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A Novel Efficient Traffic Estimation Strategy Using Hello Messaging Through Local Link Connectivity in MANETs

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Abstract

Network traffic estimation under random mobility of network nodes is one of the key challenges for effective communication in mobile ad hoc networks (MANETs). Under random movement of network nodes and uniform distribution of path durations among neighboring nodes, there must be a unified model to determine an adequate network traffic estimation strategy in MANETs. In this paper, a local link connectivity model that guarantees effective communication among the neighboring nodes inside a cluster is presented. Furthermore, a novel efficient traffic estimation (ETE) strategy is presented using a Markov chain process and Hello messaging through local link connectivity among neighboring nodes under uniform speed and random trajectories of mobile nodes. It has been observed that the ETE strategy is affected by the transmission rate of Hello messages, link probability at current time step of the Markov process, expected number of nodes inside a cluster, received signal strength, and probability of successful reception of the expected Hello messages at next time step of the Markov process. An expected increase in the critical transmission range of a network node as a result of possible overlapping with its neighboring nodes inside the cluster due to random mobility has also been investigated. Analytical and simulation results demonstrate efficacy of the proposed ETE strategy in terms of successful reachability of transmitted Hello messages, mean connection time, mean CH degree, queuing delay, and load balancing. In addition, the ETE strategy achieves better local link connectivity among neighboring nodes, lower Hello messages transmission latency, and better throughput in terms of successful reception of Hello messages by a neighboring node.

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Correspondence to Alamgir Naushad.

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Appendix

Appendix

1.1 Proof of Equation (26)

For a discrete random variable L, which represents l successes in any experiment of N trials, the probability mass function (PMF) can be written as

$$\begin{aligned} P(L=l)= {N\atopwithdelims ()l}a^{l}b^{N-l}; \quad 0\le l\ge N, \end{aligned}$$
(41)

where a represents probability of successful reception of a Hello message by an NN and \(b=1-a\), which describes the unsuccessful reception of HMs.

Hence, Eq. (40) can be rewritten as

$$\begin{aligned} P(L=l)= {N\atopwithdelims ()l}a^{l}(1-a)^{N-l}. \end{aligned}$$
(42)

Now, for the maximum number of HM transmission retries, \(t_{tot}\), the local link connectivity probability is given by

$$\begin{aligned} P(L)= 1-\left( 1-P(r/p_{r})\right) ^{t_{tot}}. \end{aligned}$$
(43)

Now rearranging Eq. (42), we get

$$\begin{aligned} \left( 1-P(r/p_{r})\right) ^{t_{tot}}= 1-P(L). \end{aligned}$$
(44)

By comparing Eq. (43) with Eq. (41), we obtain

$$\begin{aligned} P(L=l)= {N\atopwithdelims ()N-t_{tot}}\left( P\left( r/p_{r}\right) \right) ^{N-t_{tot}}\left( 1-P(r/p_{r})\right) ^{t_{tot}}. \end{aligned}$$
(45)

The mean, \(\mu _{1}\), and variance, \(\sigma ^{2}\), of L are given, respectively, by

$$\begin{aligned} \mu _{1}= N\left( P(r/p_{r})\right) , \end{aligned}$$
(46)

and

$$\begin{aligned} \sigma ^{2}= N\left( P\left( r/p_{r}\right) \right) \left( 1-P(r/p_{r})\right) . \end{aligned}$$
(47)

For the expected value of this distribution, i.e., \(N(a)\cong 1\), Eq. (44) is approximated to

$$\begin{aligned} P(L)=\frac{N\left( P\left( r/p_{r}\right) \right) }{(N-t_{tot})!}\exp \left( -N\left( P\left( r/p_{r}\right) \right) \right) . \end{aligned}$$
(48)

Now substituting \(P\left( r/p_{r}\right) = 1-(1-P_{L})^\frac{1}{t_{tot}}\) for \(\sigma\), we get

$$\begin{aligned} \sigma =\sqrt{2N\left( 1-\left( 1-P_{L}\right) ^\frac{1}{t_{tot}}\right) \left( 1-\left( 1-\left( 1-P_{L}\right) ^\frac{1}{t_{tot}}\right) \right) }. \end{aligned}$$
(49)

\(P_{L}=0.5\) represents the minimum probability that transmission of an HM is successful by an NN. By substituting this value in Eq. (48), we get

$$\begin{aligned} \sigma = \sqrt{2N\left( 1-(0.5)^\frac{1}{t_{tot}}\right) \left( 1-\left( 1-(0.5)^\frac{1}{t_{tot}}\right) \right) }. \end{aligned}$$
(50)

Similarly, \(\mu _{1}\) in Eq. (46) becomes

$$\begin{aligned} \mu _{1}=N\left( 1-(0.5)^\frac{1}{t_{tot}}\right) . \end{aligned}$$
(51)

Consequently, Eq. (47) becomes

$$\begin{aligned} P(L)=\frac{\left( N\left( 1-(0.5)^\frac{1}{t_{tot}}\right) \right) ^{N-t_{tot}}}{(N-t_{tot})!}\exp \left( -N\left( 1-(0.5)^\frac{1}{t_{tot}}\right) \right) . \end{aligned}$$
(52)

This completes the proof of Eq. (26).

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Abbas, G., Abbas, Z.H. & Naushad, A. A Novel Efficient Traffic Estimation Strategy Using Hello Messaging Through Local Link Connectivity in MANETs. Wireless Pers Commun 109, 1033–1070 (2019). https://doi.org/10.1007/s11277-019-06603-8

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