On the Performance Estimation and Resource

Optimization in Process Petri Nets

Feliciano Colella

November 25, 2014

Introduction

I Timed Process Petri Nets (TPPN).I Vector of average times of transitions;I Vector of rates associated to transitions.

I De�ning 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.

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Introduction

I Timed Process Petri Nets (TPPN).I Vector of average times of transitions;I Vector of rates associated to transitions.

I De�ning 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

Introduction

I Timed Process Petri Nets (TPPN).I Vector of average times of transitions;I Vector of rates associated to transitions.

I De�ning 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

Introduction

I Timed Process Petri Nets (TPPN).I Vector of average times of transitions;I Vector of rates associated to transitions.

I De�ning 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

Introduction

I Timed Process Petri Nets (TPPN).I Vector of average times of transitions;I Vector of rates associated to transitions.

I De�ning 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

The Problem

Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 3 / 8

The Model

The Network ...

Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 4 / 8

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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The Results

Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 6 / 8

Conclusion

I TPPN are a good formalism to model the behaviour of systems withshared resources.

I Dealing with the LP problems is useful but it quickly explodes in termsof complexity with bigger systems.

I Further attention should be put on designing betterHeuristics/Algorithms in order to reduce the time of the Experiments(more than 1 day is really a lot !).

Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 7 / 8

Thank you for the attention.

Feliciano Colella Formal Method - Process Petri Nets November 25, 2014 8 / 8