School of Mathematics, New Campus, Central South University, Changsha 410083, China
Abstract:
We investigate deviation matrix for discrete-time GI/M/1-type Markov chains in terms of the matrix-analytic method, and revisit the link between deviation matrix and the asymptotic variance. Parallel results are obtained for continuous-time GI/M/1-type Markov chains based on the technique of uniformization. We conclude with A. B. Clarke’s tandem queue as an illustrative example, and compute the asymptotic variance for the queue length for this model.