Wardrop Equilibria and Price of Stability for Bottleneck Games with Splittable Traffic

  • Vladimir Mazalov
  • Burkhard Monien
  • Florian Schoppmann
  • Karsten Tiemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


We look at the scenario of having to route a continuous rate of traffic from a source node to a sink node in a network, where the objective is to maximize throughput. This is of interest, e.g., for providers of streaming content in communication networks. The overall path latency, which was relevant in other non-cooperative network routing games such as the classic Wardrop model, is of lesser concern here.

To that end, we define bottleneck games with splittable traffic where the throughput on a path is inversely proportional to the maximum latency of an edge on that very path—the bottleneck latency. Therefore, we define a Wardrop equilibrium as a traffic distribution where this bottleneck latency is at minimum on all used paths. As a measure for the overall system well-being—called social cost—we take the weighted sum of the bottleneck latencies of all paths.

Our main findings are as follows: First, we prove social cost of Wardrop equilibria on series parallel graphs to be unique. Even more, for any graph whose subgraph induced by all simple start-destination paths is not series parallel, there exist games having equilibria with different social cost. For the price of stability, we give an independence result with regard to the network topology. Finally, our main result is giving a new exact price of stability for Wardrop/bottleneck games on parallel links with M/M/1 latency functions. This result is at the same time the exact price of stability for bottleneck games on general graphs.


Nash Equilibrium Social Cost Sink Node Latency Function Maximum Latency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vladimir Mazalov
    • 1
  • Burkhard Monien
    • 2
  • Florian Schoppmann
    • 2
  • Karsten Tiemann
    • 2
  1. 1.Institute of Applied Mathematical Research, Karelian Research CenterRussian Academy of SciencesPetrozavodskRussia
  2. 2.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany

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