Some Inequalities for Parallel-Server Queues

Shelby L. Brumelle
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Shelby L. Brumelle: University of British Columbia, Vancouver, B.C., Canada

Operations Research, 1971, vol. 19, issue 2, 402-413

Abstract: This paper obtains bounds, in terms of the first two moments of the input, on the expected wait in an A / G / k queue with stationary input. To this end, two single-server systems are constructed. The wait in queue for the first single-server system is stochastically larger than the wait in the given multiserver system, and the expected wait in the second single-server system is used to obtain a lower bound on the expected wait in the A / G / k system. The paper also develops, as a consequence of the lower bounds, some results concerning the optimum number of servers, given a fixed work capacity.

Date: 1971
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