Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T14:43:55.639Z Has data issue: false hasContentIssue false
  • English
  • Français

THE OPTIMAL CONTROL OF A GENERAL TANDEM QUEUE

Published online by Cambridge University Press:  06 March 2006

Josef Weichbold  and
Klaus Schiefermayr
Josef Weichbold
Affiliation:
Department of Stochastics, University Linz, Linz, Austria, E-mail: [email protected]
Klaus Schiefermayr
Affiliation:
Department of Engineering, Upper Austrian University of Applied Sciences, Wels, Austria, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a scheduling problem with two interconnected queues and two flexible servers. It is assumed that all jobs are present at the beginning and that there are no further arrivals to the system at any time. For each job, there are waiting costs per unit of time until the job leaves the system. A job of queue 1, after being served, joins queue 2 with probability p and leaves the system with probability 1 − p. The objective is how to allocate the two servers to the queues such that the expected total holding costs until the system is empty are minimized. We give a sufficient condition such that for any number of jobs in queue 1 and queue 2, it is optimal to allocate both servers to queue 1 (resp. queue 2).

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 307 - 327
Copyright
© 2006 Cambridge University Press

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

REFERENCES

Ahn, H., Duenyas, I., & Zhang, R.Q. (1999). Optimal stochastic scheduling of a two-stage tandem queue with parallel servers. Advances in Applied Probability 31: 1095–1117.Google Scholar
Chang, C.S., Nelson, R., & Pinedo, M. (1991). Scheduling two classes of exponential jobs on parallel processors: Structural results and worst-case analysis. Advances in Applied Probability 23: 925–944.Google Scholar
Elaydi, S.N. (1996). An introduction to difference equations. New York: Springer-Verlag.
Pandelis, D.G. & Teneketzis, D. (1994). Optimal multiserver stochastic scheduling of two interconnected priority queues. Advances in Applied Probability 26: 258–279.Google Scholar
Ross, S. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.
Schiefermayr, K. & Weichbold, J. (2005). A complete solution for the optimal stochastic scheduling of a two-stage tandem queue with two flexible servers. Journal of Applied Probability 42: 778–796.Google Scholar
Schiefermayr, K. & Weichbold, J. (2006). A scheduling problem of several parallel servers (submitted).