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First-passage-time and busy-period distributions of discrete-time Markovian queues:Geom(n)/Geom(n)/1/N

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Abstract

This paper gives simple explicit solutions of various first-passage-time distributions for a general class of discrete-time queueing models under arbitrary initial conditions, state-dependent transition probabilities and the finite waiting room. Explicit closed form expressions are obtained in terms of roots. These expressions are then used to get numerical as well as graphical results. Explicit closed-form expressions are also deduced for the continuous-time models including the busy-period distributions. The analysis is then extended to cover the case of two absorbing states.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Royal Military College of Canada, K7K 5L0, Kingston, Ontario, Canada

    Mohan L. Chaudhry

  2. Department of Mathematics and Statistics, University of Winnipeg, R3B 2E9, Winnipeg, Manitoba, Canada

    Yiqiang Q. Zhao

Authors
  1. Mohan L. Chaudhry
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  2. Yiqiang Q. Zhao
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Chaudhry, M.L., Zhao, Y.Q. First-passage-time and busy-period distributions of discrete-time Markovian queues:Geom(n)/Geom(n)/1/N . Queueing Syst 18, 5–26 (1994). https://doi.org/10.1007/BF01158772

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  • DOI: https://doi.org/10.1007/BF01158772

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