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September 2013 Heavy-traffic limits for a many-server queueing network with switchover
Guodong Pang, David D. Yao
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Adv. in Appl. Probab. 45(3): 645-672 (September 2013). DOI: 10.1239/aap/1377868533

Abstract

We study a multiclass Markovian queueing network with switchover across a set of many-server stations. New arrivals to each station follow a nonstationary Poisson process. Each job waiting in queue may, after some exponentially distributed patience time, switch over to another station or leave the network following a probabilistic and state-dependent mechanism. We analyze the performance of such networks under the many-server heavy-traffic limiting regimes, including the critically loaded quality-and-efficiency-driven (QED) regime, and the overloaded efficiency-driven (ED) regime. We also study the limits corresponding to mixing the underloaded quality-driven (QD) regime with the QED and ED regimes. We establish fluid and diffusion limits of the queue-length processes in all regimes. The fluid limits are characterized by ordinary differential equations. The diffusion limits are characterized by stochastic differential equations, with a piecewise-linear drift term and a constant (QED) or time-varying (ED) covariance matrix. We investigate the load balancing effect of switchover in the mixed regimes, demonstrating the migration of workload from overloaded stations to underloaded stations and quantifying the load balancing impact of switchover probabilities.

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Guodong Pang. David D. Yao. "Heavy-traffic limits for a many-server queueing network with switchover." Adv. in Appl. Probab. 45 (3) 645 - 672, September 2013. https://doi.org/10.1239/aap/1377868533

Information

Published: September 2013
First available in Project Euclid: 30 August 2013

zbMATH: 1282.60091
MathSciNet: MR3102466
Digital Object Identifier: 10.1239/aap/1377868533

Subjects:
Primary: 60K25
Secondary: 60F17, 90B22

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 3 • September 2013
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