Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment

A. Korhan Aras (), Xinyun Chen () and Yunan Liu ()
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A. Korhan Aras: SAS Institute
Xinyun Chen: Wuhan University
Yunan Liu: North Carolina State University

Queueing Systems: Theory and Applications, 2018, vol. 89, issue 1, No 5, 125 pages

Abstract: Abstract Extending Ward Whitt’s pioneering work “Fluid Models for Multiserver Queues with Abandonments, Operations Research, 54(1) 37–54, 2006,” this paper establishes a many-server heavy-traffic functional central limit theorem for the overloaded $$G{/}GI{/}n+GI$$ G / G I / n + G I queue with stationary arrivals, nonexponential service times, n identical servers, and nonexponential patience times. Process-level convergence to non-Markovian Gaussian limits is established as the number of servers goes to infinity for key performance processes such as the waiting times, queue length, abandonment and departure processes. Analytic formulas are developed to characterize the distributions of these Gaussian limits.

Keywords: Many-server queues; Many-server heavy-traffic limits; Nonexponential service times; Efficiency-driven regime; Customer abandonment; Gaussian approximation; Functional central limit theorem; 60B12; 60B05; 60F17; 60K25; 60M20; 90B22 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-018-9575-0

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