Bicriteria Optimization of a Queue with a Controlled Input Stream

1. E. Altman, Constrained Markov Decision Processes(Chapman and Hall/CRC Press, London, 1999).

   Google Scholar 

2. E. Altman, G. Koole and T. Jimenez, On optimal call admission control in a resource-sharing system, IEEE Trans. Commun. 49 (2001) 1659-1668.

   Article  PubMed  Google Scholar 

3. E. Altman and A. Shwartz, Markov decision problems and state-action frequences, SIAM J. Control Optim. 29 (1991) 786-809.

   Google Scholar 

4. P.S. Ansell, K.D. Glazebrook, I. Mitrani and J. Nino-Mora, A semidefinite programming approach to the optimal control of a single server queueing system with imposed second moment constraints, J. Oper. Res. Soc. 50 (1999) 765-773.

   Google Scholar 

5. V. Borkar, Topics in Controlled Markov Chains(Longman Scientific and Technical, Harlow, Essex, England, 1991).

   Google Scholar 

6. E.A. Feinberg, Constrained semi-Markov decision processes with average rewards, Z. Oper. Res. 39 (1994) 257-288.

   Google Scholar 

7. E.A. Feinberg, Optimal control of average reward constrained continuous-time finite Markov decision processes, in: Proc. of IEEE Conf. on Decision and Control, Vol. 4 (2002) pp. 3805-3810.

   Google Scholar 

8. S. Floyd, TCP and explicit congestion notification, ACM Comput. Commun. Rev. 24 (1994) 10-23.

   Google Scholar 

9. X. Guo and O. Hernandez-Lerma, Constrained continuous-time Markov control processes with discounted criteria, Stochastic. Anal. Appl. 21 (2003) 379-400.

   Google Scholar 

10. X. Guo and O. Hernandez-Lerma, Drift and monotonicity conditions for continuous-time controlled Markov chains with an average criterion, IEEE Trans. Automat. Control 48 (2003) 236-245.

    Google Scholar 

11. N. Hemachandra and Y. Narahari, A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems, Queueing Systems 36 (2001) 443-461.

    Google Scholar 

12. O. Hernandez-Lerma and R. Romera, Pareto optimality in multiobjective Markov control processes, Preprint (2001).

13. C.V. Hollot, V. Misra, D. Towsley and W. Gong, A control theoretic analysis of RED, in: Proc. of IEEE Conf. INFOCOM(2001) pp. 1510-1519.

14. A. Hordijk and F. Spieksma, Constrained admission control to a queueing system, Adv. in Appl. Probab. 21 (1989) 409-431.

    Google Scholar 

15. M. Kitaev, Semi-Markov and jump Markov controllable models. Average cost criterion, Teor. Veroyatnost. i Primenen. 30 (1985) 252-268 (in Russian).

    Google Scholar 

16. M.Y. Kitaev and V.V. Rykov, Controlled Queueing Systems(CRC Press, New York, 1995).

    Google Scholar 

17. M.E. Lewis, Average optimal policies in a controlled queueing system with dual admission control, J. Appl. Probab. 38 (2001) 369-385.

    Google Scholar 

18. R.Sh. Liptzer and A.N. Shiryaev, Theory of Martingales(Kluwer, Dordrecht, 1989).

    Google Scholar 

19. M. Mandjes, D. Mitra and W. Scheinhardt, Models of network access using feedback fluid queues, Queueing Systems (in press).

20. V. Misra, W.B. Gong and D. Towsley, A fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED, in: Proc. of ACM Conf. SIGCOMM’2000.

21. A.B. Piunovskiy, Homogeneous controllable Markov models with continuous time, Cybernetics 25 (1989) 55-61.

    Google Scholar 

22. A.B. Piunovskiy, Optimal Control of Random Sequences in Problems with Constraints(Kluwer Academic, Dordrecht, 1997).

    Google Scholar 

23. A.B. Piunovskiy, A controlled jump discounted model with constraints, Theory Probab. Appl. 42 (1998) 51-72.

    Google Scholar 

24. A.B. Piunovskiy and V.M. Khametov, New effective solutions of optimality’s equation for the controlled Markov chains with continuous parameter (the unbounded price-function), Probl. Control Inform. Theory 14 (1985) 303-318.

    Google Scholar 

25. M.L. Puterman, Markov Decision Processes(Wiley, New York, 1994).

    Google Scholar 

26. M.I. Reiman and A. Shwartz, Call admission: A new approach to quality of service, Queueing Systems 38 (2001) 125-148.

    Google Scholar 

27. R.T. Rockafellar, Conjugate Duality and Optimization(SIAM, Philadelphia, PA, 1989).

    Google Scholar 

28. V.V. Rykov, Monotone control of queueing systems with heterogeneous servers, Queueing Systems 37 (2001) 391-403.

    Article  Google Scholar 

29. S. Sanghavi, K. Avrachenkov and E. Altman, Optimal policies for admitting calls with silence suppression, Preprint (2002).

30. L. Sennott, Stochastic Dynamic Programming and the Control of Queueing Systems(Wiley, New York, 1999).

    Google Scholar 

31. H.M. Taylor and S. Karlin, An Introduction to Stochastic Modeling(Academic Press, San Diego, CA, 1998).

    Google Scholar 

32. A.A. Yushkevich and E.A. Feinberg, On homogeneous Markov models with continuous time and finite or countable state space, Teor. Veroyatnost. i Primenen. 24 (1979) 155-160 (in Russian).

    Google Scholar 

Download references