ON THE RELATIVE WAITING TIMES IN THE GI/M/s AND THE GI/M/1 QUEUEING SYSTEMS.

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Abstract

The average waiting time in a GI/M/s queue was compared with the average waiting time in an ″equivalent″ system comprised of s separate GI/M/1 queues. The results may be used to find the optimal partition of servers into several groups when designing a service system where certain restrictions eliminate the possibility of assigning all the servers in a single parallel group. The results may be qualitatively summarized as follows. If the inter-arrival times for both systems is of the ″same type″ then one would wait, on the average, at least s times as long in the separate system than in the combined one, when rho goes to 1. When rho becomes small the ratio of waiting times goes to infinity.

Original languageEnglish
Pages (from-to)325-337
Number of pages13
JournalOperational Research Quarterly
Volume28
Issue number2
DOIs
StatePublished - 1977

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