Hostname: page-component-76d6cb85b7-lrvh5 Total loading time: 0 Render date: 2026-07-13T16:05:37.482Z Has data issue: false hasContentIssue false
  • English
  • Français

A Globally Gated Polling System with a Dormant Server

Published online by Cambridge University Press:  27 July 2009

S. C. Borst
S. C. Borst
Affiliation:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

We study a globally gated polling system with a dormant server, which makes a halt at its home base when there are no customers present in the system. We derive an explicit expression for the cycle time distribution as well as for the waiting-time distribution at each of the queues. As a justification of the dormant server policy, we show the waiting time at each of the queues to be smaller (in the increasing-convex-ordering sense) than in the ordinary nondormant server case.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 239 - 254
Copyright
Copyright © Cambridge University Press 1995

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.)

Article purchase

Temporarily unavailable

References

1.Sarkar, D. & Zangwill, W.I. (1991). Variance effects in cyclic production systems. Management Science 37: 444–453.CrossRefGoogle Scholar
2.Altman, E., Konstantopoulos, P., & Liu, Z. (1992). Stability, monotonicity and invariant quantities in general polling systems. Queueing Systems 11 (Special Issue on Polling Models): 35–57.CrossRefGoogle Scholar
3.Blanc, J.P.C. & Van der Mei, R.D. (1994). The power-series algorithm applied to polling systems with a dormant server. In Labetoulle, J. & Roberts, J.W. (eds.), The fundamental role of teletraffic in the evolution of telecommunications networks, Proceedings of ITC 14. Amsterdam: North-Holland, pp. 865–874.Google Scholar
4.Borst, S.C. (1993). A polling system with a dormant server. Report BS-R9313. CWI, Amsterdam.Google Scholar
5.Borst, S.C. (1994). A pseudo-conservation law for a polling system with a dormant server. In Labetoulle, J. & Roberts, J.W. (eds.), The fundamental role of teletraffic in the evolution of telecommunications networks, Proceedings of ITC 14. Amsterdam: North-Holland, pp. 729–742.Google Scholar
6.Boxma, O.J., Levy, H., & Yechiali, U. (1992). Cyclic reservation schemes for efficient operation of multiple-queue single-server systems. Annals of Operations Research 35: 187–208.CrossRefGoogle Scholar
7.Boxma, O.J., Weststrate, J.A., & Yechiali, U. (1993). A globally gated polling system with server interruptions, and applications to the repairman problem. Probability in the Engineering and Informational Sciences 7: 187–208.CrossRefGoogle Scholar
8.Cohen, J.W. (1982). The single server queue, 2nd ed.Amsterdam: North-Holland.Google Scholar
9.Eisenberg, M. (1971). Two queues with changeover times. Operations Research 19: 386–401.CrossRefGoogle Scholar
10.Eisenberg, M. (1972). Queues with periodic service and changeover times. Operations Research 20: 440–451.CrossRefGoogle Scholar
11.Eisenberg, M. (1994). The polling system with a stopping server. Queueing Systems 18: 387–431.CrossRefGoogle Scholar
12.Gersht, A.M. & Marbukh, V.V. (1975). Queueing systems with readjustment. Engineering Cybernetics 13: 55–65.Google Scholar
13.Srinivasan, M.M. & Gupta, D. (1993). When should a roving server be patient? Report, University of Tennessee, Knoxville.Google Scholar
14.Keilson, J. & Servi, L.D. (1990). The distributional form of Little's law and the Fuhrmann-Cooper decomposition. Operations Research Letters 9: 239–247.CrossRefGoogle Scholar
15.Levy, H. & Sidi, M. (1990). Polling systems: Applications, modelling and optimization. IEEE Transactions on Communications 38: 1750–1760.CrossRefGoogle Scholar
16.Levy, H., Sidi, M., & Boxma, O.J. (1990). Dominance relations in polling systems. Queueing Systems 6: 155–171.CrossRefGoogle Scholar
17.Liu, Z., Nain, P., & Towsley, D. (1992). On optimal polling policies. Queueing Systems 11 (Special Issue on Polling Models): 59–83.CrossRefGoogle Scholar
18.Resing, J.A.C. (1993). Polling systems and multitype branching processes. Queueing Systems 13: 409–426.CrossRefGoogle Scholar
19.Takagi, H. (1986). Analysis of polling systems. Cambridge, MA: The MIT Press.Google Scholar
20.Takagi, H. (1990). Queueing analysis of polling models: An update. In Takagi, H. (ed.), Stochastic analysis of computer and communication systems. Amsterdam: North-Holland, pp. 267–318.Google Scholar
21.Takagi, H. (1991). Queueing analysis. Vol. 1. Amsterdam: North-Holland.Google Scholar
22.Takine, T. & Hasegawa, T. (1992). On the M/C/1 queue with multiple vacations and gated service discipline. Journal of the Operations Research Society of Japan 35: 217–235.CrossRefGoogle Scholar