Converge Cast: On the Capacity and Delay Tradeoffs

In this paper, we define an ad hoc network where multiple sources transmit packets to one destination as Converge-Cast network. We will study the capacity delay tradeoffs assuming that n wireless nodes are deployed in a unit square. For each session (the session is a dataflow from k different source nodes to 1 destination node), k nodes are randomly selected as active sources and each transmits one packet to a particular destination node, which is also randomly selected. We first consider the stationary case, where capacity is mainly discussed and delay is entirely dependent on the average number of hops. We find that the per-node capacity is Θ (1/√(n log n)) (given nonnegative functions f(n) and g(n): f(n) = O(g(n)) means there exist positive constants c and m such that f(n) ≤ cg(n) for all n ≥ m; f(n)= Ω (g(n)) means there exist positive constants c and m such that f(n) ≥ cg(n) for all n ≥ m; f(n) = Θ (g(n)) means that both f(n) = Ω (g(n)) and f(n) = O(g(n)) hold), which is the same as that of unicast, presented in (Gupta and Kumar, 2000). Then, node mobility is introduced to increase network capacity, for which our study is performed in two steps. The first step is to establish the delay in single-session transmission. We find that the delay is Θ (n log k) under 1-hop strategy, and Θ (n log k/m) under 2-hop redundant strategy, where m denotes the number of replicas for each packet. The second step is to find delay and capacity in multisession transmission. We reveal that the per-node capacity and delay for 2-hop nonredundancy strategy are Θ (1) and Θ (n log k), respectively. The optimal delay is Θ (√(n log k)+k) with redundancy, corresponding to a capacity of Θ (√((1/n log k) + (k/n log k)). Therefore, we obtain that the capacity delay tradeoff satisfies delay/rate ≥ Θ (n log k) for both strategies.