Skip to main content
SpringerLink
Log in

A production system with two job classes, changeover times and revisitation

  • Short Communication
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

This paper, motivated by the need to predict performance of production systems with random arrivals, setup times and revisitation, presents an imbedded Markov chain analysis of the underlyingM/G/1 queue with two customer classes, changeover times and instantaneous Bernoulli feedback. It is assumed that jobs are scheduled according to the exhaustive alternative priority queue discipline. Expressions for the mean waiting time and the nonsaturation condition are derived under two different priority assignments to the repeat customers. Sojourn times under these priority assignments are shown to possess a convex ordering. Results of the study are also applicable to data communication networks that operate under cyclic switching mechanisms.

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

References

  1. B. Avi-Itzhak, W.L. Maxwell and L.W. Miller, Queueing with alternating priorities, Oper. Res. 13 (1965) 306–318.

    Google Scholar 

  2. O.J. Boxma, Models of two queues: A few views, in:Teletraffic Analysis and Computer Performance Evaluation, eds. O.J. Boxma, J.W. Cohen and H.C. Tjims (North-Holland, Amsterdam, 1986) pp. 75–98.

    Google Scholar 

  3. J.A. Buzacott and D. Gupta, Impact of flexible machines on automated manufacturing systems, Ann. Oper. Res. 15 (1988) 169–205.

    Article  Google Scholar 

  4. A. Cobham, Priority assignment in waiting lines problems, Oper. Res. 2 (1954) 70–76.

    Google Scholar 

  5. D.R. Cox and H.D. Miller,The Theory of Stochastic Processes (Chapman and Hall, New York, 1965).

    Google Scholar 

  6. G.R. D'Avignon and R.L. Disney, Queues with instantaneous feedback, Management Sci. 24 (1977) 168–180.

    Google Scholar 

  7. R.L. Disney, D.C. McNickle and G. Simon, TheM/G/1 queue with instantaneous Bernoulli feedback, Naval Res. Logist. Quart. 27 (1980) 635–644.

    Google Scholar 

  8. R.L. Disney, A note on sojourn times inM/G/1 queues with instantaneous Bernoulli feedback, Naval Res. Logist. Quart. 28 (1981) 679–684.

    Google Scholar 

  9. B.T. Doshi, Queueing systems with vacations — A survey, Queueing Systems 1 (1986) 29.

    Article  Google Scholar 

  10. M. Eisenberg, Two queues with changeover times, Oper. Res. 19 (1971) 386–401.

    Google Scholar 

  11. M. Eisenberg, Queues with periodic service and changeover times, Oper. Res. 20 (1972) 440–451.

    Google Scholar 

  12. M.J. Ferguson and Y.J. Aminetzeh, Exact results for nonsymmetric token ring systems, IEEE Trans. Comm. COM-33 (1985) 223–231.

    Article  Google Scholar 

  13. S.W. Fuhrman and R.B. Cooper, Stochastic decompositions in theM/G/1 queue with generalized vacations, Oper. Res. 33 (1985) 1117–1129.

    Google Scholar 

  14. S.B. Gershwin, Stochastic scheduling and setups in flexible manufacturing systems,Proc. 2nd ORSA/TIMS Conf. on FMS: Operations Research Models and Applications, K.E. Stecke and R. Suri (eds.) (1986) pp. 431–442.

  15. D. Gupta, A modelling approach to understanding flexibility of manufacturing systems, Ph.D. Dissertation, University of Waterloo, Waterloo, Ontario, Canada (1987).

    Google Scholar 

  16. O. Hashida, Analysis of multiqueue, Rev. Elect. Commun. Lab. Nippon Telegraph and Telephone Public Corp. 20 (1972) 189–199.

    Google Scholar 

  17. S. Kekre, Issues in manufacturing cell design, Working Paper Series No. 13-94-85, Grad. Sch. Ind. Admin., Carnegie-Mellon University (1985).

  18. P.J. Kuehn, Multiqueue systems with non-exhaustive cyclic service, Bell Syst. Tech. J. 58 (1979) 671–698.

    Google Scholar 

  19. M.A. Leibowitz, An approximate method for treating a class of multiqueue problems, IBM J. Res. Develop. 5 (1961) 204–209.

    Article  Google Scholar 

  20. S.M. Ross,Stochastic Processes (Wiley, New York, 1983).

    Google Scholar 

  21. B. Simon, Priority queues with feedbacks, J. ACM 31 (1984) 134–149.

    Article  Google Scholar 

  22. J.G. Shanthikumar and M. Sumita, Convex ordering of sojourn times in single server queues: Extremal properties of FIFO and LIFO service disciplines, J. Appl. Prob. 24 (1987) 737–748.

    Article  Google Scholar 

  23. J.S. Sykes, Simplified analysis of an alternating priority queueing model with setup times, Oper. Res. 19 (1970) 1182–1192.

    Google Scholar 

  24. L. Takacs, Two queues attended by a single server, Oper. Res. 16 (1968) 639–650.

    Article  Google Scholar 

  25. L. Takacs, A single server queue with feedback, Bell Syst. Tech. J. 42 (1963) 505–519.

    Google Scholar 

  26. H. Takagi, Analysis of polling systems,MIT Press Series in Computer Systems, M. Schwetman (ed.) (MIT Press, Cambridge, MA, 1986).

    Google Scholar 

  27. R.W. Wolff, Poisson arrivals see time averages, Oper. Res. 30 (1982) 223–231.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Business, McMaster University, L8S 4M4, Hamilton, Ontario, Canada

    Diwakar Gupta

  2. Department of Management Sciences, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    John A. Buzacott

Authors
  1. Diwakar Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John A. Buzacott
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by Natural Sciences and Engineering Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta, D., Buzacott, J.A. A production system with two job classes, changeover times and revisitation. Queueing Syst 6, 353–368 (1990). https://doi.org/10.1007/BF02411483

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02411483

Keywords

Search

Navigation