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

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

2009-07-31

arxiv.org/abs/0907.5489v2

Computer Science

Networking and Internet Architecture

12 pages,8 figures, conference

Scientific paper

This paper studies the delay constrained multicast capacity of large scale mobile ad hoc networks (MANETs). We consider a MANET consists of $n_s$ multicast sessions. Each multicast session has one source and $p$ destinations. The wireless mobiles move according to a two-dimensional i.i.d. mobility model. 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. Given the delay constraint $D,$ we first prove that the capacity per multicast session is $O(\min\{1, (\log p)(\log (n_sp)) \sqrt{\frac{D}{n_s}}\}).$ 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 $\lim_{n\to \infty} f(n)/g(n)=0;$ and $f(n)=\omega(g(n))$ means that $\lim_{n\to \infty} g(n)/f(n)=0.$ We then propose a joint coding/scheduling algorithm achieving a throughput of $\Theta(\min\{1,\sqrt{\frac{D}{n_s}}\}).$ Our simulations show that the joint coding/scheduling algorithm achieves a throughput of the same order ($\Theta(\min\{1, \sqrt{\frac{D}{n_s}}\})$) under random walk model and random waypoint model.

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