Error bounds for perturbing nonexponential queues

A general framework is provided to derive analytic error bounds for the effect of perturbations and inaccuracies of nonexponential service or arrival distributions in single- and multiserver queues. The general framework is worked out in detail for the three types of finite or infinite buffer queues: GI/G/1/N, M/G/c/N, and GI/M/c/N. First, for the standard GI/G/1/N queue, it is illustrated how the general error bound result can lead to error bounds for different performance measures like the throughput, mean queue length, and stationary queue length distribution. Next, for the M/G/c/N queue, an error bound and monotonicity result are established for the throughput. M/G/c/N queues can so be compared even when hazard rates are not ordered. Finally, for the GI/M/c/N queue, a similar result is obtained with a perturbation of the interarrival time distribution. The error bound results are supported by asymptotic expressions for the M/M/c/N queue and numerical results for the GI/G/1/N queue.