Approximations for Heavily-Loaded G/GI/n +GI Queues

Motivated by applications to service systems, we develop simple engineering approximation formulas for the steady-state performance of heavily-loaded G/GI/n+GI multi-server queues, which can have non-Poisson and non-renewal arrivals and non-exponential service-time and patience-time distributions. The formulas are based on recently established Gaussian manyserver heavy-traffic limits, but involve important heuristic refinements. Simulation experiments show that the proposed approximations are effective for both large-scale and small-scale queueing systems in both the efficiency-driven regime and the quality-and-efficiency-driven regime for a significant range of the traffic intensity ρ and the abandonment rate θ parameters, roughly for ρ > 1.02 and θ < 2.0. keywords: queues, queues with customer abandonment, queueing approximations, steady-state performance, queues with non-exponential distributions. ∗yunan [email protected] †[email protected] ‡[email protected]