Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T06:01:46.546Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Optimality of the Generalized Shortest Queue Policy

Published online by Cambridge University Press:  27 July 2009

Arie Hordijk  and
Ger Koole
Ger Koole
Affiliation:
Department of Mathematics and Computer ScienceUniversity of Leiden, P.O. Box 9512, 2300 RA Leiden The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a queueing model in which arriving customers have to choose between m parallel servers, each with its own queue. We prove for general arrival streams that the policy which assigns to the shortest queue is stochastically optimal for models with finite buffers and batch arrivals.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 4 , October 1990 , pp. 477 - 487
Copyright
Copyright © Cambridge University Press 1990

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

Cox, D.R. & Isham, V. (1980). Point processes. London: Chapman and Hall.Google Scholar
Daley, D.J. (1987). Certain optimality properties of the first-come first-served discipline for G|G|s queues. Stochastic Processes and Their Applications 25: 301–308.CrossRefGoogle Scholar
Derman, C., Lieberman, G.J., & Ross, S.M. (1980). On the optimal assignment of servers and a repairman. Journal of Applied Probability 17: 577–581.CrossRefGoogle Scholar
Ephremides, A., Varaiya, P., & Walrand, J. (1980). A simple dynamic routing problem. IEEE Transactions on Automatic Control 25: 690–693.CrossRefGoogle Scholar
Hordijk, A. & Schassberger, R. (1982). Weak convergence for generalized semi–Markov processes. Stochastic Processes and Their Applications 12: 271–291.CrossRefGoogle Scholar
Menich, R. & Serfozo, R.F. (1986). Optimality of shortest queue routing for dependent service stations. Working paper.Google Scholar
Schassberger, R. (1973). Warteschlangen. Wien: Springer-Verlag.CrossRefGoogle Scholar
Seth, K. (1977). Optimal service policies, just after idle periods, in two-server heterogeneous queueing systems. Operations Research 25: 356–360.CrossRefGoogle Scholar
Sobel, M.J. (in press). Throughput maximization in a loss queueing system with heterogeneous servers. Journal of Applied Probability.Google Scholar
Weber, R.R. (1978). On the optimal assignment of customers to parallel queues. Journal of Applied Probability 15: 406–413.CrossRefGoogle Scholar
Whitt, W. (1980). Continuity of generalized semi-Markov processes. Mathematics of Operations Research 5: 494–501.CrossRefGoogle Scholar
Whitt, W. (1986). Deciding which queue to join: some counterexamples. Operations Research 34: 55–62.CrossRefGoogle Scholar
Winston, W. (1977). Optimality of the shortest line discipline. Journal of Applied Probability 14: 181–189.CrossRefGoogle Scholar