Delay bounds for random linear coding in multihop relay networks

In this paper we consider the problem of transmitting a collection of packets from a source node to a destination node across a relay network. We analyze a simple random network coding scheme where each node transmits a random linear combination of packets each time it has a transmission opportunity. Our goal is to determine the expected time required to transmit all packets from the source to the destination. The main result of this paper is an upper bound on the expected time to transmit a generation of packets across the network. We show that the expected time is bounded by a constant plus the number of packets divided by the capacity of the minimum cut separating the source from the destination. This extends similar results for line networks to relay networks with arbitrarily many relay nodes. To facilitate our analysis, we model the relay network by a continuous-time Markov chain. Our primary analytical tool is a general method for computing upper bounds on hitting times associated with continuous-time Markov chains. We believe that this approach will also provide a method for analyzing transmission times associated with more general network topologies.