## 1 Introduction
Therefore, sensor nodes can make use of the duty cycle mechanism to save energy when meeting the monitoring requirements. However, the node cannot receive and send data when it is in the sleep state. Therefore, when the sender needs to transmit data, if the nodes in the forwarding nodes set are all in the sleep state, then the sender needs to wait for its forwarding nodes to wake up before beginning data transmission [42]. In this paper, the time that the sender node must wait for its forwarding nodes due to the duty cycle mechanism is called sleep delay. The sleep delay depends on the duty cycle of the sensor nodes. In a period, the ratio of the time of the node in the awake state and the whole cycle time is called the duty cycle (denoted as \(\delta\)). In some environmental monitoring applications that are not strict in real time requirements, the cycle of the duty cycle may be measured in minutes when the temperature is collected [43; 44]. Therefore, in this case, sleep delay is the leading factor in end to end delay. Even in IWSNs, the sleep delay of sensor nodes has a great effect on the end to end delay [42]. Thus, how to reduce the sleep delay in data routing is a key factor in reducing end to end delay. Another delay associated with the duty cycle is the delay for detection. When a node is in the sleep state it cannot detect data packets. When a packet is sent to the node in the sleep state it is necessary to wait for the node to wake up before the packet can be perceived and received. The elapsed time between the node sending the packet and the other node perceiving the packet is called the delay for detection. The reduction of sleep delay and delay for detection are also major challenges. Because delay is caused by the duty cycle mechanism used by the sensor nodes [42], it essentially depends on the time that the node is in the sleep state. To reduce the sleep delay it is necessary to reduce the time of the node in the sleep state and increase the time that it is awake. In other words, this increases the duty cycle \(\delta\). Increasing the duty cycle will increase the energy consumption of the node and reduce its lifetime. Because of this, as far as we know, there has been no research into maintaining a high lifetime while reducing delay. In this paper, we provide an optimization method that can effectively reduce the delay and ensure that the lifetime is not less than the previous strategies. Specifically, the main innovations in this work are as follows:  
1. A novel Portion of Nodes with Larger Duty Cycle (PNLDC) scheme is proposed to reduce sleep delay and maintain a high lifetime for IWSNs. We have taken note of the following two facts: First, the sender has multiple forwarding nodes and the sleep delay is equal to 0 as long as the duty cycle of any node in the forwarding nodes set (FNS) is 1. Second, a significant number of studies show that the nodes in the near sink region bear a lot of data so their energy consumption is high while the nodes far away from the sink have residual energy. Therefore, a PNLDC scheme makes full use of the residual energy of non-hotspots to set the duty cycle of a certain proportion of nodes to 1 (\(\delta=1\)). Thus, a PNLDC scheme is able to reduce delay while ensuring that lifetime is not less than the previous strategy. 2. Through strict theoretical calculation and deduction, this paper first gives the proportion of nodes with full duty cycle (duty cycle = 1) in different regions that have different distances to the sink. Then, the relationship between the proportion of nodes with full duty cycle and the reduced delay is given. This provides the theoretical basis for the PNLDC strategy and provides the basis for the calculation of similar methods. 3. The full theoretical analysis in this paper shows that the proposed PNLDC scheme significantly reduces the delay for forwarding data by 8.9-26.4% and delay for detection by 2.1-24.6% without reducing the network lifetime when compared to the fixed duty cycle approach. The rest of this paper is organized as follows.