Dr Sonja Stuedli

Recently the additive increase multiplicative decrease (AIMD) algorithm has been applied in fields other than congestion control in communications networks. A major attribute of these new applications is that the share of each user is bounded. Simulations suggest that AIMD performs well, even in the case of individual constraints on each user. In this paper, we provide a formal proof of exponential convergence to a unique fixed-point for the AIMD algorithm under individual user constraints.

We present a convergence result for a nonhomogeneous Markov chain that arises in the study of networks employing the additive-increase multiplicative decrease (AIMD) algorithm. We then use this result to solve the network utility maximisation (NUM) problem.

The additive increase multiplicative decrease (AIMD) algorithm, that is commonly used for congestion avoidance in communication networks, has recently been suggested in other fields such as load management in electric power networks. As for congestion avoidance, in such systems a large number of agents are required to share a given resource. In recent work by Shorten, Wirth and Leith on congestion control in networking a stochastic model has been developed to analyse AIMD algorithms. However, the analysis assumes a continuous implementation of the algorithm and a constant available resource. These assumptions are no longer useful if the AIMD algorithm is applied in fields such as load management in electric power networks, where a discrete implementation is often required, and the available resource shared may be inherently variable. In this paper we develop a disturbed AIMD model based on the model introduced by Shorten et al. that includes discrete time implementation and time varying resource availability. Further, we use that model to bound the influence of these disturbances, caused by either a discrete implementation or small variations in the available resource.

This paper exploits the analogy between the electrical grid and modern communication networks to implement Electric Vehicle (EV) battery charging scheduling algorithms inspired by popular communication network techniques. In preliminary works, a similar approach was used to manage the Grid-to-Vehicle (G2V) active power flows. In this paper, we extend this framework to both implement the Vehicle-to-Grid (V2G) concept and to provide reactive power compensation capabilities that do not affect charging times. The ability of the proposed algorithms to optimally share the available/desired power in a fair way, with minimum communication requirements, in a very uncertain, dynamically changing framework, is illustrated through several examples for different scenarios of interest. © 2014 © 2014 Taylor & Francis.