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Deviation matrix and asymptotic variance for GI/M/1-type Markov chains |
Yuanyuan LIU, Pengfei WANG( ), Yanmin XIE |
| School of Mathematics, New Campus, Central South University, Changsha 410083, China |
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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.
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| Keywords
GI/M/1-type Markov chains
deviation matrix
asymptotic variance
matrix-analytic method
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Corresponding Author(s):
Pengfei WANG
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Issue Date: 26 August 2014
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