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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.

Service experiences and waiting lines are often – unfortunately – seen to go hand in hand. This chapter explains why this is the case. Beginning with an exploration of capacity and operating constraints, discussion then delves into both the mathematical origins and psychological implications of waiting lines. The final section offers hope to managers and guests alike, with a survey of different operations strategies and tactics that can eliminate or abate the need to wait.