Queueing Systems

, Volume 21, Issue 1–2, pp 125–141 | Cite as

Triggered batch movement in queueing networks

  • W. Henderson
  • B. S. Northcote
  • P. G. Taylor


A product form equilibrium distribution is derived for a class of queueing networks, in either discrete or continuous time, in which multiple customers arrive simultaneously, multiple customers complete service simultaneously, and any event occurring in the network can force/trigger the release of multiple customers to be routed through the network.


Product form batch movement triggered transitions state dependence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Boucherie and N. van Dijk, Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes, Adv. Appl. Prob. 22 (1990) 433–455.Google Scholar
  2. [2]
    R. Boucherie and N. van Dijk, Product forms for queueing networks with state dependent multiple job transitions, Adv. Appl. Prob. 23 (1990) 152–187.Google Scholar
  3. [3]
    X. Chao and M. Pinedo, On generalized networks of queues with positive and negative arrivals, Prob. Eng. Inf. Sci. 7 (1993) 301–334.Google Scholar
  4. [4]
    J.L. Coleman, W. Henderson and P.G. Taylor, Product form equilibrium distributions and a convolution algorithm, for stochastic Petri nets, to appear in Perform. Eval.Google Scholar
  5. [5]
    S. Donatelli and M. Sereno, On the product form solution for stochastic Petri nets,Proc. 13th Int. Conf. on Application and Theory of Petri Nets, Sheffield, UK (1992) pp. 154–172.Google Scholar
  6. [6]
    D. Frosch and K. Natarajan, Product form solutions for closed synchronized systems of stochastic sequential processes,Int. Computer Symp. Taichung, Taiwan (1992).Google Scholar
  7. [7]
    E. Gelenbe, Product form networks with negative and positive customers, J. Appl. Prob. 28 (1991) 656–663.Google Scholar
  8. [8]
    E. Gelenbe, G-networks with triggered customer movement, preprint (1992).Google Scholar
  9. [9]
    E. Gelenbe, Negative customers with batch removal, personal communication (1992).Google Scholar
  10. [10]
    W. Henderson, Queueing networks with negative customers and negative queue lengths, J. Appl. Prob. 30 (1993) 931–942.Google Scholar
  11. [11]
    W. Henderson, D. Lucic and P.G. Taylor, A net level performance analysis of stochastic Petri nets, J. Aust. Math. Soc. Ser. B31 (1989) 176–187.Google Scholar
  12. [12]
    W. Henderson, B.S. Northcote and P.G. Taylor, Geometric equilibrium distributions for queues with interactive batch departures, Ann. Ops. Res. 48 (1994) 493–511.Google Scholar
  13. [13]
    W. Henderson, B.S. Northcote and P.G. Taylor, State dependent signalling in queueing networks, Adv. Appl. Prob. 26 (1994) 436–455.Google Scholar
  14. [14]
    W. Henderson, B.S. Northcote and P.G. Taylor, Networks of queues with signals.Proc. Australia-Japan Workshop on Stochastic Models in Engineering, Technology and Management (World Scientific, 1993) pp. 161–171.Google Scholar
  15. [15]
    W. Henderson, C.E.M. Pearce, P.G. Taylor and N.M. Van Dijk, Closed queueing networks with batch services, Queueing Systems 6 (1990) 59–70.Google Scholar
  16. [16]
    W. Henderson and P.G. Taylor, Insensitivity of processes with interruptions, J. Appl. Prob. 26 (1989) 242–258.Google Scholar
  17. [17]
    W. Henderson and P.G. Taylor, Product form in networks of queues with batch arrival and batch services, Queueing Systems 6 (1990) 71–88.Google Scholar
  18. [18]
    W. Henderson and P.G. Taylor, Embedded processes in stochastic Petri nets, IEEE Trans. Software Eng. 17 (1991) 108–116.Google Scholar
  19. [19]
    W. Henderson and P.G. Taylor, Some new results on queueing networks with batch movement, J. Appl. Prob. 28 (1991) 409–421.Google Scholar
  20. [20]
    J.R. Jackson, Networks of waiting lines, Oper. Res. 5 (1957) 518–521.Google Scholar
  21. [21]
    F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).Google Scholar
  22. [22]
    M. Li and N.D. Georganas, Parametric analysis of stochastic Petri nets.5th Int. Conf. on Modelling and Tools for Computer Performance Evaluation, Torino, Italy (1991).Google Scholar
  23. [23]
    B.S. Northcote, Signalling in product form queueing networks, Ph.D. Thesis, Adelaide University (1993).Google Scholar
  24. [24]
    J. Walrand, A discrete time queueing network, J. Appl. Prob. 20 (1983) 903–909.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • W. Henderson
    • 1
  • B. S. Northcote
    • 1
  • P. G. Taylor
    • 1
  1. 1.Teletraffic Research Centre, Applied Maths DepartmentUniversity of AdelaideAdelaideAustralia

Personalised recommendations