with this, this manuscript analytically derives the effective discharge rate of a roadway segment by considering multi-stage merging behavior and vehicular traffic kinematics near a side entrance, for optimal bus-only lane conversion. The classic fluid-based approximation model by Newell that characterizes the queuing and dissipation process is extended to a multi-state queuing analysis framework. Three effective discharge rate discount factors are explicitly derived, for bus-only lane, general-purpose lane, and mixed-traffic lane, respectively. The derived effective discharge rates are represented by mathematically-simple expressions in a closed-form, and correctly account for the effects of demand inputs, such as arrival rate and the ratio of vehicles of different types, vehicular performance (such as acceleration rate), and traffic flow characteristics (such as backward wave speed and jam density). The bus-only lane conversion scheduling problem is then formulated as an optimization model to minimize total traffic delay. Validation, using NGSIM data, showed that our model reduced the effective discharge rate estimation error significantly on both arterials and freeways. Sensitivity analysis revealed that the optimal bus-only lane scheduling time varied in response to traffic demand and vehicle ratios, and the developed optimization model was always beneficial when compared with the demand-oriented strategy.