Increased mobility coupled with a possible reduction of cabling costs and deployment time makes wireless communication an attractive alternative for the industrial process monitoring and control. The major obstacles towards the utilisation of wireless industrial systems are predominantly the timing and reliability requirements. In this study, the authors take jointly the timing and reliability requirements, limited wireless resources and the cyclic data feature into consideration, and study the performance bounds and two-stage time- and channel-optimal convergecast scheduling algorithms for wireless industrial systems with hierarchical star and mesh architecture. Specifically, they consider the convergecast communication for wireless industrial systems operating according to the recent wireless network for industrial automation-process automation standard; and they will provide bounds on the minimum convergecast schedule length and bounds on the minimum number of channels for cluster-line and cluster-tree routing structures. In both cases, they propose time- and channel-optimal twostage scheduling algorithms. They evaluate the author's two-stage scheduling algorithms by both simulation and real hardwares. Numerical results demonstrate that their algorithms are efficient compared with traditional time division multiple access-based convergecast scheduling algorithms.