Some New Insights into Kolmogorov's Criterion, with Applications to Hysteretic Queues

#### P. Buckingham, B. Fralix

2015, v.21, Issue 2, 339-368

ABSTRACT

We give a new random-product representation for the stationary distribution of a regular, ergodic continuous-time Markov chain (CTMC), as well as an analogous representation for the distribution of any regular CTMC having no absorbing states at an independent exponential time. We then use these results to analyze both the steady-state and the time-dependent behavior of a hysteretic $M/M/1$ queue.

Keywords: circular Markov process; clearing model; continuous-time Markov chain; hysteretic queues; Kolmogorov criterion; stationary distribution; time-dependent behavior; time-reversal