Change rate models of equivalent queue length for congested traffic flow

In order to describe the evolution rules of vehicle queue in congested traffic flow, the equivalent queue length change rate models for single-lane and multi-lane links were educed by calculous method on the basis of equivalent queue length models from two-fluid theory. These models were validated by the simulated data from VISSIM. Analysis result indicates that the equivalent queue length change rate is approximately equal to traffic wave velocity when traffic flow is at congested state. The equivalent and actual queue length change rates approach in sampling interval. Error method and entropy method are used to prove that they more approach when sampling interval is longer. So these models can quantitatively describe the evolution speed of vehicle queue in congested traffic flow.