Two-sided bounds on the rate of convergence for continuous-time finite   inhomogeneous Markov chains
  We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered: birth-death-catastrophes processes, queueing models with batch arrivals and group services, chains with absorption in zero. 
A. Zeifman, V. Korolev
math.PR