Bottleneck flows in unit capacity networks
Information Processing Letters
The Impact of Oligopolistic Competition in Networks
Operations Research
Stackelberg Routing in Arbitrary Networks
Mathematics of Operations Research
ACM Transactions on Algorithms (TALG)
Congestion games with failures
Discrete Applied Mathematics
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Stronger Bounds on Braess's Paradox and the Maximum Latency of Selfish Routing
SIAM Journal on Discrete Mathematics
Conflicting Congestion Effects in Resource Allocation Games
Operations Research
The effectiveness of stackelberg strategies and tolls for network congestion games
ACM Transactions on Algorithms (TALG)
On the Efficiency-Fairness Trade-off
Management Science
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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, 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 optimal flows 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 with multiple sources and a single sink for which the price of anarchy is unbounded, even in networks with linear latencies. Furthermore, 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 latency.