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.

在网络调度中，必须在由完整图形连接的统一机器（处理器）上调度作业（任务），以最大程度地减少总加权完成时间。此设置可应用于分布式多处理器计算环境以及运筹学中。在本文中，我们研究了在以下情况下的随机分散机制的设计：一组非抢占性作业从一组要处理的统一机器中随机选择一台机器，每台机器一次最多可以处理一个作业。我们引入了近视贝叶斯-纳什激励相容性的新概念，该概念削弱了经典贝叶斯-纳什激励相容性，并在假设每个工作都是理性和自私的前提下得出了随机分散的机制。我们证明了我们的机制可以通过使用图形理论解释激励相容性约束来诱使工作真实地报告其近视贝叶斯-纳什可实施性的私人信息。此外，我们证明了该机制的性能是渐近最优的。