Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T16:04:24.964Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient behavior of multi-server queues with recurrent input and exponential service times

Published online by Cambridge University Press:  14 July 2016

U. Narayan Bhat
U. Narayan Bhat*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
Get access Rights & Permissions [Opens in a new window]

Summary

Customers arrive in a recurrent process and get served by one of the s (≧1) servers wit han exponential service time distribution. The equilibrium behavior of the queue length process has been studied by earlier authors. In this paper the transient behavior of this process is investigated.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 158 - 168
Copyright
Copyright © Sheffield: 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

Arora, K. L. (1962) Time dependent solution of the two server queue fed by general arrival and exponential service time distributions. Operat. Res. 10, 327–334.Google Scholar
Bhat, U. N. (1965) The queue GI/M/3 with service rate depending on the number of busy servers (abstract). Ann. Math. Statist. 36, 1081.Google Scholar
Bhat, U. N. (1966) The queue GI/M/2 with service rate depending on the number of busy servers. Ann. Inst. Statist. Math., Tokyo 18, 211–221.CrossRefGoogle Scholar
Jackson, R. R. P. and Henderson, J. C. (1966) The time-dependent solution to the many server Poisson queue. Operat. Res. 14, 720–722.CrossRefGoogle Scholar
Karlin, S. and Mcgregor, J. (1958) Many server queueing processes with Poisson input and exponential service times. Pacific J. Math. 8, 87–118.Google Scholar
Kendall, D. G. (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of imbedded Markov chain. Ann. Math. Statist. 24, 335–354.Google Scholar
Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 78, 1–18.CrossRefGoogle Scholar
Presman, E. L. (1965) On waiting time for many-server queueing systems. Theor. Probability Appl. 10, (1), 63–73.Google Scholar
Pollaczek, F. (1953) Sur une généralisation de la théorie des attentes. C. R. Acad. Sci. Paris. 236, 578–580.Google Scholar
Pollaczek, F. (1961) Théorie Analytique des Problèmes Stochastiques Relatifs à un Groupe de Lignes Téléphoniques avec Dispositif d'Attente, Mémorial des Sciences Mathématiques, Fasc. 150. Gauthier-Villars, Paris.Google Scholar
Roes, P. B. M. (1966) A many server bulk queue. Operat. Res. 14, 1037–1044.Google Scholar
Saaty, T. L. (1960) Time dependent solution of many server Poisson queue. Operat. Res. 8, 755–772.Google Scholar
Shyu, K. (1962) On the queueing processes in the system GI/M/n with bulk service. Chinese Math. (English Trans.) 1, 196–204.Google Scholar
Takács, L. (1959) On the queueing problem concerning telephone traffic. Acta Math. Acad. Sci. Hungar. 8, 325–335.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press (N.Y.).Google Scholar