Closure under Coupling of Cellular-DEVS for the Optimization of Memory Resource: Wildfire Spread Case Study
CClosure under Coupling of Cellular-DEVS for theOptimization of Memory Resource: Wildfire SpreadCase Study
Youcef Dahmani , Maamar El Amine Hamri , and Nesrine Driouche Ibn Khaldoun University, Tiaret, Algeria (dahmani [email protected]) Aix-Marseille Univ, Universit de Toulon, CNRS LIS, Marseille, France([email protected]) Independant software researcher, Marseille, France([email protected])September 3, 2020
Abstract
The present work aims to show one of the advantages of using the property of closure undercoupling in the DEVS specification. The advantage concerned in this paper attempts to addressthe need for memory resources during the simulation of systems by cellular-DEVS.This improvement of performance is based on the usage of the property closure undercoupling in the DEVS formalism. With this property and taking account of the iterative behaviorof each cellular-DEVS atomic model, we provide simulation of many models simultaneously.The method starts with the specification of the cellular-DEVS coupled model which is thenconverted into its equivalent DEVS atomic model. Thus, the goal of this conversion is totransform large quantities of atomic models coupled together, which require huge computationalresources, into one DEVS atomic model.A case study is presented at the end of the work on modeling and simulation of forestfire propagation using DEVS and cellular-DEVS. A specification by cellular-DEVS of theforest fire model and its non-modular equivalent DEVS atomic model are presented. Finally, acomparison between both methods is presented in term of consumption of resources.
Modeling and Simulation (M&S) have accumulated a large number of successes in a wide andvaried range of domains. However, M&S consumes time, effort and resources when you need toresolve class of problems where the analytic or modeling solution is very hard to find. This classof problems includes dynamic systems where there is a wide number of parameters with time andcausal dependencies between them, a non-linear behavior of the system, etc.Discrete event M&S deals with systems whose temporal and spatial behaviors are complexto be treated analytically. The DEVS formalism (Discrete EVent system Specification) is one1 a r X i v : . [ n li n . C G ] S e p f the common formalism used in the simulation of dynamic systems [1, 2]. It is known for itsmodularity and expressiveness. This formalism offers, compared to others, a general purpose.However, the DEVS formalism has undergone several extensions to meet specific needs. Manyvariants on DEVS were adopted by introducing appropriate theories such the parallel-DEVS [3]DS-DEVS [4], Cell-DEVS [5], etc.Although these variants exist, it is very difficult to simulate complex systems, especially thoserepresented by large-scale cellular-DEVS models. The need for computational resources becomesvital in order to ensure reliable and fast simulations. Many techniques were adopted with theiradvantages and disadvantages [6].In this work, we take advantage of the property, closure under coupling of DEVS which allowsus to reduce computational resources without changing the bases of DEVS specification.A case study of the Wildfire Spread Simulation is modeled by the cellular-DEVS coupledmodel and its equivalent DEVS atomic model. Simulation results for both techniques are givenand a comparison between these two simulations is described.The remainder of this paper is outlined as follows: Section 2 resumes the basic concepts on theDEVS formalism. Section 3 is divided into two subsections, in the first one, a literature review onoptimization methods to improve the performances of simulation within the DEVS formalism isreported, and in the second subsection, an overview on forest fire spread simulations is presented.Section 4 depicts our approach by converting the cellular-DEVS into its equivalent DEVS atomicmodel using the property closure under coupling applied to wildfire spread. Section 5 illustratessimulation experiments on our case study on forest fire spread, we specify both models: cellular-DEVS coupled model versus DEVS atomic model. At the end, conclusion and perspectives aregiven. Being based on system theory, the DEVS formalism is one of the means theoretically well-grounded to express discrete event systems in a hierarchical and modular manner. A discrete eventsystem is a dynamic system whose behavior is directed by the appearance of discrete events [7].The use of discrete event-based simulation, rather than time-driven simulation has been provento reduce computation time in many applications. DEVS formalism can be used to specify systemswhose input, state and output trajectories are piecewise constant [8]. In addition, DEVS cangive highest performance for simulation of continuous systems typified by spatial and temporalheterogeneity [9, 10].Theoretically, each system is characterized by two features: functional (behavioral) andstructural aspects. At the lowest level, a basic part called DEVS atomic, describes the autonomousbehavior of a discrete event system. At the highest level, DEVS coupled describes a system asmodular and hierarchical structure [1, 2].A DEVS atomic model is based on continuous time, inputs, outputs, states and functions(output, internal and external transitions, life states). Formally, a DEVS atomic model is describedby the following seven-tuple: AM devs = ( X, S, Y, δ int , δ ext , λ, t a ) Where X , S and Y are the sets of input events, states, and output events, respectively, δ int : S → S the internal transition function, describes the state changes, that occurs when the elapsedtime reaches the lifetime of the state, δ ext : Q × S → S is the external transition function, where2 = { ( s, e ) | s ∈ S, e ∈ R + , ≤ e ≤ t a ( s ) } is the total state set and e describes the elapsed timesince the last transition of the current state s , λ : S → Y : when the elapsed time reaches thelifetime of the state, this function generates an output event, and t a : S → R + ∪ ∞ : time advancefunction, which is the lifespan of a state.The DEVS coupled model allows formalizing the modeled system in a set of inter-connectedand reused components. A DEVS coupled model is defined as an eight-tuple: CM devs = ( X self , Y self , D, { M d | d ∈ D } , EIC, EOC, IC, Select ) Where X self : set of inputs events, Y self : set of outputs events, D : is the name set ofsub-components, { M d | d ∈ D } : set of sub-components of DEVS models, EIC : set of ExternalInput Coupling,
EOC : set of External Output Coupling, IC : defines the Internal Coupling, and Select : 2 D → D : defines a priority between simultaneous events. Several DEVS formalisms have evolved compared to the classic DEVS to fit specific needs.Cellular-DEVS models have been created to model and simulate several phenomena such as firepropagation, traffic control, etc. [9].Cellular-DEVS originates from the cellular automata formalism. The latter is based on discrete-time simulation which consumes the computation power to update all cells at each time-step. Adecrease in the time-step used in the models would increase accuracy, but would also result in alonger simulation time and requires large computational resources. In fact, in many cases, there arefew cells that are concerned to be updated at each time-step, which makes this manner inefficient.In order to overcome this problem, cellular-DEVS was adopted to offer computational resourcesto the active cells that really execute state transitions and therefore avoid useless computation oninactive cells.The cellular-DEVS formalism divides the spatial space into a set of identical cells wherecomputations are done locally. A cell is considered as a DEVS atomic model which executesthe local computations based on its own state as well as its neighbor states. The spatial space isimplemented as a DEVS coupled model where the internal couplings between cells are given byneighborhood rules [6].
The property closure under coupling, in DEVS and parallel-DEVS, reports that every coupledmodel has its own equivalent atomic model. Therefore a DEVS coupled model regroups severalDEVS models, which can be regarded as another DEVS atomic model.The transition from the parallel-DEVS coupled model into its equivalent parallel-DEVS atomicmodel is described as follows [11, 6]:The state set S of the subsequent model will be the Cartesian product of the total state sets ofall the DEVS atomic models. Thus, the time advance t a ( s ) defines the time remaining to the nextevent in component d . S = × d ∈ D Q d t a ( s ) = minimum { ρ d | d ∈ D } Where s ∈ S, s = ( . . . , ( s d , e d ) , . . . ) for all d ∈ D and ρ d = t a ( s d ) − e d The overall transition function is defined as: 3 ( s, e, x b ) = δ ext ( s, e, x b ) if ≤ e < t a ( s ) and x b (cid:54) = φδ conf ( s, e, x b ) if e = t a ( s ) and x b (cid:54) = φδ int ( s ) if e = t a ( s ) and x b = φ Where δ ext : × d ∈ D Q d × X → × d ∈ D Q d δ conf : × d ∈ D Q d × X → × d ∈ D Q d δ int : × d ∈ D Q d → × d ∈ D Q d λ : × d ∈ D Q d → Y DEVS coupled model can be reduced to a behaviorally equivalent DEVS atomic one. Thus,the concept of closure under coupling ensures that the coupled model results in a model of thesame class which has a basic specification.
In many situations, simulate complex systems with DEVS requires machines with very highperformance. To overcome this crucial need, various techniques have been used and can beclassified in two categories: those that modify the DEVS formalism by adding either specificfunctions or variables to manage in a dynamic way the structure of the models, which requiredemonstrating again some of the properties of DEVS (closure under coupling, hierarchy, etc.), andthose that preserve the DEVS formalism but which integrate information concerning the behavioralmodel structure, which decrease the modularity, flexibility and its reuse.For both categories, different techniques have been developed in the DEVS community suchas quantization [12], which helps in enhancing performance simulation by decreasing the numberof state transitions and messages. However, [6] have noted that quantization is an approximationmethod that satisfies the tolerance requirement, i.e, the simulation should stay within acceptableerror.The parallel and distributed DEVS simulations need more hardware as well as extra workfor parallelization of prevailing sequential models [13, 14, 7]. However, [15] have noted that,the overhead of check pointing and rollback operations may result in unstable and degradedperformance.DEVS components within variable structure [16], permit models and couplings to be dynam-ically added and/or removed during simulations run. This main advantage is loosen when animportant number of update (add and/or remove) of models and couplings are done during asimulation cycle [17].However, there are few works based on converting DEVS coupled into DEVS atomic toincrease performance [6]. Among these works, [7] presented a formal approach of this propertywith addition of scheduling mechanism, they introduced a composition-based method that convertsa DEVS coupled model into its equivalent DEVS atomic model at compile time in order to speedup the simulation by accounting events and messages at compile time. The main advantage isthat the resultant atomic model should keep track of all the functions of these internal models.However, this technique results in overhead as the number of the internal models grows up, and theconversion process will be more complex to be done properly. [18] followed the same approach byconverting a coupled model into atomic one in order to eliminate the message overhead based on4odelica parallel variable update. Unfortunately, this approach shows slow simulations becauseof the large number of variables used. Thereby, these two techniques proceed at compile time toallow the conversion.In [6], the idea is to convert a set of cellular-DEVS atomic model into its single DEVS atomicmodel while keeping the same accuracy and remaining an error-free approach. Thus, instead ofconsidering each cell as an atomic model, with the closure under coupling and at the specificationand development stage, the method will transform a group of cells into a non-hierarchal andnon-modular model which leads to increase the performance simulations run.Although the resulting model is not hierarchical, but this does not present any problem to theuser since they are identical sub-models. Therefore, the user will bypass the hierarchy due to theiterative and repetitive behavior and structure of cells.The present work is closely related to [6]. Our work focuses mainly on the usage of the memoryresource. We apply the property closure under coupling in the modeling of forest fire to obtainreliable simulations by decreasing the use of memory resource; and as a collateral profit, we speedup the simulation run and we increase considerably the number of concurrent simulated cells.
Wildfires continue to cause considerable losses of human lives, wildlife and houses every year andare costly to contain. In United States of America alone, about one billion dollars is spent annuallyon wildfire suppression and containment [19, 20].Fire spread is a propagation process and needs to build simulation models that relate thesystem evolution as accurately as possible to plan scenarios in order to save lives and money.However, simulating wildfire spread remains a challenging problem due to the complexity ofwildfire behavior.Such far, no model has tried to combine the different features of fire behavior (vegetation,weather, topography, etc.) that are already established separately because of the important factorsthat influence wildfire behavior and the interaction between them [21, 19], that why there are manymodels in the literature.The most common approaches to simulate fire spread are based either on vector or waveapproach, or on the cellular models [21]. For the former, the model produces vector fire perimetersat determined time intervals. For the latter, the cellular models simulate fire spread as a discreteprocess of ignitions across a regular division of the space in cells. Successive computations arecarried out on each cell to ignite its neighbors.The majority of fire models in use today are principally based on fire propagation relationsdeveloped by [22], [23] and [24]. The popular Rothermel model was in particular chosen becauseof its robustness and stability which have been extensively tested and proven [25, 19].Both categories of models (vector, cellular) are simulated either in discrete or continuous time[26]. The following non-exhaustive list of examples uses the Rothermel model. HFIRE [27]includes discrete time model, FARSITE [21] where the fire growth is based on Huygens principleof wave propagation, and BEHAVE [28] uses continuous simulation for the vector models.The forest fire simulation models include cellular space, cellular automata [25], cellular-DEVSmodels [29], DEVS-Fire [30], and cell-DEVS which uses heat transfer partial differential equationsto calculate fire spread in each cell [[31, 32]].Cellular-DEVS and Cell-DEVS simulation results were compared and the analysis concludedthe validation of both models [32]. However, the present cellular implementation knows asimulation issue whenever all cells in the cell space are created simultaneously which causes5imulation performance degradation. This degradation is attributed to the initialization of the cellsand the functions needed, and the memory that is required to run the simulation [19].A dynamic structure was proposed to overcome this issue [19, 20]. This approach keepstrack of active cells along the fire front as the simulation proceeds. The cells are created/deleteddynamically; however this implementation has computational overhead at runtime when weproceed with a large-scale cell space.Other implementations were proposed to overcome these concerns. Indeed, besides using highperformance computers, researchers still develop other techniques including innovative algorithmsthat allow handling only active cells or research on how the non-modularity/non-hierarchy inmodeling can improve simulations run [6, 33].
The M&S of forest fire spread is confronted to size of the map in a geographic information system(GIS). So, obtaining reliable and accurate simulations needs huge computation performance. Theaim of this section is to show the benefit of applying the closure under coupling property of DEVSto enhance the use of memory space and increase the size of the map on GIS during simulationruns.
The forest is represented as a 2D cell space of square cells whose dimensions depend on theresolution of the GIS. Each cell has eight neighbors and carried out its local computation of therate of fire spread and direction based on its local conditions (parameters). The literature classifiesthe parameters which set the fire spread ratio into three groups: vegetation type (caloric content,density, etc.), fuel properties (vegetation size) and environmental parameters (wind speed, humidityand slope). The flaming fire evolves principally according to the wind speed and its direction [34].We assume, in this work, that fuel, topography and weather conditions are uniform for each cell.This work is closely related to [19, 20]. The rate of fire spread of each cell relies on Rothermelmodel [22] which is decomposed thereafter into eight spreading directions according to the cellneighborhood and schedules ignition of its neighboring cells accordingly.The ignition process consists on spreading fire from a burning cell to its neighbors using Mooreneighborhood. A cell space is considered as a DEVS atomic model, therefore, the forest cell spaceis a coupled model composed of a set of cell atomic models.We consider that each cell can be in one of the following possible states: • Nonflammable (N): It can be a road, a surface of water or just an empty surface. • Unburned (U): Passive state; it represents any fuel which is not consumed yet by fire. • Burning (B): represents a consuming fire. • Ash (A): It is afterburning state, it is the final combustion process state.
The overall system proposed in this work is composed of (Figure 1):6 othermel ModelIgniter ModelVegetation Type Fuel Properties Environmental Parameters S l op e W i nd H u m i d i t y d e n s i t y V e g e t . s i z e Forest Cell Space G I S C a l o r i c c on t e n t Figure 1: Functional architecture of fire spread simulation. • Forest cell space, in which each forest cell is an atomic model. • Geographic information system interface which provides the different data that influencethe spread rate. It consists of: – Environmental parameters interface: provides weather and topography data such aswind speed, its direction, relative humidity, slope, aspect, etc., – Fuel properties: provide size of vegetation, fuel model, etc., and – Vegetation type: provides density of vegetation, its calorific content, etc. • Forest cell igniter: ignites an initial set of cells to start the simulation, and • Rothermel model: computes fire spread and its direction.In its basic form, Forest cell space is modeled as a grid composed of n rows and m columns,which depends on the data resolution. The dynamic system of the flaming front propagation speedis given by the simulator. It is based on the current cell position and its own variables, each ofwhich is given by an appropriate model. The forest cell igniter is a DEVS atomic model; it iscoupled to all forest cells to ignite cells. The Environmental interface and Fuel and Vegetationinterface provide two kinds of values: spatial-temporal and environmental data. These data are fedinto the forest cells which in turn send these data to Rothermel model to compute the rate of firespread and its main direction. In this section, we are going to describe the overall system design. As seen above, the fire spreadmodel is composed of forest cell space coupled to the igniter model, Rothermel model, and GIS7nterface (environmental, vegetation and fuel models).
For each cell O = ( a, b ) , its Moore neighborhood is given by the set: V = { O, N, N E, E, SE, S, SW, W, N W } Each neighbor is reported as one of eight compass points ( N, N E, E, SE, S, SW, W, N W ) .In Figure 2, the fire is propagated from the center of the cell to the center of the neighbor cells. NW N NEW O EW O a,b E d j SW S SES
Figure 2: Cell center-to-center fire spread.Each forest cell DEVS atomic model has four states: Nonflammable (N), Unburned (U),Burning (B) and Ash (A). All cells are assumed to be initially in unburned state, except thosedefined by the user in the passive state Nonflammable.Once a cell is ignited it computes the ignition delays for its eight neighbors, and sends outthe ignition message for each of them. Therefore, each cell is ignited either by its neighbor orby the igniter model. The ignited cell, in its turn, ignites its neighbors. Thus, an additional inputport is coupled with each forest cell DEVS atomic model. The ignition delays are calculatedby the Rothermel model. Each cell sends out its state variables (fuel model, size of vegetation,wind speed, wind direction, etc.) obtained from the GIS interface toward the Rothermel model.The latter sends out as a result the rate of fire spread and its main direction to the concerned cell.Therefore the forest cell interacts with the weather and fuel interface, and the Rothermel model viathese additional input/output ports.Consequently, each forest cell has 11 input ports and 9 output ports by which it reacts and actson its environment (Figure 3).The dynamics of fire spread is described as follows: once a cell is ignited, it sends out ignitionmessages one by one in each of the eight directions. The decomposition of fire spread in eachdirection is based on the model that defines the fire shape as an ellipse [20, 21]. The contagionprocess of fire spread across a cell considered in our case study is center-to-center as in [26].Consequently, the burning cell remains in this state at least until all the eight messages will be sentout.Let us consider: • T td = { t , t , t , t , t , t , t , t } , the set of these eight different time delays sorted respec-tively from the smallest to the largest. 8igure 3: Forest cell DEVS atomic model. • ∆ T td = { ρ , ρ , ρ , ρ , ρ , ρ , ρ , ρ } ,the set of the time interval between two adjacent ignition messages. ρ = t and ρ i = ( t i − t i − ) | i = 2 .. .The first message is sent at t + t and the last one at t + t , at this moment, the forestcell transitions from the burning state to the ash one (burned) after sending out its last ignitionmessage. The set T td can be affected by the parameters change (wind flow, speed, direction) andconsequently the set ∆ T td . In this case, the forest cell space model notifies the Rothermel modelwhich updates the rate of fire spread and subsequently the spread in each direction. The rate of firespread in each direction is depicted on Figure 4. OutNW OutN OutNEOutW O a,b
OutEOutSW OutS OutSE t1 t3 t2t5 t4t7 t8 t6 D i r ec t i on o f m ax f i r e s p r ea d Figure 4: Rate of spread calculation in eight directions.9he formal specification of the forest cell DEVS atomic model (Figure 5) is:
F orestCellAM = (
X, S, Y, δ ext , δ int , δ conf , λ, t a ) where: InP orts = { InN, InN E, InE, InSE, InS, InSW, InW, InN W, InIgn,InP ar, InRot } XInP orts = R × R d × R Where dimension 9 represents the nine ignition messages (8 from neighbors and one from ignitermodel), d is the number of parameters of each forest cell (weather, wind, humidity, etc.), and thenumber 2 is the couple, rate of fire spread and its main direction. OutP orts = { OutN, OutN E, OutE, OutSE, OutS, OutSW, OutW, OutN W,OutP ar } Y OutP orts = R × R d We have 8 output ignition messages coupled respectively to the 8 neighbor cells; and d is adimension, that represents the cell parameters, its output is coupled with Rothermel model. X = { ( in, x ) | in ∈ InP orts, x ∈ XInP orts } S = { ( N onf lammable, ∞ ) , ( U nburned, ∞ ) , ( Burning, ρ ) , ( Ash, ∞ ) }| ρ ∈ R + Y = { ( out, y ) | out ∈ OutP orts, y ∈ Y OutP orts } δ int ( Burning, ρ ) = (
Burning, ρ i ) if (∆ T td (cid:54) = ∅ ) ∆ T td = ∆ T td − ρρ i = min (∆ T td ) δ int ( Burning, ρ ) = (
Ash, ∞ ) if | ∆ T td | = 1( i.e. ∆ T td has a cardinality of 1 ) δ ext ( U nburned, ρ, ( In ? x )) = ( Burning, ρ ) δ ext ( Burning, ρ, ( InP ar ? x )) = ( Burning, ρ i ) δ conf ( s, ρ, x ) = δ ext ( δ int ( s ) , , x ) λ ( Burning ) =
Out ! ignitiont a ( phase, ρ ) = ρ The initial state of this model is ( U nburned, ∞ ) .Where In ∈ InP orts − {
InP ar, InRot } , ρ (cid:48) i is computed by the Rothermel model wheneverparameters change, Out ∈ OutP orts − {
OutP ar } , ignition ∈ R . In?x Out!ignition
Forest cell atomic model
InNInNE OutNOutNE
Out!ignition
Unburned ∞ Burning ρ i InNEInEInSEInSInSWInWI NW OutEOutSEOutSOutSWOutW
Out!ignition
Ash ∞ InNWInIgnInParInRot OutWOutNWOutPar
Figure 5: Forest cell DEVS behavior.10n Figure 5, the solid line describes the occurrence of external event, while the dashed linedepicts the internal state changes, and occurs when the elapsed time reaches the lifetime of thestate.
The Rothermel mathematical model [22] computes a one-dimensi- onal maximum fire spread rateand its direction. Fire geometry has been determined empirically [21]. However, in the literature,the fire shape is considered as an ellipse which is widely used [24]. Therefore the fire spread isinferred in all directions from the 1-D maximum rate using the mathematical properties of theellipse and the equations defined in [21, 25]. The spread rate in an arbitrary direction θ (Figure 6)is obtained by: R ( θ ) = R max − (cid:15) − (cid:15) cos θ (1) (cid:15) = √ lw − lw (2) lw = 0 . e . v + 0 . e − . v − . (3)Where R max is maximum rate of spread, lw is the ellipse ratio of the semi-major over semi-minor (Length to breath ratio) and v is the midflame wind speed (effective wind speed).Once the rate of spread is known in all directions, we compute the time delays to reach thecenter of the neighbors by this equation: t i = d i R i | i = 1 .. (4)Where t i is the time to reach the neighbor i, d i is the distance from the center of the burning cellto the center of its neighbor i and R i is the fire spread rate in this direction. In case of parameterschange (wind speed, direction, humidity, etc.), the new R newi in direction of the neighbor i , isinferred from Rothermel model if the fire hasn’t yet reached it. The new remaining time delay is: t newi = ∆ d i R newi (5) x Direction of maximum spread y R( θ ) θ R max Figure 6: Rate of spread according to an arbitrary direction.11here ∆ d i is the remaining distance to reach the neighbor i and t newi is the new time delay.As the fire propagates, the equation 5 allows the model to be dynamic and sensitive to weatherchanges. In the forest cellular approach, the forest fire spread is usually presented as a set of arranged cellswhose dimensions depend on the resolution of GIS [20]. Thus, forest cell space coupled model isa discrete dynamical system formed by coupling a finite number of forest cells. These cells arearranged uniformly in a two-dimensional space composed of n rows and m columns. Each forestcell atomic model is coupled to 8 neighbors as described in Figure 7. ForestCellSpace
Cell(1,1) Cell(n,3)Cell(n,2) Cell(2,3)Cell(1,3)Cell(2,2)Cell(1,2)Cell(2,1)Cell(n,1) Cell(1,m)Cell(2,m)Cell(n,m)
EIC IC
Forest Cell atomic modelIgnition
Figure 7: Forest cell space DEVS coupled model.The fire spread model is described in Section 4.2. It is composed of forest cell space (a grid offorest cells), igniter model, GIS interface and Rothermel model. However, simulate such a modelwill be affected by large-scale forest cell model and particularly during the simulation run andinvolves more memory usage. A huge memory is needed to simulate the overall forest and if youlack memory, you simulate just a part of it. In [19], memory required for some implementations isillustrated. 12o overcome to this issue, we propose to use the closure under coupling. This property of theDEVS formalism consists to transform a coupled model into its equivalent atomic model. Thus,the forest cell space coupled model will be converted into an atomic model.Each cell becomes a state variable of this atomic model and accedes to its neighbor state directlyby removing the ports from the atomic models that is resulted by small volume of inter-componentmessages during simulation run. In fact, the communication between cells is done directly insidethe model, except outdoor events [6].Based on the Forest Cell DEVS atomic model described in Section 4.3.1, the forest cell spaceDEVS coupled model is transformed into forest cell space DEVS atomic model and would benefitfrom the property of closure under coupling. It is described as follows:
F orestCellSpaceAM = (
X, S, Y, δ int , δ ext , δ conf , λ, t a ) • X = { ( ignite, list ) , ( inP aram, parameters ) } — list is a list of initial ignited cells • Y = ∅ , there is no output event to send out. • S = Cell × inP aram = { . . . , ( phase i,j , ρ i,j ) , . . . } × R d | i = 1 ..n j = 1 ..m Where
Cell is the set of forest cell. Each cell is identified by its position ( row , column ) whichcan be in one of the four states (Nonflammable, Unburned, Burning, Ash) and d is the number ofparameters provided by GIS interface.Each cell keeps its current state and according to external and internal events state changes willoccur to update the state of the concerning cell. It is pointed out that each cell has eight neighborsexcept those situated on the bound of the forest. Environmental parameters are assumed to beuniform at each cell except the wind which can change its speed and direction over time. Thus, thefire spread direction can change dynamically. Thus, we get a non-modular modeling structure (seeFigure 8). With a modular modeling, when a cell ignites its neighbors, it invokes internal statechange to provoke the execution of the output function λ () , which sends out the event ignitionto all neighbors. On the other hand, the non-modular modeling propagates the output eventignition directly to neighboring cells without calling the simulator for dispatching events. Sucha communication optimizes the DEVS M&S structure and decreases the number of exchangedmessages between cells.Consequently, the fire spread model in its non-modular structure is comprised of four atomicmodels: Igniter atomic model, Forest cell space atomic model, GIS interface and Rothermel modelas shown on Figure 9. It is identical to the structure depicted in Figure 1 except the Forest CellSpace which is converted to an atomic model.Note that this architecture remains an open and modular one which allows enhancing thefunctionalities of the GIS and updating the Rothermel package. In this section some output results that measure the simulation performance of the two models areprovided. The package Behave was used to compute the rate of fire spread given by the Rothermelmodel. The experiments were carried out on laptop Dell [email protected] with Intel CPU, 1.66GHz processor, 2.50 GB of RAM and Windows XP c (cid:13) operating system and as a simulator, wehave used our own simulator developed in Java and respecting DEVS specifications.13 ext ( s , e , x ) c, c´ : Cellif (x = ignite) { for each c ∈ ignite list s c = δ ext (s c , e, ignite) } if (x = inParam)update parametersrecompute the lifetime for each active cell cδ int ( s ) for each c ∈ Cell { if (lifetime(c) = lifetime(Cell)) { if (burning( s c ))for each c´ ∈ neighbor(c)s c (cid:48) = δ ext (s c (cid:48) , lifetime(Cell), ignite) s c = δ int ( s c ) } elselifetime(c) = lifetime(c) - lifetime(Cell) } δ conf ( s , e , x ) δ ext ( δ int ( s ) , , x ) lifetime ( s ) return min { lifetime(c) | c ∈ Cell } Figure 8: DEVS atomic model functions of forest fire spread
Rothermel ModelIgniter Model GIS interface (Fuel, vegetation and environment )Forest Cell SpaceAtomic model
Figure 9: The forest fire spread model via closure under coupling.
As mentioned by [19], an assessment of memory usage based on the implementation in [35] showsthat each cell needs about 35 kB memory space. This fact is time consuming and resource intensiveand therefore not very effective for large-scale cells simulation.We were tempted to see the limits of our simulator for these two specifications of forest firespread. The ForestCellSpace DEVS coupled model versus ForestCellSpace DEVS atomic model.Table 1 summarizes some important results. The model ForestCellSpace coupled model uses a14able 1: Comparison results.
Results ForestCellSpaceCoupled Model ForestCellSpaceAtomic Model
Maximum number of simulated cells[cells] 70 ×
70 2682 × ×
60 cells 8.74 1.23Used Memory [MB] for 600 ×
600 cells Out of Memory Er-ror 12Simulation Execution Time [second(sec)] for 60 ×
60 cells 109,131 13,390
Table 2: Sample of simulation performances of ForestCellSpace: Coupled vs. Atomic
Indicator ForestCellSpaceCoupled Model ForestCellSpaceAtomic Model
Simulation Execution Time[sec.] 109,131 13,390Used Heap Memory [MB] [2, 20] [2, 8]Thread Count [9, 3500] [9, 14]CPU Usage [%] 100 100 conventional architecture, where a grid of cells is used. While ForestCellSpace atomic model usesthe closure under coupling to get a unique atomic model of the forest cell space.The experiment revealed that only about 70 ×
70 cells of the overall forest space has beensimulated in coupled model, whereas the other specification, i.e., forest cell atomic model, a limitof 2682 × × cells.As mentioned before, despite the different implementations of forest fire spread, it is essentialto reminder that both models have the same behavior, whereas their simulation performances aredifferent (see Figure 11 for a cell space of 60 × a) ForestCellSpace coupled model: grid of cells.(b) ForestCellSpace atomic model: closure under coupling. Figure 10: Performances of forest fire spread simulation.16 a) DEVS coupled: time =900 sec. (b) DEVS atomic: time = 900sec. (c) DEVS coupled: time =1600 sec. (d) DEVS atomic: time=1600 sec.
Figure 11: ForestCellSpace coupled model vs. ForestCellSpace atomic model.
The validation of fire spread model is not an easy task, and few works describe validations basedon real fire [25]. Nevertheless, we are going to do a partial validation by comparing the results ofour approach by those of FARSITE. The latter is the most generally distributed and accepted firebehavior predictive model used in forestry [19].On one hand, we are going to simulate our model described in Section 4.2 by adopting thisfunctional architecture, on the other hand, we are going to simulate by FARSITE software thesame scenario and compare the different results. Therefore, the equivalence of the two forms isverified using simulation methods.In these simulations, we suppose that: • Virtual forest is constructed as a grid of 260 ×
260 cells where each cell represents an area of1 × m (m: meter). • Fire spreading is on each of the eight compass points. • Starting ignited point is the cell(130,30).We assume that uniform parameters characterize the cell space, i.e., each cell has uniform fuel,terrain, weather and fire behavior along the forest fire area.The fire shape is assumed elliptical and the decomposition scheme considered is center-to-center. We use the Rothermel model to compute the maximum fire spread rate. Fire spread in allother directions is inferred from the spread rate using the mathematical properties of the ellipse(equation 1).We consider the following values to get the rate of spread by the Rothermel model:The model of fuel considered in this experiment is Northern Fire Forest Laboratory (NFFL)Fuel Model 1: short grass (1 feet (ft)) with its standard characteristics.Besides that, we assume: − wind speed [meter/second (m/s)] wsp = 1 . − wind direction [degree( ◦ )] wdr = 0 . − slope [ ◦ ] slp = 16 . − aspect [ ◦ ] asp = 0 . The Rothermel model produces the following results: − rate of spread [m/s] ros = 0 . − direction of maximum spread [ ◦ ] sdr = 180 − effective wind speed [m/s] efw = 1 . θ R ( θ ) % ros ∓
45 0.14 53.77 ∓
90 0.066 25.41 ∓
135 0.04 16.63180 0.038 14.55 (a) time = 300 sec.: 0.29 ha (b) time = 900 sec.: 1.17 ha (c) time = 1200 sec.: 4.28 ha (d) time = 3184 sec.: 6.76 ha
Figure 12: Fire spread progression (260 ×
260 cells)Length to breath ratio lw is obtained via equation 3, its value for theses parameters is: − lw = 1 . The spreading rate in each direction is given by equation 1 based on the ratio lw . Thus, weobtain the following spreading rates according to each direction as shown on Table 3.According to these results, we simulate our forest fire model. Figure 12 shows the fire spreadtaken at different simulation times and gives us the effective burned area [hectare (ha)].On the other hand, we have done the simulation on FARSITE with the same parameters andwe obtained output results shown on Figure 13. (a) Fire perimeter. (b) Burned area curve. Figure 13: Fire spread progression on FARSITEA comparison was done on the progression of fire area over time (see Figure 14). The resultshows the likeness between both methods. Of course, the goal is not to mimic FARSITE softwarebehavior, it is possible to fine-tune or parameterize our model so that it mimics FARSITE and18 h a ) F i r e A r ea ( h FARSITEDEVS01 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Time (minutes)( )
Figure 14: Fire area: FARSITE vs. DEVS.obtain the same graph. However, the real purpose is to show the vitality of our approach. As youcan see, the same scenario can’t be simulated with the forest cell space coupled model and we willget a message as
Out of memory error . A solution suggested is, either we divide this forestspace into small areas or decrease the cell resolution (increase cell dimension) which may result inincorrect results and degrade accuracy.As cited previously, this is a partial and preliminary validation. More validation is definitelyrequired because of the many potential sources of error which can confuse the comparisons.These tests have underlined the necessity to consider errors associated with: • The spatial and temporal resolution of the inputs, • The model input data (fuels and environmental parameters) and • The nature of fire growth projections used for comparison in both methods (Huygensprinciple of wave propagation in FARSITE versus Rothermel spread equation in Behavepackage).Logically, a wildfire spread simulation should be most accurate when using accurate data athigh spatial and temporal resolutions.The acceptability of this statement is dependent on the spatial resolution required by the userand the resolution specified for the simulation. Thus, the sensitivity of fire simulation to theresolution, fire spread patterns generated (Huygens principle) and model of different fire inputparameters remain to be verified.However, it should be noted that even FARSITE needs to be validated [21], the most importantresult of FARSITE tests to date has been proven that spread rates for all fuel models tended to beover predicted by the Rothermel spread equation. Different adjustments have been added in orderto correct the observed error with real forest fire, but there is no way to guide settings for theseadjustments. Consequently, future work needs to focus more on validating our approach usingobserved fire growth patterns in several conditions of weather and vegetation.
This work attempts to foster the integration between two concepts: closure under coupling incellular-DEVS and the forest fire spread to gain memory resource during simulation run.19he study of the simulation of forest fire has increased considerably, it requires buildingsimulation models that allows for system evolution in both time and space.The most common approaches to simulate fire spread are based either on vector approach,or on the cellular models. Cellular models simulate fire spread as a discrete process of ignitionsacross a regular division of the space in cells. However, dealing with high cell resolutions naturallydefies efficient computer simulation.In this work, we tried to gain some performance in simulation run. This was achieved byconverting the cell space into atomic model in order to eliminate inter-cell messages. This approachwas initially deduced from the property closure under coupling of the DEVS formalism. Somerelevant results are presented and a comparison between our approach and the simulation byFARISTE software is given.However, this implementation needs an additional work in verification and validation (whichwe crossed an important step) to confirm more again the vitality of this approach. The functionalarchitecture needs to take into account more parameters since the fire spread process might becomecomplicated. A model for these parameters must be coupled to our architecture in order to get morerealistic results. Also we need to validate our approach by using observed fire growth patterns inseveral conditions of weather and vegetation. An issue that we hope explore in the near future.
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