Skip to main content
Log in

On truncations and perturbations of Markov decision problems with an application to queueing network overflow control

  • Computational Issues
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Conditions are provided to derive error bounds on the effect of truncations and perturbations in Markov decision problems. Both the average and finite horizon case are studied. As an application, an explicit error bound is obtained for a truncation of a Jacksonian queueing network with overflow control.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Hinderer, On approximate solutions of finite-stage dynamic programs,Dynamic Programming and its Applications, ed. M.L. Puterman (Academic Press, New York, 1978).

    Google Scholar 

  2. M. Kolonko, Bounds for the regret loss in dynamic programming, under adaptive control, Zeit. O.R. 27 (1983) 17–37.

    Google Scholar 

  3. M. Kurano, Average-optimal adaptive policies in semi-Markov decision processes including an unknown parameter, J. Oper. Res. Soc. Japan 28 (1985) 252–266.

    Google Scholar 

  4. H.J. Langen, Convergence of dynamic programming models, Math. Oper. Res. 6 (1981) 493–512.

    Google Scholar 

  5. C.D. Meyer Jr., The condition of a finite Markov chain and perturbation bounds for the limiting probabilities, SIAM J. Alg. Disc. Math. 1 (1980) 273–283.

    Google Scholar 

  6. T.J. Ott and K.R. Krishnan, State dependent routing of telephone traffic and the use of separable routing schemes,Proc. 11th Int. Teletraffic Congres, Tokyo, Japan (1985).

  7. S.M. Ross,Applied Probability Models with Optimization Application (Holden-Day, San Francisco, 1970).

    Google Scholar 

  8. T.A. Sarymsakov, Sur les chaines de Markoff à une infinité dénombrable d'états possibles, Doklady Akad. Sci. U.S.S.R. 48 (1975) 159–161.

    Google Scholar 

  9. P.J. Schweitzer, Perturbation theory and finite Markov chains, J. Appl. Prob. 5 (1968) 401–413.

    Google Scholar 

  10. E. Seneta, Finite approximations to infinite non-negative matrices, Proc. Cambridge Phil. Soc. 63 (1967) 983–992.

    Google Scholar 

  11. E. Seneta, The principles of truncations in applied probability, Comm. Math. Univ. Carolina 9 (1968) 533–539.

    Google Scholar 

  12. E. Seneta,Non-Negative Matrices and Markov Chains (Springer, 1980).

  13. H.C. Tijms,Stochastic Modelling and Analysis. A Computational Approach (Wiley, New York, 1986).

    Google Scholar 

  14. E.A. Van Doorn, On the overflow process from a finite Markovian queue, Performance Eval. 4 (1984) 233–240.

    Google Scholar 

  15. N.M. Van Dijk, Perturbation theory for unbounded Markov reward processes with applications to queueing, Adv. Appl. Prob. 20 (1988) 99–111.

    Google Scholar 

  16. N.M. Van Dijk, A proof of simple insensitive bounds for a pure overflow system, J. Appl. Prob. 26 (1989) 113–120.

    Google Scholar 

  17. N.M. Van Dijk, Truncation of Markov chains with applications to queueing, Research Report 53, Free University, Amsterdam (1989).

    Google Scholar 

  18. N.M. Van Dijk, and M.L. Puterman, Perturbation theory for Markov reward processes with applications to queueing systems, Adv. Appl. Prob. 20 (1988) 79–98.

    Google Scholar 

  19. N.M. Van Dijk, P. Tsoucas and J. Walrand, Simple bounds and monotonicity of the call congestion of finite multiserver delay systems, Prob. Eng. Inf. Sci. 2 (1988) 129–138.

    Google Scholar 

  20. W. Whitt, Approximations of dynamic programs I, Math. Oper. Res. 3 (1978) 231–243.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van Dijk, N.M. On truncations and perturbations of Markov decision problems with an application to queueing network overflow control. Ann Oper Res 29, 515–535 (1991). https://doi.org/10.1007/BF02283612

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02283612

Keywords

Navigation