Product-Form Queueing Networks

2021 ◽  
pp. 125-142
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Product Form Queueing Networks

Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

2000 ◽  
Vol 32 (01) ◽  
pp. 284-313 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Unified Approach ◽  
Stationary Distributions ◽  
Batch Arrivals ◽  
Unified View ◽  
Batch Services ◽  
Product Form Queueing Networks

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

Mean value analysis by chain of product form queueing networks

1989 ◽  
Vol 38 (3) ◽  
pp. 432-442 ◽  
Author(s):  
A.E. Conway ◽  
E. de Souza e Silva ◽  
S.S. Lavenberg
Keyword(s):  
Queueing Networks ◽  
Mean Value ◽  
Product Form ◽  
Value Analysis ◽  
Mean Value Analysis ◽  
Product Form Queueing Networks

On closed support T-Invariants and the traffic equations

1998 ◽  
Vol 35 (2) ◽  
pp. 473-481 ◽  
Author(s):  
Richard J. Boucherie ◽  
Matteo Sereno
Keyword(s):  
Petri Nets ◽  
Queueing Networks ◽  
Stochastic Petri Nets ◽  
Product Form ◽  
Approximate Analysis ◽  
Existence Of A Solution ◽  
Exact Analysis ◽  
Necessary And Sufficient ◽  
Product Form Queueing Networks

The traffic equations are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note shows that the new condition stating that each transition is covered by a minimal closed support T-invariant, is necessary and sufficient for the existence of a solution for the traffic equations for batch routing queueing networks and stochastic Petri nets.

scholarly journals A survey of product form queueing networks with blocking and their equivalences

1994 ◽  
Vol 48 (1) ◽  
pp. 31-61 ◽  
Author(s):  
Simonetta Balsamo ◽  
Vittoria de Nitto Personè
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Product Form Queueing Networks
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