A new queue shock wave theory based on platoon dispersion modeling

Abstract

Statistical platoon dispersion models are developed mainly for traffic flow macro-simulation. While the queueing theory outputs the same delay results as those applied in shock wave theory, the dynamic process of queue forming and dissipating can be simulated only by the latter. Traditional shock wave theory treats traffic flow as a compressible fluid; hence, shock waves form whenever the state of speed–density changes. Similarly, shock waves form because of signal lights when simulating traffic flow with platoon dispersion models. This paper theoretically analyzes the queueing process based on a newly proposed platoon dispersion model, with the assumption that speed follows truncated normal distribution. Besides solving the queueing equations approximately with mathematical methods, an analytical table method is proposed to find the boundary solutions. Application methods are also presented for both static and dynamic scenarios. This theory can be applied to optimize signal timing for queue management, particularly for congestion control.