# Activity-Based Discrete Event Simulation of Spatial Production Systems: Application to Fisheries

Eric Innocenti, Paul-Antoine Bisgambiglia, Dominique Urbani

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Eric Innocenti, Paul-Antoine Bisgambiglia, Dominique Urbani. Activity-Based Discrete Event Simulation of Spatial Production Systems: Application to Fisheries. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2014, Ajaccio, France. pp.240-247, 10.1007/978-3-662-44733-8_30. hal-01387188

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# Activity-based Discrete Event Simulation of Spatial
Production Systems: application to fisheries

Eric Innocenti, Paul-Antoine Bisgambiglia, Dominique Urbani

University of Corsica UCPP, UMR 6134 SPE CNRS, 20250 CORTE FRANCE
(eric.innocenti,bisgambiglia,durbani)@univ-corse.fr

***Abstract.*** In this paper, we present a modular and generic object framework us-
ing the Discrete EVent system Simulation Specification (*DEVS*) and the activity
concept. We plan to simulate coastal fishery policies in the aim of improving
harvesting and the management of fisheries.

**Keywords:** Spatial Production Systems, Cellular Automata Model, DEVS.

# 1 Introduction

Application of long-term effective policies in natural production systems needs rele-
vant decision-making indicators and quantitative assessments. This issue is critical in
fisheries management facing the decline of world productivity due to pressures from
overfishing, habitat change, pollution, and climate change [1]. It is possible to de-
velop software tools dedicated to the election of strategies for sustainable fisheries
management (fishing gear regulation, stock rebuilding projects, etc.) [2] – [4]. This
work remains part of a computer tool designed to help fishery managers. The main
goal is to assist in the definition of a responsible fishing policy in Corsica. We discuss
the opportunity to develop a modular framework using the Discrete EVent system
Specification formalism (DEVS) and the activity concept. We plan to develop soft-
ware to simulate coastal fishery policies to improve the management of resources. We
use a Cellular Automata Model (CAM) for spatial representation and taking into ac-
count the activity concept [5]-[8]. CAM are usually considered as an aggregation of
discrete components with local interactions. The model of fish population growth is
inspired by the literature [19], [20], and spatially explained with a CAM. The tech-
niques developed are discussed, including challenges, perspectives and limitations.
Section 2 reminds the theoretical concepts and section 3 details the software frame-
work before presenting an illustrative application (section 4). The last section before
the discussion and concluding remarks gives our simulation results, we want to show
that when CAM are jointly used with the DEVS formalism [9] and the activity con-
cept, both the model and the simulator objects efficiently exploit the numerous spatial
components.
# 2 Backgrounds

## 2.1 Cellular automata modelling

Cellular Automata Model (CAM) are an evolved form of von Neumman's Cellular Automata (CA) [8], [9]. These computational models are well suited to capture essential features of spatial systems in which large-scale behaviour arises from the collective effect of a great number of locally interacting simple components. As CAM inherit their basic characteristics from CA, they get the benefit of emerging phenomena. From a simple and deterministic local rule, CAM can generate a surprisingly complex global behaviour. The spatial interactions between cells are key elements of such models. At each time step, a cell changes state according to the local rule linked to its neighbourhood. The successive states of the cells follow a state trajectory, in the discrete time base. The state of the CAM is the aggregation of the cell states. Over the last years, the study of IT implementation of CAM considerably increased [11-15]. The determination of active components in this kind of model is also an essential aspect to improve the computing model elegance and to guarantee acceptable simulation times. In the next subsection we give more information on the activity concept.

## 2.2 Activity concept

The activity concept is usually formulated as a measure of change in system behaviour [9], and is used to concentrate computations on the high rates of change [14], [15]. The activity in a CAM is determined by the measure of the active cells, i.e. by the set of cells that can change state between two global state transitions. The activity is measured at the highest level of the hierarchy, i.e., at the global level of the CAM in a set of active cells. The local level informs the global level on the model activity: (1) at time t, the simulator browses the active cells and executes their transition functions $\delta_{int}$ (transition phase); (2) at the same time, the neighbouring inactive cells are tested in order to determine if they can become active at $t+1$ (propagation phase). This step is called and relies on the propagation rule. The inactive neighbouring cells of active cells are placed as active if they can become active at $t+1$. Whatever the size of the CAM considered, computations only depend on activity, thus the formulation of the propagation rule is a key element to enhance simulation times.

## 2.3 DEVS formalism

DEVS formalism was introduced in [8] as a rigorous basis for the compositional modelling and simulation of discrete event systems. A DEVS model is either an *Atomic* (AM) or a *Coupled (CM)* model. An AM is a structure: $<X, Y, S, \delta_{ext}, \delta_{int}, \lambda, t_a >$ with X the set of external events, Y the set of output events, S the set of sequential states, $\delta_{ext}$:
$Q \times X \to S$ the external state transition function, where $Q = \{(s,e) | s \text{ in } S, 0 \le e \le t_a(s)\}$ and $e$ is the elapsed time since the last state transition; $\delta_{int} S \to S$ the internal state transition function; $\lambda: S \to Y$ the output function and $t_a: S \to \mathbb{R}_{0 \to \infty}$ the time advance function. The *AM* describes the behaviour of the system. A *CM* describes the composition of several DEVS sub-models, i.e *AM* or *CM*. We have developed our DEVS simulator inspired by pythonDEVS [16] and DEVS-Ruby [17], and in this work we use the DEVS simulator taking into account the activity concept previously described.

# 3 Framework

In this section, we give a brief description of our simulation software. Our approach is not based on Cell-DEVS [18], but on the multi-component concepts [8]. One atomic model aggregates the entire environment.

## 3.1 Activity-based Discrete Event Simulation

The use of the *activity* concept implies the prediction of next active cells from a simulation procedure based on events. While applying these criteria to the *CAM* previously described, it is appropriate to use a discrete event system that cause transitions through the triggering of events based on message exchanges. For that, the model is established on the basis of *DEVS* formalism. The *CAM* used for the simulation is aggregated in an *AM*. It interacts with the simulator with ports and messages. The perimeter of the active area is updated when an internal event occurs ($\delta_{int}$).

## 3.2 Object implementation

Objects ensure modularity, genericity, and reusability and the DEVS formalism comes with well established discrete event simulation algorithms. The main objects and the interconnections are presented in figure 1. The left part describes the simulation part, it is conventional in DEVS. The right part shows the encapsulation mechanism of CAM in an atomic model.

<figure><img src="image_2.png" /><figcaption>Fig. 1. The *CAM* and its *DEVS* objects.</figcaption></figure>
# 4 Illustrative application: Fox model adaptation

To study the effect of the fishery on biomass and to estimate the Maximum Sustain-able Yield (MSY) in each cell, we implement a Fox Surplus-Production Model (SPM) [19], [20]. The MSY corresponds to the maximum capture that does not exhaust the fish population. SPM models are advantageous as they allow to simply estimate both fish stock and fish rates. Moreover, they collect in the same production model the evolution rules of the biomass, the mortality and population growth. Thus, they only require temporal series of stock abundance indexes that eases their use. The Fox SPM [18] is a particular case of the Pella and Tomlison model [20]. It allows characterising the fish population x according to a set of coefficients, as:

$$f(x_t) = \frac{(p+1)}{p} \times r \times x \times \left(1 - \left(\frac{x}{K}\right)^p\right) (1)$$

$$f(x_{t+1}) = x \times (1 - \varphi - r * \log(x/K)) \times \varepsilon (2)$$

Where $\varphi$ is the fish rate, $\varepsilon$ the environmental variability, r the population rate, K the maximum capacity of the environment, p an asymmetric coefficient.

In the Fox's model, p is near 0; this allows getting an asymmetric fish stock evolution. The model grows up to a K maximum constant, and it decreases keeping an asymptotic course. These models are relatively simple and well documented in literature. This model is implemented in each cell of the CAM with K=90.

## 4.1 SPM Model settings

The environmental map is composed by reef and fishing areas: the reef areas model the life spaces of the fish. They have a strong attraction capacity as they feed the fish. The attraction coefficient aCff allows setting the attraction capacity of the cell. The value of aCff of each cell depends on the distance between the cell and the location of the reef area. The attraction capacity of the cells around the reef areas is randomly calculated at the initialization. The fishing areas are space with fishing production determined by the fishing rate $\varphi$. In the original Fox's model, the fish rate is applied to all the cells of the space. In order to clearly study the effect of fishing, we only apply it to the cells set as fishing areas. During simulation, we apply the transition rule in charge of the fish population evolution, and the propagation rule in charge of the movement of fishes in space (Fig. 2).

1: c: current cell, nCell: neighbouring cell, x: fish, K: max cell capacity, aCff: attraction coefficient

2: If c.nbFish > 0

3: For each n in nCell {

4: . If c.aCff < n.aCff Or c.nbFish > (K-20) Then

5: #Different attraction da

6: da <- n.aCff - c.aCff

7: #Moving potential

8: pd <- int(K - c.nbFish)

9: . #Small attraction difference, little migration
10: `migrCOEF = 6 #Migration coefficient`
11: `If da <= 0.1 Then`
12: `bmin <- 0 #Min value`
13: `bmax <- pd/migrCOEF #Max value`
14: `#Medium attraction difference, medium migration`
15: `maxMigrCOEF = 4 #Max migration coefficient`
16: `minMigrCOEF = 8 #Min migration coefficient`
17: `If da > 0.1 And da < 0.2 Then`
18: `bmin <- pd / minMigrCOEF`
19: `bmax <- pd / maxMigrCOEF`
20: `Then`
21: `bmin <- pd / maxMigrCOEF, bmax <- pd`
22: `If c.nbFish >= K Then`
23: `bmin <- 0, bmax <- pd`
24: `#Number of fish moving`
25: `nFish <- random(bmin, bmax)`
26: `moveFish(nFish)From(c)To(n)Location`
27: `activateNCell(n)`
28: `removeFish(nFish)At(c)Location }`

<caption>Fig. 2. CAM Propagation phase algorithm.</caption>

## 4.2 Simulation example

We compare the fish population evolution in fishing areas and in an area where fishing is prohibited. Thanks to the activity concept we can simulate a domain of 350x250 cells. We experiment a reef area with maximal attraction (1.0). The attraction around the reef area is randomly determined between 0.5 and 0.9. These coefficients have been empirically defined. The number of active cells evolves during the simulation process. The main values of the model's coefficients are detailed in table 1.

<table><caption>Table 1. Model's setting.</caption><thead><tr><th></th><th>Ocean</th><th>Reef-Crown</th><th>Fishing area (10 cells)</th><th>Fishing area t=40 (83 cells)</th></tr></thead><tbody><tr><td>Population growth r</td><td>0.2</td><td>0.9-0.75</td><td>0.9</td><td>0.9</td></tr><tr><td>Cell capacity K</td><td>90</td><td>90</td><td>90</td><td>90</td></tr><tr><td>Fish rate φ</td><td>0.1</td><td>0.4-0.45</td><td>1</td><td>2.5</td></tr><tr><td>Attraction aCff</td><td>0</td><td>0.5-1</td><td>0.5-1</td><td>0.5-1</td></tr></tbody></table>

The simulation results point out the fish quantities evolution in the simulated time.

## 4.3 Results

The curve presented in Fig. 3 shows the activity of cells. It decreases slightly with a stronger tendency to t = 40, corresponding to the beginning of overfishing. Trawlers have emptied cells and they have become inactive.
<figure><img src="image_3.png" /><figcaption>**Fig. 3.** : Fish quantity and activity evolution. The blue curve represents the evolution of the fish population. The red curve describes the maximum capacity of the environment according to the K parameter and the number of active cells.</figcaption></figure>

The fish population evolves as the *activity* level. The activity curve is a good indicator trend of the model.

<figure><img src="image_4.png" /><figcaption>**Fig. 4.** Activity (a) and population (b) evolutions.</figcaption></figure>

Figure 4a represents the evolution of the activity, at t=0, 41, 120, 180. Active cells are greatly influenced by the reef areas and their attraction. Figure 4b shows the population of fish at 0, 41, 120, and 180. After initialization, the homogenization of the fish
population is due to the propagation rule. The fish population comes on the outskirts
of the reefs. The results highlight the influence of attractions areas in the development
of biomass, and the impact of fishing and overfishing. The activity does not directly
increases with the increase of fish quantity, it is quite stable, and clearly shows to
t=40 the increase in fishing. A targeted and intensive fishing activity quickly reduces
the fish population per cell. To improve the model, we will substitute the fishing areas
by agents following the fish population.

5 Conclusion

In this paper we described a research approach using the *activity* concept and the Dis-
crete EVent system Simulation Specification formalism to model the management
and harvesting of resources for fisheries. The *DEVS* formalism is coupled with a *Cel*-
lular Automata Model to efficiently exploit numerous spatial components. With this
approach we simulate a complex fishery production system with strong interactions
between components evolving in huge spatial areas. Spatial data are generated in a
modular and hierarchical way in reasonable computation times. We use our frame-
work to explore the maximum sustainable yield (MSY) and to fix the max sustainable
catch in a large fishing area. Using our software framework, decision makers can
explore various policies and make choices to improve the management and harvesting
of fisheries resources. Using a traditional population growth model from literature
[19], we show how our theoretical approach can be used to integrate spatial dynamics,
in spite of a huge number of components. Future works will require the integration of
the findings and insights of experimental studies. As in [21], we plan also to add an
economic model that takes into account the sales of fish and the cost of fuel. We can
thus add a propagation rule for trawlers. At the environmental level, we want to inte-
grate the dynamics of biomass (phyto/zooplankton) and currents and finally imple-
ment a propagation rule of biomass based on currents.

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