On the modeling and optimization of discontinuous network congestion control systems

AIMD is a widely-used network congestion control scheme. Despite its discontinuous control behavior, the majority of contemporary literature employed a statistically-averaged continuous model to approximate AIMD without considering its discontinuity. The design of a discontinuous control system must be based on rules that are entirely different from that of continuous control systems. Ignoring discontinuity issues results in great discrepancy between analytical models and the practice. In this paper we use the sliding mode control (SMC) theory to investigate congestion control without ignoring its discontinuity. Based on the SMC theory, the design of discontinuous (congestion) control systems must consider the relative degree and zero dynamics of the system, in order to guarantee asymptotic stability. This framework can precisely reflect the behavior of the control rules and the controlled objective of a congestion control system. We show that the relative degree of the control system of rate-based, AIMD flow-control algorithms is two. That is, to apply sound control principles to the design of AIMD algorithms, one should use both the queue length error and its first order time derivative to construct the switching function of the control model of an active queue management scheme. Based on the SMC model, one can quantify the tradeoffs among the convergence speed, the amount of throttling adjustments, and the degree of oscillations. We show quantitatively that one can guarantee stability conditions, drastically reduce oscillation of AIMD without significant loss of fairness and stability, and quantitative understanding of the tradeoffs among oscillation, delay and fairness.