Time-Varying Robust Queueing

We develop a time-varying robust-queueing (TVRQ) algorithm for the continuous-time workload in a single-server queue with a time-varying arrival-rate function. We apply this TVRQ to develop approximations for the periodic steady-state expected workload in models with a periodic arrival-rate function. We apply simulation and asymptotic methods to examine the performance of periodic TVRQ (PRQ). We find that PRQ predicts the mean of the periodic distribution and even the full distribution (specified by the quantiles) remarkably well. We show that the PRQ 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.