In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved numerically. Our solution methodology scales well to a large number of flows. As an application, we model and solve a system where RED is the AQM policy. Our results show excellent agreement with those of similar networks simulated using the well known ns simulator. Our model enables us to get an in-depth understanding of the RED algorithm. Using the tools developed in this paper, we present a critical analysis of the RED algorithm. We explain the role played by the RED configuration parameters on the behavior of the algorithm in a network. We point out a flaw in the RED averaging mechanism which we believe is a cause of tuning problems for RED. We believe this modeling/solution methodology has a great potential in analyzing and understanding various network congestion control algorithms.

Abstract — In this paper we use a previously developed nonlinear dynamic model of TCP to analyze and design Active Queue Management (AQM) control systems using RED. First, we linearize the interconnection of TCP and a bottlenecked queue and discuss its feedback properties in terms of network parameters such as link capacity, load and round-trip time. Using this model, we next design an AQM control system using the random early detection (RED) scheme by relating its free parameters such as the low-pass filter break point and loss probability profile to the network parameters. We present guidelines for designing linearly stable systems subject to network parameters like propogation delay and load level. Robustness to variations in system loads is a prime objective. We presentns simulations to support our analysis. I.

In this paper we study a previously developed linearized model of TCP and AQM. We use classical control system techniques to develop controllers well suited for the application. The controllers are shown to have better theoretical properties than the well known RED controller. We present guidelines for designing stable controllers subject to network parameters like load level, propogation delay etc. We also present simple implementation techniques which require a minimal change to RED implementations. The performance of the controllers are verified and compared with RED using ns simulations. The second of our designs, the Proportional Integral (PI) controller is shown to outperform RED significantly.

Virtual Queue-based marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to maintain small queue lengths and its robustness in the presence of extremely short flows (the so-called web mice). Using a mathematical tool motivated by the earlier work of Hollot et al, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several well-known AQM schemes such as RED, REM, PI controller and a non-adaptive virtual queue algorithm. With a view towards implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code. 1

FIFO queueing is simple but does not protect traffic from flows that send more than their share or flows that fail to use end-to-end congestion control. At the other extreme, per-flow scheduling mechanisms provide max-min fairness but are more complex, keeping state for all flows going through the router. This paper proposes RED-PD (RED with Preferential Dropping), a flow-based mechanism that combines simplicity and protection by keeping state for just the high-bandwidth flows. RED-PD uses the packet drop history at the router to detect high-bandwidth flows in times of congestion and preferentially drop packets from these flows. This paper discusses the design decisions underlying RED-PD, and presents simulations evaluating RED-PD in a range of environments.

Blue(SFB), a novel technique for enforcing fairness among a large number of flows. SFB scalably detects and rate-limits non-responsive flows through the use of a marking probability derived from the BLUE queue management algorithm and a Bloom filter. Using analysis and simulation, SFB is shown to effectively handle non-responsive flows using an extremely small amount of state information.

End-to-end congestion control mechanisms such as those in TCP are not enough to prevent congestion collapse in the Internet (for starters, not all applications might be willing to use them), and they must be supplemented by control mechanisms inside the network. The IRTF has singled out Random Early Detection (RED) as one queue management scheme recommended for rapid deployment throughout the Internet. However, RED is not a thoroughly understood scheme -- witness for example how the recommended parameter settings, or even the various benefits RED is claimed to provide, have changed over the past few years. In this paper, we describe simple analytic models for RED, and use these models to quantify the benefits (or lack thereof) brought about by RED. In particular, we examine the impact of RED on the loss and delay suffered by bursty and less bursty traffic (such as TCP and UDP traffic, respectively) . We find that (i) RED does eliminate the higher loss bias against bursty traffic obser...

In active queue management (AQM), core routers signal transmission control protocol (TCP) sources with the objective of managing queue utilization and delay. It is essentially a feedback control problem. Based on a recently developed dynamic model of TCPs congestion-avoidance mode, this paper does three things. First, it relates key network parameters such as the number of TCP sessions, link capacity and round-trip time to the underlying feedback control problem. Second, it analyzes the present de facto AQM standard: random early detection (RED) and determines that REDs queue-averaging is not beneficial. Finally, it recommends alternative AQM schemes which amount to classical proportional and proportional-integral control. We illustrate our results using ns simulations and demonstrate the practical impact of proportional-integral control on managing queue utilization and delay.

In order to stem the increasing packet loss rates caused by an exponential increase in network traffic, the IETF has been considering the deployment of active queue management techniques such as RED [14]. While active queue management can potentially reduce packet loss rates in the Internet, we show that current techniques are ineffective in preventing high loss rates. The inherent problem with these queue management algorithms is that they use queue lengths as the indicator of the severity of congestion. In light of this observation, a fundamentally different active queue management algorithm, called BLUE, is proposed, implemented and evaluated. BLUE uses packet loss and link idle events to manage congestion. Using both simulation and controlled experiments, BLUE is shown to perform significantly better than RED both in terms of packet loss rates and buffer size requirements in the network. As an extension to BLUE, a novel technique based on Bloom filters [2] is described for enforcing fairness among a large number of flows. In particular, we propose and evaluate Stochastic Fair BLUE (SFB), a queue management algorithm which can identify and rate-limit non-responsive flows using a very small amount of state information. I.

Random Early Detection (RED) is the recommended active queue management scheme for rapid deployment throughout the Internet. As a result, there have been considerable research efforts in studying the performance of RED. However, previous studies have often focused on relatively homogeneous environment. The effects of RED in a heterogeneous environment are not thoroughly understood. In this paper, we use extensive simulations to explore the interaction between RED and various types of heterogeneity, as well as the impact of such interaction on the user-perceived end-to-end performance. Our results show that overall RED improves performance at least for the types of heterogeneity we have considered.