Multicast capacity and delay trade-offs in ad hoc networks with random iid mobility model

Abstract

In this paper, multicast capacity and delay trade-offs of mobile ad hoc networks are considered under random independently and identically distributed (iid) mobility model. Compared with unicast, multicast can reduce the overall network load by a factor $\Theta \left( {\sqrt k } \right)$ with high probability (whp) in static random ad hoc networks, where k is the number of destination nodes in a multicast session. So we firstly discuss whether the law still holds in mobile random ad hoc networks, and in this case what delay should be tolerated. Through the relation between average retransmissions and multicast capacity, we prove that $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} {\sqrt k }}} \right. \kern-\nulldelimiterspace} {\sqrt k }}} \right)$ order of multicast capacity is not achievable whp, and delay for $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} {\sqrt k }}} \right. \kern-\nulldelimiterspace} {\sqrt k }}} \right)$ multicast capacity is $\Omega \left( {K{n}^K } \right)$, where $n$ is the number of ad hoc nodes in the whole networks, and $K = \left\lceil {{{\sqrt {k} } \mathord{\left/ {\vphantom {{\sqrt {\rm k} } {\rm c}}} \right. \kern-\nulldelimiterspace} {c}}} \right\rceil$ and c is a positive constant. Then achievable throughput whp is considered. The nearest neighbor transmission strategy is introduced by Grossglauser and Tse to achieve $\Theta \left( {\rm 1} \right)$ throughput which is so far the highest achievable unicast capacity. So the multicast capacity of mobile ad hoc networks under this strategy is studied. The analysis shows that under any multicast routing scheme based on the nearest neighbor transmission strategy, the upper bound on multicast capacity is $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} k}} \right. \kern-\nulldelimiterspace} k}} \right)$ whp. Then we propose a multicast routing and scheduling scheme by which mobile ad hoc networks can achieve $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} k}} \right. \kern-\nulldelimiterspace} k}} \right)$ throughput whp, and must tolerate $\Theta \left( {{kn}} \right)$ total network delay. Copyright © 2009 John Wiley & Sons, Ltd. Multicast capacity and delay trade-offs of mobile ad hoc networks are considered under random independently and identically distributed (iid) mobility model. Multicast capacity of $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} {\sqrt k }}} \right. \kern-\nulldelimiterspace} {\sqrt k }}} \right)$ order is not achievable with high probability (whp), and delay for $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} {\sqrt k }}} \right. \kern-\nulldelimiterspace} {\sqrt k }}} \right)$ multicast capacity is $\Omega \left( {K!{n}^K } \right)$, where $n$ is the whole number of ad hoc nodes, $k$ is the number of destination nodes in a multicast session, and $K = \left\lceil {{{\sqrt {k} } \mathord{\left/ {\vphantom {{\sqrt {\rm k} } {\rm c}}} \right. \kern-\nulldelimiterspace} {c}}} \right\rceil$ and $c$ is a positive constant. A multicast routing and scheduling scheme is proposed by which the network can achieve $\Theta \left( {{{\rm 1} \mathord{\left/ {\vphantom {{\rm 1} k}} \right. \kern-\nulldelimiterspace} k}} \right)$ throughput whp, and must tolerate $\Theta \left( {{kn}} \right)$ total network delay.