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Probl. Peredachi Inf., 2005, Volume 41, Issue 2, Pages 89–110 (Mi ppi99)  

This article is cited in 17 scientific papers (total in 17 papers)

Large Systems

The Problem of Optimal Stochastic Data Flow Control Based upon Incomplete Information

B. M. Millera, K. E. Avrachenkovb, K. V. Stepanyana, G. B. Millerc

a Institute for Information Transmission Problems, Russian Academy of Sciences
b Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis – Méditerranée
c Moscow Aviation Institute

Abstract: A nonlinear stochastic control problem related to flow control is considered. It is assumed that the state of a link is described by a controlled hidden Markov process with a finite state set, while the loss flow is described by a counting process with intensity depending on a current transmission rate and an unobserved link state. The control is the transmission rate, and it has to be chosen as a nonanticipating process depending on the observation of the loss process. The aim of the control is to achieve the maximum of some utility function that takes into account losses of the transmitted information. Originally, the problem belongs to the class of stochastic control problems with incomplete information; however, optimal filtering equations that provide estimation of the current link state based on observations of the loss process allow one to reduce the problem to a standard stochastic control problem with full observations. Then a necessary optimality condition is derived in the form of a stochastic maximum principle, which allows us to obtain explicit analytic expressions for the optimal control in some particular cases. Optimal and suboptimal controls are investigated and compared with the flow control schemes used in TCP/IP (Transmission Control Protocols/Internet Protocols) networks. In particular, the optimal control demonstrates a much smoother behavior than the TCP/IP congestion control currently used.

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English version:
Problems of Information Transmission, 2005, 41:2, 150–170

Bibliographic databases:

UDC: 621.395.17:519.2
Received: 29.04.2004
Revised: 25.01.2005

Citation: B. M. Miller, K. E. Avrachenkov, K. V. Stepanyan, G. B. Miller, “The Problem of Optimal Stochastic Data Flow Control Based upon Incomplete Information”, Probl. Peredachi Inf., 41:2 (2005), 89–110; Problems Inform. Transmission, 41:2 (2005), 150–170

Citation in format AMSBIB
\Bibitem{MilAvrSte05}
\by B.~M.~Miller, K.~E.~Avrachenkov, K.~V.~Stepanyan, G.~B.~Miller
\paper The Problem of Optimal Stochastic Data Flow Control Based upon Incomplete Information
\jour Probl. Peredachi Inf.
\yr 2005
\vol 41
\issue 2
\pages 89--110
\mathnet{http://mi.mathnet.ru/ppi99}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2158688}
\zmath{https://zbmath.org/?q=an:1091.94003}
\transl
\jour Problems Inform. Transmission
\yr 2005
\vol 41
\issue 2
\pages 150--170
\crossref{https://doi.org/10.1007/s11122-005-0020-8}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. V. Boldyrikhin, V. V. Khutortsev, “Control of observations over random processes fluxes”, Autom. Remote Control, 67:12 (2006), 1900–1912  mathnet  crossref  mathscinet  zmath
    2. A. V. Borisov, “Analysis of hidden Markov models states generated by special jump processes”, Theory Probab. Appl., 51:3 (2007), 518–528  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Borisov A.V., Stefanovich A.I., “Optimal state filtering of controllable systems with random structure”, Journal of Computer and Systems Sciences International, 46:3 (2007), 348–358  crossref  mathscinet  zmath  isi
    4. Winter J., “Finite horizon control problems under partial information”, Network Control and Optimization, Proceedings, Lecture Notes in Computer Science, 4465, 2007, 120–128  crossref  zmath  isi
    5. Miller B.M., “Optimization of queuing system via stochastic control”, Automatica, 45:6 (2009), 1423–1430  crossref  mathscinet  zmath  isi  elib
    6. B. M. Miller, G. B. Miller, K. V. Semenikhin, “Methods to design optimal control of Markov process with finite state set in the presence of constraints”, Autom. Remote Control, 72:2 (2011), 323–341  mathnet  crossref  mathscinet  zmath  isi  elib
    7. Nazin A.V. Miller B., “The Mirror Descent Control Algorithm for Weakly Regular Homogeneous Finite Markov Chains with Unknown Mean Losses”, 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-Ecc), IEEE, 2011, 1779–1783  crossref  isi
    8. Yu. V. Solodyannikov, “Control and observation for dynamical queueing networks. II”, Autom. Remote Control, 75:5 (2014), 880–899  mathnet  crossref  isi
    9. A. V. Borisov, “Primenenie algoritmov optimalnoi filtratsii dlya resheniya zadachi monitoringa dostupnosti udalennogo servera”, Inform. i ee primen., 8:3 (2014), 53–69  mathnet  crossref  elib
    10. A. V. Borisov, B. M. Miller, K. V. Siemenikhin, “Filtering of the Markov jump process given the observations of multivariate point process”, Autom. Remote Control, 76:2 (2015), 219–240  mathnet  crossref  isi  elib  elib
    11. E. V. Karachanskaya, “A “direct” method to prove the generalized Itô–Venttsel' formula for a generalized stochastic differential equation”, Siberian Adv. Math., 26:1 (2016), 17–29  mathnet  crossref  crossref  mathscinet  elib
    12. A. V. Borisov, “Application of optimal filtering methods for on-line of queueing network states”, Autom. Remote Control, 77:2 (2016), 277–296  mathnet  crossref  isi  elib
    13. A. V. Borisov, A. V. Bosov, G. B. Miller, “Modelirovanie i monitoring sostoyaniya VoIP-soedineniya”, Inform. i ee primen., 10:2 (2016), 2–13  mathnet  crossref  elib
    14. Miller B., Miller G., Semenikhin K., “Optimization of the Data Transmission Flow From Moving Object to Nonhomogeneous Network of Base Stations”, IFAC PAPERSONLINE, 50:1 (2017), 6160–6165  crossref  isi  scopus
    15. Avrachenkov K.E., Borkar V.S., Pattathil S., 2017 IEEE 56Th Annual Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2017  isi
    16. B. M. Miller, G. B. Miller, K. V. Semenikhin, “Optimal channel choice for lossy data flow transmission”, Autom. Remote Control, 79:1 (2018), 66–77  mathnet  crossref  isi  elib
    17. Kuznetsov N.A., Myasnikov D.V., Semenikhin K.V., “Optimal Control of Data Transmission Over a Fluctuating Channel With Unknown State”, J. Commun. Technol. Electron., 63:12 (2018), 1506–1517  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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