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Approximations for heavily loaded G/GI/n + GI queues
Author(s) -
Liu Yunan,
Whitt Ward,
Yu Yao
Publication year - 2016
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21688
Subject(s) - queue , truncation (statistics) , poisson distribution , queueing theory , range (aeronautics) , traffic intensity , computer science , gaussian , exponential function , mathematics , heuristic , mathematical optimization , statistics , physics , mathematical analysis , telecommunications , computer network , engineering , quantum mechanics , aerospace engineering
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