On AIMD Congestion Control in Multiple Bottleneck Networks.

We consider a linear algebraic model of the Additive-Increase Multiplicative-Decrease congestion control algorithm and present results on average fairness and convergence for multiple bottleneck networks. Results are presented for networks of both long-lived and short-lived flows

Modelling TCP congestion control dynamics in drop-tail environments

In this paper we study communication networks that employ drop-tail queueing and additive-increase multiplicative-decrease (AIMD) congestion control algorithms. We show that the theory of non-negative matrices may be employed to model such networks and to derive basic theorems concerning their behaviour

Scalable laws for stable network congestion control

Discusses flow control in networks, in which sources control their rates based on feedback signals received from the network links, a feature present in current TCP protocols. We develop a congestion control system which is arbitrarily scalable, in the sense that its stability is maintained for arbitrary network topologies and arbitrary amounts of delay. Such a system can be implemented in a decentralized way with information currently available in networks plus a small amount of additional signaling

Impact of Drop Synchronisation on TCP Fairness in High Bandwidth-Delay Product Networks.

In this paper we consider the performance of several well known high speed protocols in environments where individual flows experience different probabilities of seeing a drop in drop-tail buffers. Our initial results suggest the properties of networks in which these protocols are deployed can be sensitive to changes in these probabilities. Our results also suggest that AQM protocol co-design may be helpful in mitigating this sensitivity

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Distributed, Private, and Derandomized Allocation of Subsidized Goods

Efficient resource allocation is challenging when privacy of users is important. Distributed solution approaches have recently been used extensively to find a solution for such problems. In this work, we study the efficiency of distributed AIMD algorithm for allocation of subsidized goods. To this end, we assign each user a suitable utility function describing the amount of satisfaction that it has from allocated resource. We define the resource allocation as a \emph{total utilitarianism} problem that is an optimization problem of sum of users utility functions subjected to capacity constraint. Recently, a stochastic state-dependent variant of AIMD algorithm is used for allocation of common goods among users with strictly increasing and concave utility functions. We improve this algorithm to allocate subsidized goods to users with concave and nonmonotonous utility functions as well as users with quasi-concave utility functions. We also derandomize the AIMD algorithm and compare its efficiency with the stochastic version. We then model resource allocation problem as a competition game to evaluate the efficiency properties of unique equilibrium when network parameters change. To illustrate the effectiveness of the proposed solutions, we present simulation results for a public renewable-energy powered charging station in which the electric vehicles (EV) compete to be recharged