On Delay Constrained Multicast Capacity of Large-Scale Mobile Ad Hoc Networks

Abstract

This paper studies the delay constrained multicast capacity of large-scale mobile ad hoc networks (MANETs). We consider a MANET that consists of $n_{s}$ multicast sessions. Each multicast session has one source and $p$ destinations. Each source sends identical information to the $p$ destinations in its multicast session, and the information is required to be delivered to all the $p$ destinations within $D$ time-slots. Assuming the wireless mobiles move according to a 2-D independently and identically distributed mobility model, we first prove that the capacity per multicast session is $O(\min \{1, (\log p)(\log (n_{s}p)) ({{D}/{n_{s}}})^{1/2}\})$ . 1 We then propose a joint coding/scheduling algorithm achieving a throughput of $\Theta (\min \{1,{({D}/{n_{s}})}^{1/2}\})$ . Our simulation results suggest that the same scaling law also holds under random walk and random waypoint models. 1 Given non-negative functions $f(n)$ and $g(n)$ : $f(n)=O(g(n))$ means there exist positive constants $c$ and $m$ such that $f(n) \leq cg(n)$ for all $ n\geq m;~f(n)=\Omega (g(n))$ means there exist positive constants $c$ and $m$ such that $f(n)\geq cg(n)$ for all $n\geq m;~f(n)=\Theta (g(n))$ means that both $f(n)=\Omega (g(n))$ and $f(n)=O(g(n))$ hold; $f(n)=o(g(n))$ means that $\lim _{n\rightarrow \infty } f(n)/g(n)=0$ ; and $f(n)=\omega (g(n))$ means that $\lim _{n\rightarrow \infty } g(n)/f(n)=0$ .