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We study the problem of minimizing the maximum latency of flows in networks with congestion. We show that this problem is NP-hard, even when all arc latency functions are linear and there is a single source and sink. Still, one can prove that an optimal flow and an equilibrium flow share a desirable property in this situation: all flow-carrying paths have the same length; i.e., these solutions are "fair," which is in general not true for the optimal flow in networks with nonlinear latency functions. In addition, the maximum latency of the Nash equilibrium, which can be computed efficiently, is within a constant factor of that of an optimal solution. That is, the so-called price of anarchy is bounded. In contrast, we present a family of instances that shows that the price of anarchy is unbounded for instances with multiple sources and a single sink, even in networks with linear latencies. Finally, we show that an s-t-flow that is optimal with respect to the average latency objective is near optimal for the maximum latency objective, and it is close to being fair. Conversely, the average latency of a flow minimizing the maximum latency is also within a constant factor of that of a flow minimizing the average latenc

<p>Selfish routing is frequently discussed. The general framework of a system of non-cooperative users can be used to model many different optimization problems such as network routing, traffic or transportation problems.</p> <p>It is well known that the Wardrop user equilibria (i.e. the user optima) generally do not optimize the overall system cost in a traffic routing problem.</p> <p>In order to induce the equilibrium flow to be as close to the optimal flow as possible, the term “toll” is introduced. With the addition of tolls, a traffic system does not show the actual cost to the users but the displayed cost of users, which is the summation of the actual cost and the toll. A common behavioral assumption in traffic network modeling is that every user chooses a path which is perceived as the shortest path, then the whole system achieves the equilibrium of the displayed cost. It is proved that there exists an optimal toll which can induce the equilibrium flow under displayed cost to be the optimal flow in reality.</p> <p>However, this conclusion holds only if the selfish routing executes only once. If the game is played repeatedly, the users will detect the difference between the actual and displayed costs. Then, they will not completely trust the information given by the system and calculate the cost. The purpose of this thesis is to find out the optimal strategy given by the system–how to set tolls in order to maintain the flow as close to the optimal flow as possible.</p> / Master of Science (MSc)

<p>We study the application of reputation as an instigator of beneficial user behavior in selfish routing and when the network users rely on the network coordinator for information about the network. Instead of using tolls or artificial delays, the network coordinator takes advantage of the users' insufficient data, in order to manipulate them through the information he provides. The issue that arises then is what can be the coordinator's gain without compromising by too much on the trust the users put on the information provided, i.e., by maintaining a reputation for (at least some) trustworthiness.</p> <p>Our main contribution is the modeling of such a system as a repeated game of incomplete information in the case of single-commodity general networks. This allows us to apply known folk-like theorems to get bounds on the price of anarchy that are better than the well-known bounds without information manipulation.</p> / Master of Computer Science (MCS)