# Simplifying the Verification of Simulation Models through Petri Net to FlexSim Mapping

^{1}

^{2}

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*Appl. Sci.*

**2020**,

*10*(4), 1395; https://doi.org/10.3390/app10041395 (registering DOI)

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Petri Nets

#### 3.1. Basic Definition

_{0}), where:

- P = {P
_{1}, P_{2}, P_{3}, ....., P_{np}} is a finite set of places; - T = {T
_{1}, T_{2}, T_{3}, ....., T_{ne}} is a finite set of transitions; - A = {A
_{1}, A_{2}, A_{3}, ....., A_{na}} is a finite set of arcs that connect places to transitions and vice versa; - W: A
_{i}→ {1, 2, 3, ....} ∀ A_{i}is the weight associated with each arc; - M
_{0}: P_{i}→ {1, 2, 3, ....} ∀ P_{i}is the initial number of entities in each place (initial marking).

#### 3.2. Timed Petri Nets

## 4. FlexSim

^{®}[43] is a commercial simulation package that allows the execution of discrete and continuous simulation models. Being a commercial suite, it allows the definition of the simulation models following a proprietary and graphical approach, based on the connection of different simulation objects that allows representing the model behavior in a process interaction paradigm [44], see Figure 4.

## 5. Mapping Petri Nets to a FlexSim Model

#### 5.1. Sequential Execution

**Delay**activity.

#### 5.2. Conflict

**Decide**activity and can also be solved in either of the two ways.

**Decide**activity can have one or multiple inputs as well as one or multiple outputs, see Figure 7. Each output is assigned a positive integer number (the first option is 1, the second option is 2, etc.) All inputs enter the

**Decide**activity and exit to the assigned output. Therefore, the deterministic or probabilistic solution of the conflict will depend on the number that is “assigned” to each token, as the number assigned for each output is not changeable. For a deterministic solution, labels (equivalent to colors in a colored Petri net) can be used. These labels can be assigned before the

**Decide**activity or may exist from previous processes.

#### 5.3. Concurrency with Temporal Entities

**Split**activity in FlexSim deposits temporal entities at two (or more) output places.

#### 5.4. Synchronization with Temporal Entities

#### 5.5. Concurrency and Synchronization with Resources

**Join**and

**Split**activities, as explained above. However, because resources are so common in Petri nets, and in order to provide a rapid and comprehensive view of the scheme (imagine using the same resource for several concurrent Petri nets), they have specific activities. Therefore, Figure 12 can be represented in FlexSim as shown in Figure 13.

## 6. Example: Bridge Crossing Deadlock

#### 6.1. Petri Net Model

#### Alternative 1: Avoiding Deadlock

#### 6.2. FlexSim Process Simulation Flow

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Simplified modeling process for a simulation project [10], showing in red the aspects that will be affected by the proposed methodology. The conceptual model-tool mapping simplifies the verification process and encoding.

**Figure 4.**FlexSim environment with a basic model. The construction of the model is based on the selection of the elements that are presented on the left side and the configuration of those elements on the right side of the environment.

**Figure 20.**Case IV: reachability/coverability graph obtained by the PIPE simulator for the first proposed solution.

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**MDPI and ACS Style**

Fonseca i Casas, P.; Lijia Hu, D.; Guasch i Petit, A.; Figueras i Jové, J.
Simplifying the Verification of Simulation Models through Petri Net to FlexSim Mapping. *Appl. Sci.* **2020**, *10*, 1395.
https://doi.org/10.3390/app10041395

**AMA Style**

Fonseca i Casas P, Lijia Hu D, Guasch i Petit A, Figueras i Jové J.
Simplifying the Verification of Simulation Models through Petri Net to FlexSim Mapping. *Applied Sciences*. 2020; 10(4):1395.
https://doi.org/10.3390/app10041395

**Chicago/Turabian Style**

Fonseca i Casas, Pau, Daniel Lijia Hu, Antoni Guasch i Petit, and Jaume Figueras i Jové.
2020. "Simplifying the Verification of Simulation Models through Petri Net to FlexSim Mapping" *Applied Sciences* 10, no. 4: 1395.
https://doi.org/10.3390/app10041395