Delay and Capacity Tradeoff Analysis for MotionCast

In this paper, we define multicast for an ad hoc network through nodes´ mobility as MotionCast and study the delay and capacity tradeoffs for it. Assuming nodes move according to an independently and identically distributed (i.i.d.) pattern and each desires to send packets to k distinctive destinations, we compare the delay and capacity in two transmission protocols: one uses 2-hop relay algorithm without redundancy; the other adopts the scheme of redundant packets transmissions to improve delay while at the expense of the capacity. In addition, we obtain the maximum capacity and the minimum delay under certain constraints. We find that the per-node delay and capacity for the 2-hop algorithm without redundancy are Θ(1/k) and Θ(n log k), respectively; for the 2-hop algorithm with redundancy, they are Ω(1/k√(n log k)) and Θ(√(n log k)), respectively. The capacity of the 2-hop relay algorithm without redundancy is better than the multicast capacity of static networks developed by Li [IEEE/ACM Trans. Netw., vol. 17, no. 3, pp. 950-961, Jun. 2009] as long as k is strictly less than n in an order sense, while when k=Θ(n), mobility does not increase capacity anymore. The ratio between delay and capacity satisfies delay/rate ≥ O(nk log k) for these two protocols, which are both smaller than that of directly extending the fundamental tradeoff for unicast established by Neely and Modiano [IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1917-1937, Jun. 2005] to multicast, i.e., delay/rate ≥ O(n k²). More importantly, we have proved that the fundamental delay-capacity tradeoff ratio for multicast is delay/rate ≥ O(n log k), which would guide us to design better routing schemes for multicast.