Journal article
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
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Bibliographic Details
- Journal:
- Annals of Probability
- Volume:
- 34
- Issue:
- 2
- Pages:
- 493-527
- Publication date:
- 2006-05-24
- DOI:
- Source identifiers:
-
102317
Item Description
- Keywords:
- Pubs id:
-
pubs:102317
- UUID:
-
uuid:911b6a0e-7fe7-4292-bf33-6aca459f53ab
- Local pid:
- pubs:102317
- Deposit date:
- 2013-02-20
Terms of use
- Copyright date:
- 2006
- Notes:
-
Published at http://dx.doi.org/10.1214/00911790500000710 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org)
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