Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics

Patrick Eschenfeldt () and David Gamarnik ()
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Patrick Eschenfeldt: Massachusetts Institute of Technology Operations Research Center, Cambridge, Massachusetts, 02139
David Gamarnik: Massachusetts Institute of Technology Sloan School of Management and Operations Research Center, Cambridge, Massachusetts 02139

Mathematics of Operations Research, 2018, vol. 43, issue 3, 867-886

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 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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