Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-04T08:24:46.014Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic behaviour of the Ek/G/1 queue with finite waiting room

Published online by Cambridge University Press:  14 July 2016

Per Hokstad
Per Hokstad*
Affiliation:
University of Trondheim
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic behaviour of the Ek/G/1 queue with finite waiting room is studied. Using a combination of the supplementary variable and phase techniques, queue length and waiting time distributions are obtained. Also the idle period distribution and mean length of the idle and busy periods are found.

Keywords

Ek/G/1 QUEUEFINITE WAITING ROOMQUEUE LENGTHWAITING TIMEIDLE PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 358 - 366
Copyright
Copyright © Applied Probability Trust 1977 

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

Cooper, B. C. (1972) Introduction to Queueing Theory. Macmillan, New York.Google Scholar
Gnedenko, B. V. and Kovalenko, J. N. (1968) Introduction to Queueing Theory. Israel Program for Scientific Translation. Jerusalem.Google Scholar
Hokstad, P. (1975a) The M/G/1 queue with a finite number of waiting places. Statistics No 2/75, Department of Mathematics, University of Trondheim — NTH.Google Scholar
Hokstad, P. (1975b) The G/M/m queue with finite waiting room. J. Appl. Prob. 12, 779–792.Google Scholar
Hokstad, P. (1976) On the idle and busy period of a general queueing model. Statistics No 1/76, Department of Mathematics, University of Trondheim — NTH.Google Scholar
Kleinrock, L. (1975) Queueing Systems. Wiley, New York.Google Scholar
Stoyan, D. (1973) A continuity theorem for queue size. Bull. Acad. Polon. Sci. 21, 1143–1146.Google Scholar
Takács, L. (1961) Transient behavior of a single server queueing process with Erlang input. Trans. Amer. Math. Soc. 100, 1–28.Google Scholar
Truslove, A. L. (1975a) Queue length for the Ek/G/1 queue with finite waiting room. Adv. Appl. Prob. 7, 215–226.Google Scholar
Truslove, A. L. (1975b) The busy period of the Ek/G/1 queue with finite waiting room. Adv. Appl. Prob. 7, 416–430.Google Scholar
Whitt, W. (1974) The continuity of queues. Adv. Appl. Prob. 6, 175–183.Google Scholar