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The Mk/G/∞ batch arrival queue by heterogeneous dependent demands

  • Gennadi Falin (a1)

Abstract

Choi and Park [2] derived an expression for the joint stationary distribution of the number of customers of k types who arrive in batches at an infinite-server system of M/M/∞ type. We propose another method of solving this problem and extend the result to the case of general service times (not necessarily independent). We also get a transient solution. Our main result states that the k- dimensional vector of the number of customers of k types in the system is a certain linear function of a (2 k 1)-dimensional vector whose coordinates are independent Poisson random variables.

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Postal address: Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow 119899, Russia.

References

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[1] Borovkov, A. A. (1976) Stochastic Processes in Queueing Theory. Springer-Verlag, New York.
[2] Choi, B. D. and Park, K. K. (1992) The Mk/M/8 queue with heterogeneous customers in a batch. J. Appl. Prob. 29, 477481.
[3] Feller, W. (1970) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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