An analytical model for the performance of geographical multi-hop broadcast

In this paper we present an analytical model accurately describing the behaviour of a multi-hop broadcast protocol. Our model covers the scenario in which a message is forwarded over a straight road and inter-node distances are distributed exponentially. Intermediate forwarders draw a small random delay before forwarding a message such as is done in flooding protocols to avoid the broadcast storm problem. For a given node density and single-hop packet reception probability, the model is able to capture the probability distribution of (i) the delay of each hop, (ii) the length of each hop, (iii) the position of each forwarder, (iv) the required number of hops to cover the dissemination distance, and (v) the end-to-end delay to cover the dissemination distance. The model provides these quantities in terms of insightful, fast-to-evaluate closed-form expressions. The model has been validated by extensive simulations: modelling results stayed within typically 10%, depending on the source-to-sink distance and the node density.