Skip to main content
SpringerLink
Log in

Cyclic networks with general blocking and starvation

  • Articles
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We introducegeneral starvation and consider cyclic networks withgeneral blocking and starvation (GBS). The mechanism of general blocking allows the server to process a limited number of jobs when the buffer downstream is full, and that of general starvation allows the server to perform a limited number of services in anticipation of jobs that are yet to arrive. The two main goals of this paper are to investigate how the throughput of cyclic GBS networks is affected by varying (1) the total number of jobsJ, and (2) the buffer allocationk=(k1..., km) subject to a fixed total buffer capacityK=k 1 +... + km. In particular, we obtain sufficient conditions for the throughput to be symmetric inJ and to be maximized whenJ=K/2. We also show that the equal buffer allocation is optimal under the two regimes of light or heavy usage. In order to establish these results, we obtain several intermediate structural properties of the throughput, using duality, reversibility, and concavity, which are of independent interest.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I.F. Akyildiz and H. von Brand, Dual and selfdual networks of queues with rejection blocking, Computing 43 (1989) 1–11.

    Google Scholar 

  2. M.A. Ammar and S.B. Gershwin, Equivalence relations in queueing models of fork/join networks with blocking, Perf. Evaluat. 10 (1989) 233–245.

    Google Scholar 

  3. F. Baccelli and Z. Liu, Comparison properties of stochastic decision free Petri nets, IEEE Trans. Automat. Contr. 37 (1992) 1905–1920.

    Google Scholar 

  4. J.A. Buzacott and J.G. Shanthikumar,Stochastic Models of Manufacturing Systems (Prentice-Hall, Englewood Cliffs, NJ, 1992).

    Google Scholar 

  5. D.W. Cheng and D.D. Yao, Tandem queues with general blocking: A unified model and comparison results, DEDS: Theory and Appl. 2 (1993) 207–234.

    Google Scholar 

  6. Y. Dallery and D. Towsley, Symmetry property of the throughput in closed tandem queueing networks with finite buffers, Oper. Res. Lett. 10 (1991) 541–547.

    Google Scholar 

  7. P. Glasserman and D.D. Yao, Structured buffer-allocation problems in production lines, preprint (June 1991).

  8. P. Glasserman and D.D. Yao, Monotonicity in generalized semi-Markov processes, Math. Oper. Res. 17 (1992) 1–21.

    Google Scholar 

  9. P. Glasserman and D.D. Yao, Second-order properties of generalized semi-Markov processes, Math. Oper. Res. 17 (1992) 444–469.

    Google Scholar 

  10. P. Glasserman and D.D. Yao, A GSMP framework for the analysis of production lines, in:Probability Modeling and Analysis of Manufacturing Systems (SIAM, 1993).

  11. P.W. Glynn, A GSMP formalism for discrete-event systems, Proc. IEEE 77 (1989) 14–23.

    Google Scholar 

  12. W.J. Gordon and G.F. Newell, Cyclic queueing systems with restricted length queues, Oper. Res. 15 (1967) 266–277.

    Google Scholar 

  13. J. Hopcroft and J. Ullman, Introduction to Automata Theory, Languages and Computation (Addison-Wesley, Reading, MA, 1979).

    Google Scholar 

  14. B. Melamed, A note on the reversibility and duality of some tandem blocking queueing systems, Manag. Sci. 32 (1986) 1648–1650.

    Google Scholar 

  15. E. Muth, The reversibility property of production lines, Manag. Sci. 25 (1979) 152–158.

    Google Scholar 

  16. R.O. Onvural and H.G. Perros, Throughput analysis in cyclic queueing networks with blocking, IEEE Trans. Softw. Eng. SE-15, 6 (1989) 800–808.

    Google Scholar 

  17. D.V. Persone and D. Grillo, Managing capacity in finite capacity symmetrical ring networks, in:Conf. on Data and Communication Systems and their Performance, Brazil (1987) pp. 211–226.

  18. P.J. Ramadge and W.M. Wonham, Supervisory control of a class of discrete-event processes, SIAM J. Contr. and Optimization 25 (1987) 206–230.

    Google Scholar 

  19. J.G. Shanthikumar and D.D. Yao, Monotonicity and concavity properties in cyclic queueing networks with finite buffers, in:Queueing networks with Blocking: Proc. 1st Int. Workshop, Raleigh, North Carolina, May 20–21, 1988, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 325–344.

    Google Scholar 

  20. P.D. Sparaggis and W.B. Gong, A GSMP model for the buffer allocation problem in cyclic networks, in:Proc. 29th IEEE Conf. on Decision and Control, Honolulu, Hawaii (1990) pp. 903–908.

  21. G. Yamazaki, T. Kawashiha and H. Sakasegawa, Reversibility of tandem blocking queueing systems, Manag. Sci. 31 (1985) 78–83.

    Google Scholar 

  22. G. Yamazaki and H. Sakasegawa, Properties of duality in tandem queueing systems, Ann. Inst. Stat. Math. 27 (1975) 210–212.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 53706-1691, Madison, WI, USA

    Rajendran Rajan & Rajeev Agrawal

Authors
  1. Rajendran Rajan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajeev Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by NSF Grant No. ECS-8919818.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rajan, R., Agrawal, R. Cyclic networks with general blocking and starvation. Queueing Syst 15, 99–136 (1994). https://doi.org/10.1007/BF01189234

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01189234

Keywords

Search

Navigation