A Probabilistic Model of the LMAC Protocol for Concurrent Wireless Sensor Networks

We present a probabilistic model for the network setup phase of the Lightweight Medium Access Protocol (LMAC) for concurrent Wireless Sensor Networks. In the network setup phase, time slots are allocated to the individual sensors through resolution of successive collisions. The setup phase involving collisions should preferably be as short as possible for efficiency and energy consumption reasons. This concurrent stochastic process has inherent internal nondeterminism, and we model it using combinatorics. The setup phase is modeled by a discrete time Markov chain such that we can apply results from the theory of phase type distributions. Having obtained our model we are able to find optimal protocol parameters. We have simultaneously developed a simulation model, partly to verify our analytical derivations and partly to be able to deal with systems of excessively high order or stiff systems that might cause numerical challenges. Our abstracted model has a state space of limited size where the number of states are of the order binomial (
^n+r+1
_n
), where n is number of sensors, and r is the maximum back off time. We have developed a tool, named LMAC analyzer, on the MATLAB platform to assist automatic generation and analysis of the model.