Queue length analysis for multicast: Limits of performance and achievable queue length with random linear coding

Abstract

In this work we analyze the average queue backlog at a source node serving a single multicast flow consisting of M destination nodes. In the model we consider, the channel between the source node and each receiver is an independent identically distributed packet erasure channel. We first develop a lower bound on the average queue backlog achievable by any transmission strategy; our bound indicates that the queue size must scale as at least

Ω(ln(M)). We then analyze the queue backlog for a strategy in which random linear coding is performed over groups of packets in the queue; this strategy is an instance of the random linear network coding strategy introduced in. 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, the packet coding strategy is order-optimal with respect to the number of receivers.