This paper deals with optimizing end-to-end window control algorithms that achieve proportional fairness in the long run, and also investigating their steady state and transient or short-term fairness. An abstracted stochastic model of a bottlenecked connection is employed and the window control is designed to minimize the buffer queue variance while keeping the mean queue level at a target value, taking the round-trip delay into account. An optimal minimum variance window control algorithm and its generalized version are derived with the major aim of reducing the window size fluctuations. A relation between the generalized version and the (p, 1) proportionally fair algorithm is investigated. Also we derive the stability limits of the generalized minimum variance window control algorithm which can be useful during network design. The effects of both the target queue length and a weighting parameter on the steady state and short-term fairness, as measured by Jain's fairness and short-term fairness indices, calculated over short time intervals, are investigated by simulation. The generalized algorithm has better fairness properties as compared to existing algorithms such as that employed in TCP Vegas.

Using the Proportional Integral Derivative (PID) principle of classical feedback control theory, this paper develops two general congestion control algorithms for routers implementing Active Queue Management (AQM) while supporting TCP/IP traffic flows. The general designs of non-interacting (N-PID) and interacting (I-PID) congestion control algorithms are tailored for practical network scenarios using the Ziegler-Nichols guidelines for tuning such controllers. Discrete event simulations using ns are performed to evaluate the performance of an existing F-PID and new N-PID and I-PID algorithms. The performance of N-PID and I-PID is compared mutually as well as with the F-PID algorithm. It reveals that N-PID and I-PID have higher speed of response but lower stability margins than F-PID. In general the accurate following of the target queue size by the PID principle congestion control algorithms, while providing high link utilization, low loss rate and low queuing delays, is also demonstrated.