Command and Control Network Modeling and Efficiency Measure Based on Capability Weighted-Node

Command and Control Network Modeling and Efficiency Measure Based onCapability Weighted-NodeDu WeiScience and Technology on Information SystemsEngineering LaboratoryNational University of Defense TechnologyChangsha , Chinae-mail: duweithinker@ Liu ZhongScience and Technology on Information SystemsEngineering LaboratoryNational University of Defense TechnologyChangsha , Chinae-mail: phillipliu@ Xiu Bao-Xin *Science and Technology on Information SystemsEngineering Laboratory National University of Defense TechnologyChangsha , Chinae-mail: bxxiufuzzy@Zhang Wei-MingScience and Technology on Information SystemsEngineering LaboratoryNational University of Defense TechnologyChangsha , Chinae-mail: bxxiufuzzy@Cheng QingScience and Technology on Information SystemsEngineering LaboratoryNational University of Defense TechnologyChangsha , China e-mail: sgggps@Abstract —Command and contr ol (C2) or ganization and its existing r esea r ch a r e int r oduced, and C2 o r ganization efficiency measure is discussed. The C2 network model is built, and the capability of C2 network is analyzed by the method of weighted-node. The average cooperating efficiency is proposed to measur e C2 networ k’s cooper ating efficiency, and validate measurement’s validity by comparing with network efficiency . The optimal C2 networ k’s topology pr oper ty is analyzed by modulating some parameters. The property has a direction for designing the actual C2 network.Keywords-capability; weighted-node; C2 network; Average Cooperating EfficiencyI. I NTRODUCTIONWith development of information and network technology, command and control (C2) organization is facedwith a great challenge in modern battlefield. Changeful posture proposes a higher request on running C2 organization. Various missions need an effective organization to complete better different tasks. For an existent C2 organization in battlefield, what structure can adapt different tasks to complete. This is the principal problem to commanders as well as researchers of C2 organization.From the organization contingency theory, only in idiographic mission environment can organization structure match with the mission environment and organization exert*Corresponding author: Xiu Bao-Xinthe best action. So how to match the mission, environment and structure is the key of organization optimal design [1,2]. Based on this conclusion, America Naval Postgraduate School has a series of A2C2 experiments [3]. The results of experiments provide theory foundation for organizing resources effectively and designing C2 relation. [4] The paper depicts C2 organization on its layers and proposes the concept of C2 organization measurement, and proposes processes and methodology of organizational design.Foregone researches focus on how to designorganizational structure matching with mission environment.This means the organizational structure is related to the mission task. In the design methodology proposed by [6,7,8], the task is one of the three organizational designing factors.Consequently, most researches on C2 organization are todesign relevant structure according to idiographic task. Nowmany researchers pay gradual attention to adjusting organization to match with dynamic tasks[9,10]. But it isn’t effective to adjust organizational structure based on academic results in factual battlefield. So we require studying C2 organization design under condition of over-multitasks. The condition of over-multitasks denotes one organization can better execute many different tasks. Although every task can’t be executed to achieve a besteffect, the organization needn’t modulate its structure for every task. Now there are a mass of different tasks in battlefield. It has a great advantage that organization structure needn’t change. We abstract decision-maker (DM),platform (P) and their relations as a network. The operation unit is the node of network and various relations are the 2011 Ninth IEEE International Conference on Dependable, Autonomic and Secure Computing 2011 IEEE Ninth International Conference on Dependable, Autonomic and Secure Computingedges of network. This network is said as command and control network (C2 network). Then we propose a new measurement model to measure C2 network efficiency. The C2 network efficiency denotes the efficiency which the task is executed by the C2 organization. The task is the precondition of C2 organization. C2 organization executes the task by collaborating all operational units. The task may be denoted a request of capabilities and resources. Different tasks denote different capabilities or resources. This request can be satisfied by collaboration of all units’ capabilities and resources. If there are some units collaborating to satisfy the request of one task, we may think that the organization can execute this task successfully. The efficiency to execute tasks is equal to the efficiency of collaboration of all units. There are a few researches for the network efficiency. Most of them have a qualitative analysis or qualitative measurement by multi-metrics. Latora etc. proposed network efficiency to measure the efficiency of network by the shortest path in network. But this measurement doesn’t have pertinence to some particular networks. So many researchers have some improvements in network efficiency in order to solve respective domain’s problems [13,14]. Network efficiency only thinks about topology structure without weighted nodes’ and edges’ effects to the network. The network measured by network efficiency has the same type of nodes. There are some shortages to measure C2 network with network efficiency , so we propose specifically measurement to measure the C2 network. II.C2 NETWORK MODEL ABSTRACTING AND BUILDINGIn a practical C2 network, there are a lot of different entity units. We divide these units into two kinds: decision-unit (D) and action-unit (A). The decision-unit is the sponsor to execute task. Its responsibility is commanding and controlling the action-unit, as well as cooperating with other decision-units. The action-unit is the executants of task. It provides various resources and capabilities for meeting the request to execute the task. The follows are C2 network modeling.A. D D −cooperating networkThe decision-unit is the node, which is called the decision-node (also denoted as D). The cooperating relation is the edge. Nodes and edges compose the network, which is as the D D −cooperating network. It is denoted as follows:(,,)D D D D DD G Ds E α−−=(1)111222{(,,),(,,),(,,)}m m m Ds D m D m D m βββ="denotes the decision-node set. i D is decision-node i. i m is the weight of decision-node i. D βis denotes decision efficiency which per decision capability commands per action capability. It denotes the intrinsic decision capability of decision-unit. {(,)|(,)1}D D i j i j E D D D D θ−== denotes the set of edges, (,)1i j D D θ=denotes i D and j D have acollaboration. DD α is the cooperating efficiency parameter and denotes to quantificationally depict action capability’slosing when different decision-nodes have a collaboration.These losses are arisen by information attenuation, wrong operating, information wrong transferring, imperfect foundation establishment and disturbing from enemy as cooperating.B. D D −commanding and controlling networkThe action-unit is the node, which is called the action-node (also denoted as A). Decision-nodes and action-nodes are as nodes, and relations between decision-nodes and action-nodes as edges. They compose the network which is said D D −commanding and controlling network and denoted as follows:(,,,)D A D A DA G Ds As E α−−= (2)Thereinto 1122{(,),(,),(,)}n n As A w A w A w =" is the set of action-nodes. j A is the action-node j. j w is the weight of action-node j, denotes intrinsic executing capability of action-unit. {(,)|(,)1}D A i j i j E D A D A σ−== denotes i D commands and controls j A .DA αis the C2 efficiency parameter and denotes to quantificationally depict action capability’s loss when decision-node commands and controls action-node. As the same as DD α, These losses are arisen by information attenuation and so on when commanding, controlling. So ,(0,1)DA DD αα∈is satisfied. C. C2 network with capability weighted-nodeFrom above sections, C2 network with capability weighted-node may be expressed as follows:2(,)D D D A C N G G −−=(3)From Formula (3), C2 network comprises two types of edge: C2 relation D A E − and cooperating relation D D E −. From above model, we give a visual network to depict the C2 network:Figure 1. C2 network model example 1III. C2 NETWORK EFFICIENCY MEASURE MODEL C2 organization is built to organize every operational unit, in order to more effectively complete the mission task. In the process of mission executed, the mission is divided into many detailed tasks. For each task, C2 organization would choose different units to cooperate to execute. If we want to measure the efficiency which C2 organizationexecutes one task, we may measure the efficiency which different nodes cooperate with each other in the C2 network. As the sponsor of task executed, decision-node is the center of organization. Every task can be denoted that different decision-nodes command different action-nodes to cooperate. The follows are some variables to measure the cooperation:A. Mutual cooperating path(,)c i j Pdenotes the shortest path that i A passes to cooperatewith j A . This path starts from an action-node, passes through some decision-nodes, and ends in the other action-node. (,)c i j d denotes the length of the path (,)c i j P . B. Mutual cooperating efficiency (,)i j Ci A and j A need have a collaboration when they areexecuting a task. This process has to get the command and control from the decision-node. So the effect of collaboration is affected by not only capability weight of action-node but also various factors in (,)c i j P . These factors include (,)c i j d , D β, α. So (,)i j C may denote the format weighted by these factors.(,)(,)()c i j di j i j C w w βα=+ (4)Thereinto, (,)()i c i j iDD P i m W D ββ∈=∏denotes the effectthat decision-nodes affect the cooperating efficiency in the (,)c i j P . (,)1()i j i j D A W D w σ==¦denotes the sum of action-nodes’ capability controlled by the decision-node i D , so (,)i c i j D P ∈ denotes i D is in the (,)c i j P . D i m β denotes the maximal capability controlled by i D without action-capability losing. ()i D i W D m β≤ denotes the capability controlled by the decision-node is less than the maximal capability controlled by i D without action-capability loss, here set 1()iDi m W D β=. This means i D may control allcapability without action-capability loss. If ()i D i W D m β>,1()i D i m W D β<. So we know [0,1]()iD i m W D β∈.(,)(,)(,)D D c i j D A m n d d d DDDAααα=denotes the effect that the (,)c i j Paffects the cooperating efficiency. (,)m n D D d is the length of the shortest path from m D to n D . Here the path is contained in the D D G −. (,)D A d is the length of controlling path that D commands and controls A . Obviously (,)1D A d =. So Formula (4) is also denoted:(,)(,)(,)(,)1()D D m n g c i j D A g k d gi j DDDDA i j D P kE D A m C w w w βαα−∈==+∏¦(5)C. Average Cooperating Efficiency ave Cave C denotes the average value of (,)i j C in the whole C2 network. It is written as follows:(,)2(1)ave i j i j C C n n ≠=−¦ (6)ave C denotes the average efficiency of different action-nodes to cooperate within the C2 network. The executed task can be denoted the process of different operational units. So the efficiency that different nodes cooperate may reflect the efficiency to execute task. Consequently we use the ave C to measure the efficiency that decision-units command and control action-nodes to execute tasks in the C2 network. The value of ave C is affected by the constructing network cost, various parameters (,,DD DA i ααβ), the network topology structure. When designing the C2 network topology structure, ave C is the optimized goal. The constructing network cost and various parameters (,,DD DA D ααβ) are fixed, and the optimal network structure is designed to ensure the optimal ave C . The follows are several experiments to validate that the measurement ave C is effective and logical, and to analyze the property of different optimal network topology for different parameters by modulating the parameter value.IV. C2 NETWORK MODEL EXPERIMENT ANALYSIS There are 5 decision-units and 12 action-units in a C2 organization. The weights of every node and every parameter value are seen in TABLE1:TABLE I.PARAMETER TABLE1w 2w 3w 4w 5w 6w 7w 5 3 7 16 8 17 2 8w 9w 10w 11w 12w 1m 2m 6 20 11 12 7 6 43m 4m 5m DD α DA αDβ8 3 10 0.7 0.8 2.5Figure 2. C2 network model example2Figure 2(a) is a model of a practical simple C2 organization. From above parameters, we can gain () 3.2581ave C a =; Figure 2(b) is a optimal network structure that we have achieved by genetic algorithms whose fitness function is ave C . H ere () 5.7060ave C b =.Through analyzing the structures of (a) and (b), thedifference between (a) and (b) is D D E − and D A E −. This case is uniform to the property that ,DM DM DM p R R −− affectthe efficiency of C2 organization. ave C is valid to reflect this distinction, so we can use it to measure C2 network efficiency.A. Contrast experiment with different constructing cost In this experiment, D A E − is fixed, and the number of cooperating edges in various decision-node is changed to analyze the difference of ave C with different constructing network costs. Contrast networks with different D D E − numbers from 0 to 5.These network topology structuresare as follows:Figure 3. C2 network topology with D D E −of different numbersFigure 4 is ave C with different D D E − numbers. The horizontal axis is the serial number of network in Fig.3. The vertical axis is ave C ..network number in Fig.3C a v eAverage Cooperating Efficiency in different network constructing costsFigure 4.ave C with different D D E − numberProperty analysis: C2 network ave C is growing with the growth of the D D E − number. This means that the C2 network more effectively execute tasks when the network’s D D E −number is larger. Because the edge number is greater, the cooperating information can be transmitted effectively. So the C2 network can execute the task effectively. Apparently it is most effective to execute tasks when the network is fully connected. But it is unpractical. The constructing cost of fully connected network is great. In a limit fixed cost, there are some contrasts between two different network structuresby ave C . The contrast can determine which network has an advantage in executing tasks. B. Different measurement contrast exeriment with same parametersLatora etc. proposed network efficiency (NE ) to characterize the global property of the network, and to measure how efficiently information is exchanged over the network. The concept is as follows [11,12]:111/(1)(1)ij iji j i jNE e d N N N N ≠≠==−−¦¦(7)Thereinto, ij d denotes the shortest distance betweennode i and node j , satisfying 1/ij ij e d =. N is the numberof network’s nodes. Latora had some analysis to several types of networks.The following experiment analyzes the changes and relation of two measurements with same parameters:• Generate 100 different C2 networks randomly.The number of edges and nodes in these networks is same, and ,D D D A E E −− are different.• Compute corresponding NE and ave C of differentC2 networks.• Array the sequence of 100 C2 networks accordingto the trend of ave C from small to large. Then have a compareemnt. The result is as follows:Different networkA v e r a g e C o o p e r a t i n g E f f i c i e n c y a n d N e t w o r k E f f i c i e n c yMeasurement contrast in different networksFigure 5. Two measurement contrast of different networksProperty analysis: From the contrast of two measurements, we can calculate that standard deviation of ()0.0380NE σ=. The value is very small. This means thatit isn’t impressible for different topology structures. It can’t reflect the different network models. But ()0.6658ave C σ= means the change of ave C is bigger than NE. It can reflect the changing efficiency of C2 network. This means that ave C has a sensitive reflection and validity to measure the C2 network efficiency to execute tasks when the network topology structure has changed.C. O p timal C2 network analysis ex eriment with different parameter D β In the network theory, the node’s p oint centrality denotes the number of other nodes connecting with the node. Different networks have different central trend. For example, in a star network, the central node has the largest point centrality , and other nodes’ point centrality is 1. Likewise, this network has a larger central trend. In a complete network, all nodes’ point centrality are n-1, so this network has little central trend. The centralization of this network is 0. The centralization is able to reflect the property of the network that various nodes have different oint centrality . The network centralization is formulated as follows [19]:max1max 1()max[]ni i ni i CC C C C ==−=−¦¦ (8)This experiment designs the optimal network where the optimal goal is ave C , analyzes the structure of networks by the centralization of the optimal C2 network and validate the validity of ave C with different parameter by contrast between network efficiency and Average Coo erating Efficiency . The steps are as follows:• Fix ,,,DD DA ws ms αα, and change D β. Set D β from 0.5 to 10 with the step of 0.5. • Choose ave C as the fitness function, then optimize the network structure by genetic algorithms under different conditions with different D β.C e n t r a l i z a t i o n a n d N e t w o r k E f f i c i e n c yDifferent measurements contrast in different A v e r a g e C o o p e r a t i n g E f f i c i e n c y DβFigure 6. Three measurement contrast with different D β Property analysis: 1) From Figure 5, with the increase of D β, optimal C2 network ave Cis growing. But ave C retains fixedness when D βgrows to a bound. Because whenD βgrows to a bound, some decision-nodes’ decision-capability can satisfy the request of commanding andcontrolling all action-nodes. H ere 1()iD i m W D β=, andthe network topology is changeless with the increasing D β. So ave C is changeless.2) With the growth of D β, the transformation trend of centralization is from large to small, then from small to large. From Formula (8), the centralization is independent of D β. The change is arisen by the C2 network structure. The optimal C2 network central trend is from large to small(various nodes’ degrees deviation changes from large to small), then from small to large(various nodes’ degrees deviation changes from small to large). This means that C2 network is designed as a star-network when decision-capability validity (determined by D β) is very small or very large. 3) NE has a few changes when D βchanges. This means network efficiency isn’t able to reflect the change of parameters in C2 network whereas ave C may reflect the change distinctly. This tells us that ave Chas avalidity and sensitivity to measure the C2 network efficiency when parameters change.From the horizontal experiment (4.2) and vertical experiment (4.3), we have a contrast between NE and ave C . NE can’t effectively reflect the change of C2 network, including the network structure and network parameters. But ave C may have a great reflection on the practical property of C2 network. There is a good practical value in studying the efficiency of C2 network. Through the research to change D β, we find that the optimal network is different when the parameter changes. This has a better direction to how we design and construct a C2 network in a practical battlefield.V.C ONCLUSIONThis paper analyzes the property and essence of C2 and executed tasks, constructs the C2 network model and abstract the capabilities of various operational units as weights of nodes in the C2 network, builds the measure model of C2 network cooperating efficiency based on the weighted-nodes and has some experimental analyses to the measure model to have a contrast with NE to validate the validity of ave C . By adjusting the parameter, we investigate the structure property of optimal C2 network with different parameters. There is a significance to direct to construct the practical C2 network.In future work, we will analyze other parameters and the structure property of optimal C2 network with different parameters. We will enlarge the dimensionality of the node weight to denote different capabilities andpropose the new efficiency measurement of C2 network executing tasks.A CKNOWLEDGEMENTSThis research work is supported by the National Natural Science Foundation of China under Grant No. 70701038, No. 91024006 and No.71001105.R EFERENCES[1] H ollenbeck J R . Structural contingency theory andindividual differences: Examination of external and internal personteamfit. Journal of Applied Psychology. 2002,87(3): 599[2] Carley K M. Organizational design suited to highperformance under stress. 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