Technical Note—Maximum and Minimum Service Times for Batches of Jobs with an Unknown Number of Servers

Ernest M. Scheuer
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Ernest M. Scheuer: California State University, Northridge, California

Operations Research, 1973, vol. 21, issue 5, 1163-1167

Abstract: We consider the maximum and minimum times to service all jobs in a batch of random size at a facility having an unknown number of servers, where all servers have the same service-time distribution, and the batch size N and the service times { T i , i = 1, 2, …, N } are mutually independent random variables. For arbitrary service-time distribution and arbitrary batch-size probability mass function, the batch service time is bounded above by ∑ i =1 i = N T i and below by max{ T i , i = 1, 2, …, N }. We obtain the expected minimum batch service time for the special cases of exponential and uniform service-time distributions, and Poisson, binomial, and negative-binomal probability mass functions for batch size. Separate results are stated for the batch size restricted to be positive.

Date: 1973
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