Coordination mechanism for selfish scheduling under a grade of service provision

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 3/2 for two machines and Theta(log m/log log m) for m (>= 3) machines, respectively. For the second mechanism, we point out that the price of anarchy is 5/4 for two machines and 2 - 1/m-1 for m (>= 3) machines, respectively, and we finally analyze the convergence to a Nash equilibrium of the induced game. (c) 2013 Elsevier B.V. All rights reserved.