Transient Delay in Oversaturated Queues

Abstract

The estimation of queue length and delays in queues that are oversaturated for some part of a study period is of substantial importance in a range of traffic engineering applications. Whiting’s co-ordinate transformation has provided the basis for several approaches to this. We analyse this approach and present an explicit form for the derivative of queue length with respect to time, which we then use to establish various properties. We also report the results of numerical comparisons with exact formulae for certain special cases and show that these offer little or no advantage over the co-ordinate transformation approximations and can be computationally impractical in study periods of moderate duration.

Citation

Heydecker, B.G. and Verlander, N.Q. (1998), "Transient Delay in Oversaturated Queues", Griffiths, J.D. (Ed.) Mathematics in Transport Planning and Control, Emerald Group Publishing Limited, Leeds, pp. 371-380. https://doi.org/10.1108/9780585474182-036