Stability of a rate control system with averaged feedback and network delay

La, Richard J.; Ranjan, Priya

doi:10.1016/j.automatica.2006.05.018

Cited by 3 publications

(7 citation statements)

References 17 publications

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“…Hence, this suggests that the dynamical effect of heterogeneous delays in the dual algorithm, summarized by the averaging in (9) is similar to that of low pass filtering (or averaging) of the rate seen by the resource in the primal algorithm [18].…”

Section: Macdonald's Linear Chain Techniquementioning

confidence: 90%

“…We note that the delay differential system in (19) is similar to that in [18] for a variant of the primal algorithm where the price charged by a resource is a function of the averaged or low pass filtered version of the aggregate rate of the users through the resource, as opposed to the users' instantaneous rates in the original primal algorithm. Hence, this suggests that the dynamical effect of heterogeneous delays in the dual algorithm, summarized by the averaging in (9) is similar to that of low pass filtering (or averaging) of the rate seen by the resource in the primal algorithm [18].…”

Section: Macdonald's Linear Chain Techniquementioning

confidence: 96%

“…• We demonstrate that when the dispersion of round-trip delays can be modeled by a gamma kernel, the effects of the heterogeneous delays can be studied using the model of Hale and Ivanov [7] and are similar to those of introducing low pass filters in the feedback control loop [18].…”

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confidence: 99%

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Convergence of Dual Algorithm with Arbitrary Communication Delays

Ranjan

2008

SIAM J. Appl. Math.

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We study the issue of convergence of user rates and resource prices under a family of rate control schemes called dual algorithms with arbitrary communication delays. We first consider a case where a single resource is shared by many users. Then, we study a general network shared by heterogeneous users and derive sufficient conditions for convergence. We show that in the case of a single user utilizing a single resource, our condition is also necessary. Using our results we derive a sufficient condition for convergence with a family of popular utility and resource price functions. We present numerical examples to validate our analysis.

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Section: Macdonald's Linear Chain Techniquementioning

confidence: 90%

Section: Macdonald's Linear Chain Techniquementioning

confidence: 96%

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Convergence of Dual Algorithm with Arbitrary Communication Delays

Ranjan

2008

SIAM J. Appl. Math.

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“…where the first equalities in (A10) and (A11) have used the facts that E(𝛾 k+1 |𝛾 k = 1) = 1 − p and E(𝛾 k+1 |𝛾 k = 0) = q, and the second equalities in (A10) and (A11) have employed ( 9) and (10). Multiplying q p+q and p p+q on the both sides of (A10) and (A11), respectively, and using (11) yield…”

Section: Author Contributionsmentioning

confidence: 99%

Infinite‐horizon optimal control for networked control systems with Markovian packet losses

Wang

Liu

et al. 2023

Optim Control Appl Methods

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This article is concerned with the infinite‐horizon optimal control for networked control systems with Markovian packet losses. We focus on the case that packet losses may occur in an unreliable communication channel between the sensor and the controller. This sort of packet loss enables the optimal control problem to fall into the category of optimal output‐feedback control. Also, the output involves multiplicative noise. As well known, the separation principle fails to hold in a multiplicative‐noise setting. Thus the problem is very involved. By solving forward and backward stochastic difference equations and making convergence analysis, we acquire the necessary and sufficient solvability condition and the explicit optimal controller. The achieved results are illustrated by numerical examples.

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“…The papers of Ranjan et al [17,15,16,23,24,25,26] and [1,3] consider similar systems, starting from discrete ones, through ordinary and delay differential equations with constant or state-dependent delays, to general network systems. They examine these models from the engineering point of view, comparing the different rate control schemes, like the TCP (transmission control protocol) and its modifications.…”

Section: Introductionmentioning

confidence: 99%

A Differential Equation with a State-Dependent Queueing Delay

Balázs¹,

Krisztin²

2020

SIAM J. Math. Anal.

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We consider a differential equation with a state-dependent delay motivated by a queueing process. The time delay is determined by an algebraic equation involving the length of the queue for which a discontinuous differential equation holds. The new type of state-dependent delay raises some problems that are studied in this paper. We formulate an appropriate framework to handle the system, and show that the solutions define a Lipschitz continuous semiflow in the phase space. The second main result guarantees the existence of slowly oscillating periodic solutions.

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Stability of a rate control system with averaged feedback and network delay

Cited by 3 publications

References 17 publications

Convergence of Dual Algorithm with Arbitrary Communication Delays

Convergence of Dual Algorithm with Arbitrary Communication Delays

Infinite‐horizon optimal control for networked control systems with Markovian packet losses

A Differential Equation with a State-Dependent Queueing Delay

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