The document discusses using timed process Petri nets (TPPN) to model systems with shared resources. TPPNs use vectors to represent average transition times and rates. Linear programming problems (LPPs) can identify bottlenecks, but iterative strategies are weak and slow. Instead, heuristics provide better performance estimation and resource optimization. As a case study, the document applies TPPN modeling to a secure database system, examining the network, parameters, and results of sensitivity analysis. It concludes that TPPNs are useful for modeling but that heuristic algorithms are needed to reduce experiment time when modeling larger systems.

1. On the Performance Estimation and Resource
Optimization in Process Petri Nets
Feliciano Colella
November 25, 2014

2. Introduction
I Timed Process Petri Nets (TPPN).
I Vector of average times of transitions;
I Vector of rates associated to transitions.
Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 2 / 8

3. Introduction
I Timed Process Petri Nets (TPPN).
I Vector of average times of transitions;
I Vector of rates associated to transitions.
I Dening LPPs in order to nd Bottlenecks of the net.
Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 2 / 8

4. Introduction
I Timed Process Petri Nets (TPPN).
I Vector of average times of transitions;
I Vector of rates associated to transitions.
I Dening LPPs in order to nd Bottlenecks of the net.
I Iterative strategy is weak and slow
Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 2 / 8

5. Introduction
I Timed Process Petri Nets (TPPN).
I Vector of average times of transitions;
I Vector of rates associated to transitions.
I Dening LPPs in order to nd Bottlenecks of the net.
I Iterative strategy is weak and slow ! Heuristic works better.
Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 2 / 8

6. Introduction
I Timed Process Petri Nets (TPPN).
I Vector of average times of transitions;
I Vector of rates associated to transitions.
I Dening LPPs in order to nd Bottlenecks of the net.
I Iterative strategy is weak and slow ! Heuristic works better.
I Case Study: A Secure Database System (SDBS).
1. Use Case Diagram;
2. Sequence Diagram;
3. Petri Net modelling (Network + Parameters);
4. Sensitivity Analysis.
Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 2 / 8

7. The Problem
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8. The Model
The Network ...
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9. The Model
... and its parameters.
Figure: (a), (c) Duration of the exponential transition in the Net.
Figure: (b) Number of instances of each resource.
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10. The Results
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11. Conclusion
I TPPN are a good formalism to model the behaviour of systems with
shared resources.
I Dealing with the LP problems is useful but it quickly explodes in terms
of complexity with bigger systems.
I Further attention should be put on designing better
Heuristics/Algorithms in order to reduce the time of the Experiments
(more than 1 day is really a lot !).
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12. Thank you for the attention.
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