Throughput upper bounds for Markovian Petri nets: embedded subnets and queueing networks

2002 ◽  
Author(s):  
J. Campos ◽  
M. Silva
Keyword(s):  
Petri Nets ◽  
Queueing Networks ◽  
Upper Bounds

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.

G-Networks with Signals and Batch Removal

1993 ◽  
Vol 7 (3) ◽  
pp. 335-342 ◽  
Author(s):  
Erol Gelenbe
Keyword(s):  
Petri Nets ◽  
Computer System ◽  
Stationary Solution ◽  
Queueing Networks ◽  
The Other ◽  
Parallel Computer ◽  
System Modelling ◽  
Network Stability ◽  
Batch Mode ◽  
Flow Equations

We consider queueing networks containing customers and signals that were recently introduced in Gelenbe [4]. Both customers and signals can be exogenous or can be obtained by a Markovian transition of a customer after service. A signal entering a queue forces a customer to move on to another queue according to a Markovian routing rule or to leave the network in batch mode. This synchronized or triggered motion is useful in representing the effect of tokens in Petri-nets, for systems in which customers and work can be instantaneously moved from one queue to the other on the arrival of a signal as well as for other network behaviors that are encountered in parallel computer system modelling. We show that this network has product form stationary solution and establish the non-linear customer flow equations that govern it. Network stability is discussed in this new context.

Throughput upper bounds for open Markovian queueing networks with blocking

1995 ◽  
Vol 28 (2) ◽  
pp. 351-365 ◽  
Author(s):  
Dong-Wan Tcha ◽  
Chun-Hyun Paik ◽  
Won-Taek Lee
Keyword(s):  
Queueing Networks ◽  
Upper Bounds ◽  
Markovian Queueing Networks

scholarly journals Lower and upper bounds of shortest paths in reachability graphs

2004 ◽  
Vol 2004 (57) ◽  
pp. 3023-3036 ◽  
Author(s):  
P. K. Mishra
Keyword(s):  
Petri Nets ◽  
Shortest Path ◽  
Petri Net ◽  
Free Choice ◽  
Shortest Paths ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Marked Graphs ◽  
Marked Graph

We prove the following property for safe marked graphs, safe conflict-free Petri nets, and live and safe extended free-choice Petri nets. We prove the following three results. If the Petri net is a marked graph, then the length of the shortest path is at most(|T|−1)⋅|T|/2. If the Petri net is conflict free, then the length of the shortest path is at most(|T|+1)⋅|T|/2. If the petrinet is live and extended free choice, then the length of the shortest path is at most|T|⋅|T+1|⋅|T+2|/6, whereTis the set of transitions of the net.

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