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Balanced routing with partial information in a distributed parallel many-server queueing system
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AI
DOI：10.1016/j.ejor.2022.02.042.png)
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摘要
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We consider a queueing system that is comprised of multiple stations serving a single class of customers. Each station consists of many statistically identical servers, and has its own dedicated queue. In this pa-per, we propose a family of generalized load-balancing routing policies parameterized by vectors c and d with xi-choice (abbreviated as LB(xi, c , d ) ), that are suitable for dynamic routing with partial state in-formation. Under the proposed policy, upon an arrival, a subset of xi stations will be randomly collected, with their state information being retrieved, where xi is a positive integer-valued random variable satisfying P{xi >= 2 } > 0 ; then, this new customer will be routed to: (i) the station with minimum expected delay modified by c when all the collected stations are fully occupied; or otherwise (ii) the station with maximum idleness ratio modified by d among the collected stations with idle servers. The parameters c and d are employed to control the relative expected delay and utilization levels across stations. Using asymptotic analysis, we derive diffusion limits of queue-length processes as well as their stationary distributions under the LB(xi, c , d ) policy in the Halfin-Whitt regime. Based on these stationary diffusion limit results, we develop a solution procedure to determine policy parameters under different optimization criteria. Finally, we provide numerical experiments to validate the accuracy of our diffusion approximation, and compare the performances under the LB(xi, c , d ) policies with other routing policies. (C) 2022 Elsevier B.V. All rights reserved.
Keyword:
Queueing
Balanced routing
Diffusion limit
Halfin-Whitt regime
Partial information
期刊
IF:
6
论文数:
2.2W
被引数:
6.4W
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