# Efficient Resource Scheduling for Multipath Retransmission over Industrial WSAN Systems
## 2 Related Works  
The use of multiple channels in the TSCH MAC protocol enables benefits including diversity, network scalability, and optimized scheduling. In the last couple of years, a notable trend in multichannel MAC solutions can be seen in Reference [16]. [PERSON] et al. [17] present multichannel, TSCH-based source-aware scheduling schemes for WSNs. The algorithm benefits from multiple channels but fails to guarantee reliability. [PERSON] et al. [5] extend the SchedEx [18] scheme to a multichannel scenario by introducing scalable integration in existing schemes. The authors also claim to cut latencies around 20% in the schedules from ShedEx. [PERSON] et al. [19] proposed a distributed solution based on multichannel allocation that achieves max-min fairness among multiple flows. However, the fairness of channel use in such approach needs to trade off throughput. Researches, such as References [20; 21; 22; 23], deeply exploit the use of multiple channels. The approaches proposed in these literatures focus on decreasing the interferences while using multiple channels in their specific type of WSNs. Therefore, this paper also makes full use of available channels to optimize TSCH scheduling.  
Multipath routing allows multiple streams of information from source to sink, which significantly increases the reliability of data reception, especially in industrial environments. [PERSON], [PERSON] et al. [24] propose a complete process of channel assignments for adaptive and energy-efficient data collection protocol, which could schedule the node connectivity based on traffic load. [PERSON] et al. [25] proposed a scheduling algorithm for multipath routing structures, the objective of which is to reduce the message complexity. [PERSON] et al. [26] propose a novel channel-hopping methods for the exchange of data packages, which could prevent links, sharing the same destination from using channels with strong correlations. [PERSON] et al. [27] proposed a mixed criticality scheduling algorithm, which guarantees the real-time performance and reliability requirements of data flows with different levels of criticality. Through the empirical studies, the above researches also show that graph routing leads to significant improvements over source routing in terms of worst-case reliability, where graph routing protocol is a classical multipath transmission approach in the WirelessHART standard. However, none of these researches simultaneously consider the effect of collision, path crossing, and diverse period on TSCH scheduling, which also lacks concentration on schedulability in a large WSAN.  
The gateway resides at the root of all graphs in a wireless network, and it can provide multiple network access points, which are named sink nodes in this paper. The responsibility of a sink node is to maintain the connection between wireless nodes and the gateway, where most researches regard a sink node as a gateway [28]. However, the sink node is a hotspot and experiences more link conflicts than other nodes do when we schedule a multi-hop routing graph. Due to the deadline of industrial data transmission, this characteristic seriously decreases the schedulable ratio, especially in larger networks. Therefore, this paper provides multiple sink nodes to avoid the link scheduling conflicts and to improve the use of communication resources. In Reference [29], the authors apply the theory of compressive sensing on a multi-sink wireless sensor network, which could improve the capability for data gathering. However, the presented architecture of the network is not complicated enough to support routing graphs. Multiple sinks are generally used in the distributed scenario to balance the traffic load, which is responsible for packet collection as a substation [30; 31; 32; 33]. In this paper, we realize a multi-sink gateway to achieve a highly schedulable WSAN in a practical industrial application.