N-Dimensional Markov Chain Analysis of the Starvation Issue for IEEE 802.15.6 Slotted Aloha Algorithm

The performance of IEEE 802.15.6 standard for wireless body area network (WBAN) has been studied by many researchers and various techniques to improve its performance such as throughput have been proposed. For example, the throughput can be improved considerably by allowing the contention probability of each node to approach zero for each collision. But this approach leads to the situation where a single node monopolizes the channel while others are starving. The main model to analyze this phenomena and other performance issue is Markov chain, however previous efforts to use Markov chain were limited to fixed number of dimension because of the complexity of handling multi-dimensional case. This paper extends the Markov chain analysis to n-dimensional case and provides equations that computes the expected visit count at each node in this n-dimensional Markov chain. We have solved the equation numerically and have proved that indeed a single node monopolizes the channel. We also provide a simulation result that supports our conclusion for n-dimensional case.