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

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  • Marcel F. Neuts

    (Purdue University, Lafayette, Indiana)

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.

Suggested Citation

  • Marcel F. Neuts, 1966. "An Alternative Proof of a Theorem of Takács on the GI / M /1 Queue," Operations Research, INFORMS, vol. 14(2), pages 313-316, April.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:2:p:313-316
    DOI: 10.1287/opre.14.2.313
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