Multicast Queueing Delay: Performance Limits and Order-Optimality of Random Linear Coding

Abstract

In this work we analyze the average queue backlog for transmission of a single multicast flow consisting of M destination nodes in a wireless network. In the model we consider, the channel between every pair of nodes is an independent identically distributed packet erasure channel. We first develop a lower bound on the average queue backlog achievable by any transmission strategy; for a single-hop multicast transmission, our bound indicates that the queue size must scale as at least Ω(ln(M)). Next, we generalize this result to a multihop network and obtain a lower bound on the queue backlog as it relates to the minimum-cut capacity of the network. We then analyze the queue backlog for a strategy in which random linear coding is performed over groups of packets in the queue at the source node of a single-hop multicast. We develop an upper bound on the average queue backlog for the packet-coding strategy to show that the queue size for this strategy scales as O(ln(M)). Our results demonstrate that in terms of the queue backlog for single-hop multicast, the packet coding strategy is order-optimal with respect to the number of receivers.