Nonlinear dynamics of internet congestion control: A frequency-domain approach

Gentile, Franco S.; Moiola, Jorge L.; Paolini, Eduardo E.

doi:10.1016/j.cnsns.2013.08.011

Cited by 15 publications

(11 citation statements)

References 20 publications

(56 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to obtain better QoS (quality of service) performance, some AQM (active queue management) algorithms, which aim at improving QoS by managing the queues at the buffer of routers, are implemented in TCP, such as RED (random early detection) [3], REM (random early marking) [4] and AVQ (adaptive virtual queue) [5]. By simplifying these complicated mechanisms, the mathematical models of these algorithms were established and the stability and bifurcation problems were widely investigated [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function

Shu

Chung

2015

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

“…Time history plots for(7). For all the cases, s0 ¼ 0:1ðsecondsÞ; N ¼ 10, B ¼ 50ðpacketsÞ; C ¼ 200ðpackets=secondÞ, b1 ¼ 0:2; p max ¼ 0:4 and (a) gðq; _ qÞ is not activated for b2 ¼ 0:4846, (b) gðq; _ qÞ is activated for b2 ¼ 0:4846, (c) gðq; _ qÞ is not activated for b2 ¼ 0:32, (d) gðq; _ qÞ is activated for b2 ¼ 0:32.…”

mentioning

confidence: 99%

On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function

Shu

Chung

2015

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…In [3][4][5], the local stability in congestion control models is studied. In [6][7][8][9], the existence of Hopf bifurcation is analyzed in congestion control models.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

Zhao

Sun

Huicheng

2014

Abstract and Applied Analysis

View full text Add to dashboard Cite

We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.

show abstract

“…This phenomenon is called time delay [1,2]. As a main cause to the control deterioration and system instability, time delays exist widespread in the industry of communication [3], biology [4], mechanism [5], chemistry [6], society [7], and power utility [8][9][10]. Therefore, it is an important issue and frequent topic to evaluate the impact of time delays on the stability of dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag

Jia

Wang

et al. 2014

Journal of Applied Mathematics

View full text Add to dashboard Cite

One type of bifurcation named oscillation emergence bifurcation (OEB) found in time-delayed linear time invariant (abbr. LTI) systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge. Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim) time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.

show abstract

Nonlinear dynamics of internet congestion control: A frequency-domain approach

Cited by 15 publications

References 20 publications

On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function

On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function

Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag

Contact Info

Product

Resources

About