Learning-based synchronous approach from forwarding nodes to reduce the delay for Industrial Internet of Things

3.1 The network model

In this paper, the system model is based on duty-cycled wireless sensor networks [4, 32]. This kind of network adopts a common method in WSNs, duty cycling, in which nodes transform between active and sleep modes. A wakeup interval is always predefined there, which is the basis of the transformation. Combined with the opportunistic routing based on asynchronous protocol, nodes wake up at different moments and each node has multiple forwarders. Each node has a communication range; here, we think of it as a circular region with a radius of r and make the sender as the center of the circle. Other nodes in this circle have the chance to become the forwarding nodes of the sender. When a sender wants to transmit a packet, at least one of its corresponding candidate forwarders should be in an active mode. Otherwise, the sender has to wait for the receiver to wake up. In the process of being transmitted to the sink node, a packet may be forwarded by multiple relay nodes, which is affected by the metric for forwarder selection.

Due to the random and uniform distribution of the monitoring targets in the entire network, the probabilities that a target being perceived by any node are equal. Similarly, for each node, the probability of generating data is equal. The security of network such as privacy and attacks are not considered in this paper [48, 49].

3.2 System parameters

where D_COM is the duration of communication and \( {\mathrm{D}}_{\mathrm{COM}}^A \) and \( {\mathrm{D}}_{\mathrm{COM}}^S \) are the periods of the nodes when they are in active and sleep modes respectively. D_LEA is the learning duration of the nodes, and because at this time nodes are always active, here, D_LEA is equal to \( {D}_{\mathrm{LEA}}^A \).

The calculation of power consumption mainly include these three aspects: the power consumed in learning duration, the power consumed in receiving or transmission, and the power required when nodes in the sleep mode. Power consumption is connected with duty cycle.

3.3 Problem statement

where \( {\mathbb{P}}_{v_i} \) represents the routing path from the node v _i to the sink and \( {v}_j\in {\mathbb{P}}_{v_i} \) expresses that v _j is a node in the \( {\mathbb{P}}_{v_i} \).

4.1 Research motivation

Opportunistic Routing in Wireless sensor network (ORW) is a routing protocol and works on top of an asynchronous MAC protocol [50]. In this protocol, each sender has multiple candidate forwarding nodes and each forwarding nodes has the chance to receive the packet when the sender has data to transmit. When the first forwarding node receives the packet and sends the acknowledgement (ACK) to sender, the sender can finish its transmission. ORW uses a metric called Expected Duty Cycled Wakeups (EDC) to select relay nodes. EDC is a measure of the time from the sender transmitting a packet to the packet reaching the sink, which does not consider the location of relays. Thus, there is a probability that a node far away from the sink is selected as forwarder, which may cause longer packet delay. And in the FFSC approach, nodes closer to the sink should select the optimized relay nodes before forwarding, while nodes far away from the sink adopt the strategy of forwarding immediately if there is a forwarding node available. However, because nodes are not synchronized, the sender wait time will be longer and lead to the longer delay. Therefore, we are committed to designing a better way to reduce delay.

1. (1).

   Synchronization can reduce delay. As can be seen in Fig. 1, without synchronization, the expected delay is half of sleep time in the FFSC approach. If the duty cycle of the corresponding nodes is roughly synchronized before sending the data, the sender does not require to wait for the receiver to wake up or only need to wait for a shorter time than without synchronization. As Fig. 2 shows, after self-learning, the synchronization of the sender and its receiver is completed, so when sender A transmits data, one of its candidate receiver is also in the awake state, and then, the delay is reduced.

    
2. (2).

   It is difficult to implement synchronization. The trouble is that maintaining a wide range of synchronization consumes a lot of energy. But the approach presented in this paper does not require synchronization of all nodes in the entire network and only requires synchronization within the forwarding range of the sender, so it is easy to implement. Furthermore, nodes which are closer to the sink do not require to maintain synchronization, so these nodes do not need additional energy consumption, while nodes which are far away from the sink have residual energy. Using this part of energy for synchronization, the delay can be reduced without affecting the network lifetime.

    
3. (3).

   Duplicate packets will lead to the waste of energy consumption. But this problem is inevitable while reducing delay as much as possible. Because multiple forwarding nodes may be awake at the same time, duplicate packets will be generated whether forwarding nodes transmit the same packet to their next nodes or return the ACK to the sender. In the approach proposed in this paper, the selection of nodes is optimized, and for each sender, only its forwarding nodes within a small range will be synchronized, in order to avoid aggravating the problem of duplicate packets compared to other approaches.

    

4.2 LS approach

In this paper, the forwarder set of each node is defined as a region formed by the intersection of a circle and an arc through the center of the circle. As shown in Fig. 3, the distance between sink and the sender node B is l and the radius of the circle is equal to the communication range of node B. In order to avoid selecting forwarders with longer distance from the sink, there is a constraint that the distance from the candidate relay node to the sink is at least closer than node B to sink.

where the first part of Eq. (7) is used to calculate the area of sector ACD, the second part represents sector BCD area, and the third calculates the area of the quadrilateral ACBD.

Based on this model, the selection of relay nodes and the determination of duty cycle are related to self-learning. First, we define the nodes in the shaded portion of Fig. 4 as the candidate relays.

The sender node stays active in the self-learning cycle and sends preamble repeatedly to detect the state of its candidate relays in the forwarder set. After sensing their duty cycle, we need to determine a period of time where more nodes are active. Compared with sender’s duty cycle, if sender’s active period is nearly coincident with the period where the majority of forwarders are active, there is no necessary to change sender’s duty cycle temporarily. Beyond that, the distance between forwarders and sink also needs to be taken into account. In short, we should change the duty cycle of the sender, in order to synchronize the duty cycle of the nearest forwarder to sink and the sender. This approach can make one-hop distance longer and reduce delay. Meanwhile, each node remembers the number of its corresponding nodes participating in the adjustment of the cycle. After the sender has adjusted its duty cycle, the relay nodes affected by it also have to adjust their cycle. Another method is to keep the original start time of node’s cycle constant and change the main duty cycle, which cannot affect the work of the related nodes. Certainly, this method will lead to the fragmentation of the cycle; therefore, adjustment and consolidation are also necessary at last.

In several self-learning cycles, the first task to complete is to divide the area from the sender to the slot into multiple regions with a width of x, as shown in Fig. 5. The distance between each of the two areas that need to be synchronized is d, synchronizing the duty cycle of the nodes near the sender node A with the nodes in the next region closer to the sink. Then, the nodes in this area repeat the above operations until the region containing the sink. Synchronization of any two regions is completed in this multiple self-learning cycle. But it is important to note that when the A region is learning from the B region, the B region is in the normal duty cycle, so the learning of the B region toward the C region should begin after the completion of the learning of the A region. However, there is another approach that when the A region is learning from the B region and the C region is learning from the D region, the C region can learn from the B region at the same time. But one drawback of this approach is that it increases the probability of ACK conflict.

At the same time, because there are more than one sender, the intersection of candidate forwarding node sets of different senders may not be a non-empty set. In this case, the solution we take is that for any two senders, if their intersection of forwarder sets is larger, we synchronize them with their forwarding nodes; if their intersection of forwarder sets is smaller, we divide the intersection into two parts and realize the synchronization of two senders respectively. In short, the number of forwarding nodes of any sender cannot be too small.

In a complete synchronization, a self-learning duration is D_LEA and the duty cycle of each relay node is c ^A /c. In that way, assuming that a self-learning cycle can be divided into several time slots and the length of a time slot is c, then there are D_LEA/c time slots. The probability of any node waking up in each slot is c ^A /c. In the above context, each node has σ forwarders, and before a node sends a data packet, it sends the preamble at a certain frequency (denoted as V) in the self-learning state. It is assumed that the average distance between any two nodes in the two regions is d and that a node should be at least 2Vd after the delivery of a packet and then send the probe packet. When a node receives a probe packet, it sends an ACK back to the sender. In addition to ACK conflict problem, there is no guarantee that the ACKs received by the sender nodes are not returned by the nodes that returned ACK before. Therefore, it is a probability problem to estimate the time spent in self-learning.

The whole process of LS approach can be described in Algorithm 1.

Here, the probability of any node waking up in each slot is c ^A /c and the number of forwarders in forwarder set of node i is ρϑ. In Eq. (10), \( \frac{c^A}{c}\bullet {\left(1-\frac{c^A}{c}\right)}^{\rho \vartheta -1} \) represents the situation that the sender wakes up in a slot but all of its forwarders wake up in other slots. And \( \frac{c^A}{c}\bullet {\sum}_{k=1}^{\rho \vartheta -1}{C}_{\rho \vartheta -1}^k\bullet {\left(1-\frac{c^A}{c}\right)}^k \) represents that the sender wakes up in a slot and most of its forwarders wake up in the same slot, except for k forwarders, k = 1, 2, ⋯, ρϑ − 1.

Because the whole self-learning process includes simultaneous learning among multiple regions, the time required to complete self-learning within a certain range (denoted as \( {D}_{\mathrm{LEA}}^{\mathrm{TOT}} \)) is the maximum value of the self-learning time between the regions.

5.1 Delay analysis

After the completion of self-learning, all nodes in any two regions separated by d maintain the synchronization of duty cycle. Compared with other methods, in which nodes need to wait for the corresponding candidate forwarders to wake up before sending the packets because their duty cycle is not necessarily synchronous, this approach can optimize the performance of this respect, thus effectively reducing the sender wait time. Figure 6 shows one of the possible multi-hop path of the packet from the sender node A to the sink.

Proof According to [4], the probability density function of the expected vertical distance from one of the sender nodes to its forwarder is \( {\mathcal{F}}_d(x)=\frac{2\left(d-x\right)}{\vartheta_x}\bullet {\cos}^{-1}\left(\frac{{\left(d-x\right)}^2+{d}^2-{x}^2}{2\left(d-x\right)d}\right) \). The expected d _x can be calculated by the formula \( {d}_x={\int}_0^xx\bullet {\mathcal{F}}_d(x) dx \). ■

Although the duty cycle of most of the nodes in the forwarder set are synchronized with the sender’s cycle, we prefer to select the relay node closer to the sink. Therefore, there is a need to reach a balance between the minimum delay and the maximum vertical distance.

Theorem 2 When packet forwarding is basing on LS approach, the duty cycle of nodes and their forwarders almost synchronous. When the distance from a node and the sink is L, the delay of end-to-end transmission can be calculated in Eq. (13).

Proof Y_{i − 1, i} is the average delay of the transmission from (i − 1)th to ith node. According to [4], the duty cycle of each node is c/D_COM in transmission and the probability density function of the delay in each slot is \( {\left(1-\frac{c}{D_{\mathrm{COM}}}\right)}^{i\rho \vartheta}\left[1-{\left(1-\frac{c}{D_{\mathrm{COM}}}\right)}^{\rho \vartheta}\right] \), where \( i=0,1,\cdots, \frac{c}{D_{\mathrm{COM}}}-2 \). Here, the vertical distance is greater than or equal to x, so the expected hop count is \( \left\lceil \frac{L}{d_x}\right\rceil \). Then, the total delay can be obtained by single hop delay and hop count. ■

Based on this formula, Fig. 7 shows the expected delay under different number of nodes. As we can see from the diagram, the overall trend is that the more the number of forwarders is, the shorter the delay is.

And as shown in Fig. 8, with the increase of single hop distance, the single hop delay is reduced. This indicates that the longer distance can lead to the shorter delay. At the same time, as duty cycle increases, the delay will decrease.

As Fig. 9 shows, the one-hop delay increases with the increase of the distance L. Meanwhile, the distance between a sender and its forwarder also reflects one-hop delay: the longer the one-hop distance, the longer the one-hop delay.

5.2 Energy consumption analysis

where E _U is the total energy consumption, E _T is the energy consumption of a packet transmission, E_LPL represents the energy consumption in low power listening, and E_LEA is the energy consumption in self-learning. N _T and N _R are the number of packets in transmission and the packet amount in reception respectively. D_COM and D_LEA are the duration of communication and self-learning.

The second part of Eq. (17) represents the power consumption of periodic preamble transmission.

where ε _R D _P represents the power consumption of the packet reception, ε _T D_ACK is the power consumption in the transmission of acknowledgment message, and ε _R D _B represents the power consumption of the preamble reception.

The process of low power listening consists of two parts: listening and sleeping states, which correspond to the first and second part in Eq. (20). Because the energy consumption of packet transmission and reception is calculated in the equation before, \( {\psi}_T^L \) and \( {\psi}_R^L \) should be subtracted from the calculation for \( {E}_{\mathrm{LPL}}^L \).

Proof Network lifetime is defined as the period before the node which has the largest energy dies out due to its energy drain. In other words, the lifetime of the node with the maximum energy and the initial energy refer to the network lifetime. \( {E}_O^i \) is the initial energy of the ith node, and the largest energy consumption of the node is \( {\max}_{1\le i\le n}\left({E}_T{N}_T^i+{E}_R{N}_R^i+{E}_{\mathrm{LPL}}{D}_{\mathrm{COM}}+{E}_{\mathrm{LEA}}{D}_{\mathrm{LEA}}\right) \). ■

Based on Eq. (24), Fig. 10 shows the energy consumption under the different x values. It can be observed that the larger the x is, the smaller the energy consumption is, which is because the hop count decreases with the increase of x. Meanwhile, as the distance between the sender and sink increases, the energy consumption of nodes are also reduced.

As shown in Fig. 11, the trend of energy consumption changes with the total distance from sink is the same as in Fig. 10. In the approach proposed in this paper, when each node becomes the sender, it is taken as the center in the network. In the transmission of packets, the selection of relays in each packet forwarding always follow the principle of selecting nodes that are closer to the sink. Thus, the closer the distance between a node and sink, the greater the energy consumed, which can be observed from Fig. 11.

6.1 Transmission delay

Figures 12 and 13 show the total transmission delay of the LS, FFSC, and ORW under different distance from sink. All nodes have the same duty cycle in ORW approach. Therefore, the distance between sender node and sink is mainly related to the total delay. As shown in the first curve in Fig. 12, the greater the distance, the greater the total delay. Meanwhile, because ORW does not consider the location of nodes, there exists a problem that the forwarder far away from the sink may be selected. So the total delay of ORW approach is obviously longer than the other two approaches. Similarly, in FFSC approach, the communication duty cycle of one node is as same as others. The difference between ORW and FFSC lies in the forwarder selection. With the consideration of the location of nodes, candidate forwarders are delineated within a range closer to the sink. Thus, compared to ORW, the total delay of FFSC approach is shorter. Unlike the above two approach, LS has been improved on the basis of FFSC, which is mainly embodied in self-learning. In the self-learning cycle, the duty cycle of the sender and its corresponding forwarder set are synchronized. It successfully reduces the total delay of transmission. Compared with FFSC, the LS approach can reduce the transmission delay by 5.13–11.64%, while the network lifetime of these two protocols are the same. Thus, it can be seen that the approach proposed in this paper is better than other approaches in terms of transmission delay.

6.2 Energy efficiency and network lifetime

The energy utilization can reflect the performance of the protocol and also affect the selection of forwarding nodes. Meanwhile, the network lifetime is related to energy consumption of nodes. In this section, the performance of LS approach in energy consumption and network lifetime is analyzed.

Figures 14 and 15 show the energy consumption of the LS and FFSC approach under different distance from sink. Here, the vertical distance between a sender and its forwarder has to be greater than or equal to x, while x is related to other parameters in the network. As can be seen in the following figures, the longer the distance from the sink, the less the energy consumed. Compared with the FFSC approach, LS consumes energy efficiently in non-hotspot areas. By comparing the two pairs of curves in Figs. 14 and 15, it can be observed that the maximum energy consumption of LS and FFSC is relatively close, which is partly due to the large energy consumption during self-learning period. The bell-shaped is presented in Fig. 14 because there is no need to do self-learning before transmission when the sender is close to the sink, so at the beginning of the curve, the energy consumption of the two approaches is similar. And with the distance from the sink increases, because the partial synchronization is achieved in the self-learning period, the energy consumption during the transmission is effectively reduced. Thus, the bell-shaped is formed in Fig. 14.

And the trends of curves in Figs. 14 and 15 prove that the closer the distance between a node and sink, the greater the energy consumed. This trend is the same as in Fig. 11.

Figure 16 shows the column diagram of residual energy under different radius of transmission range. Compared with FFSC approach, the LS can increase the efficiency of energy utilization by 14.29–17.53%, which can be observed in the figure. In a word, while adopting the LS approach, the energy utilization reaches a better balance. Especially for the areas farther away from the sink, the energy efficiency of nodes has improved.

Figures 17 and 18 show the network lifetime of FFSC and LS approach under different number of the first nodes that use up their energy. Compared to FFSC approach, although the efficiency of energy utilization during the transmission is improved, the network lifetime of the approach proposed in this paper is unchanged. This is because that the energy saved during the transmission compared to FFSC approach is almost offset by the energy consumption during the self-learning period.

6.3 Effects of other parameters on the performance

In this section, we analyze the performance of LS approach which is affected by other factors in the network. The length of a duty cycle is an important factor influencing the end-to-end delay. We usually expect a near perfect duty cycle to promote the probability that the sender and its candidate relays will be active at the same time. Figures 19 and 20 show the total transmission delay under the different duty cycle. As they shows, compared with other approach, the total delay of the approach proposed in this paper has been reduced, which also proves the correctness of our ideas. At the same time, it can be observed that the larger the duty cycle is, the shorter the total delay is. This is the same as the conclusion obtained in Fig. 8.

In addition to duty cycle, the number of nodes is also one of the factors which we are concerned with. Figures 21 and 22 show the total delay of the different approaches under different number of nodes. Compared with ORW and FFSC, LS approach can achieve smaller total delay than others. This is because that in ORW and FFSC approach, the nodes in the forwarder set are not synchronized with the corresponding sender. So if the number of nodes increases, the sender wait time before its forwarding nodes wake up will decrease and the delay of each hop in transmission will also decrease. This trend is the same as in Fig. 7. And in LS approach, due to the synchronization between the sender and its candidate forwarding nodes, the sender does not require to wait for the receiver to wake up or only need to wait for a shorter time than without synchronization.

The parameter d mentioned in the previous section also has an effect on transmission delay. In general, the longer the one-hop distance, the less the number of forwarders that a packet will pass. As can be seen in Fig. 23, LS approach is less than the FFSC in the total transmission delay, and as d becomes longer, the total delay decreases. On the contrary, when using LS approach, the one-hop delay under different x grows with the increase of x, as can be seen in Fig. 24.