## 1 Introduction
Therefore, in the design and implementation of IWSNs, how to reduce a data routing delay is a critical issue [30; 31]. Researchers define the total time required for data to be transmitted from the source node to the sink as end to end delay [13; 14; 23; 30; 31]. In the process of routing [32; 33; 34; 35], the time that data is received from one node to be successfully transferred to the next hop is a single hop delay. Because end to end delay is the accumulation of the single hop delay for each node in the routing process [18], the farther the distance from the source node to the sink, the more hops on the routing path, and consequently the greater the end to end delay. Thus, reducing the single hop delay is a fundamental and effective way to reduce the end to end delay. But the single hop delay (or delay for short) is affected by many factors [18]. After receiving the data packet, the node first requires a certain processing time to receive and process it from the receiving port before finally entering it into the sending queue. Then, it transfers to the next hop according to the transport protocol until the next hop node successfully receives the packet [36; 37; 38; 39; 40]. Thus, the delay includes the processing time of the data, the queuing time, and the sending time. The data may be sent many times and are dependent on the transport protocol. Among them, the time of node processing data is very small, and it can be neglected in the wireless transmission environment. The queuing time is determined by the load of nodes. The more data the network needs to transmit, the longer the queuing time of the packets, and transmission will stop in the event the queuing columns are full [13; 14; 30; 31]. The sending time of data is mainly influenced by the data transport protocol and many other network factors. The sending time under different data transport protocols is different. For example, in the send-wait protocol, when the sender sends a packet, it will wait for the receiver to return the ACK message. If the sender receives the ACK message, it can be confirmed that the packet has successfully reached the receiver [41]. On the contrary, the sender will re-send the data packet after waiting for the timeout until the packet is sent successfully, or the number of retransmission times exceeds the prescribed number and then the transmission of the packet will be abandoned. The time required for different data transmission is different, and the network conditions also have a great impact on the delay under the same data transport protocol. If the success rate of the packet transmission is high, the probability of the data retransmission is small and the delay is small. Therefore, network conditions affect the probability of successful data transmission. If the sender uses greater transmission power, this can improve the signal-to-noise ratio and shorten the time required for data transmission, ensuring that the success rate of data transmission is high [41]. Under the circumstance that the network conditions and data transmission protocols have been determined, one of the most important factors that can affect delay is the duty cycle mechanism used by IWSNs. In Wireless sensor networks (WSNs), as the energy of the node is very limited, the extension of lifetime is a key factor in network design to effectively reduce energy consumption. The duty cycle mechanism is an effective way to reduce the energy consumption of sensor nodes [42]. The principle of this method is: the energy consumption of a sensor node in the awake state is more than 100 times of its energy consumption in the sleep state. In order to reduce the energy consumption of the nodes, the nodes must sleep when they do not need to work. As a result, the duty cycle mechanism means a periodic transformation of nodes between awake and sleep states to reduce energy consumption. Generally speaking, the cycle frequency of the duty cycle is relatively high, while the cycle time of physical events is very large relative to the duty cycle.