论文信息 - Perturbation theory for Markov reward processes with applications to queueing systems

Perturbation theory for Markov reward processes with applications to queueing systems

We study the effect of perturbations in the data of a discrete-time Markov reward process on the finite-horizon total expected reward, the infinite-horizon expected discounted and average reward and the total expected reward up to a first-passage time. Bounds for the absolute errors of these reward functions are obtained. The results are illustrated for a finite as well as infinite queueing systems (M/M/1/S and ). Extensions to Markov decision processes and other settings are discussed.

M. Puterman | N. van Dijk

[1] D. Widder,et al. The Laplace Transform , 1943, The Mathematical Gazette.

[2] D. V. Widder,et al. The Laplace Transform , 1943 .

[3] John G. Kemeny,et al. Finite Markov Chains. , 1960 .

[4] A. Ralston. A first course in numerical analysis , 1965 .

[5] P. Schweitzer. Perturbation theory and finite Markov chains , 1968 .

[6] J. Kemeny,et al. Denumerable Markov chains , 1969 .

[7] Arie Hordijk,et al. Dynamic programming and Markov potential theory , 1974 .

[8] Erhan Çinlar,et al. Introduction to stochastic processes , 1974 .

[9] John G. Kemeny,et al. Finite Markov chains , 1960 .

[10] Ward Whitt,et al. Approximations of Dynamic Programs, I , 1978, Math. Oper. Res..

[11] K. Hinderer. ON APPROXIMATE SOLUTIONS OF FINITE-STAGE DYNAMIC PROGRAMS , 1978 .

[12] CARL D. MEYER,et al. The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities , 1980, SIAM J. Algebraic Discret. Methods.

[13] Chelsea C. White,et al. Parameter Imprecision in Finite State, Finite Action Dynamic Programs , 1986, Oper. Res..