The M/M/Infinity Service System with Ranked Servers in Heavy Traffic
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 S1, S2, ... 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 SL 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].
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