Competitive Packet Routing with Priority Lists

Abstract

In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.

Equilibria in Routing Games with Edge Priorities

“…al. [14], we can show that the socially optimal state of a given symmetric game with edge priorities is an earliest arrival flow, too. Similar to the model with player priorities, there is always a socially optimal solution with edge priorities, where players only wait at the source node in an earliest arrival flow in a network with unit capacities due to the fact that an earliest arrival flow fulfills strong flow conservation.…”

“…They focus on the comparison between Nash equilibria and equilibria in a game with full control (subgame perfect equilibria) on acyclic graphs. In the paper at hand, we will use the subordinated tie-breaking of Cao et al [5] as our main criterion in a non FIFO setting similar to the model in Harks et al [14].…”

“…The throughput capacity of a node v can be limited by replacing this node by an edge (v ′ , v ′′ ) with the desired capacity and costs zero. Similar to the work of Harks et al [14], we restrict to integral transit times, since each player blocks exactly one capacity unit for one time unit on each edge of its path.…”

“…Depending on applications, there is a huge range of models. There are games with non-atomic [16] as well as atomic players [15], further there are games with continuous time [15] as well as games with discrete time steps [14].Usually, players are allowed to enter an edge directly at their arrival time. An essential ingredient of these models is the priority rule for tie-breaking.…”

“…Some models maintain the overall arrival order with a first-in firstout rule [8,15,16], i.e., only players with the exact same arrival time are re-arranged. Other models allow overtaking by higher prioritized players with global priority lists [14,15] or local priority lists [14] of players, that is, priority is a player inherent property and players are linearly ordered.…”