TCP-AQM Interaction: Periodic Optimization via Linear Programming

Avrachenkov, Konstantin; Finlay, Luke; Gaitsgory, Vladimir

doi:10.1007/0-387-33815-2_1

Cited by 3 publications

(6 citation statements)

References 13 publications

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“…Comparing it with (33), one can conclude that the admissible pair which has been constructed is an approximation to the solution of (2).…”

Section: From This Data One May Conclude Thatmentioning

confidence: 95%

“…As shown in [9] (under certain natural and easily verifiable conditions), there exists the limit of the optimal value G N,∆ of the LPP (15) and this limit is equal to the optimal value G per of the periodic optimization problem (2):…”

Section: Linear Programming Approachmentioning

confidence: 97%

“…3) Extrapolate the definition of the function ψ (16), the constructed admissible pair is a "good" approximation to the solution of the periodic optimization problem (2).…”

Section: Linear Programming Approachmentioning

confidence: 99%

“…Since we consider long-run time average criteria, our TCP-AQM interaction model falls into the framework of the periodic optimization (as outlined in the next section). This paper is an updated version of the earlier authors' work [2]. The main difference from [2] is that in the current paper we consider (and present numerical results for) a practically important case of a sigmoidal utility function.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is an updated version of the earlier authors' work [2]. The main difference from [2] is that in the current paper we consider (and present numerical results for) a practically important case of a sigmoidal utility function.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of TCP-AQM Interaction Via Periodic Optimization and Linear Programming: The Case of Sigmoidal Utility Function

Avrachenkov

Finlay

Gaitsgory

2006

Next Generation Teletraffic and Wired/Wireless Advanced Networking

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Abstract. We investigate the interaction between Transmission Control Protocol (TCP) and an Active Queue Management (AQM) router, that are designed to control congestion in the Internet. TCP controls the sending rate with which the data is injected into the network and AQM generates control signals based on the congestion level. For a given TCP version, we define the optimal strategy for the AQM router as a solution of a nonlinear periodic optimization problem, and we find this solution using a linear programming approach. We show that depending on the choice of the utility function for the sending rate, the optimal control is either periodic or steady state. Main attention is paid to a problem with a sigmoidal utility function, in which the evolution of the optimal sending rate resembles a "saw-tooth" behavior of the "instantaneous" TCP sending rate.

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“…Comparing it with (33), one can conclude that the admissible pair which has been constructed is an approximation to the solution of (2).…”

Section: From This Data One May Conclude Thatmentioning

confidence: 95%

Section: Linear Programming Approachmentioning

confidence: 97%

“…3) Extrapolate the definition of the function ψ (16), the constructed admissible pair is a "good" approximation to the solution of the periodic optimization problem (2).…”

Section: Linear Programming Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of TCP-AQM Interaction Via Periodic Optimization and Linear Programming: The Case of Sigmoidal Utility Function

Avrachenkov

Finlay

Gaitsgory

2006

Next Generation Teletraffic and Wired/Wireless Advanced Networking

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Occupational Measures Formulation and Linear Programming Solution of Deterministic Long Run Average Problems of Optimal Control

Gaitsgory

Rossomakhine

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Linear programming solutions of periodic optimization problems: approximation of the optimal control

Finlay

Gaitsgory

Lebedev³

2007

Journal of Industrial &Amp; Management Optimization

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Deterministic long run average problems of optimal control are "asymptotically equivalent" to infinite-dimensional linear programming problems (LPP) and the latter are approximated by finite dimensional LPP. The solutions of this finite dimensional LPP can be used for numerical analysis of periodic optimization problems. In the present paper we establish the convergence of controls constructed on the basis of the solution of the finite dimensional LPP to the optimal control of a periodic optimization problem. Results are illustrated with a numerical example.

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TCP-AQM Interaction: Periodic Optimization via Linear Programming

Cited by 3 publications

References 13 publications

Analysis of TCP-AQM Interaction Via Periodic Optimization and Linear Programming: The Case of Sigmoidal Utility Function

Analysis of TCP-AQM Interaction Via Periodic Optimization and Linear Programming: The Case of Sigmoidal Utility Function

Occupational Measures Formulation and Linear Programming Solution of Deterministic Long Run Average Problems of Optimal Control

Linear programming solutions of periodic optimization problems: approximation of the optimal control

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