Markov Chains with Quasitoeplitz Transition Matrix: First Zero Hitting, Journal ofApplied Mathematics and Simulation 3(1989), 205-216. 152 Journal of Applied Mathematics and Stochastic Analysis Volume 3, Number 2

Application problems are investigated for the Markov chains with quasitoeplitz transition matrix. Generating functions of transient and steady state probabilities, first zero hitting probabilities and mean times are found for various particular cases, corresponding to some known patterns of feedback ("warm-up, " "switch at threshold," etc.). Level-depending dams and queue-depending queueing systems of both M/G/1 and GI/M/1 types with arbitrary random sizes of arriving and departing groups are studied