Performance Comparison of MISP-based MANET Strong DAD Protocol

Abstract

A broadcast operation is the fundamental transmission technique in mobile ad-hoc networks (MANETs). Because a broadcast operation can cause a broadcast storm, only selected forwarding nodes have the right to rebroadcast a broadcast message among the one-hop and two-hop neighboring nodes of a sender. This paper proposes the maximum intersection self-pruning (MISP) algorithm to minimize broadcasting redundancy. Herein, an example is given to help describe the main concept of MISP and upper bounds of forward node have been derived based on induction. A simulation conducted demonstrated that when conventional blind flooding (BF), self-pruning (SP), an optimized link state routing (OLSR) multipoint relay (MPR) set, and dominant pruning (DP), are replaced with the MISP in executing Strong duplicate address detection (DAD), the performances in terms of the energy consumption, upper bounds of the number of forward nodes, and message complexity have been improved. In addition, to evaluate the performance in reference to the link error probability, P_e, an enhancement was achieved by computing a proposed retransmission limit, S, for error recovery based on this probability. Retransmission limit control is critical for efficient energy consumption of MANET nodes operating with limited portable energy where Strong DAD reacts differently to link errors based on the operational procedures.

1. Introduction

Owing to the quick growth in the number of mobile ad-hoc network (MANET) applications, short-range wireless applications, and robotic networks applications, more powerful and efficient MANET technology is strongly needed. A MANET consists of a set of sensor nodes with routing capability to forward packets. Each sensor host becomes a member of a self-organizing wireless network, where the hosts communicate with one another over multi-hop wireless links without relying on a fixed communication infrastructure, such as a base station or access point. Because a broadcast request can be issued at any time by any host with a packet to be delivered throughout the entire network, a broadcast operation has an important role in a MANET. A single transmission sent by each node will be received by all nodes within the node’s transmission range because the transmission is broadcasted on a wireless channel. All other nodes need to cooperate in propagating the packet by rebroadcasting it because when a sender transmits a packet, all nodes within the sender’s transmission range will be affected by this radio transmission [1].

Address auto-configuration is an important issue because an address pre-configuration is not always possible in a MANET. It is essential that all nodes be able to perform the operations required for the configuration of unique addresses to execute the proper routing of data packets in a MANET. In a conventional network, the address auto-configuration protocol (AAP) is categorized as either a stateless or stateful protocol [2]. The dynamic host configuration protocol (DHCP) is an example of a stateful protocol, where a DHCP server assigns unique addresses to non-configured nodes and maintains the state address information in an address allocation table. In stateless protocols, a node can select an address and verify its uniqueness in a distributed manner using DAD algorithms. Using a DAD algorithm, a node lacking an IP address in an MANET can determine whether the candidate address it selects is available. A node already equipped with an IP address also depends on DAD to protect its IP address from being accidentally used by another node in the MANET. Based on a conventional method [2], DAD can be classified as Strong DAD or Weak DAD. Strong DAD uses an address discovery mechanism where a node randomly selects and requests an address within the MANET, and verifies whether the address is already being used in the network. Based on a reply to the claimed request, which must arrive at the node within a finite-bounded time interval, the node can detect address duplications in the MANET.

To assign a new IP address to a newly joining node, a MANET conducts AAPs based on stateless or stateful approaches, where control messages are generated and transmitted from the source to destination through unicasting, multicasting, or broadcasting. Because a broadcast operation can trigger a broadcast storm when mobile nodes implement AAPs, this paper proposes a novel selective broadcasting technology called maximum intersection self-pruning (MISP), where only selected forwarding nodes have the right to rebroadcast a broadcast message. One of the application areas of this proposed MISP algorithm is in wireless sensor networks (WSNs), where sensor nodes operated by limited portable batteries need to save network costs for network maintenance, and where broadcast storms are a significant issue when delivering control messages. Many factors influence the performance of a MANET. A reduction of the control overhead is always a major concern because it relates to the power consumption of the mobile nodes and takes up a significant portion of the very limited wireless channel resources. One essential measure of the quality of a MANET routing or control protocol is scalability to the increase in MANET nodes.

The remainder of this paper is organized as follows. Section 2 summarizes the characteristics of related works, particularly concerning broadcast technologies and broadcast redundancy. Section 3 proposed several claims and corollaries leading to the mathematical expressions of the proposed algorithm, allowing the readers to easily understand the difference in the operation mechanisms between conventional SP, OLSR MPR Set, and DP algorithms and the proposed MISP algorithm. The big O-notation is used in order to derive the upper bound of the forward node of each protocol. Section 4 describes the numerical experiments conducted along with their results. Finally, Section 5 summarizes this work and provides some concluding remarks. The acronyms used in this paper are summarized in Table 1.

Table 1.Acronym Table

 

2. Related Work

2.1 Selective-Broadcasting Technology

Several selective broadcasting techniques have been proposed to overcome the redundancy of flooding. In [1], the authors addressed the issue of broadcast operations causing a broadcast storm if forwarding nodes are not carefully designated. A dominating set (DS) is a subset of nodes in a network such that every node in the network is either a member node of the DS or a neighboring node of the member node of the DS. A member node of the DS can become a forwarding node when the wireless network does not have an isolated node, and has been fully connected through the wireless connection of the member node.

The concept of an MPR set was proposed to minimize the flooding of broadcast packets by reducing duplicate retransmissions [3]. The MPR set is a subset of one-hop neighbors of node that must cover all of the node’s two-hop neighbors. The OLSR protocol uses Hello messages at each node to discover two-hop neighbor information, and conducts a distributed election of the MPR set.

In [4], the authors suggested that flooding should not be performed blindly, and proposed several schemes, including probabilistic, counter-based, distance-based, location-based, and cluster-based schemes, to reduce redundant rebroadcasts and differentiate their timing. The enhanced partial dominant pruning (EPDP) algorithm was proposed in [5]. Because the total dominant pruning (TDP), partial dominant pruning (PDP), and EPDP cause a defer time and additional IP packet fragmentation before a message is transmitted, additional wireless network resources are consumed. This paper focuses on and analyzes the SP, OLSR MPR, and DP algorithms, which do not experience message segmentation or additional wireless network resource consumption. Considering this concept, the proposed algorithm was developed in a simplistic fashion because there is no defer time or further steps required to broadcast a message. However, it is sufficiently robust to operate within MANET area where the contention-based medium address control (MAC) has been adopted.

2.2 Broadcasting Issue of Address Auto-Configuration Protocols

The Lucent WaveLAN IEEE 802.11 wireless network interface respectively consumes 1,327 and 967 mW of power when transmitting and receiving at a transmission rate of 2 Mbps [6]. In [7], a reduction in the number of broadcast messages is considered. The authors have focused on the concept of efficiency, which is represented as the number of forward nodes, rather than on reliability, which is described as the percentage of nodes receiving a broadcast packet.

In [8], the authors addressed two research approaches, probabilistic and deterministic, to obtain an efficient broadcast. A probabilistic approach uses no or a limited amount of neighbor information and requires high broadcasts to maintain an acceptable packet delivery ratio. A deterministic approach determines the list of forward nodes to guarantee full network coverage. In [9], the authors indicate that, unlike in a wired network, a packet transmitted by a node in an ad hoc wireless network can reach all neighbors. Therefore, the total number of transmissions is used as the performance metric for broadcasting. A node does not forward a broadcast packet if the SP algorithm is satisfied based on the neighborhood information. Although only a set of nodes forward a broadcast packet, this process guarantees complete network delivery. SP-based broadcast protocols collect neighborhood topology information based on a Hello message and form a connected DS through the forward nodes. DP also offers a promising approach to reducing redundant transmissions caused by BF [9], which is considered an approximation to the minimum flood tree problem. In [10], various AAPs for MANET are analyzed. One essential measure of the quality of a MANET protocol is its scalability with regard to an increase in the number of MANET nodes. Message complexity is defined as the overhead of an algorithm measured in terms of the number of messages required to satisfy the algorithm request [10].

2.3 MISP algorithm in Strong DAD

This paper proposes a new SP algorithm called MISP and verifies whether AAP algorithms are able to reduce the broadcast redundancy using this new algorithm. Furthermore, because the improvement achieved when the SP, DP, and MISP replace the conventional BF in the AAP, particularly for Strong DAD, is unknown, the performance is investigated in reference to the message complexity and energy consumption. Because Strong DAD uses additional recursive broadcast mechanisms to resolve duplicated IP addresses compared with other AAPs, the reduction rate achieved by MISP is expected to be significant compared with the reduction rate achieved by the BF, SP, OLSR, and DP algorithms. Therefore, the first objective of this paper is to obtain a quantitative ratio of the percentage of reduction for a broadcasting operation when the selected broadcasting algorithms are used in Strong DAD. The detailed operation of Strong DAD is shown in Fig. 1. This research adopts an analysis of a worst-case scenario [10] to conduct a quantitative analysis of the message complexity, upper bounds of the number of forward nodes, and energy consumption.

Fig. 1.Pseudo code of Strong DAD

2.4 Wireless Channel Condition and Link Error Probability

The wireless communication environment and the mobility of the nodes make a link unstable, thereby resulting in link errors. In this paper, a generalized approach to the link error probability (Pe) is considered. Pe is the same for all inter-node links within each MANET group. We use this type of approach because different mobility and channel models result in different error rates under specific conditions. Therefore, the performance evaluation is dependent on the mobility model and wireless communication environment such as Rayleigh and Rician fading channels used in the computer simulation.

A generalized approach to using Pe provides a level of independence to any mobility model and fading channel. By averaging the link error events to obtain the link error rate, and applying this value to the Pe, the results of this paper are directly applicable to a performance analysis of a MANET that uses a specific mobility model and fading channel [11]. For a given Pe, the retransmission count limit value (S) can be defined based on the network manager’s desired settings, some optimal criteria, and/or the priority of the mobile node. For a given Pe, the average number of transmissions (NTM) required for a successful reception is provided in (1), which can be used as a reference value for the S [11].

Because a link error can stop the propagation of AQ messages, a node that experiences link errors needs to retry broadcasting the AQ message to its neighboring nodes. Point-to-Point (PPP) protocol uses link control protocol (LCP) to negotiate, set up links, and detect link error occurred on the Wide Area Network (WAN) data link where PPP provides a standard method for transporting multiprotocol datagrams over point-to-point links. When the LCP closes the link, it notifies network layer protocols so that they may take appropriate action [12]. Therefore, this paper adopts this kind of notification mechanism from the lower layers such that an IP node can be able to learn of the link failure of a transmission using LCP.

 

3. Proposed Algorithm

3.1 Introduction of Selective-Broadcasting Technology

The broadcast storm problem is a serious issue in a MANET. Hence, several algorithms have been introduced to reduce the number of broadcast messages. In [8], the authors concluded that finding a minimum flood tree that provides the minimum number of forward nodes is nondeterministic polynomial (NP) time-complete [8]. They argued that although a minimum flood tree is constructed, the maintenance cost of the tree in a mobile environment is too high to be useful in practice. The DP algorithm [9] can reduce redundant transmissions using two-hop neighborhood information [8]. Because a source node knows the list of forward nodes, based on its neighboring nodes selected using the SP or DP algorithm, it is not necessary for all neighboring nodes to rebroadcast a packet issued by the source node. Conversely, all neighboring nodes rebroadcast a packet issued by the source node in BF. The SP and DP algorithms can reduce the total number of rebroadcasted packets and rebroadcast nodes compared to BF. By adopting the SP and DP algorithms, the performance of the Strong DAD algorithm when using the decision by the nodes to rebroadcast packets can be evaluated.

There seem to be few studies that have described in a systematic and easy to understand way the exact differences among broadcasting algorithms, such as BF, MPR, SP, and DP, for a sample MANET. Therefore, the following section describes the basic differences between the BF, MPR, SP, and DP algorithms.

3.2 Analysis of SP Algorithm

Fig. 2 (a) and (b) illustrate sample MANETs at an instantaneous time, where the differences among the SP, DP, MPR, and MISP algorithms can be seen. In the SP, when a receiver node (r) receives a packet that piggybacks a neighboring list of a sender node (s), it calculates if the set of N(r) - N(s) is empty. If the set is empty, r does not rebroadcast the packet because N(r) is covered by s. Otherwise, r rebroadcasts the packet.

Fig. 2.Sample networks

Claim 1. The upper bound of the number of forward nodes of SP can be denoted as O(∪ [n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}] for j=1,…, NT and i=1,…, NT) where i is the index number of node (n), j is the index number of neighboring nodes of the node i, and n(i), n(j) indicates the ith and jth node. In addition, when i is used as the index number of outer loop, j is used as the index number of inner loop where i and j are substituted from 1 to NT, respectively and NT indicates the total number of nodes in a network.

Proof. Fig. 2(a) is provided to explain the systematic procedure of the SP. Because node 7 (or n(i) which is ith node when i=1) is a source node, N(s) (or N(i) where i=1, the neighboring nodes of ith node) becomes {1, 2, 7}. Node 1 (or n(j) which is jth node (j=1) when i=1) and node 2 (or n(j) which is jth node (j=2) when i=1) are receiver nodes. Because node 1 (or n(j) which is jth node (j=1) when i=1) is considered to be a receiver node, N(r) (or the neighboring nodes N(j) where j=1, i=1) becomes {1, 2, 4, 6, 7, 10} and N(r) - N(s) equals {4, 6, 10}, which is not a null set. This process can be expressed as ∃n{n:n∈N(j) and n∉ N(i)} because ∃n means there exist nodes such as {4, 6, 10} satisfying the rule of {n:n∈N(j) and n∉ N(i)}. Therefore, node 1 should be a member of the forwarding node (Fn), which can be written as Fn = {1}. This process is represented as ∪(n(i), n(j)) which results in n(j) = {1} because the source node 7 (n(i)) is not counted as forward node. Furthermore, this process can be generalized as ∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}] for j=1, i=1. Because node 2 (or n(j) which is jth node (j=2) when i=1) is considered a receiver node, N(r) (or the neighboring nodes N(j) where j=2, i=1) becomes {1, 2, 4, 6, 7, 10}. Here, N(r) - N(s) equals {4, 6}, which is not a null set. This process can be expressed as ∃n{n:n∈N(j) and n∉ N(i)} because ∃n means there exist nodes such as {4, 6} satisfying the rule of {n:n∈N(j) and n∉ N(i)}. Therefore, node 2 should be a member of Fn, which can be written as Fn = {1, 2}. This process is represented as ∪(n(i), n(j)) which results in n(j) = {2} because the source node 7 (n(i)) is not counted as forward node. Furthermore, this process can be generalized as ∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}] for j=2, i=1.Therefore, the upper bound of the number of forward nodes of the first step can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}]) for j=1,…, NT, i=1.

In the next step, for Fn = {1, 2}, because node 1 (or n(i) which is ith node when i=2) becomes a source node, N(s) (or N(i) where i=2, the neighboring nodes of ith node) becomes {1, 2, 4, 6, 7, 10}. Because node 10 (or n(j) which is jth node (j=1) when i=2) is considered a receiver node, N(r) (or the neighboring nodes N(j) where j=1, i=2) becomes {1, 6, 10}. Here, N(r) - N(s) equals a null set, which violates the rule of ∃n{n:n∈N(j) and n∉ N(i)}. Therefore, node 10 should not be a member of Fn, which can be written as Fn = {1, 2}. This process can be represented as ∪(n(i), n(j)) which results in Fn = {1, 2} because the previous forward nodes found in i=1 have been accumulated. Because node 6 (or n(j) which is jth node (j=2) when i=2) is then considered as a receiver node, N(r) (or the neighboring nodes N(j) where j=2, i=2) becomes {1, 2, 4, 5, 6, 10}. Here, N(r) - N(s) equals {5}, which is not a null set, which complies with the rule of ∃n{n:n∈N(j) and n∉ N(i)}. Therefore, node 6 should be a member of Fn, which can be written as Fn = {1, 2, 6}. This process can be represented as ∪(n(i), n(j)) which results in n(j) = {6} because the source node 1 (n(i)) is already counted as forward node and the forward nodes previously found have been accumulated. Because node 4 (or n(j) which is jth node (j=3) when i=2) is then considered a receiver node, N(r) (or the neighboring nodes N(j) where j=3, i=2) becomes {1, 2, 4, 5, 6}. In this case, N(r) - N(s) equals {5}, which is not null set, which complies with the rule of ∃n{n:n∈N(j) and n∉ N(i)}. Therefore, node 4 should be a member of Fn, which can be written as Fn = {1, 2, 4, 6}. This process can be represented as ∪(n(i), n(j)) which results in n(j) = {4} because the source node 1 (n(i)) is already counted as forward node and the forward nodes previously found have been accumulated. Because node 2 (or n(j) which is jth node (j=4) when i=2) is thus considered to be a receiver node, N(r) (or the neighboring nodes N(j) where j=4, i=2) becomes {1, 2, 4, 6, 7}, and N(r) - N(s) equals a null set, which violates the rule of ∃n{n:n∈N(j) and n∉ N(i)}. Therefore, node 2 should not be a member of Fn, which can be written as Fn = {1, 2, 4, 6}. The upper bound of the number of forward nodes of the second step can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}]) for j=1,…, NT, i=2. Therefore, the upper bound of the number of forward nodes of SP can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}] for j=1,…, NT and i=1,…, NT) which summarizes the upper bounds of the number of forward nodes generated from the first step (i=1) through the last step (i= NT). ■

Corollary 1. A summary of the systematic operation of the SP can be written as below. Nodes 4 and 6 should rebroadcast the message because nodes 4 and 6 have node 5 as a neighboring node. Node 5 receives duplicated messages transmitted from nodes 4 and 6. This operation can be considered a disadvantage of the SP. The following operation yields a termination point of the SP. Although node 2 has already broadcast the message in Step I, in Step II, based on s = 1 and r = 2, yielding the result of a null set, node 2 is not required to rebroadcast the message. This means that node 2 terminates the broadcast at Step II. The following illustrates a comparison between the conventional BF and SP algorithms. In BF, even if the set of N(r) - N(s) is empty, r always rebroadcasts the packet, thereby increasing broadcast redundancy. In the above example, although node 10 achieves a null set result based on s = 1 and r = 10, it broadcasts the message, which results in an increase in network cost.

3.3 Analysis of OLSR Algorithm

Claim 2. The upper bound of the number of forward nodes of OLSR can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}] for j=1,…, NT and i=1,…, NT) where i is the index number of node (n) and j is the index number of neighboring nodes of the node i and n(i), n(j) indicates the ith and jth node.

Proof. Fig. 2(a) is provided to explain the systematic procedure of the MPR set algorithm. In the OLSR algorithm, the MPR set of node 7 (or n(i) which is ith node when i=1, j=1) should cover all two-hop neighbors of node 7, which is {4, 6, 10} (or {N(N(i))-N(i)} where i=1, j=1). To cover node 10 (or n(i) of {N(N(i))-N(i)} where i=1, j=1, one of nodes among n(i)’s two-hop neighboring nodes), node 1 (or N(j), where i=1, j=1, one of nodes among n(i)’s one-hop neighboring nodes) must be the subset of the one-hop neighbors of node 7 (or N(i) where i=1, the neighboring nodes of ith node). Therefore, the MPR set becomes {1}. Fn can be written as Fn = {1}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {1} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. To cover the node 6 (or n(i) of {N(N(i))-N(i)} where i=1, j=2, one of nodes among n(i)’s two-hop neighboring nodes), node 1 and node 2 (or N(j), where i=1, j=2, one of nodes among n(i)’s one-hop neighboring nodes) must be a subset of the one-hop neighbors of node 7 (or N(i) where i=1, the neighboring nodes of ith node). Therefore, the MPR set becomes {1, 2}. Fn can then be written as Fn = {1, 2}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {2} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. To cover node 4 (or n(i) of {N(N(i))-N(i)} where i=1, j=3, one of nodes among n(i)’s two-hop neighboring nodes), the one-hop neighboring nodes 1 and 2 (or N(j), where i=1, j=3) should be the subset of the one-hop neighbors of node 7 (or N(i) where i=1, the neighboring nodes of ith node). Therefore, the MPR set becomes {1, 2}. Fn can thus be written as Fn = {1, 2}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {2} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. Because Fn already includes 2 as its element, for uniqueness, Fn can be written as Fn = {1, 2}. Therefore, the upper bound of the number of forward nodes of the first step can be denoted as O(∪ [n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}]) for j=1,…, NT and i=1.

In the second step, the above procedure is executed recursively for each member node of the MPR set, which is {1, 2} (or n(i) which is ith node when i=2, j=1, 2). The MPR set of node 1 should cover all two-hop neighbors of node 1. To cover node 5 (or n(i) of {N(N(i))-N(i)} where i=2, j=1, one of nodes among n(i)’s two-hop neighboring nodes), node 6 (or N(j), where i=2, j=1, one of nodes among n(i)’s one-hop neighboring nodes) must be a subset of the one-hop neighbors of node 1 (or N(i) where i=2, the neighboring nodes of ith node). Therefore, the MPR set becomes {1, 2, 6}. Fn can be written as Fn = {1, 2, 6}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {6} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. To cover node 5 (or n(i) of {N(N(i))-N(i)} where i=2, j=2, one of nodes among n(i)’s two-hop neighboring nodes), node 4 (or N(j), where i=2, j=2, one of nodes among n(i)’s one-hop neighboring nodes) must be a subset of the one-hop neighbors of node 1(or N(i) where i=2, the neighboring nodes of ith node). Therefore, the MPR set becomes {1, 2, 4, 6}. Fn can then be written as Fn = {1, 2, 4, 6}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {4} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. The upper bound of the number of forward nodes of the second step can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} for j=1,…, NT, i=2. Therefore, the upper bound of the number of forward nodes of SP can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}] for j=1,…, NT and i=1,…, NT) which summarizes the upper bounds of the number of forward nodes generated from the first step (i=1) through the last step (i= NT). ■

Corollary 2. As with the SP algorithm, nodes 6 and 4 are counted recursively in the MPR set to cover node 5. Because node 5 receives duplicate messages transferred from nodes 4 and 6, this can be considered a disadvantage of the OLSR MPR set algorithm.

3.4 Analysis of DP Algorithm

Based on the sample network shown in Fig. 2(a), the detailed procedure of DP can be explained through the following two steps. The first step determines the forward nodes (fn) of the source node based on the information regarding the one-hop and two-hop neighboring nodes of the source node. The second step is identifying the next forward node based on the one-hop and two-hop neighboring node information of the previously found fn. To describe the DP and MISP algorithms, Fig. 3 is provided to illustrate the operational steps of the SP, OLSR, DP, and MISP algorithms. Based on a literature review, the SP, OLSR, DP, and MISP algorithms were shown to identify recursively the forward nodes based on the previously found forward nodes. When the union set of the forward nodes covers the entire network, the SP, OLSR, DP, and MISP algorithms terminate.

Fig. 3.Operational flowchart of SP, OLSR, DP, and MISP algorithms

Claim 3. The upper bound of the number of forward nodes of DP can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}] for j=1,…, NT and i=1,…, NT) where i is the index number of node (n) and j is the index number of neighboring nodes of the node i and n(i), n(j) indicates the ith and jth node.

Proof. The following describes the method used to determine fn based on the information regarding the source node’s one-hop and two-hop neighboring nodes. Here, N(j) is {1, 2, 7}, and N(N(i)) becomes {1, 2, 4, 6, 7, 10} based on Fig. 2(a). The set of the difference between N(N(i)) and N(i), represented as N(N(i)) - N(i), (where i=1, j=1) becomes {4, 6, 10}. For the one-hop neighboring node set of node 7 (or n(i) which is ith node when i=1, j=1), which is {1, 2, 7}, the following procedure indicates what node should be selected as the forward node to efficiently cover the set of N(N(i)) - N(i), that is, {4, 6, 10}. For DP, N(1) ∩ {N(N(i)) - N(i)} is calculated as {1, 2, 4, 6, 7, 10} ∩ {4, 6, 10}, which yields {4, 6, 10}. Because N(1) ∩ {N(N(i))-N(i)} is not a null set, node 1 (or N(j) where i=1, j=1, one of nodes among n(i)’s one-hop neighboring nodes) should be selected as one of the forward nodes, fn={1}. This means that node 1 should be used for broadcasting because this operation has significance in covering the remaining nodes that have not yet been covered.

The forwarding node (Fn) performed by the DP algorithm can be written as Fn = {1}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {1} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}.

Corollary 3. The following summary can be provided based on the observation of the above DP operation. Because N(N(v)) indicates the potential coverage area by node v, N(v) indicates the nodes already being covered by node v, and N(N(v)) - N(v) indicates the nodes to be covered. Here, N(1) ∩{N(N(v)) - N(v)} indicates the number of uncovered nodes (or remaining nodes) that can be covered by the broadcasting of node 1. If the result is a null set, the broadcasting of node 1 is without value because it does not cover any of the remaining nodes. If the result is not a null set, the broadcasting of node 1 is significant because it does cover the remaining nodes.

The same procedure can be adopted if node 2 (or N(j) where i=1, j=2, one of nodes among n(i)’s one-hop neighboring nodes) is selected as the forward node to efficiently cover the set of N(N(i)) - N(i), which is {4, 6, 10}. Therefore, in DP, N(2) ∩ {N(N(i)) - N(i)} is calculated as {1, 2, 4, 6, 7, 10} ∩ {4, 6, 10}, which yields {4, 6, 10}. Because N(2) ∩ {N(N(v)) - N(v)} is not a null set, node 2 (or N(j) where i=1, j=2, one of nodes among n(i)’s one-hop neighboring nodes) is selected as a forward node. This means that node 2 should be broadcasted because it covers the remaining nodes {4, 6, 10}. Because node 2 is newly counted as a forward node, the forward node set becomes fn = {1, 2}. Fn can be written as Fn = {1, 2}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {2} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}.

The same procedure can be adopted to determine whether node 7 (or N(j) where i=1, j=3, one of nodes among n(i)’s one-hop neighboring nodes) should be selected as a forward node to efficiently cover the set of N(N(i)) - N(i), which is {4, 6, 10}. Therefore, in DP, N(7) ∩ {N(N(v)) - N(v)} is calculated as {1, 2, 7}∩{4, 6, 10}, which yields a null set. Because N(7) ∩ {N(N(v)) - N(v)} is a null set, node 7 cannot be selected as a forward node, which means that a broadcasting by node 7 is without value because this action does not cover any of the remaining nodes. Because there is no change in the set of the forward nodes, the forward node set remains as fn = {1, 2}, and is called the first forward nodes. The first step of the DP algorithm is complete at this point. Fn can be written as Fn = {1, 2}. Because there does not exist nodes satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}, this process does not satisfy the requirement of ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}. The upper bound of the number of forward nodes of the firsr step can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} for j=1,…, NT, i=1.

The second step is determining the next forward node based on the information of the previously found fn where the information regarding the one-hop and two-hop neighboring nodes of the previously found fn is used. This begins with the calculation of N(1) ∩ {N(N(i)) - N(i)} and N(2) ∩ {N(N(i)) - N(i)}, where N(1) and N(2) indicate the one-hop neighboring nodes of fn, N(i) indicates the one-hop neighboring nodes of the source node, and N(N(i)) indicates the two-hop neighboring nodes of the source node i, which yield {4, 6, 10} and {4, 6, 10}, respectively. To determine the second forward nodes based on the first forward nodes fn = {1, 2}, N(N(fn)) and N(fn) for node 1 are calculated as {1, 2, 4, 5, 6, 7, 10} and {1, 2, 4, 6, 7, 10}, respectively. The difference in the set of N(N(fn)) - N(fn) is the presence of {5}. The difference in sets N(fn) - N(i), which is {1, 2, 4, 6, 7, 10} - {1, 2, 7}, equals {4, 6, 10}.

Corollary 4. Based on the above selection procedure for forward nodes in the DP algorithm, the observations can be summarized as below. Here, N(N(i)) and N(N(fn)) indicate the potential coverage area by node i in the first forward nodes and by node fn in the second forward nodes, respectively. In addition, N(i) and N(fn) indicate the nodes already covered by node i in the first forward nodes and by node fn in the second forward nodes, N(i) - i and N(fn) - N(i) indicate the first and second forward candidate nodes, and N(N(i)) - N(i) and N(N(fn)) - N(fn) indicate the nodes to be covered for the first and second forward nodes, respectively.

Moreover, N(N(fn)) of node 1 indicates the two-hop neighboring nodes of forward node 1, which are {1, 2, 4, 5, 6, 7, 10}, and N(fn) of node 1 indicates the one-hop neighboring nodes of forward node 1 (or n(i) which is ith node when i=2, j=1), which are {1, 2, 4, 5, 6, 7, 10}. The difference between sets N(N(fn) - N(fn) is {5}. This means that one of the one-hop neighboring nodes of forward node 1, i.e., {4, 6, 10}, could be a candidate node for the second forward node; however, the candidate nodes of the second forward node must include {5} as its one-hop neighboring node.

First, node 4 (or N(j) where i=2, j=1, one of nodes among n(i)’s one-hop neighboring nodes) are determined as {1, 2, 4, 5, 6}. Because node 4 incudes node 5 as its one-hop neighboring node, which should be covered by a forward node, node 4 can be a candidate node. Fn can be written as Fn = {1, 2, 4}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {1} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. The node 6 (or N(j) where i=2, j=2, one of nodes among n(i)’s one-hop neighboring nodes) are then determined as {1, 2, 4, 5, 6, 10}. Because node 6 includes node 5 as its one-hop neighboring node, which should be covered by a forward node, node 6 can be a candidate node of the second forward node. Fn can be written as Fn = {1, 2, 4, 6}. This process can be expressed as ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} because ∃n means there exist nodes such as {1} satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}. In the last step, node 10 (or N(j) where i=2, j=3, one of nodes among n(i)’s one-hop neighboring nodes) are determined as {1, 6, 10}. Because node 10 does not include node 5 to be covered by a forward node, node 10 cannot become a candidate node of the second forward node. Fn can then be written as Fn = {1, 2, 4, 6}. Because there does not exist nodes satisfying the rule of {n:n∈N(j) and n∉{N(N(i))-N(i)}}, this process does not satisfy the requirement of ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}.

The following section illustrates the last step used for selecting the forward nodes. Because the candidate nodes of the second forward node such as nodes 4 and 6 cover the same node 5, there is no need for both nodes 4 and 6 to become a forward node to cover the same node 5. Therefore, only node 4 is selected as a forward node of the second forward node in the DP because node 1 has the information regarding the two-hop neighboring nodes of nodes 4 and 6. The forwarding node (Fn) determined by the DP can thus be written as Fn = {1, 2, 4}. The upper bound of the number of forward nodes of the second step can be denoted as O(∪[n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}} for j=1,…, NT, i=2. Therefore, the upper bound of the number of forward nodes of SP can be denoted as O(∪ [n(i), n(j) only if when ∃n{n:n∈N(j) and n∉{N(N(i))-N(i)}}] for j=1,…, NT and i=1,…, NT) which summarizes the upper bounds of the number of forward nodes generated from the first step (i=1) through the last step (i= NT). ■

3.5 Analysis of MISP Algorithm

Fig. 2(b) is used to describe the proposed MISP, where node 1 is a source node. Here, node 6 locally broadcasts its Hello message to node 1, reporting that its neighbors are N(6) = {1, 2, 6, 7, 8}. Node 8 also broadcasts its Hello message to node 1, reporting that its neighbors are N(8) = {1, 2, 5, 6, 8}. When r = 6, source node 1 calculates N(s) = {1, 4, 6, 7, 8, 9} and N(r) = {1, 2, 6, 7, 8}, and determines N(r) - N(s) = {2}. When r = 8, source node 1 calculates N(s) = {1, 4, 6, 7, 8, 9} and N(r) = {1, 2, 5, 6, 8}, and determines N(r) - N(s) = {2, 5}. Therefore, source node 1 can select node 8 as its forward node because node 8 can cover nodes 2 and 5, whereas node 6 can only cover node 2. In a conventional SP, nodes 6 and 8 are selected as forward nodes. However, in the proposed MISP, only node 8 is selected as the forward node, and node 6 is not selected. This results in a reduction of the number of unnecessary flooding nodes by eliminating the unnecessary forward nodes in each step of the algorithm.

Claim 4. The upper bound of the number of forward nodes of MISP can be denoted as O(∪[max(|n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}| for j=1,…, NT and i=1, …, NT)]) where i is the index number of node (n), j is the index number of neighboring nodes of the node i, n(i), n(j) indicates the ith and jth node, and |∙| represents the number of nodes from the difference in set {N(j)-N(i)}.

Proof. The procedure of the MISP can be written as the seven steps generalized below.

-. Step 1: Calculate {N(j)-N(i)} (or {n:n∈N(j) and n∉ N(i)}) for a neighboring node j of source node i.

-. Step 2: Determine whether {N(j)-N(i)} for j of i is a null set.(or n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}).

-. Step 3: If {N(j)-N(i)} is a null set, stop considering j as a forward node.

-. Step 4: If {N(j)-N(i)} is not a null set, calculate the number of nodes from the difference in set {N(j)-N(i)} (or | n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}| ).

-. Step 5: Repeat the above Steps 1 through 4 for the other neighboring nodes (or | n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}| for j=1,…, NT and i=1).

-. Step 6: Choose node j as the forward node of source node i when it gives the maximum number of nodes from the difference in set {N(j)-N(i)} obtained from Steps 4 and 5 or max(|n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}| for j=1,…, NT and i=1)).

- Step 7: The forward node j chosen becomes the new source node i, and repeat Steps 1 through 6 until the network has been fully covered O(∪[max(|n(i), n(j) only if when ∃n{n:n∈N(j) and n∉ N(i)}| for j=1,…, NT and i=1, …, NT)]). ■

To begin, the proposed MISP calculates the intersection set between N(r) - N(s) of node 6 and N(r) - N(s) of node 8, which can be represented as {2}∩{2,5}, to determine whether the candidate forward nodes such as nodes 6 and 8 cover the same remaining network area. If the intersection set is not a null set, it means that the candidate forward nodes ({2}∩{2, 5} = {2}, which is not a null set) cover the same remaining network area. Therefore, the MISP chooses only one node yielding the maximum number of set elements among the candidate forward nodes. Because N(r) - N(s) of node 6 equals {2}, the number of set elements of N(r) - N(s) of node 6 is 1 and because N(r) - N(s) of node 8 equals {2, 5}, the number of set elements of N(r) - N(s) of node 8 is 2. That is, node 8 provides the maximum number of set elements among the candidate forward nodes 6 and 8. If the intersection set is a null set, it means that the candidate forward nodes (for example, {2}∩{5} = {}, which is a null set), cover a different remaining network area. Therefore, we call the proposed algorithm the maximum intersection SP algorithm, or MISP. The term intersection indicates the verification that the candidate forward nodes cover the same remaining network area, whereas the term maximum illustrates the process of removing the redundancy of rebroadcasting when the candidate forward nodes cover the same remaining network. In the above case, for the three candidate forward nodes, after investigating every intersection set of N(r) - N(s) of the candidate forward nodes of source node u (or forward node u), source node u (or forward node u) selects the forward node that provides the maximum number of element nodes in the set of N(r) - N(s). If the element nodes in the set of N(r) - N(s) of the candidate forward nodes are the same, only one forward node is selected in MISP in order to consider the network coverage. Based on systematic procedure of SP, in the conventional SP, source node 1 selects nodes 4 and 6 as its forward nodes; however, in MISP, node 4 is selected as its forward node in order to consider the network coverage. In here, the selection of node 6 yields same network coverage compared to the network coverage of node 4. Table 2 summarizes the results of the upper bounds of the number of forward node (Fn) and the its real number of forward nodes based on the sample network shown in Fig. 2. It is found that the upper bounds of MPR and DP have the same mathematical expression.

Table 2.Comparison of upper bound of the number of Forward node (Fn) and their number

 

4. Numerical Results and Observations

4.1 Energy Model

For sending a k-bit data packet in a WSN, a model of the energy consumption of the wireless transmitter and receiver was studied in [13]. For a sensor node, to transmit a k-bit packet, the node that operates the radio electronics consumes an energy amount of k∙Eelec, and the transmit power amplifier consumes an energy amount of k∙εamp∙d4 or k∙εfs∙d2, where d indicates the transmission distance between the transmitter and receiver. To receive a k-bit packet, the node operates the radio electronics, where an energy amount of k∙Eelec is consumed [13]. In [13], it was determined that to achieve an acceptable Eb/N0, the radio should dissipate Eelec = 50 nJ/bit to operate the transmitter or receiver circuitry, and εamp =100 pJ/bit/m2 for the transmit amplifier. The equation of the energy consumption was derived in [13], where it was assumed that the squared value of the distance is used for the energy loss owing to the channel transmission in the simulation model. Therefore, to transmit a k-bit message a distance of dnm2 using the radio model, where dnm indicates the distance between a node (n) to its neighboring node (m), the transmitter expends the following:

To receive a k-bit message, the receiver expends

In this research, we used this energy equation to transmit a k-bit message. In the simulation, 10 pJ/bit/m2 was used for εfs, 50 nJ/bit was used for Eelec, and 525 and 1,485 bytes were used as the lengths of a single packet, where 500 and 1,460 bytes are assigned to the data message [14] and 25 bytes is assigned to the packet header. In the simulation, the case of a single node joining the largest clustered network among several clustered sub-networks was evaluated. Clustering is randomly generated based on the network size and transmission range. A computer-based simulator was written to implement the proposed algorithm. During the simulation, the forward node list (F) implemented by the MPR, SP, DP, and MISP algorithms was selected to rebroadcast the messages. Because only the forward nodes in the neighboring list can broadcast a Strong DAD message, it was shown that the message complexities of Strong DAD are significantly reduced compared with the BF method.

The energy consumption of BF is determined based on Equation (4), where each node in the cluster member dissipates energy to locally broadcast packets. Therefore, the total energy consumption of BF is the summation of the energy consumed in each member node, which is represented as Etx_local_broad, where n and m represent member nodes in a cluster.

Because only forward nodes selected by the SP, OLSR, DP, and MISP algorithms have the right to broadcast messages, the energy consumption model of the forward nodes is the same as that of the cluster heads in the energy consumption model in [13], where the forward nodes have the same role as the cluster heads.

Therefore, based on Equations (5) and (6), the energy consumption of the SP, OLSR, DP, and MISP algorithms is composed of two steps, as described below. First, the forward nodes transmit 525-byte and 1,485-byte packets among the forward nodes, which are represented as Etx_cluster in (5). Then, each forward node locally conducts a broadcast represented as Etx_local_dominant in (6). Therefore, the total energy consumption of the SP, OLSR, DP, and MISP algorithms is the summation of the energy consumed in the forward nodes plus the energy consumed during the broadcasting, which can be represented as Etx_cluster + Etx_local_dominant, where i and j represent the forward nodes, and din represents the distance between a forward node i (which is the same as cluster head i) and a cluster member node n. Because every link in a cluster is composed of one hop, the maximum distance between a cluster and the farthest node was selected to reach all member nodes.

4.2 Simulation Environment

The system model used to analyze the proposed MISP algorithm follows the system model introduced in [10]. A standalone MANET environment is required to compare the number of algorithms used, as well as the energy consumption, message complexity, and number of forward nodes among the MPR, SP, DP, and MISP algorithms, where the MANET nodes have no connection to an external network such as the Internet. A computer-based simulator was developed with nodes randomly distributed with a uniform density within a network area of 1 km2. A discrete-event simulator was developed in Matlab to verify the various network topologies and calculate the message complexity and energy consumption. The random node generator and simulator performance verified (number of nodes, 100, 125, 150, and 175) that the average number of nodes per cluster and several of the specifications in the adaptive dynamic backbone (ADB) algorithm [10] matched the results in [10] with less than a 1% difference in most cases, where QualNet was used to simulate ADB.

In our analysis, the conflict probability (Pc) is defined as the probability that the IP address requested by a node is in use in the MANET group. The conflict probability depends on the size of the address and the number of nodes in the MANET group. BF used in the simulation, which is compared to the SP, OLSR, DP, and MISP algorithms, has every node retransmit a message to all of its one-hop neighbors whenever it receives the first copy of a message. In the computer simulation, two values of 0.25 and 0.75 are used for Pe, and a value of 0.5 is used for Pc. In ad hoc networks, it is found that the Transmission Control Protocol (TCP) throughput degradation remains at less than 10 percent for packet error probabilities ranging from 0 to 0.1, especially for one-hop ad hoc networks. This is attributed to the link-level retransmissions of error packets in IEEE 802.11, which can largely reduce the impairment of the channel error. However, the throughput has been severely deteriorated from the range of 0.1 to 1 [14]. Therefore, in this paper, Pe of 0.25 (> 0.1) and Pe of 0.75 (< 1) including the packet loss due to channel errors, MAC layer medium contention, and mobility have been selected from the range of 0.1 to 1. Table 3 summarizes the simulation parameters.

Table 3.Simulation parameters

4.3 Simulation Results

Fig. 4 compares the energy consumption of the BF, SP, OLSR, DP, and MISP when a Strong DAD algorithm is applied with a Pc of 0.5 and a Pe of 0.25 (Fig. 4 (a)) and 0.75 (Fig. 4 (b)) with the packet lengths of 525 and 1,485 Bytes. As it can be expected, in all cases of Pe,, the energy consumption of 1,485 Bytes consumed more energy of 184%, 183%, 182%, 183%, and 182% than the energy consumption of 525 Bytes with BF, SP, OLSR, DP and MISP, respectively. In addition, in all cases of Pe, the total energy consumption of MISP can be reduced by 280%, 163%, 123%, and 23% compared with the BF, SP, OLSR, and DP, respectively.

Fig. 4.Energy consumption of BF, SP, OLSR, DP, and MISP

Fig. 5 illustrates the upper bounds of the number of forward nodes among BF, SP, OLSR, DP, and MISP when the Strong DAD algorithm is applied with a Pc of 0.5 and with a Pe of 0.25 and 0.75 with the packet lengths of 525 and 1,485 Bytes. In all cases of Pe the upper bounds of the number of forward nodes of MISP can be reduced by 107%, 65%, 51%, and 11% compared with the BF, SP, OLSR, and DP, respectively.

Fig. 5.Upper bounds of the number of forward nodes (Packet lengths of 525 and 1,485 Bytes)

Fig. 6 illustrates the message complexity among BF, SP, OLSR, DP, and MISP when the Strong DAD algorithm is applied with a Pc of 0.5 and with a Pe of 0.25 and 0.75 with the packet lengths of 525 and 1,485 Bytes. The message complexity of MISP can be reduced by 98%, 61%, 48%, and 10% compared with the BF, SP, OLSR, and DP algorithms, respectively. Because the optimal design of packet fragmentation is beyond the scope of this paper, 525 and 1,485 Bytes of packet lengths did not affect to the results of upper bounds of the number of forward nodes and message complexities, but affect to the results of energy consumption.

Fig. 6.Message complexity (Packet lengths of 525 and 1,485 Bytes)

4.4 Observation

Figs. 4, 5, and 6 show that, in the case of Pe =0.75, the energy consumption, the number of forward nodes, and the message complexity of BF, SP, OLSR, DP, and MISP in Strong DAD have been increased nearly 200% compared to the case of Pe =0.25. It was also shown that in the case of Pe =0.75, the energy consumption, message complexity, and number of forward nodes of the BF, SP, OLSR, DP, and MISP in Strong DAD are increased nearly 50% compared to the case of Pe = 0.25. Therefore, it can be stated that with an increased degree of link error probability (Pe), the network cost used for recovering from the link failure is increased. For a given Pe, the mechanism of re-broadcasting (e.g., AQ) and re-unicasting (e.g., AP) messages result in different control signaling overhead in the Strong DAD protocol, and finally causes increased energy consumption and an increased number of forward nodes in the network. The main contribution of this paper is that when the Strong DAD algorithm is applied to configure the IP address in a MANET automatically, the proposed MISP algorithm significantly reduces the consumption of energy, the number of forward nodes, and the message complexity.

Because the performance of the MISP is much better than that of the DP, the steps of which are much more complex that those of MISP, this paper focuses on this factor as an important contributor. The amount of network resources is saved by reducing the number of unnecessary flooding nodes when the Strong DAD is applied along with the MISP. The main idea of MISP comes from an earlier examination to determine whether nodes can become candidate forward nodes. The earlier elimination of nodes from the set of candidate forward nodes reduces of the number of unnecessary flooding nodes. In addition, the MISP adopts the concept of an intersection to verify that when the candidate forward nodes cover the same remaining network, the MISP finds the node that covers the maximum amount of network area by removing redundancy in the rebroadcasting.

 

5. Conclusion

The proposed MISP algorithm was modified and updated from a conventional SP algorithm to minimize the retransmissions of broadcasting operations, where only selected forwarding nodes among one-hop neighboring nodes of the sender have the right to rebroadcast a broadcast message when a generalized approach to the link error probability is considered. The proposed MISP algorithm is equipped with a novel property, i.e., an intersection operation is conducted to verify whether the areas covered by the candidate forward nodes are the same as the network area. By implementing an intersection operation into a conventional SP algorithm, unnecessary forward nodes are eliminated and the network resource requirements for broadcasting a message are reduced. When the number of intersected nodes (or covered nodes) incurred by the broadcasting of candidate forward nodes is the same, the MISP algorithm selects one candidate forward node in order to consider the network coverage. An example is given to help describe the main concept of MISP. Upper bounds of the number of forward node have been derived based on induction. It is found that the upper bounds of the number of MPR and DP forward nodes have the same mathematical expression. It was determined that the MISP algorithm yields a smaller number of forward nodes compared to the SP, OLSR, and DP algorithms because the MISP algorithm reduces the number of candidate forward nodes that need to be examined. Moreover, the total energy consumption of MISP can be reduced by 280%, 163%, 123%, and 23% compared with the BF, SP, OLSR, and DP algorithms, respectively. The proposed MISP algorithm also saves 107%, 65%, 51%, and 11% in the number of forward nodes compared to the BF, SP, OLSR, and DP algorithms, respectively. A simulation indicated that the MISP-based Strong DAD algorithm reduces the number of broadcasting nodes by 107% compared to a conventional Strong DAD with BF within a transmission range of 300 m when the link error probability is considered. Moreover, the proposed MISP algorithm saves 98%, 61%, 48%, and 10% in message complexity compared to the BF, SP, OLSR, and DP algorithms, respectively. As a future research, because adopting selective-broadcasting technologies may not guarantee giving the maximized network connectivity, the combined research between the selective-broadcasting and network connectivity algorithms could be conducted. In addition, as usual in WSNs, the research on the lifetime extension for the selected forward nodes can be another topic because the nodes tend to consume more power in order to service (transfer or relay) packets coming from their neighboring nodes. Because this research has mainly focused on designing the efficient energy consumption instead of providing quality of service (such as low error rates, high bandwidth, high throughput, low transmission delay, and low jitter, etc.), there might be several trade-off settings between the energy consumption and the quality of service in controlling protocols according to the purpose of network design.