Three-velocity Queueing Model for Congested Traffic Flow Simulation

Abstract

Pinned Localized Clusters (PLC), Stop-and-Go Waves (SGW), Oscillating Congested Traffic (OCT), and Homogeneous Congested Traffic (HCT) are frequently observed vehicle queueing phenomena around ramping regions. In order to explain the origins and transition conditions of these congested traffic flow patterns, a concise two-velocity (free flow velocity and congested flow velocity) queueing model was recently designed by Chen et al., 2012b to quantitatively analyze the formation, evolution and dissipation of jam queues. It can be viewed as a specialized Newell's simplified car-following model (Newell, 2002) which assumes inflow rate dependent jam queue joining times and constant jam queue departing times. PLC/HCT patterns can be well reproduced via this model, but no correct SGW/OCT patterns can be achieved. To solve this problem, a new queueing model is proposed in this paper that adopts three kinds of vehicles velocities (free flow velocity, slow flow velocity and jam flow velocity). The transitions between slow and jam flows are controlled by duration of slow flow queues. Simulations show that this new model could well reproduce SGW/OCT patterns observed in practice. Analysis reveals that convective instability of this new queueing model makes it generate oscillation features. This conclusion is consistent with Ward and Wilson, 2011 and Treiber and Kesting, 2011.