Congestion Control Model Research Articles

Improved scheme of internet congestion control under moving average filter

An important task of Internet congestion control is inhibiting sporadic data flow to maintain a suitable window size or route queue length. Such a requirement is just consistent with the basic idea and function of a moving average filter. In this paper one prior Internet congestion control model, named transmission control protocol (TCP)/random early detection (RED) stroboscopic model, is studied, and then one new scheme is proposed to enlarge its stable domain, where a simple moving average filter is introduced to inhibit sporadic data flow as possible. In the novel scheme the bifurcation phenomenon is postponed without any extra controller. The effectiveness of the new scheme is verified by theoretical analyses and numerical simulations.

State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy

We consider a connection-level model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighted $\alpha$-fair bandwidth sharing policy introduced by Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567] [$\alpha\in (0,\infty)$]. Assuming Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. A fluid model (or functional law of large numbers approximation) for this stochastic model was derived and analyzed in a prior work [Ann. Appl. Probab. 14 (2004) 1055--1083] by two of the authors. Here, we use the long-time behavior of the solutions of the fluid model established in that paper to derive a property called multiplicative state space collapse, which, loosely speaking, shows that in diffusion scale, the flow count process for the stochastic model can be approximately recovered as a continuous lifting of the workload process.

A novel congestion control model for interworking AAA in heterogeneous networks

In the 3rd generation partnership project (3GPP) and wireless local area network (WLAN) interworking networks, 3GPP authentication, authorization, accounting (AAA) server located in 3GPP core network will be responsible for the AAA request from WLAN access network (AN). However, centralized AAA deployment is bound to give rise to the single point failure, resulting in system congestion. In order to solve this problem, this paper presents a novel congestion control model for AAA. In addition, through analyzing the model, the conclusion can be drawn that the average congestion rate of extensible authentication protocol (EAP) user request is related with factors, such as the arrival rate of EAP request, the number of EAP re-authentication, and the system buffer queue length. Finally, the simulation results show that EAP request arrival rate is directly proportional to the congestion rate, and when the number of EAP re-authentication and system buffer queue length are fixed, the number of corresponding user authentication vectors should be directly proportional to the EAP request arrival rate, so as to ensure the average congestion rate of EAP request is less than 0.005.

Nonlinear dynamics in Internet congestion control model with TCP Westwood under RED

This article develops a discrete time dynamic feedback model of a congestion control system for a simple network with TCP Westwood (TCPW) connections and a single bottleneck link with random early detection (RED) gateway. By using this model, the nonlinear dynamics of the TCPW/RED network are analyzed and its parameter sensitivities are studied. It is shown that periodic doubling bifurcation occurs when the RED control parameters or other parameters are varied. By theoretical analysis, the fixed point, the critical value of parameters and the nature of the bifurcation are determined. Moreover, by using bifurcation diagrams and Lyapunov exponent, the result of theoretical analysis is validated and the bifurcation and chaotic phenomena are numerically studied of the congestion control system with TCPW connections and RED gateway.

Linear stability and Hopf bifurcation in an exponential RED algorithm model

We consider a novel congestion control model, i.e., the exponential RED algorithm with a single link and single source. Using the gain parameter of the system instead of the delay as the bifurcation parameter, the linear stability and Hopf bifurcation are investigated, and the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. Numerical simulations are carried out to illustrate our theoretical results.

Fluid limits for networks with bandwidth sharing and general document size distributions

We consider a stochastic model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows in a network where bandwidth is shared among document transfers. In contrast to an earlier work by Kelly and Williams [Ann. Appl. Probab. 14 (2004) 1055--1083], the present paper allows interarrival times and document sizes to be generally distributed, rather than exponentially distributed. Furthermore, we allow a fairly general class of bandwidth sharing policies that includes the weighted $\alpha$-fair policies of Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567], as well as certain other utility based scheduling policies. To describe the evolution of the system, measure valued processes are used to keep track of the residual document sizes of all flows through the network. We propose a fluid model (or formal functional law of large numbers approximation) associated with the stochastic flow level model. Under mild conditions, we show that the appropriately rescaled measure valued processes corresponding to a sequence of such models (with fixed network structure) are tight, and that any weak limit point of the sequence is almost surely a fluid model solution. For the special case of weighted $\alpha$-fair policies, we also characterize the invariant states of the fluid model.

Hopf bifurcation control in a congestion control model via dynamic delayed feedback

A typical objective of bifurcation control is to delay the onset of undesirable bifurcation. In this paper, the problem of Hopf bifurcation control in a second-order congestion control model is considered. In particular, a suitable Hopf bifurcation is created at a desired location with preferred properties and a dynamic delayed feedback controller is developed for the creation of the Hopf bifurcation. With this controller, one can increase the critical value of the communication delay, and thus guarantee a stationary data sending rate for larger delay. Furthermore, explicit formulae to determine the period and the direction of periodic solutions bifurcating from the equilibrium are obtained by applying perturbation approach. Finally, numerical simulation results are presented to show that the dynamic delayed feedback controller is efficient in controlling Hopf bifurcation.

Performance analysis of a threshold-based discrete-time queue using maximum entropy

The provision of guaranteed QoS for various Internet traffic types has become a challenging problem for researchers. New Internet applications, mostly multimedia-based, require differentiated treatments under certain QoS constraints. Due to a rapid increase in these new services, Internet routers are facing serious traffic congestion problems. This paper presents an approximate analytical performance model in a discrete-time queue, based on closed form expressions using queue threshold, to control the congestion caused by the bursty Internet traffic. The methodology of maximum entropy (ME) has been used to characterize closed form expressions for the state and blocking probabilities. A discrete-time GGeo/GGeo/1/{ N 1, N 2} censored queue with finite capacity, N 2, external compound Bernoulli traffic process and generalised geometric transmission times under a first come first serve (FCFS) rule and arrival first (AF) buffer management policy has been used for the solution process. To satisfy the low delay along with high throughput, a threshold, N 1, has been incorporated to slow the arrival process from mean arrival rate λ 1 to λ 2 once the instantaneous queue length has been reached, otherwise the source operates normally. This creates an implicit feedback from the queue to the arrival process. The system can be potentially used as a model for congestion control based on the Random Early Detection (RED) mechanism. Typical numerical experiments have been included to show the credibility of ME solution against simulation for various performance measures and to demonstrate the performance evaluation of the proposed analytical model.

Esquema de controle adaptativo de tráfego de redes baseado em um algoritmo de predição fuzzy

Neste trabalho, propomos um esquema de controle adaptativo de fluxos de tráfego de redes de computadores baseado no modelo fuzzy Takagi-Sugeno (TSK). O esquema de controle proposto evita a ocorrência de congestionamento utilizando o modelo fuzzy TSK para prever adaptativamente o tamanho da fila no buffer nos enlaces. Com o objetivo de ajustar dinamicamente os parâmetros do modelo fuzzy TSK, desenvolvemos um algoritmo de treinamento adaptativo para o mesmo. Os parâmetros das partes de premissa e das partes conseqüentes do modelo são atualizados na primeira etapa do algoritmo de treinamento desenvolvido. Já a segunda etapa consiste de um algoritmo de refinamento dos parâmetros do modelo baseado em gradiente descendente. A eficiência do preditor proposto é avaliada com o uso de traços de tráfego reais em comparação a outros preditores. A partir dos parâmetros do modelo fuzzy TSK, deduzimos uma expressão para a taxa da fonte de tráfego de modo a minimizar a variância do tamanho de fila no buffer e que é parte essencial do nosso esquema de controle. O controle de congestionamento proposto é então aplicado em um cenário de rede composto de vários nós alimentados com fluxos de tráfego real. Comparações realizadas com outros métodos de controle de congestionamento demonstram que o controle de congestionamento proposto provê menores taxas de perdas, assim como a manutenção da taxa de ocupação no buffer abaixo do valor desejado.

The Role of Information Update in Flow Control

A common feature of congestion control protocols is the presence of information packets used to signal congestion. We address here the question of how frequently such protocols need to generate information packets in order to optimize their performance. Through a number of congestion control models, we identify and quantify different types of effects of the frequency of generating information packets. We consider both TCP-type protocols, in which controlling the frequency of information packets is done through static or dynamic delayed ACK options, as well as ATM type flow control, where the optimal time spacing between the generation of network management packets is computed. We show how the spacing between information packets influences the throughput and the stability of the system.

Product form stationary distributions for diffusion approximations to a flow-level model operating under a proportional fair sharing policy

We consider a flow-level model of Internet congestion control introduced by Massoulié and Roberts [2]. We assume that bandwidth is shared amongst elastic documents according to a weighted proportional fair bandwidth sharing policy. With Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. In [1], under a mild local traffic condition, we establish a diffusion approximation for the workload process (and hence for the flow count process) in this model. We first recall that result in this paper. We then state results showing that when all of the weights are equal (proportional fair sharing) the diffusion has a product form invariant distribution with a strikingly simple interpretation in terms of dual random variables, one for each of the resources of the network. This result can be extended to the case where document sizes are distributed as finite mixtures of exponentials, and to models that include multi-path routing (these extensions are not described here, but can be found in [1]).

Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay

In this paper, we investigated Hopf bifurcation by analyzing the distributed ranges of eigenvalues of characteristic linearized equation. Using communication delay as the bifurcation parameter, linear stability criteria dependent on communication delay have also been derived, and, furthermore, the direction of Hopf bifurcation as well as stability of periodic solution for the exponential RED algorithm with communication delay is studied. We find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical simulation is presented to verify the theoretical results.

Scalable robust stability for nonsymmetric heterogeneous networks

Scalable decentralized stability certificates in networks i.e. decentralized stability guarantees for an arbitrary interconnection of heterogeneous dynamical systems, are often based on certain symmetry assumptions in the way the systems are interconnected. Such structure simplifies the mathematical analysis significantly, nevertheless a potential pitfall needs to be addressed: the stability proof might offer no robustness guarantees to deviations from protocol symmetry. This is, for example, the case for Internet congestion control stability results for arbitrary networks i.e. the stability proofs break down with an arbitrarily small deviation from protocol symmetry. We propose in the paper conditions that can guarantee scalable robust stability in a nonsymmetric interconnection setting for a class of networks that includes Internet congestion control models and consensus protocols. The certificates derived are decentralized and scale with the degree of nonsymmetry.

Stability analysis of a novel exponential-RED model with heterogeneous delays

Active Queue Management (AQM) schema provides an early indication of incipient congestion to the sources. However, in developing the AQM schema, there are some urgent problems to be solved, which are how to achieve higher bandwidth utility and smaller queuing delay, keep the stability of congestion control model, and derive some sufficient conditions for the stability. In this paper, we firstly demonstrate that the stability of most of the AQM algorithm is achieved by modifying the packet drop/mark probability function, and then analyze the merit and drawback of RED and its variants. We develop a discrete-time dynamical feedback system model with delay for a TCP/Reno network. By analyzing the dynamical model proposed based on frequency domain, the sufficient conditions are derived. The local stability conditions are validated by some simulation results in ns2. The simulation results show the proposed schema here can achieve the stable average queue length with high link utilization.

A positive systems model of TCP-like congestion control: asymptotic results

We study communication networks that employ drop-tail queueing and Additive-Increase Multiplicative-Decrease (AIMD) congestion control algorithms. It is shown that the theory of nonnegative matrices may be employed to model such networks. In particular, important network properties, such as: 1) fairness; 2) rate of convergence; and 3) throughput, can be characterized by certain nonnegative matrices. We demonstrate that these results can be used to develop tools for analyzing the behavior of AIMD communication networks. The accuracy of the models is demonstrated by several NS studies

Combined Model for Congestion Control

The growth of multimedia applications on the Internet made at least one fifth of the total network traffic to run over UDP. Unlike TCP, UDP is unresponsive to network congestion. This may cause, inter alia, bandwidth starvation of responsive flows, severe and prolonged congestions or, in the worst-case scenario, a congestion collapse. Hence, the coexistence of both protocols on fair-share premises converges towards impossibility. The paper deals with a new approach to solving the problem of taming down the unresponsive flows. By using some of the desirable properties of mobile agents, the system is able to control the influx of non-TCP or unresponsive flows into the network. Various functions performed by mobile agents monitor non-TCP flows, calculate sending rates and modify their intensity according to the needs of the network to attain as good performance as it is possible.

Delay induced Hopf bifurcation in a simplified network congestion control model

Abstract This paper studies delay induced Hopf bifurcation in a simplified network congestion control model. It is shown that there exists a critical value of delay for the stability of the network. When the value of feedback delay passes through the critical value, the system will lose its stability and Hopf bifurcation will occur. The stability and direction of the bifurcating periodic solutions are determined by perturbation procedure. A numerical example is also worked out to verify the theoretical analysis.

Asymptotic properties of a TCP model with time-outs

We examine a simple discrete time Markov model of TCP congestion control, which contains congestion avoidance, fast retransmit and time-out, and we prove that it has a unique invariant measure. If the process is scaled by a factor $\sqrt{p}$, then the invariant measures converge as $p \to 0$, where $p$ is the probability of error in any given data packet. This is the $1/\sqrt{p}$-behavior of TCP throughput. <br> If the scaled process is transformed to continuous time, we show that it converges to a piecewise linear limit process. The unique invariant measure of the limit process coincides with the limit of the invariant measures above and can be easily computed. <br> Finally, we examine a slightly more sophisticated way of modelling time-outs.

NEW CONGESTION CONTROL SCHEMES OVER WIRELESS NETWORKS: STABILITY ANALYSIS

The objective of this work is to introduce two original flow control schemes for wireless networks. The mathematical underpinnings lie on the recently-developed congestion control models for Transmission-Control-Protocol(TCP)-like schemes; more precisely, the model proposed by Kelly for the wired case is taken as a template, and properly extended to the more involved wireless setting. We introduce two ways to modify a part of the model; the first is through a static law, and the second via a dynamic one. In both cases, we prove the global stability of the schemes, and present a convergence rate study and a stochastic analysis.

A Fuzzy Congestion Control Algorithm Based on Queue

Internet applications are developed rapidly. It is increasingly important for router itself to improve the ability to deal with networking congestion. Traditional Poisson model is unfit for Internet networks with burst flow. But self-similarity model suitable for Internet networks has not been used widely in practice because of its complex model and complicated calculation. By describing the practical buffer performance in routers, a new fuzzy congestion control model based on queues and a congestion control algorithm based on the model are presented. In the algorithm, all kinds of packets are firstly classified into queues according to their own priorities. Then the buffer state is divided into three phases, including normal, congestion avoidance, and congestion according to their buffer usage ratio. The three phases are crossover each other because of their fuzziness. Then by combining the whole congestion control, with the part congestion control, the fuzzy algorithm is carried out. Theoretical analysis and NS stimulation results show that the proposed algorithm has better networking performance in the fairness of all connections, compared with the traditional schemes, especially keeping from being affected by the connections with congestion. It really improves the routers' ability to deal with network congestion.