Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T01:26:32.454Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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