  The Industrial Internet of Things (IIoT) has become a critical technology to
accelerate the process of digital and intelligent transformation of industries.
As the cooperative relationship between smart devices in IIoT becomes more
complex, getting deterministic responses of IIoT periodic time-critical
computing tasks becomes a crucial and nontrivial problem. However, few current
works in cloud/edge/fog computing focus on this problem. This paper is a
pioneer to explore the deterministic scheduling and network structural
optimization problems for IIoT periodic time-critical computing tasks. We first
formulate the two problems and derive theorems to help quickly identify
computation and network resource sharing conflicts. Based on this, we propose a
deterministic scheduling algorithm, \textit{IIoTBroker}, which realizes
deterministic response for each IIoT task by optimizing the fine-grained
computation and network resources allocations, and a network optimization
algorithm, \textit{IIoTDeployer}, providing a cost-effective structural upgrade
solution for existing IIoT networks. Our methods are illustrated to be
cost-friendly, scalable, and deterministic response guaranteed with low
computation cost from our simulation results.
