Analytical Model for Performance Evaluation of Random Wireless Sensor Networks

Today Wireless Sensor Networks (WSNs) can be found in many application areas, e.g. they are used in smart home systems or in industrial settings in order to monitor and control machinery. The latter usually requires a guaranteed performance of the network. This mainly addresses the real-time capability of the network, i.e. knowledge of possible delays which occur on the multi-hop route between sender and receiver is needed. In this paper, a novel approach to model multi-hop networks with a fixed number of nodes uniformly distributed on a square area is proposed. Accordingly, no explicit knowledge of the routing and the topology is needed. That is, no specific network is reflected, but a class of random networks sharing common properties is modelled. In our model, all nodes generate frames according to a Poisson process with the same rate and send them to a common gateway. Based on this scenario, we deduce a mathematical model for the probability of simultaneous transmissions assuming that a generic CSMA MAC protocol is implemented. We use this result in order to derive an expression for the mean delays arising on the links, i.e. the medium access and queueing delay, of the multi-hop route in the special case of the IEEE 802.15.4 MAC and PHY protocols being used. The model results correspond well to an OMNeT++ simulation if the offered traffic does not exceed a certain limit. Beyond this limit, up to the capacity of the network, the model still captures the behaviour of the simulation but the deviation grows.