Waiting times in a two-queue model with exhaustive and Bernoulli service | Mathematical Methods of Operations Research
Skip to main content
Springer Nature Link
Log in

Waiting times in a two-queue model with exhaustive and Bernoulli service

  • Articles
  • Published:
Zeitschrift für Operations Research Aims and scope Submit manuscript

Abstract

This paper deals with waiting times in a two-queue polling system in which one queue is served according to the Bernoulli service discipline and the other one attains exhaustive service. Exact results are derived for the LST's of the waiting time distributions via an iteration scheme. Based on those results the mean waiting times are expressed in the system parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blanc JPC, van der Mei RD (1992) Optimization of polling systems with Bernoulli schedules. Report FEW 563, To appear in Performance Evaluation. Department of Economics, Tilburg University The Netherlands

    Google Scholar 

  2. Blanc JPC, van der Mei RD (1992) Optimization of polling systems by means of gradient methods and the power-series algorithm. Report FEW 575, Department of Economics, Tilburg University The Netherlands

    Google Scholar 

  3. Boxma OJ (1986) Models of two queues: A few new views. In: Teletraffic Analysis and Computer Performance Evaluation, Boxma OJ, Cohen JW, Tijms HC (eds) North-Holland, Amsterdam, The Netherlands 75–98

    Google Scholar 

  4. Boxma OJ (1989) Workloads and waiting times in single-server systems with multiple customer classes. Queueing Systems 5:185–214

    Google Scholar 

  5. Boxma OJ, Groenendijk WP (1988) Two queues with alternating service and switching times. In: Queueing Theory and its Applications — Liber Amicorum for J.W. Cohen, Boxma OJ, Syski R (eds) North-Holland, Amsterdam, The Netherlands 261–282

    Google Scholar 

  6. Cohen JW (1982) The single server queue (North-Holland, Amsterdam, The Netherlands; 2nd ed)

    Google Scholar 

  7. Cohen JW (1988) A two-queue model with semi-exhaustive alternating service. In: Performance '87, Courtois PJ, Latouche G (eds) North-Holland, Amsterdam, The Netherlands 19–37

    Google Scholar 

  8. Eisenberg M (1972) Queues with periodic service and changeover time. Operations Research 20:440–451

    Google Scholar 

  9. Fricker C, Jaïbi R (1992) Monotonicity and stability of periodic polling models, Report FEW 559, Department of Economics, Tilburg University The Netherlands. To appear in Queueing Systems

    Google Scholar 

  10. Fuhrmann SW (1992) A decomposition result for a class of polling models. Queueing Systems 11:109–120

    Google Scholar 

  11. Groenendijk WP (1990) Conservation laws in polling systems. PhD Dissertation, University of Utrecht The Netherlands

    Google Scholar 

  12. Keilson J, Servi LD (1986) Oscillating random walk models forGI/G/1 vacation systems with Bernoulli schedules. Journal of Applied Probability 23:790–802

    Google Scholar 

  13. Levy H (1991) Binomial-gate service: A method for effective operation and optimization of polling systems. IEEE Transactions on Communications 39:1341–1350

    Google Scholar 

  14. Levy H (1988) Optimization of polling systems: The fractional exhaustive service method. Dept of Comp Sc Tel Aviv University Israel

    Google Scholar 

  15. Ramaswamy R, Servi LD (1988) The busy period of theM/G/1 vacation model with a Bernoulli schedule. Comm Stat-Stoch Models 4:507–521

    Google Scholar 

  16. Resing JAC (1993) Polling systems and multi-type branching processes. Queueing Systems 13:409–426

    Google Scholar 

  17. Servi LD (1986) Average delay approximations ofM/G/1 cyclic service queues with Bernoulli schedules. IEEE Sel Areas Comm 4:813–822

    Google Scholar 

  18. Takagi H (1990) Queueing analysis of polling models. In: Stochastic Analysis of Computer Communication Systems, H. Takagi (ed) North-Holland, Amsterdam, The Netherlands 267–318

    Google Scholar 

  19. Tedijanto TE (1992) Exact results for the cyclic-service queue with a Bernoulli schedule. Performance Evaluation 15:89–97

    Google Scholar 

  20. Watson KS (1985) Performance evaluation of cyclic service strategies — a survey. In: Performance '84, E Gelenbe (ed) North-Holland, Amsterdam, The Netherlands, 521–533

    Google Scholar 

  21. Weststrate JA (1990) Waiting times in a two-queue model with exhaustive and Bernoulli service. Report FEW 437, Department of Economics, Tilburg University, The Netherlands

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shell Nederland Informatieverwerking, Shell Nederland B. V., Postbus 5835, 2280, HV Rijswijk, The Netherlands

    Jan A. Weststrate

  2. Faculty of Economics, Tilburg University, P.O. Box 90153, 5000, LE Tilburg, The Netherlands

    Rob D. van der Mei

Authors
  1. Jan A. Weststrate
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rob D. van der Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weststrate, J.A., van der Mei, R.D. Waiting times in a two-queue model with exhaustive and Bernoulli service. ZOR - Methods and Models of Operations Research 40, 289–303 (1994). https://doi.org/10.1007/BF01432970

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01432970

Keywords

Search

Navigation