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...

### Access Document

Publisher copy:
10.1214/00911790500000710

### Authors

Journal:
Annals of Probability
Volume:
34
Issue:
2
Pages:
493-527
Publication date:
2006-05-24
DOI:
Source identifiers:
102317
Keywords:
Pubs id:
pubs:102317
UUID:
uuid:911b6a0e-7fe7-4292-bf33-6aca459f53ab
Local pid:
pubs:102317
Deposit date:
2013-02-20

If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP