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Batch Routing Queueing Networks with Jump-Over Blocking

Published online by Cambridge University Press:  27 July 2009

Richard J. Boucherie
Richard J. Boucherie
Affiliation:
Department of Econometrics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
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Extract

This paper shows that the equilibrium distribution of a queueing network with batch routing continues to be of product form if a batch that cannot enter its destination — for example, as a consequence of capacity constraints — immediately triggers a new transition that takes up the whole batch.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 287 - 297
Copyright
Copyright © Cambridge University Press 1996

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References

1.Boucherie, R.J. & Sereno, M. (1994). A structural characterisation of product form stochastic Petri nets. In Boxma, O. J. & Koole, CM. (eds.), Performance evaluation of parallel and distributed systems—Solution methods. Tract 106. Amsterdam: CWI, pp. 157–174.Google Scholar
2.Boucherie, R.J. & van Dijk, N.M. (1991). Product forms for queueing networks with statedependent multiple job transitions. Advances in Applied Probability 23: 152–187.CrossRefGoogle Scholar
3.Henderson, W., Luck, D., & Taylor, P.G. (1989). A net level performance analysis of stochastic Petri nets. Journal of the Australian Mathematical Society, Series B 31: 176–187.CrossRefGoogle Scholar
4.Henderson, W., Pearce, C.E.M., Taylor, P.G., & van Dijk, N.M. (1990). Closed queueing networks with batch services. Queueing Systems 6: 59–70.CrossRefGoogle Scholar
5.Henderson, W. & Taylor, P.G. (1990). Product form in networks of queues with batch arrivals and batch services. Queueing Systems 6: 71–88.CrossRefGoogle Scholar
6.Jackson, J.R. (1963). Jobshop-like queueing systems. Management Science 10: 131–142.CrossRefGoogle Scholar
7.Lazar, A.A. & Robertazzi, T.G. (1991). Markovian Petri net protocols with product form solution. Performance Evaluation 12: 67–77.CrossRefGoogle Scholar
8.Pittel, B. (1979). Closed exponential networks of queues with saturation: The Jackson-type stationary distribution and its asymptotic analysis. Mathematics of Operations Research 4: 357–378.CrossRefGoogle Scholar
9.Serfozo, R.F. (1989). Markovian network processes: Congestion dependent routing and processing. Queueing Systems 5: 5–36.CrossRefGoogle Scholar
10.van Dijk, N.M. (1988). On Jackson's product form with ‘jump-over’ blocking. Operations Research Letters 7: 233–235.CrossRefGoogle Scholar