Wireless Networking

APPENDIX D

Discrete Event Random Processes

D.1 Stability Analysis of Discrete Time Markov Chains (DTMCs)

In analyzing queuing models, one of the first questions one asks is whether the system is “stable.” When a queuing system is modeled by a (time homogeneous) Markov chain then one of the criteria for stability is that the Markov chain characterizing the queuing system be positive recurrent. This at least ensures that there is a steady state distribution of the associated processes. One method for determining whether an irreducible DTMC (with transition probability matrix P) is positive recurrent is to look for a positive solution for the system of equations π = πP, Σ_iεSπ_i = 1. Although this can be done in many simple cases, in general this ...