# Effective Link Operation Duration: a New Routing Metric for Mobile Ad Hoc Networks

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3 should have a uniform distribution. Then, we can determine f Z {z} for the following distinct cases: Case :if the relative distance between nodes A and B stays fixed during their movement, the average Θ for the link during the prediction period is with d t = e d 2 x + d 2 y; Pth P t d α t (5) Case 2:if the two nodes only move away from each other during the prediction period, the pdf of Z is 0, z < d t ; f Z {z} = R d t, d t z R; (6) 0, z > R. The average Θ for the link in connection is R e P t z α dz. (7) R d t d t For example, when α = 2, π 2ρ(R d t ) [Φ(ρR) Φ(ρd t)] (8) P where ρ = th P t, and Φ(x) = 2 x π dt; 0 e t2 Case 3:if the two nodes first move toward each other, then apart some time later, the pdf of Z is 2 d, z < d t+r t; f Z {z} = d, d t+r t z R; (9) 0, z > R. The average Θ for the link in connection is For α = 2, + + dt 0 R d t P 2 th d t + R e P t Z α dz (0) d t + R e P t Z α dz. π ρ(d t + R) Φ(ρd t) () π 2ρ(d t + R) (Φ(ρR) Φ(ρd t)). Then, for these three cases, we can estimate the ELOD for a link l as D l = T f E[Θ]. (2) IV. ROUTING PROTOCOL WITH ELOD In this section, we describe how to incorporate the ELOD into the routing protocol. We implement ELOD in and call it -ELOD. We define D r, the ELOD for a path r, as the minimum ELOD over all links in the path, such that D r = min l r [D l ]. Using ELOD as the routing metric, we will obtain paths composed of links with longer durations, free of fading. However, such a path might have many more hops than the shortest one. When packet relaying involves more hops, since the radio channel is shared among neighbouring nodes in the network, it will increase medium access contention, interference, congestion, and packet collisions. Therefore, path length should also be considered when selecting a suitable path based on stability. A. Routing Metric First, we illustrate the impact of path length on network performance. Assume that there are N nodes in an ad hoc network which are independently and uniformly distributed in a rectangular area L 2 with length L on each edge. The node spatial intensity is λ = N/L 2. For a node with transmission range R, the average number of neighbours is n = λπr 2. Assume C is the number of connections in the network. Tthe expected distance between source and destination for each connection is L 3 ( 2+ln(+ 2)) [3]. The expected number of hops H required to deliver a packet can be approximated as H = ( 2 + ln( + 2))L. (3) 3R Thus, the maximum number of nodes in the network which might be involved in packet deliveries is N a = { HC, HC < N; N, HC N. (4) Then, the probability that a node has packets to transmit is N a /N. In networks using the IEEE 802. distributed coordination function (DCF), nodes within each other s transmission ranges cannot transmit at the same time. When operating under heavy traffic conditions (every node always has packets to transmit), 802. DCF provides long term per packet fairness in single-hop networks [4]. Thus each node in the shared radio has a probability of /n of occupying the channel. Combining the probability that a node has packets to transmit, the average node transmission probability is N a /(nn). For a transmitting node on an active path, the probability that it can occupy the channel, or the probability that the channel won t be occupied by any of the n neighbours, is q = N a(n ). (5) nn For transmission over one-hop, q is the average achievable throughput due to channel access contention. Assume a path is composed of h hops. The average achievable path throughput Ψ is ( Ψ = D r q h = D r N ) h a(n ). (6) nn The throughput, Ψ, combines the impacts of ELOD and path length. In -ELOD, we use Ψ as the routing metric to select stable paths with higher throughput. B. The Proposed Routing Protocol -ELOD We implement the routing metric, Ψ, into routing protocol -ELOD. The routing path establishment and maintenance procedure of -ELOD is similar to that of.

6 [6] W. Su and M. Gerla, IPv6 flow handoff in ad hoc wireless networks using mobility prediction, GLOBECOM 99, vol. A, pp , 999. [7] S. Jiang, D. He, and J. Rao, A prediction-based link availability estimation for routing metrics in MANETs, IEEE/ACM Transactions on Networking, vol. 3, no. 6, pp , [8] M. Gerharz, C. de Waal, M. Frank, and P. Martini, Link stability in mobile wireless ad hoc networks, In Proceedings of IEEE Conference on Local Computer Networks, Nov [9] W. C. Jakes, Microwave mobile communications, 2nd, Ed. WILEY INTERSCIENCE, 200. [0] T. S. Rappaport, Wireless communications, principles and practice, 2nd ed. Prentice Hall, [] M. Haenggi, Routing in ad hoc networks - a wireless perspective, BroadNets, pp , [2] J. Broch et al, A performance comparison of multi-hop wireless adhoc network routing protocols, MOBICOM, pp , Oct [3] S. Panichpapiboon, G. Ferrari, and O. K. Tonguz, Optimal transmit power in wireless sensor networks, IEEE Transactions on Mobile Computing, vol. 5, no. 0, pp , [4] M. Heusse, F. Rousseau, G. Berger-Sabbatel, and A. Duda, Performance anomaly of 802.b, INFOCOM, vol. 2, pp , [5] [6] R. J. Punnoose, P. V. Nikitin, and D. D. Stancil, Efficient simulation of Ricean fading within a packet simulator, Vehicular Technology Conference, vol. 2, pp , Sep

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