The Cluster Formation Schemes

Published Date: 02 Nov 2017

3.1 INTRODUCTION

Clustering helps in reuse of resources, better coordinate in its transmission events with the help of Cluster controller head (CCH) routing of information in inter/intra cluster communication, if any changes occur in the clusters then the particular cluster information alone need to be updated, there by reducing the information stored and processed by each and every cluster is greatly reduced.

In this chapter, three different kinds of Clustering schemes were discussed and it is suitable for mobile users, military and teleconferencing. The members are formed as subgroups based on one of the proposed techniques and the secure group communication will takes place in an authenticated and confidential manner. The ‘n’ members of a group are partitioned into subgroups and the communication is done efficiently with in finite time. If concentration is on wireless nodes then the nodes distance must be considered while forming the subgroup. When two nodes lie within same transmission range and set up a bidirectional link between them then they are said to be neighbor of each other.

Depending on the diameter of the clusters there exist two kinds of cluster control architectures, known as one-hop clustering and multi-hop (d-hop) clustering. In one-hop clustering every member node is at most 1-hop distance away from a central coordinator called as the Cluster Head (CH). Thus all the member nodes remain at most two hops distance away from each other within a logical cluster. But in multi hop clustering, the constraint of immediate neighborhood of members from the head is eliminated by allowing the nodes to be present at most dhop distance away from each other to form a cluster. The proposed three schemes follow one-hop clustering.

The proposed tree model is derived from the decentralized architectures like, IGKMP, IOLUS, HYDRA and KRONOS. All the above are supporting common sub grouping within the large group, but each technique have differences and use different techniques to achieve the distribution.

The Intra-domain protocol (IGKMP) employs a common central controller known as Domain Key Distributor (DKD) for controlling the subgroup controllers called Area Key Distributor (AKDs). But there is a main draw back if the DKD is compromised the whole group will be disrupted. Also, if an AKD is not available then the members in that area are not able to access the group communication, because it is impossible to access AKDs from any other areas.

The Iolus uses independent keys for each and every subgroup and the membership changes in a subgroup to be treated locally. Here the changes that affect a subgroup will not be reflected to other subgroups. Mainly this supports fault-tolerance of the system and also if a subgroup controller (namely, for instance, GSA) fails only that particular subgroup is affected. But Iolus affects the data path in the sense that is a need for translating the data that goes from one subgroup, and thereby one key, to another. The GSA has to manage the subgroup and also has to perform the translations so it may become a bottleneck. Iolus gives the solution for the 1-to-ncommunication, but leaving the n-to-n communication groups.

Yet another approach Kronos does not have common central controller and the subgroup controllers can generate the new keys independently, which makes the system fault-tolerant but it compromises the group security because the new group key will be generated based on the previous one. If any one key is disclosed then all keys will be compromised and thus no forward secrecy will be maintained.

Hydra uses keys that are independently generated, so that they cannot be used to recover either past keys or future keys. First of all, Hydra does not employ a central controller like DKD. The Hydra-Master appears only during setup time and it is not contacted for group-key updates. Furthermore, Hydra is more flexible regarding the subgroup formation. Whenever an HS stops working, its members can always find the new nearest HS and re-join the group session. Hydra presents the undesirable feature of one change affecting the whole group that Iolus manages to avoid. But, on the other hand, Hydra separates the control path (key management) from the data path (group communication). But Hydra needs a longer time to re-key the whole group after a membership change, the delay will be noticed in the group-key updates (control path) but the group communication (data path) will not be affected by that.

From the survey the following draw backs were notified

Common group key for a whole group in IGKMP

GSA will become bottle neck and the group data must be translated when it moves from one subgroup to another in IOLUS

The new group key will be formed after certain period irrespective of the group membership, it generates the new key based on the previous one and the servers clocks perfectly synchronized to exchange the keys exactly at the same time in KRONOS

A longer time is needed to rekey the whole group after a membership change in Hydra

In order to overcome the above drawbacks the proposed OCHT is constructed so as to accept the HSMA supporting the decentralized key management approach with contributory to achieve better scalability, reliability, and cost effectiveness with the supporting architecture, here the large group is divided into so many subgroups called Cluster Controllers(CC) with independent key and all CCs will be controlled by a Head called Cluster Controller Head(CCH). During group dynamic the particular subgroup key alone will be updated and it wont affect the other subgroups.

3.2 THE PROPOSED TREE MODEL

The subgroup concept is based on the Divide-and-conquer algorithm technique, in this the members of size ‘n’ is divided into sub problems of size ‘n/m’. The Figure 3.1 shows the proposed OCHT with Cluster Controller Head which is the head of all the Cluster Controllers each consisting of group members with the maximum count which equal to the number Cluster Controllers. The members joining the group are giving their contribution of keys in constructing the common key. The proposed OCHT model is concentrating much more on reducing the number of keys that are stored in CCs and the CCH while group dynamics takes place. Here the group of ‘N’ members is divided into clusters with size M, where N = Ma and ‘a’ is the degree of the tree. The Figure 3.1 shows the Optimal Cluster Hierarchical Tree with degree 2 and 8 cluster controllers. For example if cluster size M = 4, degree a = 2 then the total number of members in the group is N = Ma = (4)2 = 16. Since group of ‘N’ members are divided into cluster size of M with the constraint that the number of members in the cluster is equal to the number of clusters under the CCH, i.e. if the cluster size M is 4 then each cluster will have at the maximum of 4 members. Each and every cluster is assigned a unique id based on the application concerned. To obtain an optimal tree, there are [N/M] clusters with the height of .

Figure 3.1 Optimal Cluster Hierarchical Tree (OCHT)

3.3 CLUSTER FORMATION TECHNIQUES

The proposed clustering architecture is based on One-hop i.e. the distance between the member and the Cluster head called Cluster Controllers(CC) is always one and all the CC’s were one-hop to the Cluster Controller Head (CCH) which is head of all CC’s. The three different types of clustering algorithms proposed in this section are

Time Based Clustering (TBC)

Position Based Clustering (PBC)

Key Based Clustering (KBC)

The above clustering schemes were designed in such a way that they will support both wired and wireless environment. The following figure 3.2 shows the layered architecture for initialization, cluster formation and updation.

Figure 3.2 Cluster Formation Techniques

The algorithm for cluster formation is shown below generates an OCHT in an efficient manner and its main aim is to generate the tree competent at the time of tree dynamics while join/leave operations takes place. The OCHT is formed with any one of the proposed clustering schemes. The formation tree is done based on the application concerned and the group of ‘N’ members are divided into clusters with size M, where N = Ma and ‘a’ is the degree of the tree.

Algorithm 1. Cluster Formation

Input: Cluster Formation Parameters (UserTotal, TypeCluster).

Output: OCHT Generation.

Digit:=TotalDigit(UserTotal);

Digit/=2;

assert(UserTotal<=power(2,PowerDigit*Digit));

if(true) begin

CreateDummyNode(GetMemberAddress(dbgm.Pointer));

end

if(TypeCluster==0) begin

AssignMember(dbgm.Key);

ClusterTree(Sort(dbgm.Member));

else if(TypeCluster==1)

AssignMember(dbgm.Location);

ClusterTree(Sort(dbgm.Member));

else

AssignMember(dbgm.TimeStamp);

ClusterTree(Sort(dbgm.Member));

end

ClusterUpdation(db.Member,Cluster) begin

CreateDummyNode(GetMemberAddress(dbgm.Pointer));

AssignMember(dbgm.Cluster); ClusterTree(Sort(dbgm.Member));

End

3.3.1 TIME BASED CLUSTERING (TBC)

The TBC scheme is well suited for the time related applications like prepaid mobile users, pay per view in TV, webinars etc. If we take the application of prepaid mobile users, the members leaving time for a particular group will be known before hand. The users may group under how long they may have their validity to use that particular service. But for certain services that are provided by the group can be preferred based mainly on how the service is being provided. The users may prefer validity as life time, 5 years or even for one year etc. and also they may opt services like messaging service, internet service, MMS, Chatting etc. Within a time period many users join to a particular network like BSNL, Airtel, Aircel, IDEA, Vodafone etc. and based on the users willing they may be grouped and the services will be provided.

In TBC, within the allotted time span many numbers of users may join/leave in that particular group. If we group them based on any one of the service like messaging service, internet service then too many groups have to be formed. Since Wireless devices consumes lot of energy, power and less battery life time then care must be taken while forming the groups. In the proposed TBC based clustering scheme a time is allotted for joining to that particular group and after that a new group will be formed with the newly joining members for the next slot. In this every CC will have a database which is used to store the time related entities like the members joining time, leaving time, services opted be maintained. The OCHT will be balanced based on the number of CCs available automatically.

The prepaid mobile users are paying certain amount before hand and getting the required service. The newly joined member’s mobile number, and the service what they need will be registered with that particular group. If the particular user’s service is not available with that CC then the request is made to corresponding CC to render the service what the user needs. Then CC will communicate CCH and get the necessary security keys to contact other CC’s or all CC’s. Due to technical problem if any one of the CC is unable/down then automatically a new CC will be elected immediately and the new CC will take of care of the rest of the communication. The Cluster head selection is discussed at the end of this chapter in detail.

Each and every members joining/arrival time will be taken and the members will be joining in that group by comparing the already joined members and the newly joining members. Let us consider Ti and the Tj are the joining time of i and j then their arrival time must be, Ti <= Tj and the clustering has been done by using joining time of the members. In the following diagram the Cluster Controllers CC1, CC2, CC3 and CC4 are controlling the cluster members {M1, M2, M3, M4}, {M5, M6, M7, M8}, {M9, M10, M11, M12} and {M13, M14, M15, M16} respectively. Cluster Controller CC1 maintains the member {M1, M2, M3, M4} based on Arrival Time Ti where i = [1, 2, 3, 4] and T1≤T2 ≤T3≤T4.

Figure 3.3 Shows Cluster with 4 members Limit = 4 Members

CCH

CC1

CC2

CC4

CC3

T3

T2

T6

T9

T7

T10

T1

T5

T8

T4

T11

T12

T13

T14

T15

T16

Cluster 1

Cluster 2

Cluster 3

Cluster 4

M1

M16

M 7

M 8

M 9

M1 0

M11

M12

M13

M14

M15

M2

M3

M4

M 5

M 6

3.3.1.1 CLUSTER FORMATION ALGORITHM

Step 1 : The total number of members in a cluster is equal to the number

of cluster controllers in a group so assign CC.size = M and Initial

= 0

Step 2 : The member who wants to join the group(M1) will send the hello

message along with its ID and the time stamp. The time stamp

will consists of the joining time and the Time-to-Live(TTL)

Step 3 : CC.Time = threshold; {Min.threshold & Max.threshold}

CC checks if its threshold value of its time meets then

{ if { M1.intime < CC. Max.threshold) &&

(M1.intime > CC. Min.threshold)}}

CC -> responds that request is accepted and Initial ++;

Step 4 : repeat Step 2 to 3 until Initial = CC.size

Step 5 : CC calculates GSK and distributes GSK to all M in CC.

3.3.1.3 PERFORMANCE METRICS

Simulation Time

100s

Topology Size

3400m x 1300m

Number Of Nodes

75

MAC Type

MAC 802.11

Initial Energy

100J

Transmit Power

0.4W

Receive Power

0.3W

CBR Rate

512 bytes x 6 per second

Number of Connections

50

Encryption Algorithm

Elliptic curve cryptography

Key Length

128 bits

Key Encryption Time

1.42 msec

Key Generation Time

1.40 msec

Authentication Rate

1441 KB.sec

Memory overhead:

This will be calculated as the

(Total number of root request packet + The control root reply packet) / The total number of control packets

There are four control messages available, request, reply, acknowledgement and error

Throughput = number of packets received in bytes / time in seconds

Packet delivery ratio (PDR) measures the percentage of data packets generated by nodes that are successfully delivered, expressed as

(Total number of data packets successfully delivered) / (Total number of data packets sent) × 100%

End to end latency = inter arrival between first key and second key / total delivery key time Interval = .41s

Packet latency measures the average time it takes to route a data packet from the source node to the hub. It is expressed as Σ Individual data packet latency / Total number of data packets delivered

Energy Consumption: This measure the energy expended per delivered data packet. It is expressed as Σ Energy exhausted by each node / Total number of data packets delivered

4 states idle, sleep, transmit and receive state

3.3.2 POSITION BASED CLUSTERING (PBC)

The main design concept of the proposed position based clustering is that a distributed scheme be used for key generation and management within the particular region to achieve robustness. Since the position based clustering scheme is more suitable for battle oriented group in which the group members must share their secret information’s and communicate with each other securely and opportune for mission execution. The proposed clustering schemes are following one-hop clustering i.e. every member node is at most 1-hop distance away from a central coordinator and also suitable for wired / wireless communication. If wireless communication is considered then the nodes can move freely and even some time network partitioning or merging may also occur. Here the nodes are belonging to a single group not belonging to several groups at a time thus avoiding the operations like key bundling and sending which increases heavily the communication cost and the network traffic. For scalability and efficiency, the proposed position based group key management scheme divides a group into region-based subgroups based on decentralized key management like IGKMP, which uses a single group key for the whole group and this will lead to single point of failure. This draw back is overcome by the subgroup controllers named CC’s, each group member is equipped with GPS and knows its position as it moves across regions. When a member crosses the boundary or leaves the group then automatically the subgroup key called Group Session Key (GSK) and Domain Key (DK) has to be refreshed. In forming the group key each member’s contribution is taken into account thus achieving the robustness as in the distributed key management scheme. Here the contributory key agreement protocol such as ECGDH is used for this purpose. The subgroup size is also very important parameter that determines the cost of group key management.

We have to determine the large region and it has to be divided into small regions based on the location (distance between the members) and the CC. Here the overlapping of clusters is not allowed and the CCH will take care of sending the information to other clusters. The PBC can be achieved by differentiating position or area like Military, Computer Lab, building that contains number of systems, city etc. When military like applications are considered then based on the position only a large group of members is divided and secret information’s are passed between them.

3.3.2.1 CLUSTER FORMATION ALGORITHM

Step 1 : The total number of members in a cluster is equal to the number

of cluster controllers in a group, so assign CC.size = M and initial

= 0

Step 2 : The member who wants to join the group(M1) will send the hello

message along with its ID, location and its public key

Step 3 : CC checks if its threshold value of its time meets then

CC.distance = threshold; {Min.threshold & Max.threshold}

Step 4 : if (M1.location(X,Y) > CC. Min.threshold) &&

(M1.location(X,Y) > CC. Max.threshold)) then CC sends

request Accepted and Initial ++;

Step 5 : repeat Step 2 to 4 until Initial = CC.size

Step 6 : CC calculates GSK and distributes GSK to all M in CC.

We have to determine the area after that we have to calculate the members who are belongs to that particular area. Based on that area we have done clustering and it is said to be as position based clustering.

WS1

WS2

WS3

WS4

WS5

WS5

WS2

WS3

WS4

WS1

WS1

WS2

WS3

WS4

WS5

WS1

WS2

WS3

WS4

WS5

CLUSTER CONTROLLER HEAD

WS5

WS2

WS3

WS4

WS1

Cluster 1

Cluster 5

Cluster 2

Cluster 4

Cluster 3

Cluster Limit = 5 Members

Figure. 5 Position Based Clustering

Figure.5 shows how to perform position based clustering. Here, Group Controller maintains 5 clusters (Namely Cluster 1, 2, 3, 4, and 5). So the limit range of Group Controller is 5.

Simulation Time

100s

Topology Size

3400m x 1300m

Number Of Nodes

75

MAC Type

MAC 802.11

Radio Propagation Range

250m

Initial Energy

100J

CBR Rate

512 bytes x 6 per second

Encryption Algorithm

Elliptic curve cryptography

Key Length

128 bits

Key Encryption Time

1.72 msec

Key Generation Time

1.70 msec

Authentication Rate

1521 KB.sec

3.3.2.3 PERFORMANCE METRICS

3.3.3 KEY BASED CLUSTERING

KBC is constructed in a different way, i.e., not only here considering the location but also the similarities of public key {x1, y1} of the members, clustering is being done. The public key is constructed with the help of the member’s private keys and the contribution to the group key formation is done. KBCis done by grouping the members those are having same key. Each and every member will hold its public & private key pair and also every member will know the group session key for communicating with in the group. This type of clustering is well suited where security is more important [7], [8], [9]. Take the application like online question paper downloading from Internet. For example for downloading the question paper from the Internet then a group people contribution is needed like the head of the institution, the concern institutions university representative and the university representatives. Here every member is giving a part of their key in downloading the question paper from the University.

If security is more important then this type of clustering may consider. Here we are considering not only the position but also the member’s contribution in forming the groups. If any one of the member is leaving/joining the group then automatically a new group key is formed by the CC’s and information will be communicated immediately to the existing members. The session key and the domain key formation is well discussed in [8][9]. Since these clustering schemes supports wired/wireless the asymmetric key cryptography ECC is used in forming the key, exchanging the keys between the members and in key agreement. This ECC is more secure than RSA because even for a smaller key size also this is providing more security.

3.3.3.1 CLUSTER FORMATION ALGORITHM

Step 1 : The total number of members in a cluster is equal to the number

of cluster controllers in a group, so assign CC.size = M and initial

= 0

Step 2 : The member who wants to join the group(M1) will send the hello

message along with its ID, location and its public key

Step 3 : CC checks if its threshold value of its key(X,Y) coordinates

meets then If(CC.X = = M1.X) then respond to the member

request accepted Initial ++;

Step 4 : repeat Step 2 & 3 until the Initial = cluster size limit is met

Step 5 : Calculate GSK where GSK = n * P{ Pkm1 + Pkm2 + …+ Pkmn}

n is the random number and P is number of cluster members

Step 6 : CC calculates GSK and distributes GSK to all M in CC.

Simulation Time

100s

Topology Size

3400m x 1300m

Number Of Nodes

75

Initial Energy

100J

Transmit Power

0.4W

Receive Power

0.3W

CBR Rate

512 bytes x 6 per second

Number of Connections

50

Encryption Algorithm

Elliptic curve cryptography

Key Length

128 bits

Key Encryption Time

1.42 msec

Key Generation Time

1.40 msec

Authentication Rate

1441 KB.sec

Signature rate

512 bits

Signature key length

314 kb /sec

Signature type

ECDSA

BEFORE CLUSTERING

Cluster Limit = 3 Members

GC0

10

11

12

K2

K1

K3

K3

K1

K2

K1

K2

K3

M1

M2

M3

M4

M5

M6

M7

M8

M9

Cluster 1

Cluster 2

Cluster 3 (Groups that are having different Keys)

Figure.3 Before Clustering

From Figure.3, The Cluster Controllers are 10, 11 and 12 and Cluster Members are M1, M2, M3, M4, M5, M6, M7, M8 and M9. Here, the Cluster Controller 10 controls the cluster member M1, M2, M3.

AFTER CLUSTERING

CC0

10

11

12

K1

K1

K1

K3

K2

K2

K3

K3

K2

M2

M5

M7

M1

M6

M9

M3

M4

M8

Cluster 1

Cluster 2

Cluster 3

Cluster Limit = 3 Members

(Groups that are having same Keys using KBC)

Figure.4 After KBC

Figure.4 shows the usage of Key Based Clustering. The structure of above figure can be modified by using KBC. Here the Cluster Controller 10, 11 and 12 controls the cluster members {M2, M5, M7}, {M1, M6, M9} and {M3, M4, M8} respectively.

3.3.3.3 PERFORMANCE METRICS

CLUSTER HEAD SELECTION

For selecting a cluster head, minimal spanning tree algorithm specifically Kruskal algorithm is used because it provides lesser time complexity, power consumption when it is implemented for wireless network and also well suited for wired network too. Since the proposed concept is based on decentralized distributed architecture for that Kruskal is the best spanning tree.

Before selecting or forming the cluster, each node must be assigned with a unique identifier and a timestamp which describes the time of join. Cluster is formed based on any one of the proposed clustering techniques and also considering certain parameters like the transmission range, timestamp, tamper resistance of a node, residual battery power of a node. A Threshold value is also assigned to form a cluster based on the distance among the nodes in the same transmission range. If the length of an edge formed between two nodes is greater than the threshold value then the edge must be removed from the list to form the cluster with same transmission range. Here no overlapping of two heads in the same transmission range. The following algorithm shows how cluster head will be selected after the cluster formed with any one of the proposed technique.

Algorithm :

/* after cluster formation */

Initialize e.threshold = 0;

Initialize c.head = null;

n.list = null;

A node which wants to join a cluster must first transmit its ID with timestamp value.

Calculate neighbor node list for each node ‘u’ in N where N consists of all the nodes in same transmission range.

Find a node ‘v’ in N which has greater neighbor node list and put the node to the set N’. Repeat step 3 until there is no node with greater neighbor list in N

/* e.threshold is the threshold value for energy consumption */

Calculate energy consumption for each node ‘w’ in N’ such that

E = max{ Transmission Range + tamper resistance + ↑ residual battery power + ↑ neighbor list}

c.node = first node in N’;

set e.threshold = c.node’s E;

Find a node ‘u’ in N’ such that ‘u’ has E >e.threshold

c.head = ‘u’;

e.threshold = E;

/* if cluster head fails or leaves the cluster */

Set e.threshold = 0;

Set c.head= null;

Repeat step 8 to 10 until a node ‘w’ in N’-{u} /*where u is acted as previous cluster head*/ has greater E.

/* if all the nodes in N’ left the group then follow the below mentioned steps*/

Find a set S = N – N’

Repeat the steps from 1 to 10

Steps to be followed for selecting a Cluster head

Step 1: Each node is assigned a unique ID.

Step 2: Each node maintains neighbor node lists.

Step 3: Threshold value is set for energy calculations.

Step 4: Energy is calculated based on the tamper resistance, transmission

range of individual node.

E -> Threshold

E = Max {Transmission Range + Tamper resistance + residual battery power

+ neighbor list}

Assumption:

A node with greater tamper resistance is able to act as cluster head.

Neighbor node:

1) 2, 5, 4

2) 1, 5, 3

3) 2, 5, 8

4) 1, 2, 5, 6

5) 1, 2, 3, 4, 6, 7, 8

6) 4, 5, 7

7) 6, 5, 8, 4

8) 3, 5, 7

 Node 5 has greater neighbor list.

Step 1:

N = {set of nodes}

- Find neighbor for each node using kruskal algorithm.

N’ = {V}, ‘V’ has greater neighbor nodes.

Step 2:

 Calculate E for each V in N.

Such that E = Max {Transmission Range + Tamper resistance + residual battery power + neighbor list}

Step 3:

Choose a V which has High E

Step 4:

 If V gets failed / leaves the group, choose a node from N and calculate E.

 If all the N gets failed / leaves the group,

Calculate E for all

In S = {N} – {N’}

 If E of "V" in S is greater than threshold and the high priority then elect "U" as head.

 For this, all nodes must have a field called priority (Based on the time of joining the cluster).

Broadcast Hello message to all nodes. Each node has its own unique ID

Hello Message

ID

Priority

Field

Calculate neighboring nodes of each ‘u’ in N (Using Kruskal). N consists of all nodes in same transmission range

Find a node V in N with large neighbor list and put the node in set N’

Calculate ‘E’ for all nodes in N where E = Max {Transmission Range + Tamper resistance + residual battery power + neighbor list} where Battery power, transmission range and tamper resistance has threshold values.

Choose a node with high E as a cluster head

When a new node wants to join the group then the corresponding new node ‘u’ has to broadcast its id to cluster head. When a cluster head fails / leaves the group then a new cluster head ‘U’ has to be elected with high E in the set of nodes N. The threshold value has to be updated for calculating ‘E’ and now the elected cluster head ‘U’ will have the highest priority.

Theorem: 3.1

Given the set of nodes ‘N’ and the node ‘a’ has lesser power consumption compared to all other nodes in the cluster.

Proof:

Where ‘i’ is the intermediate neighbor between the source ‘a’ and the sink ‘j’.

Denotes the total distance from source to sink.

For calculating the power consumption, we must assume the following:

- denotes the probability of member to leave the group.

- Energy required for

- denotes the average update energy required for updating the group session key GSK and DK. We need this because each member may require different energy expenditure so that is measured.

Theorem: 3.2

The energy consumed to deliver a message to group of member in a cluster is optimal.

Proof:

Assume that:

(i.e.)

- Energy consumed by sub group cluster controller

- Energy consumed by cluster controller head

Key update massages required is for different sub group cluster

Let, be the number of routes.

Proof:

Let

Where n = number of nodes in the tree.

In order to deliver the message, the neighbor nodes must be calculated using

These neighbor nodes are called as c – neighbor and are stored in the set (CN)

For delivering the message, each has to travel through the neighbor node called CNi in the set CN:

Where ‘i’ is the c – neighbor to the sender.

Hence,

Average energy calculated as in Equation 1.

Energy required to deliver a message to sub group is calculated as,

Where N is the number C – neighbor to that sub group

Therefore the energy expenditure for a member to leave the group is calculated as,

Wired/Wireless:

Join =

Leave =

The Ea is calculated as,

C – Neighbor energy expenditure

Where is the probability for the member ‘i’ to leave the group.

The three different schemes and their results were discussed in detail.