Understanding time-dependent queues is essential for reliable journey time prediction in periods involving transient over-saturation. Detailed mathematical and simulation methods are available but practical traffic modelling also requires computationally efficient models. The best known is the sheared queue model, obtained by transforming a deterministic time-dependent and a probabilistic steady-state equilibrium model, but this can be inaccurate in certain cases. The inaccuracy can be traced to the quasi-equilibrium formulation and incomplete information about the queue length probability distribution. A formula for the variance of queue length is derived and is used to both test and improve the accuracy of the queue model. Further improvement is potentially available by incorporating the initial utilization as well as the initial queue size and variance into the model. (A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E134766.
Abstract