The M/M/Infinity Service System with Ranked Servers in Heavy Traffic
Probability
2011-07-11 v1 Performance
Abstract
We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first two terms in the asymptotic expansions of the moments of L as lambda tends to infinity, where L is the index of the server S_L serving a newly arriving customer in equilibrium, and lambda is the ratio of the arrival rate to the service rate. The leading terms of the moments show that L/lambda tends to a uniform distribution on [0,1].
Keywords
Cite
@article{arxiv.1107.1536,
title = {The M/M/Infinity Service System with Ranked Servers in Heavy Traffic},
author = {Patrick Eschenfeldt and Ben Gross and Nicholas Pippenger},
journal= {arXiv preprint arXiv:1107.1536},
year = {2011}
}
Comments
i+6 pp