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Closed queueing networks with batch services

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Abstract

In this paper we study queueing networks which allow multiple changes at a given time. The model has a natural application to discrete-time queueing networks but describes also queueing networks in continuous time.

It is shown that product-form results which are known to hold when there are single changes at a given instant remain valid when multiple changes are allowed.

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References

  1. K. Chandy, J. Howard and D. Towsley, Product form and local balance in queueing networks, J. Assoc. Comp. Mach. 24 (1977) 250–263.

    Google Scholar 

  2. K. Chandy and J. Martin, A characterisation of product form queueing networks, J. Assoc. Comp. Mach. 30 (1983) 286–299.

    Google Scholar 

  3. H. Daduna and R. Schassberger, Networks of queues in discrete time, Z. Oper. Res. 27 (1983) 159–175.

    Article  Google Scholar 

  4. W. Henderson and P.G. Taylor, Product form in networks of queues with batch arrivals and batch services, Queueing Systems 6 (1990) 71–88.

    Google Scholar 

  5. A. Hordijk and N. Van Dijk, Networks of queues with blocking,Performance 81, ed. K. Kylstra (North-Holland, 1981) 51–65.

  6. A. Hordijk and N. Van Dijk, Networks of queues, Proc. Int. Seminar onModelling and Performance Evaluation Methodology, INRIA, vol. 1 (1983) pp. 79–135.

    Google Scholar 

  7. A. Hordijk and N. Van Dijk, Adjoint processes, job local balance and insensitivity for stochastic networks, Bull. 44th Session Int. Stat. Inst. 50 (1983) 776–788.

    Google Scholar 

  8. J. Jackson, Networks of waiting lines, Oper. Res. 5 (1957) 518–521.

    Article  Google Scholar 

  9. F. Kelly, Networks of queues with customers of different types, J. Appl. Prob. 12 (1975) 542–544.

    Article  Google Scholar 

  10. F. Kelly (1975), Markov processes and Markov random fields, Bull. Inst. Int. Statist. 46 (1975) 397–404.

    Google Scholar 

  11. F. Kelly, Networks of queues, Adv. Appl. Prob. 8 (1976) 416–432.

    Article  Google Scholar 

  12. F. Kelly,Reversibility and Stochastic Networks (Wiley, London, 1979).

    Google Scholar 

  13. G. Pujolle, J.P. Claude and D. Seret, A discrete queueing system with a product form solution,Computer Networking and Performance Evaluation, eds. T. Hasegawa, H. Takagi and Y. Takahashi (Elsevier Science, North-Holland, Tokyo, 1986) pp. 139–147.

    Google Scholar 

  14. R.F. Serfozo, Markovian network processes with system-dependent transition rates, preprint.

  15. J. Walrand, A discrete-time queueing network, J. Appl. Prob. 20 (1983) 903–909.

    Article  Google Scholar 

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Henderson, W., Pearce, C.E.M., Taylor, P.G. et al. Closed queueing networks with batch services. Queueing Syst 6, 59–70 (1990). https://doi.org/10.1007/BF02411465

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  • DOI: https://doi.org/10.1007/BF02411465

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