The M -Server Queue with Poisson Input and Gamma-Distributed Service of Order Two

Saul Shapiro
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Saul Shapiro: International Business Machines, Inc., Yorktown Heights, New York

Operations Research, 1966, vol. 14, issue 4, 685-694

Abstract: Analysis is made of the multiserver-queuing systems with Poisson input and service times distributed according to a second order gamma distribution. A set of difference equations involving the time-invariant state-probabilities is derived and a unique solution of these equations is found. The method used is that of treating the gamma-distributed service times or order two as the sum of two independent and identically distributed service times, which are exponentially distributed. It is shown that the time invariant probability of n customers being in the system is of the form, P n = ∑ i =0 i = m C i β i n , where m is the number of servers, and a method for finding the C i 's and β i 's is given.

Date: 1966
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