Approximations for heavily loaded G/GI/n + GI queues

Approximations for heavily loaded G/GI/n + GI queues

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Article ID: iaor20162642
Volume: 63
Issue: 3
Start Page Number: 187
End Page Number: 217
Publication Date: Apr 2016
Journal: Naval Research Logistics (NRL)
Authors: , ,
Keywords: simulation, queues: theory, engineering
Abstract:

Motivated by applications to service systems, we develop simple engineering approximation formulas for the steady‐state performance of heavily loaded G/GI/n+GI multiserver queues, which can have non‐Poisson and nonrenewal arrivals and non‐exponential service‐time and patience‐time distributions. The formulas are based on recently established Gaussian many‐server heavy‐traffic limits in the efficiency‐driven (ED) regime, where the traffic intensity is fixed at ρ > 1, but the approximations also apply to systems in the quality‐and‐ED regime, where ρ > 1 but ρ is close to 1. Good performance across a wide range of parameters is obtained by making heuristic refinements, the main one being truncation of the queue length and waiting time approximations to nonnegative values. Simulation experiments show that the proposed approximations are effective for large‐scale queuing systems for a significant range of the traffic intensity ρ and the abandonment rate θ, roughly for ρ > 1.02 and θ > 2.0. 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 187–217, 2016

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