Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics
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1502.00999.pdf
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367.75 KB
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Author(s)
Eschenfeldt, Patrick Clark
Gamarnik, David
Date Issued
February 2018
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Eschenfeldt, Patrick and David Gamarnik. “Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics.” Mathematics of Operations Research 43, 3 (August 2018): 867–886 © 2018 INFORMS
Version
Original manuscript
Abstract
We consider queueing systems with n parallel queues under a Join the Shortest Queue (JSQ) policy in the Halfin-Whitt heavy-traffic regime. We use the martingale method to prove that a scaled process counting the number of idle servers and queues of length exactly two weakly converges to a two-dimensional reflected Ornstein-Uhlenbeck process, while processes counting longer queues converge to a deterministic system decaying to zero in constant time. This limiting system is comparable to that of the traditional Halfin-Whitt model, but there are key differences in the queueing behavior of the JSQ model. In particular, only a vanishing fraction of customers will have to wait, but those who do incur a constant order waiting time. Keywords: queueing theory; parallel queues; diffusion models
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MOOR.2017.0887
