Skip to main content Accessibility help

Some results for infinite server poisson queues

  • Mark Brown (a1) and Sheldon M. Ross (a2)


We consider a queueing model in which arrivals occur according to a non-homogeneous Poisson process in batches of varying size, and in which a customer is served immediately upon arrival by one of an infinite number of servers.



Hide All
[1] Brown, M. (1968) An invariance property of Poisson processes arising in traffic flow theory. Stanford University Technical Report.
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.
[3] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.
[4] Pyke, R. (1958) On renewal processes related to type I and type II counter models. Ann. Math. Statist. 29, 737754.
[5] Rao, , Sudarsana, J. (1966) An application of stationary point processes to queueing and textile research. J. Appl. Prob. 3, 231246.
[6] Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.
[7] Shanbhag, D. N. (1966) On infinite server queues with batch arrivals. J. Appl. Prob. 3, 274279.
[8] Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung. III, 169191.
[9] Benes, V. E. (1965) Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, 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? *


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