Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T08:19:44.974Z Has data issue: false hasContentIssue false
  • English
  • Français

THE ISRAELI QUEUE WITH INFINITE NUMBER OF GROUPS

Published online by Cambridge University Press:  19 November 2013

Nir Perel  and
Uri Yechiali
Nir Perel
Affiliation:
Department of Statistics and Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel. E-mail: perelnir@post.tau.ac.il; uriy@post.tau.ac.il
Uri Yechiali
Affiliation:
Department of Statistics and Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel. E-mail: perelnir@post.tau.ac.il; uriy@post.tau.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

The so called “Israeli Queue” is a single server polling system with batch service of an unlimited size, where the next queue to be visited is the one in which the first customer in line has been waiting for the longest time. The case with finite number of queues (groups) was introduced by Boxma, Van der Wal and Yechiali [3]. In this paper we extend the model to the case with a (possibly) infinite number of queues. We analyze the M/M/1, M/M/c, and M/M/1/N—type queues, as well as a priority model with (at most) M high-priority classes and a single lower priority class. In all models we present an extensive probabilistic analysis and calculate key performance measures.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 1 , January 2014 , pp. 1 - 19
Copyright
Copyright © Cambridge University Press 2013 

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.Ammar, M.H. & Wong, J.W. (1987). On the optimality o cyclic transmission in teletext systems. IEEE Transactions on Communications COM 35(1): 68–73.Google Scholar
2.Boon, M.M.A, Van der Mei, R.D & Winands, E.M.M. (2011). Applications of polling systems. Surveys in Operations Research and Management Science 16(2): 67–82.CrossRefGoogle Scholar
3.Boxma, O.J., Van der Wal, Y. & Yechiali, U. (2008). Polling with batch service. Stochastic Models 24(4): 604–625.Google Scholar
4.Dykeman, H.D., Ammar, M.H. & Wong, J.W. (1986). Scheduling algorithms for videotex systems under broadcast delivery. In Proceedings of the International Conference on Communications (ICC’86), pp. 1847–1851.Google Scholar
5.Gasper, G. & Rahman, M. (2004). Basic hypergeometric series, 2nd ed.Cambridge: Cambridge University Press.Google Scholar
6.He, Q.-M. & Chavoushi, A.A. (2013). Analysis of queueing systems with customer interjections. Queueing Systems 73: 79–104.CrossRefGoogle Scholar
7.Latouche, G. & Ramaswami, V. (1999). Introduction to matrix analytic methods in stochastic modeling. ASA-SIAM Series on Statistics and Applied Probability. Philadelphia: SIAM.Google Scholar
8.Liu, Z. & Nain, P. (1992). Optimal scheduling in some multiqueue single-server systems. IEEE Transactions on Automatic Control 37(2): 247–252.CrossRefGoogle Scholar
9.Neuts, M.F. (1981). Matrix-geometric solutions in stochastic models. An algorithmic approach. Baltimore: The Johns Hopkins University Press.Google Scholar
10.Takagi, H. (1986). Analysis of polling systems. Cambridge: The MIT Press.Google Scholar
11.Van Oyen, M.P. & Teneketzis, D. (1996). Optimal batch service of a polling system under partial informtion. Methods and Models in OR 44(3): 401–419.Google Scholar
12.Van der Wal, J. & Yechiali, U. (2003). Dynamic visit-order rules for batch-service polling. Probability in the Engineering and Informational Sciences 17(3): 351–367.Google Scholar
13.Yechiali, U. (1993). Analysis and control of polling systems. Performance Evaluation of Computer and Communication Systems. Heidelberg: Springer-Verlag, 630–650.Google Scholar