Utility Functionals Associated With Available Congestion Control Algorithms

This paper is concerned with understanding the connection between the existing Internet congestion control algorithms and the optimal control theory. The available resource allocation controllers are mainly devised to derive the state of the system to a desired equilibrium point and, therefore, they are oblivious to the transient behavior of the closed-loop system. To take into account the real-time performance of the system, rather than merely its steady-state performance, the congestion control problem should be solved by maximizing a proper utility functional as opposed to a utility function. For this reason, this work aims to investigate what utility functionals the existing congestion control algorithms maximize. In particular, it is shown that there exist meaningful utility functionals whose maximization leads to the celebrated primal, dual and primal/dual algorithms. An implication of this result is that a real network problem may be solved by regarding it as an optimal control problem on which some practical constraints, such as a real-time link capacity constraint, are imposed

Congestion control algorithms from optimal control perspective

This paper is concerned with understanding the connection between the existing Internet congestion control algorithms and the optimal control theory. The available resource allocation controllers are mainly devised to derive the state of the system to a desired equilibrium point and, therefore, they are oblivious to the transient behavior of the closed-loop system. This work aims to investigate what dynamical functions the existing algorithms maximize (minimize). In particular, it is shown that there exist meaningful cost functionals whose minimization leads to the celebrated primal and dual congestion algorithms. An implication of this result is that a real network problem may be solved by regarding it as an optimal control problem on which some practical constraints, such as a real-time link capacity constraint, are imposed

Effects of Delay on the Functionality of Large-scale Networks

Networked systems are common across engineering and the physical sciences. Examples include the Internet, coordinated motion of multi-agent systems, synchronization phenomena in nature etc. Their robust functionality is important to ensure smooth operation in the presence of uncertainty and unmodelled dynamics. Many such networked systems can be viewed under a unified optimization framework and several approaches to assess their nominal behaviour have been developed. In this paper, we consider what effect multiple, non-commensurate (heterogeneous) communication delays can have on the functionality of large-scale networked systems with nonlinear dynamics. We show that for some networked systems, the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions; whereas in other cases the loop gains have to be compensated for by the delay size, in order to render functionality delay-independent for arbitrary network sizes. Consensus reaching in multi-agent systems and stability of network congestion control for the Internet are used as examples. The differences and similarities of the two cases are explained in detail, and the application of the methodology to other technological and physical networks is discussed

Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance

This paper analyzes dynamic user equilibrium (DUE) that incorporates the notion of boundedly rational (BR) user behavior in the selection of departure times and routes. Intrinsically, the boundedly rational dynamic user equilibrium (BR-DUE) model we present assumes that travelers do not always seek the least costly route-and-departure-time choice. Rather, their perception of travel cost is affected by an indifference band describing travelers’ tolerance of the difference between their experienced travel costs and the minimum travel cost. An extension of the BR-DUE problem is the so-called variable tolerance dynamic user equilibrium (VT-BR-DUE) wherein endogenously determined tolerances may depend not only on paths, but also on the established path departure rates. This paper presents a unified approach for modeling both BR-DUE and VT-BR-DUE, which makes significant contributions to the model formulation, analysis of existence, solution characterization, and numerical computation of such problems. The VT-BR-DUE problem, together with the BR-DUE problem as a special case, is formulated as a variational inequality. We provide a very general existence result for VT-BR-DUE and BR-DUE that relies on assumptions weaker than those required for normal DUE models. Moreover, a characterization of the solution set is provided based on rigorous topological analysis. Finally, three computational algorithms with convergence results are proposed based on the VI and DVI formulations. Numerical studies are conducted to assess the proposed algorithms in terms of solution quality, convergence, and computational efficiency