Randomized mechanism design for decentralized network scheduling

In the network scheduling, jobs (tasks) must be scheduled on uniform machines (processors) connected by a complete graph so as to minimize the total weighted completion time. This setting can be applied in distributed multi-processor computing environments and also in operations research. In this paper, we study the design of randomized decentralized mechanism in the setting where a set of non-preemptive jobs select randomly a machine from a set of uniform machines to be processed on, and each machine can process at most one job at a time. We introduce a new concept of myopic Bayes–Nash incentive compatibility which weakens the classical Bayes–Nash incentive compatibility and derive a randomized decentralized mechanism under the assumption that each job is a rational and selfish agent. We show that our mechanism can induce jobs to report truthfully their private information referred to myopic Bayes–Nash implementability by using a graph theoretic interpretation of the incentive compatibility constraints. Furthermore, we prove that the performance of this mechanism is asymptotically optimal.