A control theoretic analysis of PID-controller based active queue management algorithms

基於 PID 控制器的主動隊列管理算法的控制論分析

Student thesis: Doctoral Thesis

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  • Yi LI

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Awarding Institution
Award date15 Feb 2006


Congestion control in the Internet consists of two main components: the Transmission Control Protocol (TCP) Additive-Increase Multiplicative-Decrease (AIMD) mechanism on sending window implemented by the end-user, and the Active Queue Management (AQM) scheme implemented at the router which can improve the effectiveness of congestion control. Recently, some Proportional- Integral-Derivative (PID) controllers based algorithms have been proposed as new AQM schemes for TCP congestion control. However, most of the proposed PID-controllers for AQM are validated for their performance and stability via intuitive explanations and simulation studies instead of theoretic analysis and performance evaluation. This study focuses on the control theoretic analysis of PID-controller based AQM algorithms. Based on some well-known TCP models, we analyze and enhance the PID-controller based AQMs by regarding the TCP congestion control mechanism as a feedback control system. The main findings of this research work can be summarized as follows: In this work, the stability of PID-controller based AQMs is analyzed. Stability is of great importance for the design of AQM algorithms. When an AQM controller stabilizes the queue length of the router around a given target, the link utilization can be improved, the buffer overflow can be significantly reduced, and the queuing delay or Quality of Service (QoS) can also be consistent. We review related work and propose some new solutions on the stability of TCP/PIDcontroller based AQM system. We derive a closed-form solution for the stable region of the control gains in PI-controller for AQM. Any control gain selected inside this region is stable. We also establish a sufficient condition under which the stability of the system is preserved. After obtaining the stable region, we develop a methodology for systematic selection of parameter values for PID-controller based AQMs. We propose three methods to parameterize the controllers based on Zzegler-Nichols Tuning Rule, Internal Model Control, and Gain and Phase Margins. Simulation results demonstrate that all of the three methods are effective in parameterizing the controllers. Among these methods, the parameter values based on Zzegler-Nichols Tuning Rule can speed up the response, while it is too aggressive in producing the packet drop probability. The Internal Model Control based PID-controller design reduces the complexity and takes the robust performance into account. The Gain and Phase Margins method results in a compromise between the stability and effectiveness. The above-mentioned parameterizing methods all require an accurate TCP reference model, which is rarely achieved with the time-varying nature of the Internet. As a result, PID-controller based AQMs are likely to show reduced effectiveness if fixed parameter values are used. In order to enhance effectiveness and stability of the network, we take uncertainties of the system described by the TCP model into consideration. A TCP/PI-controller system can be optimized if the controller is designed to minimize an H, norm of a certain function when the uncertainties are within some given ranges. We demonstrate that the simulation results are consistent with the theoretic analysis. Time delays, such as propagation delay, queuing delay in the buffer of the router, cause degradation of performance and instability of the network. When the time delay is small, PID-controller based AQMs can be effective if the controllers are elaborately tuned. Unfortunately, PID-controller based AQMs could lead to poor performance when the time delay is large. To handle large time delay, Smith Predictor is commonly adopted to implement effective compensation. In this work, a Smith-Predictor-based PI-controller for AQM (SPPA) is proposed as a new enhancement of PI-controller. When a mismatch exists in between the actual model of the TCP process and the reference model employed by the SPPA, we demonstrate conditions under which the stability of the network can be maintained. The results of simulations are presented to demonstrate the excellent consistency with the theoretic analysis of SPPA. Finally, many control theoretic techniques have been used in the study for the implementation of AQM schemes as well as the maintenance of their stability under varying network condition. We find such control theoretic techniques effective in the design of PID-controller based AQM schemes.

    Research areas

  • Telecommunication, Internet, Traffic, Management