Research ArticleCommunication Analysis of Network-Centric Warfare viaTransformation of System of Systems Model into IntegratedSystem Model Using Neural Network

Bong Gu Kang ,1 Kyung-Min Seo ,2 and Tag Gon Kim 1

1Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea2Naval & Energy System R&D Institute, Daewoo Shipbuilding & Marine Engineering (DSME) Co., Ltd., Seoul, Republic of Korea

Correspondence should be addressed to Kyung-Min Seo; kmseo.kumsung@gmail.com

Received 11 December 2017; Accepted 11 March 2018; Published 24 June 2018

Academic Editor: Arturo Buscarino

Copyright © 2018 Bong Gu Kang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Communication system in the network-centric warfare (NCW) has been analyzed from the perspective of the system of systems(SoS), which consists of a combat systemand anetwork system so that the two reflect each other’s effects.However, this paradoxicallycauses a prolonged execution time. To solve this problem, this paper proposes an advanced integrated modeling method for thecommunication analysis in theNCWvia the transformation of the SoS, which reduces the simulation execution timewhile ensuringthe accuracy of the communication effects.The proposedmodels mainly cover interentity traffic and intraentitymobility developedin the formof feed-forward neural networks to guarantee two-way interactions between the combat system and the network system.Because they are characterized as discrete events, the proposed models are designed with the discrete-event system specification(DEVS) formalism. The experimental results show that the proposed transformation reduced an error by 6.40% compared to theexisting method and reduced the execution time 3.78-fold compared to the SoS-based NCW simulation.

1. Introduction

Network-centric warfare (NCW) is an emerging theory ofwar based on the concepts of nonlinearity and complexity[1, 2]. According to the doctrine of NCW, all combat entities,such as war-fighters, manned and unmanned platforms, andcommand and control (C2) centers, are linked via a networkarchitecture for sharing the combat situation [3, 4]. For exam-ple, network nodes are dynamically located as the entities aremoved; traffic between the nodes is also changed wheneverthey interact in joint operations. Thus, NCW should beanalyzed based on the communication interactions, whichmainly cover interentity traffic and intraentity mobility [5, 6].

For communication analysis in NCW, modeling andsimulation (M&S) techniques have been widely used; and awell-known approach is to simulate communication factorsseparately within the whole NCW simulation [7, 8]. Inother words, an M&S engineer separates a network systemfor explicit communication information from a combatsystem that generates the overall combat scenario. Then, the

engineer interacts with the two systems under standardizedarchitectures such as high-level architecture (HLA) or testand training enabling architecture [9, 10]. This is a typicalapproach for system of systems (SoS) development, whichsupports the high reality of component systems and flexibilityin changing them [11, 12].

Despite these advantages, the SoS-based simulationcauses a prolonged simulation execution time. Simulationanalysis generally requires performing simulation evalua-tions of all possible input combinations as a “what if”analysis; thus, it consumes a lot of execution time due tothe many repeated experiments [13]. In the SoS approach,the simulation overhead due to the use of the interoperationarchitecture is a primary reason for the time-consumingproblem [14, 15].

To overcome this weakness, this paper focuses on atransformation approach that shifts from an SoS-basedNCWsimulation to an integrated form without using the interop-eration infrastructure. For simulation analysis of the networksystem, we distinguish two main factors: interentity traffic

HindawiComplexityVolume 2018, Article ID 6201356, 16 pageshttps://doi.org/10.1155/2018/6201356

2 Complexity

and intraentity mobility. Based on the factors, we propose(1) a new combat model that includes them and we describe(2) how the model is connected to the network model in themanner of an integrated simulation.

Traffic and mobility, in the integrated simulation, shouldbe two-way interactive with the combat model and thenetwork model. For example, the combat model requeststhe traffic situation, such as packet delivery ratio and delay,between the source and the destination nodes to the networkmodel. Then, the network model eventually responds to therequest based on the network conditions. Thus, the combatmodel proposed in this paper facilitates the representationof interactive changeability according to the current state ofthe network; and the network model enables an analysis ofthe communication effect more realistically. This interactivedesign for the two models represents a clear difference fromprevious studies on the development of traffic and mobilitymodels.

To this end, this paper proposes a transformation processconsisting of the following three major phases: (1) trafficandmobility data acquisition from SoS-based simulation, (2)data preprocessing for training, and (3) traffic and mobilitymodels hypothesis and variable estimation of them usinga neural network. In the third phase, we design regres-sion models in the form of feed-forward neural networks.Specifically, inputs of the models are the communicationeffects, for example, packet delivery ratio (PDR) and end-to-end delay, and outputs are the variables, for example,interdeparture time of traffic generation and the movementspeed of the network node. Because the inputs and theoutputs are characterized as discrete events, the traffic andthe mobility models are designed with discrete-event systemspecification (DEVS) formalism [16].

For training of the communication effects, in the firsttwo phases, we preferentially performed SoS-based simu-lation. The SoS simulation consists of two systems and aninteroperable middleware between them: a combat systemcontaining military operations of various combat entities,which is implemented through DEVSim++ [17], a networksystem that includes the depiction of amobile ad hoc network(MANET)with network simulator 3 (NS3) [18, 19], and a run-time infrastructure (RTI) for interoperating them [20]. In thispaper, we assume that the simulation results for SoS-basedNCW are already validated.

As an experiment, wemeasured the accuracy and simula-tion speed of the procedure of transformation by comparingthe previous traffic and mobility model in the existingstudy. The experimental result shows that the proposed workreduced the error by about 6.40% compared to the previouswork and within an acceptable added time for trainingthe proposed model. Finally, we expect that our study willprovide an alternative way for the user, when operating anSoS requiring long execution times, to conduct a simulationanalysis of various scenarios including network parameterssuch as a sensitivity analysis.

This study is organized as follows. Section 2 describesthe background. Section 3 analyzes previous work and itslimitations. Section 4 defines our problem and explainsthe proposed method and model. Section 5 discusses the

experimental results by comparing previous studies. Finally,Section 6 presents our conclusions.

2. Background

This section provides background knowledge regarding sys-tematic views and the main factors affecting communicationanalysis in NCW.

2.1. Two Systematic Views for Communication Analysis inNCW. The power of NCW is derived from the effectivelinking or networking of knowledgeable entities that aregeographically or hierarchically dispersed [21]. The combatentities in NCW can independently move in any direction;also, they are interconnected with wireless communication.Thus, we assume that the network for NCW is realizedwith MANET, which is effective in enabling highly mobile,highly responsive, and quickly deployable entities [22]. In thiscontext, one of the purposes of NCW simulation is to analyzethe performance of the network, for example, packet deliveryration or end-to-end delay, in consideration of the network’sdynamic configuration [23].

Figure 1 shows two systematic views on communicationanalysis in MANET. The first approach is based on theSoS-based simulation. In the SoS view, a combat systemgenerates the tactical behaviors of all entities and a networksystem computes the configuration of nodes inMANET. Twomain data sets, that is, traffic and mobility, are interactedwith each other via a predefined interface. The next viewis to develop an integrated network system comprisinga network model and an abstracted combat model. Thecombatmodel abstractsmobility and trafficdata and interactswith the network model at the model level not the systemlevel.

The interoperation method assumes that each subsystemperforms its tasks autonomously to take detailed actionsfor the SoS [11]. Thus, the biggest benefit of the SoS-basedNCW is enhancing the accuracy of mobility and traffic data.Nevertheless, it inevitably remains a practical problem dueto the prolonged simulation execution time. On the otherhand, the integration method implies that each submodelinteracts with others, sharing common information to forma unified system. Since they are operated within a standaloneenvironment, the simulation is executedmore quickly than inthe interoperation method. However, the abstracted modelshave lower fidelity compared with the independent systemsin the SoS.

Therefore, this paper proposes an advanced integrationmethod for communication analysis in NCW, which reducesthe simulation execution time and ensures the accuracy of themobility and traffic models.

2.2. Two Factors for Communication Analysis in NCW:Mobil-ity and Traffic. Figure 2 illustrates how two factors, that is,traffic and mobility, influence the linking of combat entitiesin NCW. We assume that there is a one-to-one correspon-dence between a combat entity and a network node. For astraightforward understanding, we explain this by separating

Complexity 3

Output:Communicationeffect

What if ? Input: Communication

parameter

Communication effect analysisin MANET (mobile ad hoc network)

Integrated system view

Traffic model

OutputInput

Mobility model

Networkmodel

Interface

Combat system

System of systems view

OutputInput Node

Network system

Trafficdata

Mobilitydata

Entity

Abstractedcombat model

Integrated network system

LCC HQs

BRIGADE CP

DIVISION CPBATTALION CP

COMPANY

PLATOON

Figure 1: Communication analysis from two systematic perspectives: system of systems (SoS) and integrated system views.

the combat entities from their nodes, which is relevant to anSoS approach.

In Figure 2, a C2 center, for example, headquarters, triesto send an infantry troop a command message to moveto a specific location. Under normal situations, EntityC2 inthe combat system sends a request message, including thecommand to the network system. Then, the network systemfinds a proper routing path fromNodeC2 to NodeA and sendsa response message to EntityA in the combat system. Afterreceiving the message, EntityA moves to the desired location.On the contrary, when the network is in a bad condition, thetransmission from NodeC2 to NodeA fails, and the networksystem cannot send a response to the combat system. In thiscase, EntityC2 has difficulty controlling EntityA, and EntityAmay generate different maneuvering behavior. If EntityAmoves, whether it behaves correctly or not, it sends a finalposition to the network system to update its node. In otherwords, this ad hoc configuration of the network may changewith time as the nodes move or adjust their transmission andreception messages.

In this way, the combat system exchanges two types ofdata, that is, traffic and mobility, with the network via aninteroperation infrastructure. The traffic data regarding thecommandmessage in Figure 2 is composed of the traffic flowin the connection of the pair of the source and the destination

entities and the requested time for the connection. Themobility data has the position of the entity at the specific time.

With these data, when we transform the SoS-basedNCW simulation into the integrated simulation, includingthe combat and the network models, the following tworequirements should be considered. First, traffic andmobilityoccur eventually in the combat model; thus, the two modelsare specified with discrete-event simulations. Next, becausethese data influence both models, it is necessary to constructthem with inputs as well as outputs.

Although many research studies have been conductedon the construction of the traffic and mobility model inthe network system [24, 25], these regard the models as agenerator model with only output. In the following section,we will discuss some related work and its limitations indetail.

3. Related Works and Limitations

Over the last decade, several studies have been conductedto construct a traffic and mobility model for evaluation ofthe network system in the NCW. Each of these studies hasdescribed this model in the form of a generator that can beclassified in terms of whether data is used in the process of themodel’s construction or not. The generator model not based

4 Complexity

Combat system

Communicationresponse

Network system

Communicationrequest

Communicationrequest

Communication considering dynamic mobility of each entityCommunication considering network traffic between entities in the combat system

Desiredlocation

Maneuveringby command ％ＨＮＣＮＳ！

％ＨＮＣＮＳC2

．Ｉ＞？！(t + 1)

．Ｉ＞？！(t + 1)

．Ｉ＞？！(t)

．Ｉ＞？＃2(t)

Command

Maneuvering

without command

Figure 2: Traffic and mobility data exchanged between the combat system and the network system.

on the data has an advantage in that it can be used regardlessof the presence or absence of data, whereas it is difficult toreflect the real world completely. On the other hand, thegenerator model based on data enhances the reality of thetraffic and mobility, although it requires data from the realworld. Table 1 shows the related traffic and mobility modelsaccording to the criteria for this classification.

To evaluate the performance of the network system, eventhough there is no available data, several studies have used thestatistical traffic models based on probabilistic distribution,such as constant bit ratio and exponential. Some of themhave represented the network with homogeneous nodes withthe same traffic [26–28] or with heterogeneous nodes withdifferent traffic according to the type of the combat entity[29]. On the other hand, other studies have tried to constructthe traffic model with available data from the real world[30, 31].They have extracted the data set of the interdeparturetime from the real world and have made the empiricalcumulative distribution function using the data set.Theyhavethen generated the traffic based on the distribution function.Although these models play a role in generating traffic, theycannot generate the different traffic against a change in thesituation, because they are only in the form of a generatorwith the output.

Similar to the traffic model, some researchers havefocused on developing a mobility model to evaluate thenetwork system under a condition in which there is noavailable data. Bindra et al. and Kioumourtzis et al. used thereference point group mobility model that regards mobilenodes as a moving group based on a random waypointmodel (RWP) [32, 33]. Also, Fongen et al. used the hierar-chical group mobility model that divides the battlefield areaaccording to the organization structure andmoves within thearea using the RWP model [34], while Reidt and Wolthuseused the ad hoc mobility model with the tactical maneuvertrace predefined by the user [35]. Although their studiescan be an alternative when there is no available data, thestereotypedmodel is somewhat different from the situation inthe real world. On the other hand, other studies have tried toconstruct a similar mobility model that reflects the real worldfrom the data [36, 37]. In these studies, they hypothesizeda mobility model that includes the combat entity’s propertyas the parameter, such as speed, the angle of movement,and the duration time of the movement, and then tunes theparameters based on the traced data acquired from the realworld. In the end, two such models can only generate thepredefined positions regardless of the change of the situation,because they are only generator models.

Complexity 5

Table 1: Related works for construction of the traffic and mobility model.

Model type Pros and cons Kinds of traffic and mobility model

Generator model notbased on the data

Pros(i) Can be used as an alternative if there is no availabletraffic or mobility dataCons(i) Is limited in terms of expressiveness

Traffic model(i) Statistical traffic model [26–29]Mobility model(i) Reference point group mobility model [32, 33](ii) Hierarchical group mobility model [34](iii) Ad hoc user-defined model [35]

Generator modelbased on the data

Pros(i) Enhances the reality of the traffic and mobilityCons(i) Requires the traffic or mobility data for learning

Traffic model(i) Traffic model from data in the real world [30, 31]Mobility model(i) Mobility model from data in the real world [36, 37]

System of systems

Combatsystem

NetworksystemInput Output

Interoperation

Network modelas it is

Abstracted modelfor combat system

Integrated system

Abstractedcombat model

Network model

Input Output

Interface model

Trafficmodel

Mobilitymodel

Transformation

Figure 3: Transformation of the SoS into the integrated system for NCW simulation.

To summarize, even though some researchers have triedto construct the traffic and mobility models regardless ofthe presence or absence of data for the analysis of theNCW, they have represented the models in the form of aconventional generator, only having an output from the viewof the standalone system and not the system of systems.Unfortunately, to apply these generatormodels to the analysisof the network system in the SoS-based NCW simulationcauses the degradation of the accuracy, because the trafficand mobility data are changed according to the status of thecommunication, as we previously explained. For this reason,it is inevitable that we will need to construct a new type oftraffic and mobility model that includes the input and outputto generate the different traffic and mobility traces accordingto the status of the network system. Therefore, we suggest a

new type of traffic andmobility model that satisfies the aboveconstraints of the previous studies. The following sectionfocuses on this proposed model.

4. Proposed Work

In this section, we clarify the problem definition and proposea transformationmethod for NCW simulation.The proposedmodel in the method is an NCW model including anabstracted combat model and network model.

4.1. Problem Definition. Figure 3 shows how this studytransforms the SoS based on an interoperation environment(upper left part) to the integrated system (lower right part).In this process, the network system remains as it is, whereas

6 Complexity

the combat system is abstracted into an abstracted combatmodel, which includes the traffic and mobility generating thetraffic and position data, and an interface model connectingthe models with the network model. Then, the model isintegrated with the unchanged network model.

In the process of the abstraction of the combat system,to deal with the aforementioned limitations, the proposedabstracted combat model should satisfy two requirements:(1) a discrete-event model for discrete-event simulation and(2) a model generating the different output according to thestates of the adjacent system. In this respect, we define sucha situation as a problem to (1) hypothesize a DEVS coupledmodel including atomic models and (2) estimate the relatedvariables.

4.2. Proposed Transformation Method. In general, the outputof the system (𝑌 = 𝑓(𝑋; 𝑉)) can be expressed as a function(𝑓) of input, that is, parameters (𝑋) and variables (𝑉). Fromthis perspective, Figure 4 shows how formalism expresses thetransformation, where

𝑓 is the combat system to be abstracted𝑔 is the network system to be analyzed𝑋𝑔 is the input parameter set of 𝑔;𝑌𝑔 is the output set of 𝑔;𝑉𝑔 is the variable set of 𝑔;

𝑌𝑓𝑔 is the output set from 𝑓 to 𝑔;𝑌𝑔𝑓 is the output set from 𝑔 to 𝑓;

𝑓𝑔 is the abstracted model of 𝑓 from the perspectiveof 𝑔;

𝑉𝑓𝑔 is the variable set of 𝑓𝑔;

ℎ is the estimation function for 𝑉𝑓𝑔;

𝑌𝑓𝑔 = 𝑓𝑔(𝑌𝑔𝑓; 𝑉𝑓𝑔) is the estimated output from 𝑓𝑔;

𝑉𝑓𝑔 = ℎ(𝑌𝑔𝑓) is the estimated variable of the model(𝑓𝑔);

𝑌𝑔 = 𝑔(𝑋𝑔, 𝑓𝑔(𝑌𝑔𝑓; ℎ(𝑌𝑔𝑓)); 𝑉𝑔) is the integratedsystem.

In the SoS, the output of the network system is 𝑌𝑔 =𝑔(𝑋𝑔, 𝑌𝑓𝑔; 𝑉𝑔), and 𝑌𝑓𝑔 is acquired from the combat system(𝑌𝑓𝑔 = 𝑓(𝑌𝑔𝑓; 𝑉𝑓)). Unfortunately, because the combatsystem does not exist in the integrated system, 𝑌𝑓𝑔 cannot beacquired directly.

To solve this problem, we hypothesize an abstractedmodel (𝑌𝑓𝑔 = 𝑓𝑔(𝑌𝑔𝑓; 𝑉𝑓𝑔)). 𝑓𝑔 and 𝑉𝑓𝑔 refer to an abstractedcombat model and a variable of the combat model fromthe perspective of the analysis of the network system. Forexample, among the various combat system logics, factorsonly related to the traffic and position are necessary for

System of systems Integrated system

XgXg YgYg

fg

YfgYgf YgfYfg

f: System

g: Systemg: System

Figure 4: Systematic representation of the proposed transforma-tion.

the network system’s analysis. In this context, 𝑉𝑓𝑔 meansthe variable for expressing the factors and 𝑓𝑔 means theabstracted combat model, including the variable. In addition,to represent the fact that 𝑉𝑓𝑔 is influenced by the responseof the network system (i.e., 𝑌𝑔𝑓), we assume an estimationfunction (ℎ) against the relation between 𝑉𝑓𝑔 and 𝑌𝑔𝑓; thatis, 𝑉𝑓𝑔 = ℎ(𝑌𝑔𝑓).

With 𝑓𝑔 and ℎ, this paper can acquire the output,𝑌𝑓𝑔 = 𝑓𝑔(𝑌𝑔𝑓; ℎ(𝑌𝑔𝑓)), from the abstracted combat model,and furthermore, by using this model, we can finally findthe output of the integrated network system 𝑌𝑔 = 𝑔(𝑋𝑔,𝑓𝑔(𝑌𝑔𝑓; ℎ(𝑌𝑔𝑓)); 𝑉𝑔) by integrating the network model. Thenext subsection shows its detailed process.

4.3. Overall Process of System Transformation. Figure 5depicts the process of the transformation consisting of thefollowing three major phases: (1) data acquisition from thesimulation of the SoS-based NCW, (2) data preprocessing,and (3) traffic and mobility model hypothesis and vari-able estimation of the models using the neural network.In the model hypothesis step, Figure 6 and the followingspecification indicate an abstracted combat model (𝐴𝐶𝑀)constructed as a DEVS coupled model, including three kindsof DEVS atomic models: traffic (𝑇𝑀), mobility (𝑀𝑀), andinterface model (𝐼𝑀). The role of the traffic model is togenerate data from the source node to the destination node;each traffic model is mapped onto the node’s pair of thesource node and the destination node. The mobility modelgenerates the position of the corresponding node; eachmodelis mapped to each node.

In the last phase, we hypothesized the traffic andmobilitymodel and the function for estimating the variables of themodels using the neural network; we trained the neuralnetwork using the preprocessed data set.Thenwe constructedthe integrated system for the NCW by embedding theneural network in the traffic and mobility model. The nextsubsection gives a description of the last phase.

4.4. Proposed NCW Model. In the first phase, we extractedsome experimental points against the input of the networksystem (i.e., communication parameters) from the entiredesign space using the design of the experiment (DOE). We

Complexity 7

SoS for NCW

Transformation

Embedded NNin the traffic &mobility model

Feed-forwardneural network

Data preprocessing

Training

Data acquisitionfrom

NCW simulation

Combat system

Network system

Message info.Position info.

Integrated system for NCW

Time

Messages

Interdeparture time

Posit

ion

Time

Traffic analysis with message info. Mobility analysis with position info.

ManeuverCommand

Feed-forwardneural network

Network model

Interface model

Trafficmodel

Mobilitymodel

Trafficmodel

Mobilitymodel

Combat model

∈ VTM ∈ VMM

Data set for traffic model Data set for mobility model

Ygf = {PDR, delay} is communication effectsVMM = variable related to the mobility model

VMMi), i: id for an experimental point}{(Ygfi,Ygf = {PDR, delay} is communication effectsVTM = variable related to the traffic model

VTMi), i: id for an experimental point}{(Ygfi,

Nodei Nodej

Ygfpdr ∈

Ygfdelay ∈

Ygfpdr ∈

Ygfdelay ∈

Figure 5: Proposed transformation procedure of the SoS into the integrated system.

Mobility model (MM)for node (i)

Interface model(IM)

Traffic model(TM)

for node (i, j)

C resultC result

TrafficPosition

PositionTraffic

C response

C result

C request

Abstracted combat model (ACM)

Network model

C request

C request

C response

C response

Integrated NCW model

Figure 6: Overall NCW model structure including the abstractedcombat model and the network model.

then executed the NCW simulation against the extractedexperimental points by acquiring the message and positioninformation for the traffic and mobility analysis. After that,for the preprocessing of the data for training, we constructedthe data set for traffic and mobility from the acquiredinformation against the experimental points. The former is{(𝑌𝑔𝑓𝑖, 𝑉𝑇𝑀𝑖)} and the latter is {(𝑌𝑔𝑓𝑖, 𝑉𝑀𝑀𝑖)}, where 𝑌𝑔𝑓𝑖 iscommunication response, that is, end-to-end delay and PDR,and 𝑉𝑇𝑀𝑖 and 𝑉𝑀𝑀𝑖 are the variables related to the traffic andmobility model, respectively.

In addition, to represent the property of the trafficand mobility affected by the network system, the interfacemodel performs a role to connect the communication effectsfrom the network model to the input of the traffic andmobility model according to the following procedure. Theinterface model transmits the traffic generated from thetraffic model to the network model through the C requestduring the initial period of the simulation. The modelthen receives the communication effect of each event fromthe network model through the C response port, calcu-lates the average communication effect, and transmits itto the traffic and mobility model using the C result port.Once it has received the effects, the traffic and mobilitymodel completes the simulation model by calculating thevalue of the variables of the model based on the effects

8 Complexity

predictC, predictIDT,predictTST, predictTET

!Traffic

INIT WAIT

GEN START

C result Traffic

External transition, Transition Syntax: [Condition] ?input/

ta = IDT

Internal transition, Transition Syntax: [Condition] !output/

[1 − PC] ?C result/predictC

[T＝ＯＬ > ４％４]

[４３４ ≤ T＝ＯＬ ≤ ４％４] !Traffic

Ｎ； = ∞

Ｎ； = ４３４ − T＝ＯＬ

Ｎ； = T）＄４

C] ?C result/[P

Object model

Object model

[T＝ＯＬ < T３Ｎ；ＬＮ] !Traffic

[T＝ＯＬ ≥ T３Ｎ；ＬＮ] !Traffic

Figure 7: Traffic model design using the DEVS formalism.

and the neural network and proceeds with the simula-tion.

𝐴𝐶𝑀 = ⟨𝑋, 𝑌, {𝑀𝑖} , 𝐸𝐼𝐶, 𝐸𝑂𝐶, 𝐼𝐶, 𝑠𝑒𝑙⟩ , (1)

where

𝑋 = {𝐶 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒};𝑌 = {𝐶 𝑟𝑒𝑞𝑢𝑒𝑠𝑡}{𝑀𝑖} = {⋃

𝑛𝑖=1 𝑇𝑀𝑖, ⋃

𝑛𝑖=1𝑀𝑀𝑖, 𝐼𝑀};

𝐸𝐼𝐶 = {(𝐴𝐶𝑀.𝐶 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒, 𝐼𝑀.𝐶 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒)};𝐸𝑂𝐶 = {(𝐼𝑀.𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, 𝐴𝐶𝑀.𝐶 𝑟𝑒𝑞𝑢𝑒𝑠𝑡)};𝐼𝐶 = {(𝐼𝑀.𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, ⋃𝑛𝑖=1 𝑇𝑀𝑖.𝐶 𝑟𝑒𝑠𝑢𝑙𝑡)

(𝐼𝑀.𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, ⋃𝑛𝑖=1𝑀𝑀𝑖.𝐶 𝑟𝑒𝑠𝑢𝑙𝑡),(⋃𝑛𝑖=1 𝑇𝑀𝑖.𝑇𝑟𝑎𝑓𝑓𝑖𝑐, 𝐼𝑀.𝑇𝑟𝑎𝑓𝑓𝑖𝑐)(⋃𝑛𝑖=1𝑀𝑀𝑖.𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛, 𝐼𝑀.𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛)};

𝑠𝑒𝑙 = 𝐼𝑀.

Figure 7 and the following specification show the struc-ture of the traffic DEVS atomic model (𝑇𝑀) consisting offour variables: 𝑉𝑇𝑀 = {𝐼𝐷𝑇, 𝑃𝐶, 𝑇𝑆𝑇, 𝑇𝐸𝑇}. 𝐼𝐷𝑇 and 𝑃𝐶refer to the time interval between the generation of the trafficand whether or not the source and destination node areconnected. 𝑇𝑆𝑇 and 𝑇𝐸𝑇 are the times when the packetgeneration is started and ended.

𝑇𝑀 = ⟨𝑋,𝑌, 𝑆, 𝛿𝑝𝑒𝑥𝑡, 𝛿𝑖𝑛𝑡, 𝜆, 𝑡𝑎⟩ , (2)

where

𝑋 = {𝐶 𝑟𝑒𝑠𝑢𝑙𝑡};𝑌 = {𝑇𝑟𝑎𝑓𝑓𝑖𝑐}𝑆 = {𝐼𝑁𝐼𝑇,𝑊𝐴𝐼𝑇, 𝑆𝑇𝐴𝑅𝑇, 𝐺𝐸𝑁}𝛿𝑝𝑒𝑥𝑡 : (𝑊𝐴𝐼𝑇, 𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, 𝑃𝐶) → 𝑆𝑇𝐴𝑅𝑇

execute ∀𝑜𝑚 ∈ 𝑂𝑀𝑇𝑀;(𝑊𝐴𝐼𝑇, 𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, 1 − 𝑃𝐶) → 𝑊𝐴𝐼𝑇

execute 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝐶;

𝛿𝑖𝑛𝑡 : (𝑆𝑇𝐴𝑅𝑇, 𝑇𝑆𝑇 − 𝑇𝑐𝑢𝑟) → 𝐺𝐸𝑁

(𝐺𝐸𝑁, 𝐼𝐷𝑇) → 𝐺𝐸𝑁 where 𝑇𝑆𝑇 ≤ 𝑇𝑐𝑢𝑟 ≤ 𝑇𝐸𝑇(𝐺𝐸𝑁, 𝐼𝐷𝑇) → 𝑊𝐴𝐼𝑇; where 𝑇𝐸𝑇 < 𝑇𝑐𝑢𝑟(𝐼𝑁𝐼𝑇, 𝑇𝐼𝐷𝑇) → 𝐼𝑁𝐼𝑇; where 𝑇𝑐𝑢𝑟 < 𝑇𝑆𝑇𝐴𝑅𝑇(𝐼𝑁𝐼𝑇, 𝑇𝐼𝐷𝑇) → 𝑊𝐴𝐼𝑇; where 𝑇𝑆𝑇𝐴𝑅𝑇 ≤ 𝑇𝑐𝑢𝑟

𝜆 : {𝑆𝑇𝐴𝑅𝑇,𝐺𝐸𝑁, 𝐼𝑁𝐼𝑇} → 𝑇𝑟𝑎𝑓𝑓𝑖𝑐𝑡𝑎 : 𝐼𝑁𝐼𝑇 → 𝑇𝐼𝐷𝑇;

𝑊𝐴𝐼𝑇 → ∞;𝑆𝑇𝐴𝑅𝑇 → 𝑇𝑆𝑇 − 𝑇𝑐𝑢𝑟𝐺𝐸𝑁 → 𝐼𝐷𝑇.

𝑉𝑇𝑀 = {𝐼𝐷𝑇, 𝑃𝐶, 𝑇𝑆𝑇, 𝑇𝐸𝑇} (3)

is 𝑇𝑀’s variable:

𝐼𝐷𝑇 is the interdeparture time of traffic genera-tion;𝑃𝐶 is the probability of existence of the trafficmodel;𝑇𝑆𝑇 is the start time of the traffic generation;𝑇𝐸𝑇 is the end time of the traffic generation.

𝑂𝑀𝑇𝑀 = {𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐼𝐷𝑇, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝐶, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑇𝑆𝑇,

𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑇𝐸𝑇}(4)

is 𝑉𝑇𝑀’s object model:

𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐼𝐷𝑇 is the prediction function of 𝐼𝐷𝑇;𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝐶 is the prediction function of 𝑃𝐶;𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑇𝑆𝑇 is the prediction function of 𝑇𝑆𝑇;𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑇𝐸𝑇 is the prediction function of 𝑇𝐸𝑇;

𝑇𝑆𝑇𝐴𝑅𝑇 is the time for the initial traffic generation;𝑇𝐼𝐷𝑇 is the interdeparture time of the traffic in the𝐼𝑁𝐼𝑇 state.

The traffic model is a probabilistic discrete-event modelin which packets are generated at intervals of 𝐼𝐷𝑇 fromthe 𝑇𝑆𝑇 to the 𝑇𝐸𝑇 time according to the probabilityof the existence of the connection (𝑃𝐶) [38]. The modelhas four states: 𝐼𝑁𝐼𝑇,𝑊𝐴𝐼𝑇, 𝑆𝑇𝐴𝑅𝑇, and 𝐺𝐸𝑁. In the𝐼𝑁𝐼𝑇 state, traffic occurs in the 𝑇𝐼𝐷𝑇 interval time during

Complexity 9

predictSPD, predictANG, maneuver MOVE

WAIT STOP

PositionC result

Ｎ； = ∞

[P－／６％] !Position/maneuver

[P－／６％] ?C result/predictP－／６％ , predictD－／６％ , predictD３４／０ ,

Ｎ； = D－／６％

Ｎ； = D３４／０

[P－／６％][1 − P－／６％] !Position/maneuver

[1 − P－／６％] ?C result/predictP－／６％ ,predictD３４／０

[1 − P－／６％]

Figure 8: Mobility model design using the DEVS formalism.

the 𝑇𝑆𝑇𝐴𝑅𝑇 time and then waits in the 𝑊𝐴𝐼𝑇 state. Afterreceiving the communication effect from the interfacemodel through the C result, the 𝐼𝐷𝑇, 𝑃𝐶, 𝑇𝑆𝑇, and 𝑇𝐸𝑇values are calculated by calling the object model: 𝑂𝑀𝑇𝑀 ={𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐼𝐷𝑇, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝐶, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑇𝑆𝑇, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑇𝐸𝑇}. If theconnection exists, it transits to the 𝑆𝑇𝐴𝑅𝑇 state and to the𝐺𝐸𝑁 state after the 𝑇𝑆𝑇 − 𝑇𝑐𝑢𝑟 time for traffic generationand generates the traffic at the 𝐼𝐷𝑇 interval. Then, when the𝑇𝐸𝑇 time is reached, the traffic generation is stopped andthe state transits to the𝑊𝐴𝐼𝑇 state. On the other hand, if Cdoes not exist, it does not generate traffic. In such a form,this traffic model plays the role of generating different typesof traffic according to the communication effect calculatedin the network model.

Figure 8 and the following specification show the struc-ture of the mobility DEVS atomic model (𝑀𝑀) consistingof five variables:𝑉𝑀𝑀 = {𝑃𝑀𝑂𝑉𝐸, 𝐷𝑀𝑂𝑉𝐸, 𝐷𝑆𝑇𝑂𝑃, 𝑆𝑃𝐷,𝐴𝑁𝐺}.𝑃𝑀𝑂𝑉𝐸 refers to the transition probability to the𝑀𝑂𝑉𝐸 state,and 𝐷𝑀𝑂𝑉𝐸 and 𝐷𝑆𝑇𝑂𝑃 refer to the time for remaining inthe 𝑀𝑂𝑉𝐸 and 𝑆𝑇𝑂𝑃 state, respectively. In this model, theprobability of staying in the 𝑀𝑂𝑉𝐸 state is determined by𝑃𝑀𝑂𝑉𝐸, and the position information is generated based onthe 𝑆𝑃𝐷 and 𝐴𝑁𝐺 in that state.

𝑀𝑀 = ⟨𝑋,𝑌, 𝑆, 𝛿𝑝𝑒𝑥𝑡, 𝛿𝑝𝑖𝑛𝑡, 𝜆, 𝑡𝑎⟩ , (5)

where

𝑋 = {𝐶 𝑟𝑒𝑠𝑢𝑙𝑡}𝑌 = {𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛};𝑆 = {𝑊𝐴𝐼𝑇,𝑀𝑂𝑉𝐸, 𝑆𝑇𝑂𝑃}𝛿𝑝𝑒𝑥𝑡 : (𝑊𝐴𝐼𝑇, 𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, 𝑃𝑀𝑂𝑉𝐸) → 𝑀𝑂𝑉𝐸

execute ∀𝑜𝑚 ∈ 𝑂𝑀𝑀𝑀(𝑊𝐴𝐼𝑇, 𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, 1 − 𝑃𝑀𝑂𝑉𝐸) → 𝑆𝑇𝑂𝑃

execute 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝑀𝑂𝑉𝐸, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑆𝑇𝑂𝑃

𝛿𝑝𝑖𝑛𝑡 : (𝑀𝑂𝑉𝐸,𝐷𝑀𝑂𝑉𝐸, 𝑃𝑀𝑂𝑉𝐸) → 𝑀𝑂𝑉𝐸

execute𝑚𝑎𝑛𝑒𝑢V𝑒𝑟(𝑀𝑂𝑉𝐸,𝐷𝑀𝑂𝑉𝐸, 1 − 𝑃𝑀𝑂𝑉𝐸) → 𝑆𝑇𝑂𝑃

execute𝑚𝑎𝑛𝑒𝑢V𝑒𝑟(𝑆𝑇𝑂𝑃,𝐷𝑆𝑇𝑂𝑃, 𝑃𝑀𝑂𝑉𝐸) → 𝑀𝑂𝑉𝐸(𝑆𝑇𝑂𝑃,𝐷𝑆𝑇𝑂𝑃, 1 − 𝑃𝑀𝑂𝑉𝐸) → 𝑆𝑇𝑂𝑃

𝜆 : 𝑀𝑂𝑉𝐸 → 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛;𝑡𝑎 : 𝑊𝐴𝐼𝑇 → ∞;

𝑀𝑂𝑉𝐸 → 𝐷𝑀𝑂𝑉𝐸;𝑆𝑇𝑂𝑃 → 𝐷𝑆𝑇𝑂𝑃.

𝑉𝑀𝑀 = {𝑃𝑀𝑂𝑉𝐸, 𝐷𝑀𝑂𝑉𝐸, 𝐷𝑆𝑇𝑂𝑃, 𝑆𝑃𝐷,𝐴𝑁𝐺} (6)

is𝑀𝑀’s variable:

𝑃𝑀𝑂𝑉𝐸 is the transition probability to the𝑀𝑂𝑉𝐸state;𝐷𝑀𝑂𝑉𝐸 is the duration time in the𝑀𝑂𝑉𝐸 state;𝐷𝑆𝑇𝑂𝑃 is the duration time in the 𝑆𝑇𝑂𝑃 state;𝑆𝑃𝐷 is the speed of the movement;𝐴𝑁𝐺 is the angle of direction change.

𝑂𝑀𝑀𝑀 = {𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝑀𝑂𝑉𝐸, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑀𝑂𝑉𝐸,

𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑆𝑇𝑂𝑃, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑆𝑃𝐷, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐴𝑁𝐺,

𝑚𝑎𝑛𝑒𝑢V𝑒𝑟}

(7)

is 𝑉𝑀𝑀’s object model:𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝑀𝑂𝑉𝐸 is the prediction function of 𝑃𝑀𝑂𝑉𝐸;𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑀𝑂𝑉𝐸 is the prediction function of𝐷𝑀𝑂𝑉𝐸;

𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑆𝑇𝑂𝑃 is the prediction function of𝐷𝑆𝑇𝑂𝑃;𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑆𝑃𝐷 is the prediction function of 𝑆𝑃𝐷;

𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐴𝑁𝐺 is the prediction function of 𝐴𝑁𝐺;

𝑚𝑎𝑛𝑒𝑢V𝑒𝑟 is the maneuver function using𝑆𝑃𝐷,𝐴𝑁𝐺.

This model is a probabilistic discrete-event model inwhich themodel varies stochastically according to the𝑃𝑀𝑂𝑉𝐸.The model has three states, 𝑊𝐴𝐼𝑇,𝑀𝑂𝑉𝐸, 𝑎𝑛𝑑 𝑆𝑇𝑂𝑃, andwaits initially in the 𝑊𝐴𝐼𝑇 state. Similar to the traf-fic model, after receiving input through the C result,five parameter values are calculated by the object model:𝑂𝑀𝑀𝑀 = {𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑃𝑀𝑂𝑉𝐸, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑀𝑂𝑉𝐸, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐷𝑆𝑇𝑂𝑃,𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑆𝑃𝐷, 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝐴𝑁𝐺,𝑚𝑎𝑛𝑒𝑢V𝑒𝑟}. In the 𝑀𝑂𝑉𝐸 state,the position is updated through the 𝑆𝑃𝐷 and𝐴𝑁𝐺 during the𝐷𝑀𝑂𝑉𝐸 time, but the position is not updated during the𝐷𝑆𝑇𝑂𝑃time in the 𝑆𝑇𝑂𝑃 state. At the end of each state, it decides theprobability of staying in the𝑀𝑂𝑉𝐸 state according to𝑃𝑀𝑂𝑉𝐸.

10 Complexity

?C response

?Position, Traffc

INIT START

SEND

Position C resultTrafficC response

C request

!C result/calCommResult

Ｎ； = ∞Ｎ； = TSTART

Ｎ； = 0

?Position, Traffc

[T＝ＯＬ ≥ T３４！２４] !C request

[T＝ＯＬ < T３４！２４] !C request

Figure 9: Interface model design using the DEVS formalism.

In this way, the influence of the network model affects thevalues of the five variables through the object model, therebygenerating different types of mobility.

Finally, the specification for the interface DEVS atomicmodel (𝐼𝑀) is described in Figure 9. This model calculatesthe cumulative communication effect through the C responsefrom the network model during the initial 𝑇𝑆𝑇𝐴𝑅𝑇 time andpasses the result to the traffic and mobility model throughthe C result port. Then, the traffic and position informationgenerated from each model is transmitted to the networkmodel through the C request port. The interface modelconsists of three states: 𝐼𝑁𝐼𝑇, 𝑆𝑇𝐴𝑅𝑇, 𝑎𝑛𝑑 𝑆𝐸𝑁𝐷. After the𝑇𝑆𝑇𝐴𝑅𝑇 time in the 𝐼𝑁𝐼𝑇 state, the model calculates the aver-age communication effects using the 𝑐𝑎𝑙𝐶𝑜𝑚𝑚𝑅𝑒𝑠𝑢𝑙𝑡 andtransmits them to the traffic and mobility model. Throughthis process, the model enables the generation of the differenttypes of traffic and mobility data according to the state of thenetwork model.

𝐼𝑀 = ⟨𝑋, 𝑌, 𝑆, 𝛿𝑒𝑥𝑡, 𝛿𝑖𝑛𝑡, 𝜆, 𝑡𝑎⟩ , (8)

where

𝑋 = {𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛, 𝑇𝑟𝑎𝑓𝑓𝑖𝑐, 𝐶 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒}𝑌 = {𝐶 𝑟𝑒𝑠𝑢𝑙𝑡, 𝐶 𝑟𝑒𝑞𝑢𝑒𝑠𝑡};𝑆 = {𝐼𝑁𝐼𝑇, 𝑆𝑇𝐴𝑅𝑇, 𝑆𝐸𝑁𝐷}𝛿𝑒𝑥𝑡 : (𝐼𝑁𝐼𝑇, 𝐶 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒) → 𝐼𝑁𝐼𝑇

(𝐼𝑁𝐼𝑇, 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑟 𝑇𝑟𝑎𝑓𝑓𝑖𝑐) → 𝑆𝐸𝑁𝐷(𝑆𝑇𝐴𝑅𝑇, 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑟 𝑇𝑟𝑎𝑓𝑓𝑖𝑐) → 𝑆𝐸𝑁𝐷

𝛿𝑖𝑛𝑡 : 𝐼𝑁𝐼𝑇 → 𝑆𝑇𝐴𝑅𝑇;

𝑆𝐸𝑁𝐷 → 𝐼𝑁𝐼𝑇 where 𝑇𝑐𝑢𝑟 < 𝑇𝑆𝑇𝐴𝑅𝑇

𝑆𝐸𝑁𝐷 → 𝑆𝑇𝐴𝑅𝑇 where 𝑇𝑆𝑇𝐴𝑅𝑇 ≤ 𝑇𝑐𝑢𝑟

𝜆 : 𝐼𝑁𝐼𝑇 → 𝐶 𝑟𝑒𝑠𝑢𝑙𝑡;

execute 𝑐𝑎𝑙𝐶𝑜𝑚𝑚𝑅𝑒𝑠𝑢𝑙𝑡𝑆𝐸𝑁𝐷 → 𝐶 𝑟𝑒𝑞𝑢𝑒𝑠𝑡;

𝑡𝑎 : 𝐼𝑁𝐼𝑇 → 𝑇𝑆𝑇𝐴𝑅𝑇;

𝑆𝑇𝐴𝑅𝑇 → ∞;𝑆𝐸𝑁𝐷 → 0.

𝑐𝑎𝑙𝐶𝑜𝑚𝑚𝑅𝑒𝑠𝑢𝑙𝑡 is the function for calculation on theeffects of communication.

After the model hypothesis step, we are going to focuson the variable (𝑉𝑇𝑀, 𝑉𝑀𝑀) estimation step. As mentionedin the previous subsection, it is necessary to transform raw-data {𝑌𝑔𝑓, 𝑌𝑓𝑔} from the SoS-based NCW simulation to thedata set {𝑌𝑔𝑓, 𝑉𝑓𝑔} for learning (referring to Figure 5).We thenconstructed a regressionmodelwith the formof feed-forwardneural network using the data set [39–41].

The upper part of Figure 10 shows the detailed structureincluding 𝑌𝑔𝑓 as an input and 𝑉𝑓𝑔 as an output. It consists ofthree kinds of layers: input, hidden, and output; each layer hasneurons, and they have a weighted connectivity with neuronsin the other layers. The value of neurons in the hidden andoutput layer is acquired from the weighted sum of neurons inthe previous layer and the activation function. To make thisidentified regression model in an executable form, as shownin the lower part of Figure 10, this paper regards the regressionmodel as a function and generates the model to the sourcecodes, which can be implemented to the prediction functionsof the object model (𝑂𝑀𝑇𝑀, 𝑂𝑀𝑀𝑀) in the above traffic andmobility model.

5. Case Study: Simulation-Based Analysis ofthe Network System

The objective of this case study is to demonstrate how muchthe proposed method improves the accuracy compared tothe existing method while conducting the transformation ofthe SoS-based NCW [42, 43]. Also, this paper compares thesimulation speeds before and after the transformation.

5.1. Experimental Design. The objective of the SoS-basedNCW simulation is to analyze the communication effects(i.e., end-to-end delay and PDR) against the communication-related parameters under the battlefield environment inwhich the exchange of information between combat entitiesoccurs through the communication. The SoS-based NCWconsists of two systems (combat and network system), whichhave already been validated.

The combat system represents the army’s military logicat an infantry company level and consists of 131 combatentities.These entities exchange information between entitiesthrough communication (traffic) and conduct the maneuver(mobility). This system is implemented in the DEVSimHLAusing DEVS formalism. On the other hand, the network

Complexity 11

Input layer Hidden layer Output layer

pdr

delay

Object model generation

∑

∑ ∑

∑

...

...

∈ Vfg

∈ Vfg

Ygfpdr ∈

Ygfdelay ∈

Ygfpdr ∈

Ygfdelay ∈

Figure 10: Realization of the object model from the trained feed-forward neural network.

Table 2: Network system parameters and their description.

Parameter name Parameter level DescriptionPacket size (PPS) 100, 200, 400, . . ., 6400 (byte) The size of packetTransmission power (PTP) −10, 5, 0, . . ., 40 (dbm) The transmission power of nodeTransmission gain (PTG) 0, 2, 4, . . ., 20 (dB) The transmission gain of nodeReception gain (PRG) 0, 2, 4, . . ., 20 (dB) The reception gain of nodePhyMode (PPM) 1, 2, 5.5, 11 (Mbps) The 802.11 phy layer mode of DsssRate

system describes the MANET using destination sequenceddistance vector (DSDV) routing protocol and consists of131 network nodes, which correspond to the entities of thecombat system [44, 45]. This system calculates the effects ofcommunication (traffic) by updating the position of nodes(mobility). This system is implemented in the ns-3 discrete-event network simulator.

The two systems participate in the HLA-based inter-operable simulation through an RTI and use a federationobject model that includes the traffic and mobility data. Inaddition to the data management, the systems advance thesimulation time using the application program interfacesrelated to time management. The network system calculatesthe effects of communication against the traffic data from the

combat system and transmits them to the destination nodeby updating information on the position from the mobilitydata.

This combat scenario depicts the complex and hierar-chical information exchange among combat entities [46,47]. The blue force conducts a defense operation againstthe red force with three times the military strength in a2 km × 2 km operation area. The combat entities performthreat evaluation and weapons assignment and transmit theresults to another entity through communication. Accordingto the communication performance, the entity makes adifferent decision and generates a different type of traffic andmobility data. Table 2 shows the parameters’ names and theirdescriptions.

12 Complexity

Table 3: Linear regression model of packet delivery ratio.

Coefficient SE 𝑡Stat 𝑝 valueC 0.3844 0.0498 7.7202 1.63𝑒 − 10PPS −1.59𝑒 − 05 7.00𝑒 − 06 −2.2756 0.0265PTP 0.0102 9.4723𝑒 − 04 10.7808 1.43𝑒 − 15PTG 0.0088 0.0024 3.7153 4.5282𝑒 − 04PRG 0.0084 0.0024 3.5254 8.2480𝑒 − 04PPM −0.0160 0.0043 −3.6865𝑒 − 04 4.9648𝑒 − 04Adj. 𝑅2 = 0.712; 𝑝 value = 8.14𝑒 − 16.

Table 4: Linear regression model of end-to-end delay.

Coefficient SE 𝑡Stat 𝑝 valueC 0.0775 0.0660 1.1737 0.2452PPS 4.68𝑒 − 05 9.28𝑒 − 06 5.0439 4.64𝑒 − 06PTP 0.0033 0.0013 2.6683 0.0098PTG 9.3956𝑒 − 04 0.0031 0.2987 0.7662PRG 6.5681𝑒 − 04 0.0031 0.2088 0.8354PPM −0.0234 0.0057 −4.0851 1.34749𝑒 − 04Adj. 𝑅2 = 0.39; 𝑝 value = 1.66𝑒 − 06.

5.2. Experimental Procedure. Before conducting the trans-formation, we executed the SoS-based NCW simulation. Inour five-dimensional network parameters in Table 2, the fullfactorial design size is 7 (for 𝑃𝑃𝑆) × 11 (for 𝑃𝑇𝑃) × 11 (for𝑃𝑇𝐺) × 11 (for 𝑃𝑅𝐺) × 4 (for 𝑃𝑃𝑀) = 37,268, which requiresa long execution time, approximately 1,128,084 hours if weconduct 30 trials against each experimental point (1.01 hoursper one execution) [48–50]. For this reason, we selectedthe first 65 experimental points for training from the entiredesign space: 43 points using face-centered central compositeand 22 points using a Latin hypercube design [51]. We thenchose an extra 22 points at random from among the fulldesign to evaluate the transformation. Using the acquireddata from the SoS-basedNCWsimulation, we constructed anabstracted combatmodel consisting of the 908 trafficmodels,131 mobility models, and an interface model. In the process,we trained the feed-forward neural network with a 2-5-1structure using Levenberg-Marquardt algorithm.

From the perspective of accuracy and simulation execu-tion performance, we regarded the output of the networksystem and the execution time as the effectiveness index.Theenvironment for this case study is as follows. For the combatsystem, CPU: I5-3550 3.3 GHz, RAM: 4GB, DEVSim++ v.3.1are used. For the network system, we used NS3 v.3.18. Thesetwo systems used RTI 1.3-NG and progressed simulation timeover 5,000 sec including 𝑇𝑆𝑇𝐴𝑅𝑇 300 sec. For the training, weused MATLAB neural network toolbox v.8.2.1 and MATLABCoder v. 2.7.

5.3. Experimental Results. Before the analysis of the accuracyand the speed,we constructed the first-order linear regressionmodel (𝑦 ∼ 1 + 𝑃𝑃𝑆 + 𝑃𝑇𝑃 + 𝑃𝑇𝐺 + 𝑃𝑅𝐺 + 𝑃𝑃𝑀) toidentify whether the selected network parameters influencethe communication effects [52, 53]. In Tables 3 and 4, thecolumn refers to the parameters, while the row refers to

Accuracy comparison of packet delivery ratio

Proposed methodExisting method

0.2 0.4 0.6 0.8 10Packet delivery ratio in the SoS-based NCW

0

0.2

0.4

0.6

0.8

1

Estim

ated

pac

ket d

eliv

ery

ratio

Figure 11: Simulation results for packet delivery ratio comparingbetween the existing and the proposed methods.

Accuracy comparison of end-to-end delay

Proposed methodExisting method

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5Es

timat

ed en

d-to

-end

del

ay (l

og(s

ec))

0 0.5−1.5 −1 −0.5−2.5 −2−3End-to-end delay in the SoS-based NCW (log(sec))

Figure 12: Simulation results for end-to-end delay comparingbetween the existing and the proposed methods.

the coefficient estimates, the standard errors (SEs) of theestimates, the 𝑡-statistic values of the hypothesis tests forthe corresponding coefficients (𝑡Stat), and the significantprobability (𝑝 value). Tables 3 and 4 show that the fiveparameters influence at least one of the two communicationeffects based on the fact that the 𝑝 value is smaller than thesignificance level (0.05); therefore, we used these parametersin the case study.

To conduct an analysis from the perspective of accuracy,we compared the results of the transformation through theproposed method and the conventional method, which onlygenerates the output regardless of the input. Figures 11 and12 show the graphs for the accuracy comparison of thecommunication effects (i.e., PDR and end-to-end delay).The 𝑥-axis and 𝑦-axis refer to the communication effectsfrom the SoS-based NCW execution and integrated system,respectively. The more symmetry of the 𝑥- and 𝑦-axes, the

Complexity 13

Traffic in the SoS and the proposed integrated system for NCW

Normal network condition: NCW SoS

Poor network condition: NCW SoS

Normal network condition: integrated system

Poor network condition: integrated system

# of traffic

300

250

200

150

100

50

Figure 13: Traffic model results of the SoS and the proposed integrated system for NCW.

higher the accuracy. In Figures 11 and 12, the simulationresults of the proposed method have higher accuracy thanthose of the conventional method. For the quantitate analysisof this difference, we measured the root mean square error(RMSE). In the case of Figure 11, each case indicates 0.0425and 0.0997 RMSE, whichmeans 4.6281% and 10.8407%whenconsidering the minimum and maximum value (0.0491,0.9691). Also, Figure 12 indicates 0.0520- and 0.1304-secondRMSE, which means 4.3721 and 10.9647% when consideringthe minimum and maximum value (0.0018, 1.1915). Thisimproved accuracy stems from the proposed traffic andmobility model, as shown in the following figures.

Figure 13 shows the flow of the traffic, which is one ofthe causes of enhanced accuracy.The left and right part showthe traffic between entities in the SoS-based NCW and theproposed integrated system. The upper and lower part showthe traffic in the normal and poor network condition; theformer implies a case of having high PDR and small end-to-end delay, and the latter implies a case of having small PDRand high end-to-end delay. In the left part, the two figuresshow that more traffic occurs in the normal communicationcondition than in the poor condition, because the normalnetwork condition allows for more exchanged informationand more connection of information owing to the delivery ofthe hierarchical command. From this perspective, the rightpart describes a similar trend to the left part in that trafficchanges according to the communication condition, whichhelps to reduce the error from the transformation.

Table 5: Comparison of the simulation speeds of the SoS and theintegrated system for NCW.

Execution time(min.)

# of processed events in the networksystem

SoS 60.539 2.539𝑒 + 08Integratedsystem 16.025 2.569𝑒 + 08

Figure 14 shows another cause of enhanced accuracy,mobility data; it shows the average position change of thenodes against the experimental points at the end of thesimulation time. In the SoS-based NCW simulation, theposition change in the experimental points with a normalcommunication condition is larger than the experimentalpoints with a poor condition, as the orders between the enti-ties related to maneuver are normally transmitted throughthe communication. In the proposed integration system, themobility also indicates a similar trend, although it does nothave the same results; it also plays a role in enhancing theaccuracy.

From the perspective of the simulation speed, we com-pared the average execution times and the average numbersof executed events per one trial in the SoS-based NCWand integrated system. Table 5 shows that the integratedsystem reduced the execution time 3.78-fold compared tothe SoS-based NCW. Also, judging by the fact that the

14 Complexity

system for NCWMobility in the SoS and the proposed integrated

0

200

400

600

800

1000

of n

odes

(m)

Aver

age p

ositi

on ch

ange

20 30 40 50 60 70 800 10Experimental point number

SoSIntegrated system

Figure 14: Mobility model results of the SoS and the proposedintegrated system for NCW.

number of executed events in the network system is similarbetween the SoS-based NCW and the integrated system andis much higher than the number of the executed events inthe combat system of the SoS-based NCW, we can infer thatthe elimination of the interoperation architecture of the SoS-based NCWplays a prominent role in reducing the executiontime.

Furthermore, they recorded 2633.45, 697.07 hours withthe 87 experiment points, that is, 2610 trials. In addition to theexecution time for the simulation, the proposed integratedsystem requires a time for training in machine learning ofabout 8.55 hours, including 7.27 hours for the traffic modelsand 1.28 hours for the mobility models. Fortunately, however,the time is quite small compared to the execution time of theSoS-based NCW simulation.

6. Conclusion

In network-centric warfare (NCW), due to the importanceof communication, which is responsible for the flow ofinformation, it is necessary to analyze the performance ofthis communication against the communication parametersin an environment with high complexity, such as a battlefield.For this reason, many studies have conducted a simulation-based analysis of the NCW from the perspective of theSoS, which consists of the combat system and the networksystem so that the two reflect each other’s effects. However,this paradoxically causes a prolonged execution time anddifficulty in conducting the analysis of the various parametersdue to the problem of time.

To overcome this weakness, we need to abstract the com-bat system to an abstracted combat model that includes thetraffic and mobility models required for the network system’sanalysis. We also need to integrate the abstracted combatmodel with the network system. Some studies have beenconducted on the construction of the traffic and mobilitymodel for the analysis of communication. However, as theanalysis has been performed in a standalone system, not anSoS, the resulting model has a form with only an output,

and therefore themodel cannot generate the different outputsaccording to the state of the adjacent system, although it is animportant characteristic of the SoS with high complexity.

This paper proposed the transformation of the SoS-based NCW into an integrated system. For this, we firsthypothesized an abstracted combat coupled model thatincludes the traffic, mobility, and interface atomic modelsusing discrete-event systems specification (DEVS) formalismfor the discrete-event simulation. We then estimated thevariables of the models in the form of the neural network,which can be updated from the state of the adjacent system,and identified the variable using the machine learning andthe data acquired from the SoS-based NCW simulationexecution.

The case study shows that the integrated system, as a resultof the proposed method, significantly improves the accuracycompared to the existing method and reduces the executiontime compared to the SoS-basedNCWsimulation.We expectthat this paper will help in the analysis of various parametersin various domains based on the SoS as well as the militarydomain.

Glossary

C2: Command and controlCPU: Central processing unitDEVS: Discrete-event system specificationHLA: High-level architectureMANET: Mobile ad hoc networkM&S: Modeling and simulationNCW: Network-centric warfareNS3: Network simulator 3PDR: Packet delivery ratioRAM: Random-access memoryRMSE: Root mean square errorRTI: Run-time infrastructureRWP: Random waypoint modelSE: Standard errorSoS: System of systems.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

Thisworkwas supported by Institute for Information&Com-munications Technology Promotion (IITP) grant funded bythe Korean Government (MSIP) (no. 2017-0-00461, Devel-opment Platform for User-Level Customizable, General Pur-pose Discrete-Event Simulation Software).

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