NORTON'S THEOREM FOR BATCH ROUTING QUEUEING NETWORKS

This paper shows that the aggregation and decomposition result known as Norton's theorem for queueing networks can be extended to a general class of batch routing queueing networks with product-form solution that allows for multiple components to simultaneously release and receive (batches of) customers.

[1]  Simonetta Balsamo,et al.  Product-Form Synthesis of Queueing Networks , 1985, IEEE Transactions on Software Engineering.

[2]  Richard J. Boucherie,et al.  Norton's equivalent for batch routing queueing networks with independently routing customers , 1996 .

[3]  C. E. M. Pearce,et al.  Closed queueing networks with batch services , 1990, Queueing Syst. Theory Appl..

[4]  Guy Pujolle,et al.  Product-Form Discrete-Time Queues in Series with Batch Transition: Late Arrival Case , 1995, Perform. Evaluation.

[5]  Peter Buchholz,et al.  Aggregation and disaggregation in product form queueing Petri Nets , 1997, Proceedings of the Seventh International Workshop on Petri Nets and Performance Models.

[6]  Simonetta Balsamo,et al.  An Extension of Norton's Theorem for Queueing Networks , 1982, IEEE Transactions on Software Engineering.

[7]  Aurel A. Lazar,et al.  An extension to Norton's equivalent , 1989, Queueing Syst. Theory Appl..

[8]  K. Mani Chandy,et al.  Parametric Analysis of Queuing Networks , 1975, IBM J. Res. Dev..

[9]  Hendrik Vantilborgh.  Exact Aggregation in Exponential Queueing Networks , 1978, JACM.

[10]  Richard J. Boucherie,et al.  Product forms for queueing networks with state-dependent multiple job transitions , 1991, Advances in Applied Probability.

[11]  Peter Buchholz,et al.  Queueing Petri Nets with Product Form Solution , 1998, Perform. Evaluation.

[12]  Peter Whittle,et al.  Systems in stochastic equilibrium , 1986 .

[13]  J. Walrand.  A NOTE ON NORTON'S THEOREM FOR QUEUING NETWORKS , 1983 .

[14]  N. M. van Dijk,et al.  Product forms for queueing networks with limited clusters , 1988 .

[15]  Richard J. Boucherie,et al.  A generalization of Norton's theorem for queueing networks , 1993, Queueing Syst. Theory Appl..

[16]  Donald F. Towsley,et al.  Queuing Network Models with State-Dependent Routing , 1980, JACM.

[17]  Matteo Sereno,et al.  On closed support T-Invariants and the traffic equations , 1998, Journal of Applied Probability.

[18]  Pieter S. Kritzinger,et al.  A generalisation of Norton's theorem for multiclass queueing networks , 1982, Perform. Evaluation.

[19]  W. Henderson,et al.  Some new results on queueing networks with batch movement , 1991, Journal of Applied Probability.

[20]  J. R. Jackson.  Networks of Waiting Lines , 1957 .

[21]  Peter G. Taylor,et al.  A net level performance analysis of stochastic Petri nets , 1989, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[22]  Richard J. Boucherie,et al.  Norton's Equivalent for Queueing Networks Comprised of Quasireversible Components Linked by State-Dependent Routing , 1998, Perform. Evaluation.

[23]  Peter G. Taylor,et al.  Product form in networks of queues with batch arrivals and batch services , 1990, Queueing Syst. Theory Appl..

[24]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.