Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-07T03:13:42.232Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results for infinite server poisson queues

Published online by Cambridge University Press:  14 July 2016

Mark Brown  and
Sheldon M. Ross
Mark Brown
Affiliation:
Cornell University
Sheldon M. Ross
Affiliation:
University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 604 - 611
Copyright
Copyright © Applied Probability Trust 

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] Brown, M. (1968) An invariance property of Poisson processes arising in traffic flow theory. Stanford University Technical Report. Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.Google Scholar
[3] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[4] Pyke, R. (1958) On renewal processes related to type I and type II counter models. Ann. Math. Statist. 29, 737–754.Google Scholar
[5] Rao, , Sudarsana, J. (1966) An application of stationary point processes to queueing and textile research. J. Appl. Prob. 3, 231–246.CrossRefGoogle Scholar
[6] Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar
[7] Shanbhag, D. N. (1966) On infinite server queues with batch arrivals. J. Appl. Prob. 3, 274–279.Google Scholar
[8] Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung. III, 169–191.Google Scholar
[9] Benes, V. E. (1965) Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, New York.Google Scholar