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

Stability and Hopf bifurcation of controlled complex networks model with two delays

none3siopenJinde Cao, Luca Guerrini, Zunshui ChengCao, Jinde; Guerrini, Luca; Cheng, Zunshu

Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes

We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model

Chaos in the tourism industry

The paper presents an application of the chaos theory to tourism, a sector in which operators' choices are particularly elaborate and complex. The dynamics of the tourist industry are, in fact, the result of close interactions between units of production, tourist flows, local authorities and natural resources. These interactions do not necessarily lead to a regular trend in the development of the tourist industry as proposed by Butler; on the contrary, irregularities of various types are very possible. The model microfounds rigorously on both the demand and the supply side. Firms and tourists operate under the hypothesis of limited rationality, the former in an oligopolistic context, the latter on the basis of mechanisms of evolutionary selection. Although not exhaustive, the model forms a theoretical platform that can be easily adapted to hypotheses and situations that differ from those originally hypothesized. As a consequence, this paper presents a series of numerical simulations. The results show the chaotic nature of a tourist flow, which limits the practicability of measures introduced to stabilise the system. In their place, measures are needed that stimulate a continuous reshaping of the system in relation to the factors that tend to change it.sustainable tourism; chaos; evolutionary games; Butler's cycle

Stabilizing RED queue oscillation using the logistic map in AutoRED mechanism

Active queue management (AQM) is one of the ways to control congestion at Internet Routers. One of the widely used AQM's is the random early detection (RED) scheme. The RED scheme suffers from chaotic queue oscillation problem particularly in a highly congested network. It causes jitter, high queuing delay when the queue size stays high, and underutilization when the queue size is low. Recently AutoRED algorithm has been proposed as a solution to the chaotic queue oscillation problem in that AutoRED calculates the weight, wq, continuously as opposed to a constant value set by a user [1]. AutoRED displays the reduction of the chaotic queue oscillation by network performance metrics and queue behavior graphs, but there has been no metric known to measure the degree of queue oscillation in terms of its effect on the Quality of Service (QoS). The purpose of the present study is twofold. Firstly, the possibility of an improvement by modifying AutoRED using a Logistic Map is investigated. This new technique introduces a user control parameter that can contribute to further improvements. Secondly, a new metric is proposed to show the degree of queue oscillation with regards to its effect on the QoS. The experiments are done by applying the new technique to network simulations in TCP only and TCP and UDP combined traffic environments. The results are compared with RED and AutoRED with regards to the proposed metric coupled with the network performance measurements and the statistical measurements of the queue behavior