An Alternative Proof of a Theorem of Takács on the GI / M /1 Queue

Marcel F. Neuts
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Marcel F. Neuts: Purdue University, Lafayette, Indiana

Operations Research, 1966, vol. 14, issue 2, 313-316

Abstract: An analytic proof is given of the fact that the stationary distribution for the imbedded Markov chain in a GI / M /1 queue is geometric. A generating function for the stationary transition probabilities is obtained as the unique solution to an integro-differential equation, which may be solved by reduction to a Wiener-Hopf equation.

Date: 1966
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