Price of Anarchy for Machines Models

Years and Authors of Summarized Original Work

• 2002; Czumaj, Vöcking

Problem Definition

This entry considers a selfish routing model formally introduced by Koutsoupias and Papadimitriou [10], in which the goal is to route the traffic on parallel links with linear latency functions. One can describe this model as a scheduling problem with m independent machines with speeds s₁, …, s _m and n independent tasks with weights w₁, …, w _n . The goal is to allocate the tasks to the machines to minimize the maximum load of the links in the system.

It is assumed that all tasks are assigned by noncooperative agents. The set of pure strategies for task i is the set {1, …, m}, and a mixed strategy is a distribution on this set.

Given a combination (j₁, …, j _n ) ∈ { 1, …, m}ⁿ of pure strategies, one for each task, the cost for task i is $\sum \nolimits_{j_{k}=j_{i}}\frac{w_{k}} {s_{j_{i}}}$, which is the time needed for machine j _i chosen by task ito complete all tasks allocated to that machine....