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

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  • Yunan Liu
  • Ward Whitt
  • Yao Yu

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

Suggested Citation

  • Yunan Liu & Ward Whitt & Yao Yu, 2016. "Approximations for heavily loaded G/GI/n + GI queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 187-217, April.
    • Handle: RePEc:wly:navres:v:63:y:2016:i:3:p:187-217
    DOI: 10.1002/nav.21688
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    References listed on IDEAS

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    Cited by:

    1. S. A. Grishunina, 2020. "Limit Theorems for Queueing Systems with Various Service Disciplines in Heavy-Traffic Conditions," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1529-1538, December.
    2. Ward Whitt & Jingtong Zhao, 2017. "Many‐server loss models with non‐poisson time‐varying arrivals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 177-202, April.

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