Design a congestion controller based on sliding mode variable structure control☆
Introduction
TCP congestion control mechanisms, while necessary and powerful, are not sufficient to provide good services in all circumstances, especially with the rapid growth in size and the strong requirement for QoS guarantee, because there is a limit how much control can be accomplished at the end system. It is needed to implement some measures in the intermediate nodes to complement the end system congestion avoidance mechanisms. Active Queue Management, as one class of packet dropping/marking mechanism in the router queue, has been recently proposed to support the end-to-end congestion control in the Internet [1]. It has been a very active research area in the Internet community.
The goals of AQM are to (1) reduce the average length of queue in routers and thereby decrease the end-to-end delay experienced by packets, and (2) ensure efficient use of network resources by reducing the packet loss due to queue overflow. AQM highlights the trade-off between delay and throughput. By keeping the average queue size small, AQM can provide greater capacity to accommodate nature-occurring bursts without dropping packets, while at the same time, it can reduce the delays seen by flow. This is particularly important for real-time interactive applications. RED [2] was originally proposed to achieve fairness among sources with different burst attributes and to control queue length. Because it meets the requirements of AQM, RED was the only algorithm recommended for AQM in RFC 2309.
RED is a heuristic algorithm, and dependents on experience. Partial simulations and experiments on special network configurations are the only measures used to validate the algorithm performance, while the systematic and theoretic analysis and evaluation are neglected. Thus we lack the complete understanding of the algorithm performance and efficiency. Once the problems occur in practice, remediation is made through new simulations or experiments. For instance, the original paper about RED presented the impact of configuration parameter on performance, and suggested the guidelines towards the appropriate values based on heuristics and simulation. Subsequently, some further investigations found that they were not optimal, and then gave the current suggestion [11], where wq (weighted factor) is increased from 0.001 to 0.002 because wq is too low to timely detect the congestion in a relative high speed network; maxp (maximum packet dropping probability) is set to 0.1 instead of to 0.02 because 2% drop probability is not enough to force multiple TCP sources to sufficiently reduce their window sizes, especially in many short-lived and burst HTTP sessions. The heuristic design has not always been scientific and reasonable for all conditions. Of course, since the Internet is a rather complex huge system, it is very difficult to have a full-scale and systematic comprehension, but the importance has been considerably noted.
The mathematical modeling of Internet is the first step towards an in-depth understanding, and the algorithms designed based on the rational model should be more reliable than one originated from experience. The non-linear dynamic model for TCP flow control [12] inspired Hollot et al. to design the PI controller for AQM [13]; Kunniyur and Srikant also proposed the Adaptive Virtual Queue (AVQ) algorithm for AQM based on this non-linear model [14]. Kelly et al. constructed a unified framework [15], in which the problem of congestion control was formulated as a convex program, and the aggregate source utility was maximized subject to bandwidth constrain. Random Early Marking [16] was a controller designed in a dual formulation to obtain optimal source rates.
In this paper, we will follow the design approach based on the theoretical model. However, The linear model used in Ref. [13] differs from the real network model in the following ways (1) the model considers TCP flows only and ignores other kinds of flows. (2) The different versions of TCP implementation, such as TCP Reno, TCP New-Reno and TCP Vegas, etc. will coexist in the Internet. Actually, the model only describes the TCP Reno congestion control mechanism exactly. (3) The model describes the AIMD behavior of TCP while ignores slow start and timeout, thus it is accurate under most conditions where congestion avoidance is the primary operating state of TCP, especially for long-lived transmissions like FTP flows. In the case of short-lived flows like Telnet and Web, slow start and timeout will frequently occur when more than one packet is dropped consecutively in a single window. (4) When evaluating partials at the operating point during linearization [13], either the number of active TCP connections or their round-trip times are assumed constant. However, these parameters are highly variable in time-varying networks. In view of the model inaccuracy mentioned earlier, a regulation mechanism should be chosen to be able to eliminate the mismatch caused by the simple linear system model from a control standpoint. Moreover, the performance of the selected controller should be insensitive to the drift of system parameters as well. The robust sliding mode variable structure controller is able to tolerate the model mismatch, and resist against the noise. This idea motivates our work in this paper.
The remainder of the paper is organized as follows. In Section 2, we provide an introduction to the related works, the background on TCP flow control model and Sliding Mode Variable Structure control. Section 3 develops the SMVS controller, and presents design guidelines. In Section 4, we testify to the validity of SMVS controller, and then compare its performance with that of the PI controller by numerical simulation results. Finally the conclusion is drawn in Section 5.
Section snippets
Related works
Since RED was recommended as candidate algorithm for AQM, there had been many full-scale investigations into its integrated performance. Many subsequent studies have verified that RED suffers from the defects of instability and unfairness in some network environments. Christiansen et al. [5], taking an experiment approach, conclude that tuning RED for stable operation is difficult. As for theoretical analysis about RED stability, Firoiu and Borden [3] modeled the relationship between queue
SMVS algorithm
In this section, we discuss the design of SMVS controller for AQM. First, suppose that The plant depicted in Fig. 1 is described by a second-order system of differential equations:where
F(t) can be regarded as the external disturbance. For the convenience
Performance evaluation
We evaluate the effectiveness and performance of the SMVS controller by simulations using ns2 simulator [18]. The network topology is shown in Fig. 5. The only bottleneck link lies between node A and node B. The buffer size of node A is 300 packets, and the packet default size is 500 bytes. Queue A is SMVS scheme, and the others are Drop Tail. All sources are classed into three groups. The first group is N1 greedy sustained FTP application sources. The second group is composed of N2 burst HTTP
Conclusion and furture works
AQM is an effective mechanism to support end-to-end congestion control. Most of works mainly focus on the analysis of stability and fairness of the existing various schemes, and the exploration of the heuristic algorithms. Since the experience and partial simulations are not absolutely reliable, the theoretical and systematic approaches should be used in designing and evaluating algorithms for flow and congestion control. According to the operation mechanism of AQM, it is reasonable to regard
Acknowledgements
The authors faithfully appreciate the anonymous reviewers for their valuable comments. This work is funded by the National Natural Science Foundation of China (No. 60273009), and the Projects of Development Plan of the State Key Fundamental Research (No. 2003CB314804).
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The abbreviated version of this paper was published in Proceedings of IEEE INFOCOM2002, San Francisco, USA, July, 2002.
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Present Address: Academy of Opto-Electronics, Chinese academy of Sciences, Beijing, 10083, China.