Time-Varying Robust Queueing

The natural queueing models for many operations research applications have time-varying arrival rates. In addition, the natural models often are not Markov stochastic processes, so that they are not amenable to exact mathematical analysis. In “Time-Varying Robust Queueing,” Ward Whitt and Wei You propose a time-varying robust queueing algorithm to approximate the time-varying distribution of the workload (virtual waiting time) in a non-Markovian single-server queue with a time-varying arrival-rate function. They apply simulation and asymptotic methods to examine the performance of periodic robust queueing. They show that periodic robust queueing converges to a proper limit in appropriate long-cycle and heavy-traffic regimes and coincides with long-cycle fluid limits and heavy-traffic diffusion limits for long cycles. Simulation examples show that the mean and the full distribution (specified by the quantiles) of the periodic steady-state workload are remarkably well approximated.