scholarly journals Approximating closed fork-join queueing networks using product-form stochastic Petri-nets

2015 ◽  
Vol 110 ◽  
pp. 264-278 ◽  
Author(s):  
Rasha Osman ◽  
Peter G. Harrison
Keyword(s):  
Petri Nets ◽  
Queueing Networks ◽  
Stochastic Petri Nets ◽  
Product Form

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.

On closed support T-Invariants and the traffic equations

1998 ◽  
Vol 35 (02) ◽  
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.

Product-form and stochastic Petri nets: a structural approach

2005 ◽  
Vol 59 (4) ◽  
pp. 313-336 ◽  
Author(s):  
S. Haddad ◽  
P. Moreaux ◽  
M. Sereno ◽  
M. Silva
Keyword(s):  
Petri Nets ◽  
Structural Approach ◽  
Stochastic Petri Nets ◽  
Product Form
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