Tobias Harks

Utility proportional fair bandwidth allocation: an optimization oriented approach

In this paper, we present a novel approach to the congestion control and resource allocation problem of elastic and real-time traffic in telecommunication networks. With the concept of utility functions, where each source uses a utility function to evaluate the benefit from achieving a transmission rate, we interpret the resource allocation problem as a global optimization problem. The solution to this problem is characterized by a new fairness criterion, utility proportional fairness. We argue that it is an application level performance measure, i.e. the utility that should be shared fairly among users. As a result of our analysis, we obtain congestion control laws at links and sources that are globally stable and provide a utility proportional fair resource allocation in equilibrium. We show that a utility proportional fair resource allocation also ensures utility max-min fairness for all users sharing a single path in the network. As a special case of our framework, we incorporate utility max-min fairness for the entire network. To implement our approach, neither per-flow state at the routers nor explicit feedback beside ECN (Explicit Congestion Notification) from the routers to the end-systems is required.

Strong Nash Equilibria in Games with the Lexicographical Improvement Property

We provide an axiomatic framework for the the well studied lexicographical improvement property and derive new results on the existence of strong Nash equilibria for a very general class of congestion games with bottleneck objectives. This includes extensions of classical load-based models, routing games with splittable demands, scheduling games with malleable jobs, and more.

Characterizing the Existence of Potential Functions in Weighted Congestion Games

Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let

Stackelberg Strategies and Collusion in Network Games with Splittable Flow

\mathcal{C}

Strong equilibria in games with the lexicographical improvement property

be an arbitrary set of locally bounded functions and let

Stackelberg Routing in Arbitrary Networks

\mathcal{G}(\mathcal{C})

On the existence of pure nash equilibria inweighted congestion games

be the set of weighted congestion games with cost functions in

Optimal Cost Sharing for Resource Selection Games

\mathcal{C}

Priority pricing in utility fair networks

. We show that every weighted congestion game

Computing pure Nash and strong equilibria in bottleneck congestion games

G\in\mathcal{G}(\mathcal{C})