The Expected Competitive Ratio for Weighted Completion Time Scheduling

A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a so called diffuse adversary chooses the distribution F j of the random processing time P j from a certain class of distributions \(\mathcal{F}_{j}\). The scheduler is given the expectation \(\mu_{j}=\mathbb{E}[P_{j}]\), but the actual duration is not known in advance. A positive weight w j is associated with each job j and all jobs are ready for execution at time zero. The objective is to minimise the expected competitive ratio max\(_{F\in f} \mathbb{E}[\frac{\Sigma_{j}\omega_{j}C_{j}}{OPT}]\), where C j denotes the completion time of job j and OPT the offline optimum value. The scheduler determines a list of jobs, which is then scheduled in non-preemptive static list policy.

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