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A star-linear industry wireless sensor network (IWSN) for narrow process industries is proposed in this paper. Based on the proposed IWSN, we focus on time-efficient convergecast solutions. We present algorithms to achieve optimal convergecast performance in terms of time slots use. In the proposed IWSN, the field devices (FDs) constitute a set of TDMA (time division multiple access) based star topology clusters, and the cluster heads present a multihop linear backbone. Time slots are scarce communication resource for convergecast in a narrow IWSN. Aiming to use slots efficiently, we design optimal algorithms to improve the polling scheduling in the cluster and the packets forwarding over the backbone. In a cluster, we design a multicycle scheduling algorithm and a fair polling algorithm to improve slots utility of the communication reliability and integrity. Over the backbone, an optimal slots allocating algorithm is designed to maximize the slots performance in terms of the end-to-end communication reliability, based on which a slot-efficient multisuperframe scheduling algorithm is presented. 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