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On the maximum queue length in the supermarket model

Abstract:

There are $n$ queues, each with a single server. Customers arrive in a Poisson process at rate $\lambda n$, where $0<\lambda<1$. Upon arrival each customer selects $d\geq2$ servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove th...

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Publisher copy:
10.1214/00911790500000710

Authors


Luczak, MJ More by this author
McDiarmid, C More by this author
Journal:
Annals of Probability
Volume:
34
Issue:
2
Pages:
493-527
Publication date:
2006-05-24
DOI:
URN:
uuid:911b6a0e-7fe7-4292-bf33-6aca459f53ab
Source identifiers:
102317
Local pid:
pubs:102317

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