Multicast Scaling Law in Multichannel Multiradio Wireless Networks

Abstract

This paper addresses the issue of multicast scaling performance in multichannel multiradio (MC-MR) networks. Under the assumption of both limited bandwidth and node tunability, a total fixed bandwidth W is equally split into c channels with 0 <; m ≤ c interfaces equipped on each node for channel switching. The network contains totally n nodes, each serving as a source with k randomly and uniformly selected destinations. We try to give a comprehensive picture of multicast scalings by investigating both the static and mobile networks, with the metrics being capacity and delay. Previous literature [9] has indicated that unicast capacity is solely determined by the ratio of channels to interfaces c/m in MC-MR networks. However, in multicast our problem is made more complicated by the interplay among k, c/m and node mobility (if considered in mobile scenario). We characterize their impact on multicast scaling and obtain three remarkable findings from our results. First, we find capacity loss exists in static networks even if the ratio c/m = O(log n) (We use the following notation throughout our paper: f(n) = O(g)(n))⇔ limsupn→∞g(n)/f(n)<; ∞, f(n) = Ω(g(n) ⇔ lim infn→∞g(n)/f(n) <;, ∞ f(n) = Θ(g(n)) ⇔ f(n) = O(g(n)) and g(n) = O(f(n)), f(n) = Θ(·): The corresponding order Θ(·) which contains a logartihmic order.) when k is close to Θ(n). This differs from unicast that is free of capacity loss as long as c=m 1/4 O(log n). Second, mobility is manifested to improve multicast capacity in MC-MR networks, where two major capacity bottlenecks, i.e., connectivity and interference constraints, in static networks can be effectively broken. Third, a largely reduced delay is possible by simply seeking for multichannel reuse in 2-hop algorithm without redundancy. This even outperforms the delay scaling in single channel framework [26], where a delay smaller than Θ(√n long k) is not achievable even with more than Θ(√n log k) relay nodes involved in 2-hop mode. As a high-level summary of our results, our work discloses analytically where the performance improvement and degradation exhibit in MC-MR networks, meanwhile unifying the previous bounds on unicast (setting k 1/4 1) in [9].