| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 428554 | Information Processing Letters | 2013 | 4 Pages |
In this paper, we study the problem of selfish scheduling game under a grade of service provision, where all machines and all jobs are labeled with the different grade of service (GoS) levels such that a job J can be assigned to execute on machine M only when the GoS level of machine M is not higher than the GoS level of job J . We consider two coordination mechanisms for this selfish scheduling game: the makespan policy and the LG-LPT policy. For the first mechanism, we show that the price of anarchy is exactly 32 for two machines and Θ(logmloglogm) for m (⩾3)(⩾3) machines, respectively. For the second mechanism, we point out that the price of anarchy is 54 for two machines and 2−1m−1 for m (⩾3)(⩾3) machines, respectively, and we finally analyze the convergence to a Nash equilibrium of the induced game.
► We study two coordination mechanisms for the selfish scheduling game under a GoS provision: makespan policy and LG-LPT policy. ► For first mechanism, the POA is 32 for two machines and Θ(logmloglogm) for m (>3)(>3) machines, respectively. ► For second mechanism, the POA is 54 for two machines and 2−1m−1 for m (>3)(>3) machines, respectively. ► We finally analyze the convergence of the second mechanism to a Nash equilibrium of the induced game.
