We study bounds on the rate of convergence to the stationary distribution in monotone separable networks which are represented in terms of stochastic recursive sequences. Monotonicity properties of this subclass of Markov chains allow us to formulate conditions in terms of marginal network characteristics. Two particular examples, generalized Jackson networks and multiserver queues, are considered.
Foss, S. G., & Sapozhnikov, A. (2006). Convergence rates in monotone separable stochastic networks. Queueing Systems: Theory and Applications, 52(2), 125-137. https://doi.org/10.1007/s11134-006-4261-z