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Time dependent solution of a correlated queueing problem with variable capacity

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Abstract

This paper considers the transient behaviour of a queueing problem wherein (i) the arivals at the two consecutive transition marks are correlated, (ii), the queue discipline is first-come-firstserved, (iii) service time distribution is exponential, and (iv) the capacity of the service channel is a random variable. TheLaplace transforms of the probability generating functions are obtained for two models. Finally, some particular cases are derived.

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References

  1. Mohan, C.: Some Problems in the Theory of Random Walk, Ph. D. Thesis, London University 1958.

  2. Chaudhry, M. L.: Some Queueing Problems with Phase-type Service., Operations Research, Vol.14, No. 3, 1966.

  3. Tuteja, R. K.: A Queueing Problem with Arrivals Correlated and Finite Number of Servers CORS, Vol.4, No. 3, 1967.

  4. Murari, K.: A Queueing Problem with Correlated Arrivals and Correlated Phase-type Service, Metrika (to appear).

  5. Saaty, T. L.: Elements of Queueing Theory, McGraw Hill, New York, 1961.

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Mohan, C., Murari, K. Time dependent solution of a correlated queueing problem with variable capacity. Metrika 19, 209–215 (1972). https://doi.org/10.1007/BF01893297

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Keywords

  • Generate Function
  • Stochastic Process
  • Probability Theory
  • Economic Theory
  • Service Time