No abstract

Abstract-We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)-casting as a generalization of all forms of one-to-one, one-to-many and many-to-many information dissemination in wireless networks. In this context, n, m, and k denote the total number of nodes in the network, the number of destinations for each communication group, and the actual number of communication-group members that receive information (i.e., k ≤ m), respectively.We compute upper and lower bounds for the (n, m, k)-cast throughput capacity in random wireless networks. When m = k = Θ(1), the resulting capacity equals the well-known capacity result for multi-pair unicasting by Gupta and Kumar. We demonstrate that Θ(1/ √ mn log n) bits per second constitutes a tight bound for the capacity of multicasting (i.e., m = k < n) when m ≤ Θ (n/(log n)). We show that the multicast capacity of a wireless network equals its capacity for multi-pair unicasting when the number of destinations per multicast source is not a function of n. We also show that the multicast capacity of a random wireless ad hoc network is Θ (1/n), which is the broadcast capacity of the network, when m ≥ Θ(n/ log n). Furthermore, we show that Θ( √ m/(k √ n log n)), Θ(1/(k log n)) and Θ(1/n) bits per second constitutes a tight bound for the throughput capacity of multicasting (i.e., k < m < n) when Θ(1) ≤ m ≤ Θ (n/ log n), k ≤ Θ (n/ log n) ≤ m ≤ n and Θ (n/ log n) ≤ k ≤ m ≤ n respectively.

No abstract

The conventional approach to routing in computer networks consists of using a heuristic to compute a single shortest path from a source to a destination. Single-path routing is very responsive to topological and link-cost changes; however, except under light traffic loads, the delays obtained with this type of routing are far from optimal. Furthermore, if link costs are associated with delays, single-path routing exhibits oscillatory behavior and becomes unstable as traffic loads increase. On the other hand, minimumdelay routing approaches can minimize delays only when traffic is stationary or very slowly changing.We present a "near-optimal" routing framework that offers delays comparable to those of optimal routing and that is as flexible and responsive as single-path routing protocols proposed to date. First, an approximation to the Gallager's minimum-delay routing problem is derived, and then algorithms that implement the approximation scheme are presented and verified. We introduce the first routing algorithm based on link-state information that provides multiple paths of unequal cost to each destination that are loop-free at every instant. We show through simulations that the delays obtained in our framework are comparable to those obtained using the Gallager's minimum-delay routing. Also, we show that our framework renders far smaller delays and makes better use of resources than traditional single-path routing.

No abstract