Throughput and Delay with Network Coding in Hybrid Mobile Ad Hoc Networks: A Global Perspective

Abstract

In this paper, we study throughput and delay scaling laws of wireless networks with network coding under different mobility models. Specifically, we consider 2-hop and multi-hop schemes with n nodes and k original packets for each pair of source-destination. We consider two ad hoc network mobility models- hybrid random walk models (HRWM) and discrete random direction models (DRDM). For the hybrid random walk models, we divide the unit square into n ^2β cells with an area of 1/n ^2β, where 0 ≤ β ≤ 1/2, each cell is further divided into n ^{1 − 2β} subcells. For the discrete random direction models, the unit square is divided into n ^2α cells with an area of 1/n ^2α, where 0 ≤ α ≤ 1/2. At the beginning of each time slot, every node moves from its current cell to the adjacent cell. We find that (1) under 2-hop relay scheme with network coding, there is a logn gain on delay only when the mobility model is random walk model; (2) under multi-hop relay scheme, there is a turning point and a critical turning point for delay in these two models. For hybrid random walk models, we take k = Θ(n ^β), and obtain that the delay is halved by the turning point β = 1/4. Compared to the network without network coding, our results show that there is a critical turning point β = 1/5, which means when 0 ≤ β < 1/5, the delay will be better without network coding for the network, and when 1/5 ≤ β ≤ 1/2, network coding helps decrease the delay. The same results also hold in discrete random direction models. At last, we propose the network model with network coding and infrastructure mode together. And in this mode, we obtain the results of throughput and delay.