ON THE STEADY-STATE DISTRIBUTION OF NUMBER IN THE QUEUE Geom/G/1

  • Authors:

  • M. L. Chaudhry

  • Affiliations:

  • Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, Ontario K7K 7B4, Canada

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 1999

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Abstract

Discrete-time queues are frequently used in telecommunication networks. This paper proposes a new method which is based only on probabilistic arguments. It derives the distributions of numbers of customers in the discrete-time systems Geom/G/1 and Geom/G/1/M. Though the derivation does not involve use of the transforms, the transforms may be obtained, if desired. Another advantage of this is that the numerical results obtained are stable as there are no negative signs involved in summations. Further, the method can be easily used to solve more complex problems in discrete- and continuous-time queues.