Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
R. Boucherie and N. van Dijk, Product forms for queueing networks with state dependent multiple job transitions, Adv. Appl. Prob. 23 (1990) 152–187.
X. Chao and M. Pinedo, On generalized networks of queues with positive and negative arrivals, Prob. Eng. Inf. Sci. 7 (1993) 301–334.
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.
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.
D. Frosch and K. Natarajan, Product form solutions for closed synchronized systems of stochastic sequential processes,Int. Computer Symp. Taichung, Taiwan (1992).
E. Gelenbe, Product form networks with negative and positive customers, J. Appl. Prob. 28 (1991) 656–663.
E. Gelenbe, G-networks with triggered customer movement, preprint (1992).
E. Gelenbe, Negative customers with batch removal, personal communication (1992).
W. Henderson, Queueing networks with negative customers and negative queue lengths, J. Appl. Prob. 30 (1993) 931–942.
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.
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.
W. Henderson, B.S. Northcote and P.G. Taylor, State dependent signalling in queueing networks, Adv. Appl. Prob. 26 (1994) 436–455.
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.
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.
W. Henderson and P.G. Taylor, Insensitivity of processes with interruptions, J. Appl. Prob. 26 (1989) 242–258.
W. Henderson and P.G. Taylor, Product form in networks of queues with batch arrival and batch services, Queueing Systems 6 (1990) 71–88.
W. Henderson and P.G. Taylor, Embedded processes in stochastic Petri nets, IEEE Trans. Software Eng. 17 (1991) 108–116.
W. Henderson and P.G. Taylor, Some new results on queueing networks with batch movement, J. Appl. Prob. 28 (1991) 409–421.
J.R. Jackson, Networks of waiting lines, Oper. Res. 5 (1957) 518–521.
F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).
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).
B.S. Northcote, Signalling in product form queueing networks, Ph.D. Thesis, Adelaide University (1993).
J. Walrand, A discrete time queueing network, J. Appl. Prob. 20 (1983) 903–909.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Henderson, W., Northcote, B.S. & Taylor, P.G. Triggered batch movement in queueing networks. Queueing Syst 21, 125–141 (1995). https://doi.org/10.1007/BF01158577
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01158577