## 1 Introduction  
Industrial intelligent technology has attracted the considerable attention of the manufacturing industries of all countries in the world. Industry and academia have invested a large number of funds, technology, and efforts in this area. Its main objective is to digitize and intelligentize the information of supplies, manufacturing and sale information by cyber-physical systems (CPS), and achieve a fast, efficient and personalized product supply [1; 2]. Smart industrial wireless sensor networks (SIWSNs) is identified as an essential technology to pave the way to this goal [2; 3; 4]. With SIWSNs, data sensing, gathering and communicating are performed intelligently by all kinds of industrial wireless sensors (e.g., photoelectric sensor, ultrasonic sensor, gas sensor, video sensor [5; 6; 7; 8]). Thus, data can be exchanged and managed autonomously and efficiently [9; 10]. Additionally, sensors can self-organize the routing path in the network [11; 12; 13] and automatically update the path according to the application. This feature gives SIWSNs a superior performance that the inherent drawbacks of wired industrial networks can be well overcome [14; 15]. Nowadays, smart WSNs have been widely applied in industrial application scenarios, ranging from environment monitoring to urban health monitoring [14; 16], vehicular communication networks [6; 17], cyber-physical cloud systems [18; 19; 20; 21; 22], multi-channel cognitive radio networks [8; 23], crowdsourcing networks [24; 25; 26], social network [27; 28; 29; 30]. The growing demand for wireless sensors in the smart industry makes Quality-of-Service (QoS) one of the paramount issues in wireless sensor-based applications [31; 32; 33; 34]. For SIWSNs, the two most significant QoS indicators are the energy efficiency [11; 15; 21; 23; 35; 36; 37; 38] and delay [2; 35; 37; 39; 2; 8; 33; 2]. Delay is vital for industrial sensor networks. The studies in energy efficiency focus on how to reduce the energy consumption to improve network lifetime. For the optimization of energy consumption, data aggregation is an effective method [28; 40; 41]. In the data transmission process, data packets can be aggregated into the packets with a smaller size. Therefore, energy consumption can be reduced [40; 41; 42]. This is categorized as aggregation routing problem. In the previous research of data aggregation routing, all nodes have the same values of \(N_{t}\) and \(T_{t}\). Small value of \(N_{t}\) and \(T_{t}\) are set to make the data with small delay deadline satisfy its QoS requirement. However, this keeps a low network lifetime. In most industrial applications, most of the data is delay-insensitive, and there is small proportion of delay-sensitive data. Adopting the top QoS parameters setting (setting \(N_{t}\) and \(T_{t}\) to satisfy the QoS requirement of the most emergent data) can ensure that all the data meet their requirements of application, but the frequency of aggregation is improved and the lifetime is significantly reduced. In this scenario, differentiated data aggregation routing is a wise option [43]. The main idea is to set different dominant parameters for different QoS requirements. Based on the premise of meeting different QoS requirements, the energy consumption and delay are reduced and the performances increase. However, the special nature of data aggregation routing makes the scheme difficult to be fully implemented. Each node in the network prepares various \(N_{t}\) and \(T_{t}\) for QoS requirements. When the data in a node satisfies some aggregation condition, all data packets in the queue should be aggregated and transferred. However, this strategy makes the data with restrict QoS requirement difficult to be keep valid, and gives the data with loose QoS requirement an unnecessary and superfluous service guarantee. Moreover, if we use the strategy that only the data with corresponding service requirement is aggregated when a requirement is satisfied, the data storage structure is more complex and the energy consumption in transmission increases.