FIFO and Randomized Competitive Packet Routing Games

Abstract

In competitive packet routing games, packets route over time through a network from a start to a destination node. The packets selfishly minimize their arrival time, which depends on one hand on the transit times of the edges and on the other hand on the suffered waiting times. These occur whenever several packets try to enter an edge simultaneously. In those situations, scheduling policies determine which packet is allowed to enter this edge first and which has to wait.

We analyze the impact of two different scheduling policies on the inefficiency of equilibria, namely of a FIFO policy and a randomized policy. In a FIFO policy conflicts between interacting packets are resolved by their arrival time. In a randomized policy, an ordering of the packets is drawn uniformly at random and in any conflict the packet with the lower position is prioritized. While the existence of pure Nash equilibria in single/commodity games with the FIFO policy is already known, we provide a constructive proof for the existence of pure Nash equilibria in games with a randomized policy. In contrast, in multi/commodity games, there are examples without a pure Nash equilibrium for both policies. We provide several bounds on the price of anarchy and stability in single/commodity games and analyze the total price of anarchy in multi-commodity games. Surprisingly, the price of anarchy in single/commodity games is linear in the number of packets for both examined priority policies. For randomized priorities, we furthermore show a connection of parallel networks to singleton congestion games with affine linear cost functions. From this, we derive a tight constant bound on the price of stability and the price of anarchy.

We want to thank the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – UnRAVeL-Research Training Group 2236/1 for funding this research.