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

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Gennadi Falin
Gennadi Falin*
Affiliation:
Moscow State University
*
∗ Postal address: Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow 119899, Russia.
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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 (2k – 1)-dimensional vector whose coordinates are independent Poisson random variables.

Keywords

INFINITE SERVER QUEUEHETEROGENEOUS CUSTOMERSDEPENDENT SERVICE TIMESTRANSIENT REGIME

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 841 - 846
Copyright
Copyright © Applied Probability Trust 1994 

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References

[1] Borovkov, A. A. (1976) Stochastic Processes in Queueing Theory. Springer-Verlag, New York.Google Scholar
[2] Choi, B. D. and Park, K. K. (1992) The Mk/M/8 queue with heterogeneous customers in a batch. J. Appl. Prob. 29, 477–481.Google Scholar
[3] Feller, W. (1970) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar