State-space analysis of static and dynamic Markovian access control protocols

A state-space approach to the problem of analysis of static and dynamic Markovian access control protocols in large decentralized communication networks is presented. The state is chosen to be the number of users having at least i packets in their buffers, i = 1, ..., N. Asymptotic analysis of the resulting state-space model constitutes the basis for the developed method. The method gives analytical formulae for calculating (i) steady state throughput, (ii) steady state time delay, (iii) steady state buffer occupancy, (iv) local stability of each equilibrium, and (v) residence time in the domain of attraction of every metastable steady state. Global behavior and state-space portraits are also discussed. Numerical experiments are reported (using the ALOHA and Symmetric ALOHA systems as examples) which support the described findings.