Theory Of Markovian Access to Collision Channels

In this paper, a unified, analytical framework for analysis of Markovian access control protocols in collision channels with a finite number of buffered users is presented. The theory developed is based on: 1) an appropriate state-space modeling of a network, 2) the averaging theory for the slow-in-the-average Markov walks used for the local analysis, and 3) an asymptotic large deviations theory used for the global analysis. Specific new results obtained here are: 1) formulas for the steady-state buffer OCCupancy and the probability of packet rejection, 2) a relationship between the capacity of the users buffers and the steady-state throughput, time delay, and the probability of packet rejection, 3) an asymptotic formula for the saturation period, and 4) a new adaptive protocol, the adaptive TDMA, is constructed, and it is shown that it is superior to the adaptive ALOHA system.