Skip to main content Accessibility help

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

  • Gennadi Falin (a1)


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.


Corresponding author

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


Hide All
[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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed