Analysis and control of bifurcation and chaos in averaged queue length in TCP/RED model

This paper studies the bifurcation and chaos phenomena in averaged queue length in a developed Transmission Control Protocol (TCP) model with Random Early Detection (RED) mechanism. Bifurcation and chaos phenomena are nonlinear behaviour in network systems that lead to degradation of the network performance. The TCP/RED model used is a model validated previously. In our study, only the average queue size k q − is considered, and the results are based on analytical model rather than actual measurements. The instabilities in the model are studied numerically using the conventional nonlinear bifurcation analysis. Extending from this bifurcation analysis, a modified RED algorithm is derived to prevent the observed bifurcation and chaos regardless of the selected parameters. Our modification is for the simple scenario of a single RED router carrying only TCP traffic. The algorithm neither compromises the throughput nor the average queuing delay of the system

Symbolic dynamical model of average queue size of random early detection algorithm

In this paper, a symbolic dynamical model of the average queue size of the random early detection (RED) algorithm is proposed. The conditions on both the system parameters and the initial conditions that the average queue size of the RED algorithm would converge to a fixed point are derived. These results are useful for network engineers to design both the system parameters and the initial conditions so that internet networks would achieve a good performance

New RED-type TCP-AQM algorithms based on beta distribution drop functions

In recent years, Active Queue Management (AQM) mechanisms to improve the performance of TCP/IP networks have acquired a relevant role. In this paper we present a simple and robust RED-type algorithm together with a couple of dynamical variants with the ability to adapt to the specific characteristics of different network environments, as well as to the user needs. We first present a basic version called Beta RED (BetaRED), where the user is free to adjust the parameters according to the network conditions. The aim is to make the parameter setting easy and intuitive so that a good performance is obtained over a wide range of parameters. Secondly, BetaRED is used as a framework to design two dynamic algorithms, which we will call Adaptive Beta RED (ABetaRED) and Dynamic Beta RED (DBetaRED). In those new algorithms certain parameters are dynamically adjusted so that the queue length remains stable around a predetermined reference value and according to changing network traffic conditions. Finally, we present a battery of simulations using the Network Simulator 3 (ns-3) software with a two-fold objective: to guide the user on how to adjust the parameters of the BetaRED mechanism, and to show a performance comparison of ABetaRED and DBetaRED with other representative algorithms that pursue a similar objective

Stabilizing Chaotic Behavior of RED

The Internet is a so complex nonlinear network that many results show how the data flow exhibits chaotic attributes and the fractal nature of aggregate TCP/IP traffic. In this work, we study a new model of Random Early Detection (RED) using beta distribution configured by tuning decisions of dropping or accepting packets so that the queue occupancy level is kept at a given target level, thereby eliminating aggressive fluctuations of buffer underflow and overflow. Our proposed model programmed with Python incorporates new parameters (a, B) that make it possible to stabilize oscillations of averaged router queue length and to be close to the stationary state. We present study and numerical analysis from the same perspective of former studies for congestion control

Internet congestion control: From stochastic to dynamical models

Since its inception, control of data congestion on the Internet has been based on stochas tic models. One of the first such models was Random Early Detection. Later, this model was reformulated as a dynamical system, with the average queue sizes at a router’s buffer being the states. Recently, the dynamical model has been generalized to improve global stability. In this paper we review the original stochastic model and both nonlin ear models of Random Early Detection with a two-fold objective: (i) illustrate how a random model can be “smoothed out” to a deterministic one through data aggregation and (ii) how this translation can shed light into complex processes such as the Internet data traffic. Furthermore, this paper contains new materials concerning the occurrence of chaos, bifurcation diagrams, Lyapunov exponents and global stability robustness with respect to control parameters. The results reviewed and reported here are expected to help design an active queue management algorithm in real conditions, that is, when sys tem parameters such as the number of users and the round-trip time of the data packets change over time. The topic also illustrates the much-needed synergy of a theoretical approach, practical intuition and numerical simulations in engineerin

Generalized TCP-RED dynamical model for Internet congestion control

Adaptive management of traffic congestion in the Internet is a complex problem that can gain useful insights from a dynamical approach. In this paper we propose and analyze a one-dimensional, discrete-time nonlinear model for Internet congestion control at the routers. Specifically, the states correspond to the average queue sizes of the incoming data packets and the dynamical core consists of a monotone or unimodal mapping with a unique fixed point. This model generalizes a previous one in that additional control param eters are introduced via the data packet drop probability with the objective of enhancing stability. To make the analysis more challenging, the original model was shown to exhibit the usual features of low-dimensional chaos with respect to several system and control pa rameters, e.g., positive Lyapunov exponents and Feigenbaum-like bifurcation diagrams. We concentrate first on the theoretical aspects that may promote the unique stationary state of the system to a global attractor, which in our case amounts to global stability. In a sec ond step, those theoretical results are translated into stability domains for robust setting of the new control parameters in practical applications. Numerical simulations confirm that the new parameters make it possible to extend the stability domains, in comparison with previous results. Therefore, the present work may lead to an adaptive congestion control algorithm with a more stable performance than other algorithms currently in use

Quadratic exponential random early detection: a new enhanced random early detection-oriented congestion control algorithm for routers

Network congestion is still a problem on the internet. The random early detection (RED) algorithm being the most notable and widely implemented congestion algorithm in routers faces the problems of queue instability and large delay arising from the presence of an ineffectual singular linear packet dropping function. This research article presents a refinement to RED, named quadratic exponential random early detection (QERED) algorithm, which exploits the advantages of two drop functions, namely quadratic and exponential in order to enhance the performance of RED algorithm. ns-3 simulation studies using various traffic load conditions to assess and benchmark the effectiveness of QERED with two improved variants of RED affirmed that QERED offers a better performance in terms of average queue size and delay metrics at various network scenarios. Fortunately, to replace/upgrade the implementation for RED algorithm with QERED’s in routers will require minimal effort due to the fact that nothing more besides the packet dropping probability profile got to be adjusted