Towards the analysis of TCP with the aid of stochastic control

Alexander Miller, Boris Miller

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

The article considers the optimal stochastic control approach to the analysis of various TCP. Generally the analysis of TCP schemes relates to so-called liquid models which provide the asymptotic behavior of the queuing system where the number of jobs is huge. At this level of consideration only the asymptotic results could be obtained and the real performance of existing protocols is still unclear particularly for the case of seasonal changes and congestions. Meanwhile, the models of controllable Markov chains (CMC) are more appropriate to the analysis of control of flows in the Internet that has been observed by many authors long ago. The principal difficulty of the application of CMC is the problem of the models high dimension particularly for connected controllable Markov chains (CCMC). But nowadays this problem is less important due to the development of multiprocessor supercomputers that make the numerical solution of the optimal control problems for CMC more achievable. Models of CCMC arise in queuing systems with many service lines where some idle lines may be used to avoid the congestion if the principal lines have been subjected the huge workload. Here we suggest the tensor form of the representation for such CMC and give the dynamic programming equation in corresponding tensor form. As an example we consider the system with two service lines, namely the main and reserve ones, having different service rates and the cost of service. Numerical approach to the solution of the access and service rate control has been proposed.
Original languageEnglish
Title of host publicationProceedings of the IX International Conference: Systems Identification and Control Problems
EditorsV A Lototsky
Place of PublicationMoscow
PublisherMAIK Nauka
Pages326 - 346
Number of pages21
ISBN (Print)9785914500983
Publication statusPublished - 2012
EventInternational Conference on System Identification and Control Problems (SICPRO 2012) - V.A. Trapeznikov Institute of Control Sciences, Moscow, Russian Federation
Duration: 30 Jan 20122 Feb 2012
Conference number: 9th
http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=10043

Conference

ConferenceInternational Conference on System Identification and Control Problems (SICPRO 2012)
Abbreviated titleSICPRO 2012
CountryRussian Federation
CityMoscow
Period30/01/122/02/12
Internet address

Cite this

Miller, A., & Miller, B. (2012). Towards the analysis of TCP with the aid of stochastic control. In V. A. Lototsky (Ed.), Proceedings of the IX International Conference: Systems Identification and Control Problems (pp. 326 - 346). Moscow: MAIK Nauka.
Miller, Alexander ; Miller, Boris. / Towards the analysis of TCP with the aid of stochastic control. Proceedings of the IX International Conference: Systems Identification and Control Problems. editor / V A Lototsky. Moscow : MAIK Nauka, 2012. pp. 326 - 346
@inproceedings{f28b4c0e150c4c29a0bd803662f88427,
title = "Towards the analysis of TCP with the aid of stochastic control",
abstract = "The article considers the optimal stochastic control approach to the analysis of various TCP. Generally the analysis of TCP schemes relates to so-called liquid models which provide the asymptotic behavior of the queuing system where the number of jobs is huge. At this level of consideration only the asymptotic results could be obtained and the real performance of existing protocols is still unclear particularly for the case of seasonal changes and congestions. Meanwhile, the models of controllable Markov chains (CMC) are more appropriate to the analysis of control of flows in the Internet that has been observed by many authors long ago. The principal difficulty of the application of CMC is the problem of the models high dimension particularly for connected controllable Markov chains (CCMC). But nowadays this problem is less important due to the development of multiprocessor supercomputers that make the numerical solution of the optimal control problems for CMC more achievable. Models of CCMC arise in queuing systems with many service lines where some idle lines may be used to avoid the congestion if the principal lines have been subjected the huge workload. Here we suggest the tensor form of the representation for such CMC and give the dynamic programming equation in corresponding tensor form. As an example we consider the system with two service lines, namely the main and reserve ones, having different service rates and the cost of service. Numerical approach to the solution of the access and service rate control has been proposed.",
author = "Alexander Miller and Boris Miller",
year = "2012",
language = "English",
isbn = "9785914500983",
pages = "326 -- 346",
editor = "Lototsky, {V A}",
booktitle = "Proceedings of the IX International Conference: Systems Identification and Control Problems",
publisher = "MAIK Nauka",

}

Miller, A & Miller, B 2012, Towards the analysis of TCP with the aid of stochastic control. in VA Lototsky (ed.), Proceedings of the IX International Conference: Systems Identification and Control Problems. MAIK Nauka, Moscow, pp. 326 - 346, International Conference on System Identification and Control Problems (SICPRO 2012) , Moscow, Russian Federation, 30/01/12.

Towards the analysis of TCP with the aid of stochastic control. / Miller, Alexander; Miller, Boris.

Proceedings of the IX International Conference: Systems Identification and Control Problems. ed. / V A Lototsky. Moscow : MAIK Nauka, 2012. p. 326 - 346.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

TY - GEN

T1 - Towards the analysis of TCP with the aid of stochastic control

AU - Miller, Alexander

AU - Miller, Boris

PY - 2012

Y1 - 2012

N2 - The article considers the optimal stochastic control approach to the analysis of various TCP. Generally the analysis of TCP schemes relates to so-called liquid models which provide the asymptotic behavior of the queuing system where the number of jobs is huge. At this level of consideration only the asymptotic results could be obtained and the real performance of existing protocols is still unclear particularly for the case of seasonal changes and congestions. Meanwhile, the models of controllable Markov chains (CMC) are more appropriate to the analysis of control of flows in the Internet that has been observed by many authors long ago. The principal difficulty of the application of CMC is the problem of the models high dimension particularly for connected controllable Markov chains (CCMC). But nowadays this problem is less important due to the development of multiprocessor supercomputers that make the numerical solution of the optimal control problems for CMC more achievable. Models of CCMC arise in queuing systems with many service lines where some idle lines may be used to avoid the congestion if the principal lines have been subjected the huge workload. Here we suggest the tensor form of the representation for such CMC and give the dynamic programming equation in corresponding tensor form. As an example we consider the system with two service lines, namely the main and reserve ones, having different service rates and the cost of service. Numerical approach to the solution of the access and service rate control has been proposed.

AB - The article considers the optimal stochastic control approach to the analysis of various TCP. Generally the analysis of TCP schemes relates to so-called liquid models which provide the asymptotic behavior of the queuing system where the number of jobs is huge. At this level of consideration only the asymptotic results could be obtained and the real performance of existing protocols is still unclear particularly for the case of seasonal changes and congestions. Meanwhile, the models of controllable Markov chains (CMC) are more appropriate to the analysis of control of flows in the Internet that has been observed by many authors long ago. The principal difficulty of the application of CMC is the problem of the models high dimension particularly for connected controllable Markov chains (CCMC). But nowadays this problem is less important due to the development of multiprocessor supercomputers that make the numerical solution of the optimal control problems for CMC more achievable. Models of CCMC arise in queuing systems with many service lines where some idle lines may be used to avoid the congestion if the principal lines have been subjected the huge workload. Here we suggest the tensor form of the representation for such CMC and give the dynamic programming equation in corresponding tensor form. As an example we consider the system with two service lines, namely the main and reserve ones, having different service rates and the cost of service. Numerical approach to the solution of the access and service rate control has been proposed.

UR - http://www.sicpro.org/sicpro12/code/e12_08.htm

M3 - Conference Paper

SN - 9785914500983

SP - 326

EP - 346

BT - Proceedings of the IX International Conference: Systems Identification and Control Problems

A2 - Lototsky, V A

PB - MAIK Nauka

CY - Moscow

ER -

Miller A, Miller B. Towards the analysis of TCP with the aid of stochastic control. In Lototsky VA, editor, Proceedings of the IX International Conference: Systems Identification and Control Problems. Moscow: MAIK Nauka. 2012. p. 326 - 346