### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the IX International Conference: Systems Identification and Control Problems |

Editors | V A Lototsky |

Place of Publication | Moscow |

Publisher | MAIK Nauka |

Pages | 326 - 346 |

Number of pages | 21 |

ISBN (Print) | 9785914500983 |

Publication status | Published - 2012 |

Event | International Conference on System Identification and Control Problems (SICPRO 2012) - V.A. Trapeznikov Institute of Control Sciences, Moscow, Russian Federation Duration: 30 Jan 2012 → 2 Feb 2012 Conference number: 9th http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=10043 |

### Conference

Conference | International Conference on System Identification and Control Problems (SICPRO 2012) |
---|---|

Abbreviated title | SICPRO 2012 |

Country | Russian Federation |

City | Moscow |

Period | 30/01/12 → 2/02/12 |

Internet address |

### Cite this

*Proceedings of the IX International Conference: Systems Identification and Control Problems*(pp. 326 - 346). Moscow: MAIK Nauka.

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-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 -