An adaptive retransmit mechanism for delay differentiated services in industrial WSNs

The retransmission protocol is an important mechanism to ensure the reliability of wireless transmission and is one of the most important research contents in WSNs. As mentioned earlier, the communication quality of WSNs is often very different due to the communication distance between nodes, transmission power, and the surrounding environment. In some networks, the packet loss rate is as high as 20–23%, so some reliability measures are needed to ensure the reliability of packet transmission. At the same time, the strategy of guaranteeing the reliability of data transmission often affects the delay of data transmission. Therefore, the strategy of ensuring the reliability of data transmission is considered simultaneously with the delay optimization strategy.

(1) Send-and-wait automatic repeat-request (SW-ARQ) protocols. The SW-ARQ protocol is a basic data transmission protocol that guarantees the reliability of wireless communication [38]. It mainly guarantees the reliability of data transmission through the retransmission mechanism. Its main operating mechanism is as follows: Sender starts to send packets after establishing a connection with the receiver, and the receiver returns an acknowledge (ACK) to the sender after receiving the packet. After receiving the ACK, sender knows that the data packet has been successfully received by the receiver, so it can start the transmission of the next packet. If the packet sent by the sender is lost during the transmission, the receiver will not return an ACK back because of not having received the packet [38]. Thus, after the sender waits for a timeout period and does not receive the ACK, it considers that the transmitted data packet has been lost, and thereby retransmits the data packet. The sending and receiving process is the same as that of the first sending of the data packet. From the above process, the reliability of the SW-ARQ protocol data transmission is guaranteed by retransmitting the data packet multiple times. Let the probability of successful data transmission be \( {p}_i^s \), then n data retransmissions can probabilistically guarantee the probability of successful transmission is 1 − \( {\left(1-{p}_i^s\right)}^n \). It can be seen that multiple retransmission mechanisms can significantly improve the reliability of data transmission but will increase the delay of data transmission. In data communication, the time it takes for the sender to send a packet to receive an ACK is called round-trip time (RTT), and the sender takes longer to perform a retransmission. It needs to wait for a time to out (RTO) time before starting a retransmission, while the RTO duration is longer than the RTT, because delay is the accumulation of time taken by multiple retransmissions. Thus, the more data retransmissions, the greater the delay [38]. In order to control the delay within the allowable range, it is often necessary to set a maximum number of retransmissions m. That is, when the maximum number of retransmissions of the same packet reaches m, the packet is not retransmitted, but discarded. It is easy to get the maximum number of retransmissions: Since the reliability of data transmission for m times is required to be 1 − \( {\left(1-{p}_i^s\right)}^m>\delta \), the reliability of data transmission can be guaranteed to meet the requirement when \( m=\left\lceil \lg \left(1-\delta \right)/\lg \left(1-{p}_i^s\right)\right\rceil \). Setting the maximum number of retransmissions prevents extreme situations during a packet transmission: always unsuccessful transmission. Of course, in general, the packet transmission success rate \( {p}_i^s \) is relatively high, which is 80% or more. Therefore, in practice, the value of the data transmission success rate \( {p}_i^s \) is relatively high. Therefore, although the maximum number of retransmissions m is set, the average number of successful data transmissions is not large in the case where δ is less than 1, much smaller than m [38].

The above retransmission mechanism is mainly aimed at the reliability transmission of hop to hop. According to source node routing and multi-hop routing of the data packet, the above retransmission mechanism also has control strategies divided into end to end (E2E) and hop by hop (HBH) [38]. The control mode of E2E is that the source node sends the data packet to the sink; then, the latter returns the ACK after receiving the data packet. In this control mode, once the source node receives the ACK, it knows that the data packet has been successfully received by the sink, and thus begins to send the next packet. However, in this mode, the data packet has to go through multiple hops to reach the sink. Assuming that the hop count of the data packet from the source node to the sink is h, the success rate of the packet to the sink through k hops’ routing is p^h. Obviously, if the success rate of one hop of the ACK when it returns is β, the probability that the ACK successfully returns to the source node is β^h. Therefore, the probability that the source node successfully receives the ACK returned is p^h ∙ β^h. If ρ = 90%, β = 95%, and h = 10, the probability that the source node can receive the ACK after sending the data packet < 21%. To make the reliability rate of the data successfully reaching the sink, δ = 90%, the source node needs to send 10 times on average to guarantee the rate. For each retransmission, the packet needs to go through 10 hops to reach the sink, and the ACK returned by the sink needs to go through 10 hops to return to the source node, so the elapsed time (delay) is very long, and the RTO time of a retransmission will be longer. This shows that in the E2E control mode, the number of retransmissions of the source node is large, and the delay is large too [38]. However, this control method has one advantage that has not been noticed in previous studies: In an ideal wireless sensor network with high reliability of data transmission (the transmission reliability rate can be considered as 100%), since sink is the end point of data transmission of all nodes, the nodes that are close to the sink area bear a large amount of data, which is called hotspots. Due to the hotspots, the energy consumption of nodes near the sink area is much higher than in other areas, which may lead to early network death. This situation seriously damages the lifetime of the network. In the reliability control mode of E2E, since part of the data packets sent by the source node will gradually lose during their transmission to the sink, which will reduce the impact of hotspots. Hop by hop (HBP) reliability control is a hop-by-hop reliability control method [38]. In this way, if the reliability of receiving the data packet by the sink is δ, and the data packet needs to go through h hops to reach the sink, and when the data transmission reliability of each hop is \( \sqrt[h]{\delta } \), the reliability after the h-hop routing of the data packet is guaranteed to be δ. In the HBP mode, to require the reliability of each hop to be \( \sqrt[h]{\delta } \), that is, to require this process, the sender sends the data packets to the receiver, then receiver returns the ACK to the sender after having received, but if the sender does not receive the ACK, timeout retransmission is implemented. If the sender sets its maximum number of retransmissions \( m=\left\lceil \lg \left(1-\sqrt[h]{\delta}\right)/\lg \left(1-{p}_i^s\right)\right\rceil \), the end to end reliability of data transmission will be guaranteed to be δ. In this HBP control mode, the control mode adopted by each node is single-hop control, and thus its end to end delay is the delay accumulation of each hop. Relatively speaking, the nodes of the HBP mode bear less data.

It can be seen from the above SW-ARQ mechanism that the biggest feature of this retransmission mechanism is that the protocol is simple and easy to implement [38]. Moreover, in this way, the extra energy consumption of the node is due to the energy consumption by transmitting the ACK, and the length of the ACK is relatively smaller than the length of the data packet, so the additional energy consumption is relatively small, and thus the energy consumption of the protocol is relatively small compared to the mechanism introduced later. However, the biggest shortcoming of this method is that each retransmission generates a timeout period, and the data packets may be needed to be retransmitted multiple times, resulting in a larger delay for this protocol.

In order to reduce delay and the large deficit of the SW-ARQ protocol, the researchers proposed an improved protocol for SW-ARQ. Go-Back-N protocol (GBN) [39] is just one of the improved protocols. The main operation of the GBN protocol is the following: The sender is no longer a serial mode that it sends a packet at a time and waits for an ACK to return like the SW-ARQ protocol [39]. In the GBN protocol, the sender continuously sends multiple data packets, and the data packet contains the sequence number of itself. If the receiver finds that the sequence number of the received packet is not continuous, which indicates that there is a packet loss during the transmission, therefore, the receiver sends a NACK to the sender, indicating the smallest sequence number of the packet in the unreceived packets. After the sender receives the NACK, it retransmits from the sequence number of the packet indicated in the NACK. The GBN protocol speeds up the transmission of data packets, thereby reducing delay [39].

Selective repeat protocol (SR) [40] is an improvement to the GBN protocol. In this protocol, the sender sends the packet in a similar manner to the GBN protocol. However, when the receiver returns the NACK of the unreceived packets, the SR protocol only retransmits the packets that were not successfully transmitted, thus reducing the system overhead.

The delay of the retransmission protocol mainly comes from the retransmission of the data packet, and the retransmission of the data packet will inevitably go through a TTO time, so the time taken is long. Multiple retransmissions and multi-hop routing will make the end to end delay very large. Therefore, if using the mechanism that does not return ACK, the delay can be reduced. Therefore, some researchers have proposed the mechanism of s packet rerouting. In this mechanism, the sender repeatedly sends the same data packet m times, and the s data packets all have a certain probability of reaching the sink. Therefore, after repeated transmissions for m times, the value of data transmission reliability can be ensured to meet the application requirements δ. Compared with the SW-ARQ protocol, since the receiver does not need to return ACK in this protocol, the delay is the least, but the node has the highest energy consumption. As previously analyzed, in the SW-ARQ protocol, the average expected number of times that a sender sends a packet is much smaller than the maximum number of retransmissions m. However, in the mechanism without feedback, the number of times the data packet is sent by each node is the maximum number of retransmissions m. Therefore, the energy consumption of this protocol is very large and rarely used in wireless sensor networks.

In a network with high reliability of the communication link, the data packet does not need to be retransmitted, so its delay is small. While in a network with low reliability of the communication link, the data needs to be retransmitted multiple times, and the time consumed by one retransmission far exceeds the time of the first data transmission. Therefore, the method of improving the reliability of the communication link can be used to reduce delay and improve data transmission reliability. Thus, there are also some methods to reduce delay and improve data transmission reliability by improving the quality of communication links [46]. One of the more effective methods is to improve the data transmission power. The central idea of this approach is that the communication success rate between nodes in a wireless router network is not only related to the distance between the nodes but also related to the transmit power of the sender nodes. The higher the transmit power of the sender nodes, the higher the signal-to-noise ratio (SNR) of the received signal of the receiver and the higher the success rate of receiving data [46]. It can be seen from the foregoing discussion that if the data transmission success rate is higher, the number of retransmissions required by the node is smaller, so that the delay caused by the retransmission can be effectively reduced. For example, in a network with a data transmission success rate of 98%, the probability of successfully reaching the sink after 10 hops is 81.7%. While in a network with a data transmission success rate of 80%, the success rate of the packet reaching the sink after a 10-hop routing is only 10.7%. It can be seen that increasing the success rate of data transmission can significantly reduce the number of retransmissions thus reducing delay [46]. Based on the above ideas, some researchers have proposed the strategy of increasing the transmission power of the sender to improve the reliability of data transmission, thus to reduce the delay. But the real strategy of improving the node’s transmit power is more complicated. Because increasing the transmit power of a node requires more energy consumption, but the energy of the node is very limited. Thus, to increase the transmit power of the node, it should minimize the energy consumption of data per bit successfully transmitted [46]. The sender’s transmit power is a nonlinear relationship with the successful transmission of the packet (see Fig. 1). If the communication distance between the nodes is fixed, increasing the transmit power of the sender can increase the receiver’s reception rate. However, after the receiver’s receiving rate reaches a certain value, it rises very little if the sender’s power continues to be increased. Therefore, when the transmit power of the sender can be adjusted to the optimized value, the energy consumption for successfully transmitting each bit of data can be minimized. In terms of reducing the delay, increasing the sending power of the sender helps to reduce the number of retransmissions, thereby reducing delay [46].

Due to the development of current microprocessors, multiple applications can run in the same WSNs at the same time. Because different applications require different QoS indicators, research on differentiated services has only just begun, but there have been some researches about this.

Zhang et al. [16] proposed an integrity and delay differentiated routing (IDDR) scheme, which is such a differentiating service strategy. In IDDR scheme, there are two different types of network applications. One is data integrity, which is an application of packet loss sensitivity, requiring an extremely low packet loss ratio. The other type is an application of delay sensitivity, which has high requirements for delay. In WSNs, the shortest routing method is generally adopted, which causes hotspots near the sink area. The hotspot area bears a large amount of data, which on the one hand makes the energy consumption of nodes in this area large. On the other hand, congestion occurs in the hotspots area, due to the large amount of data transmitted by the nodes in this area. The result of congestion is high packet loss rate and large data routing delay. Therefore, the solution adopted by the IDDR scheme is using the shortest routing method for delay-sensitive packets to reduce their delay. For data packets with high data integrity requirements, a detour is used. By bypassing the hotspots area, although the length of the route is increased, the congestion is small, thus meeting the requirements of data integrity. Therefore, IDDR can differentiate services.

Huang et al. [47] proposed a very effective delay in differentiated services (DDS) for data fusion networks. In a data fusion network, if a packet waits for a period of time for more packets on the intermediate node of the route, the amount of data reduced will be larger after more data packets are merged, thereby reducing the energy consumption of the route and improving the network life. Therefore, from the perspective of reducing energy consumption, the longer the data packet stays on the node, the more data fusion can be performed, which can reduce energy consumption and thus help to improve network life. However, the longer the packet stays on the node, the greater the delay of the packet reaching the sink, which affects its usability. Thus, the method adopted by Huang et al. [47] is the following: For data with high delay requirements, set a smaller dwell time threshold to speed up data routing and reduce delay, and for data with less demanding delay, set a larger dwell time threshold to make more data packets meet for data fusion thus reducing energy consumption and improving network life.

In this paper, a system model of a classical planar wireless sensor network is used. The system model is referenced to [48]. The system model structure is as follows:

The local energy model used in this paper is referred to [50]. Let ϖ_s represent the energy consumption of data transmission, as shown in Eq. (1).The energy consumption ϖ_rec of the received data is given by Eq. (2).

Among them, the transmission circuit loss is represented by E_elec. The energy consumption of data transmission uses the free space (s² power loss) and multi-path fading (s⁴ power loss) channel model according to whether the distance exceeds the threshold s_td. When the power amplifier loss is based on the free space model, ℓ_s is used instead; when the transmission distance is greater than or equal to the threshold s_td, ℓ_m is selected as the power amplifier loss of the multi-antenna model. α is the number of bits in the data packet. The above parameter settings are shown in Table 1 [50]. The system parameters adopted in this paper are listed in Table 2. 

The main goal of this paper is to design a communication approach to reduce the transmission delay of WSNs by improving the network energy utilization, and to ensure that the increase of Adaptive Retransmit Mechanism for Delay Differentiated Services (ARM-DDS) protocol.

The problem of the ARM-DDS protocol can be described as differentiated services for different transmission delay requirements, to meet the broad delay requirements. Data packets with different delay requirements and reliability requirements are processed differently to optimize the delay and energy utilization of the entire network. WSN data collection routing can be characterized by several performance indicators, as described below:

In summary, the research questions in this paper can be summarized as follows. And the parameters related to the calculation are shown in Table 3. 

The Adaptive Retransmit Mechanism for Delay Differentiated Services (ARM-DDS) scheme is mainly proposed for the research problem in which no effective methods work on the distinction of delay differentiated service. The main goal of ARM-DDS is to reduce the energy consumption of nodes as much as possible. Under the premise of ensuring the reliability of data transmission to meet the application requirements, it can provide a wide range of differentiated services for the delay. The research motivation of this paper mainly comes from the following points.

Based on the above three points, the ARM-DDS protocol uses differentiated services for different requirements data to reduce transmission delay. When transmitting data streams with different reliability requirements, set different maximum retransmission times for different required data streams and the maximum number of retransmissions near the sink, improving network life, meeting higher reliability requirements, and improving energy utilization at far-sink nodes.

In this section, the algorithm of the ARM-DDS scheme differentiated service is given by analyzing the data transmission mode.

Figures 2 and 3 represent the difference and improvement between the ARM-DDS strategy and the traditional SW-ARQ protocol. The data transmission of the SW-ARQ protocol is shown in Fig. 2. The sender sends a packet every time it transmits. Sending a packet to the receiver requires \( \frac{1}{2}{\tau}_{\mathrm{round}} \) time. The success rate is \( {p}_i^s \). Receiver immediately sends an ACK to the sender when a packet is received. The ACK also needs \( \frac{1}{2}{\tau}_{\mathrm{round}} \) time to the sender. The rate is \( {q}_i^a \). When sender receives the ACK, it can be determined that the data transmission is successful. After sender sends the data packet, if the ACK is not received after waiting for τ_round + μ time, it is considered that the sending of the data packet failed, and then sender needs to send the data packet again. Therefore, under the SW-ARQ protocol, additional τ_round + μ time is required for each data retransmission. The sender will resend the data. Therefore, the SW-ARQ protocol requires τ_round + μ time for each data to be retransmitted.

The ARM-DDS scheme proposed in this paper can continuously send multiple sets of data. When using ARM-DDS scheme transmission, first determine the c value according to the requirements of the application. As shown in Fig. 3, the time when the data packet is sent to the receiver is \( \frac{1}{2}{\tau}_{\mathrm{round}} \), which is the same as the traditional protocol. When sending c packets in succession, the interval of sending each packet is s. Therefore, when the packets of group c arrive at receiver, the time is \( \frac{1}{2}{\tau}_{\mathrm{round}}+\left(s-1\right)c \). The algorithm of receiver and the SW-ARQ protocol is consistent, and when a packet is received, an ACK is returned. The minimum interval for sending ACK is b. As long as one ACK is received by sender, it is regarded as successful. The transmission of the c-group data packets using the transmission strategy of the ARM-DDS scheme requires τ_round + (s + b − 2)c delay. If the traditional protocol is used, this delay becomes (τ_round + μ)c. In the network, the data transmission time τ_round is much larger than the minimum interval between data and ACK transmission (s + b − 2). Therefore, according to the above analysis, it can be obtained. The following conclusions are drawn: (1) When the number of retransmissions is small, the time required for the ARM-DDS protocol to transmit data with the SW-ARQ protocol is similar.

(2) When multiple retransmissions are required, the transmission delay of ARM-DDS will increase (s + b − 2)c. The transmission delay of the SW-ARQ protocol is increased by (τ_round + μ)c. At this point, ARM-DDS has an advantage in latency. That is to say, the ARM-DDS scheme has a greater advantage in delay when it is required to retransmit data multiple times.

The algorithm of the ARM-DDS scheme is as follows: In a planar wireless sensor network, all nodes are awake and all nodes know their next hop node. When transmitting data, depending on the timeliness of the data, the data has different delay requirements. Time-sensitive data needs to arrive as quickly as possible, so the node must transmit the data as much as possible to ensure that its latency is low. Data with relatively low timeliness does not require more energy. Distinguish data with latency requirements so that each data can be transmitted within its required delay.

The algorithm of the receiving node is as follows: In the ARM-DDS protocol, the receiving node waits to receive a data packet, and if a group of data is received, it sends an ACK, otherwise, it continues to listen to the data packet.

Algorithm 2 assigns the appropriate c value to applications according to different delay requirements. The ARM-DDS protocol does not send multiple sets of data at one time to hotspots in the near-sink area. Because hotspots increase the number of sending groups, the energy consumption increases, the node death rate increases, and the network life decreases, which is undesirable for the research. Therefore, for a node with a hop count of 1, it is consistent with the SW-ARQ protocol, that is, c = 1. In this way, it is possible to differentiate the data stream without reducing the network life and reduce the purpose of delay.

Figure 4 is an E2E delay comparison of the two protocols. The experimental environment is a planar network with a radius of 400 m centered on the sink node. Its emission radius is 80 m, reliability δ=0.8\( , {p}_i^s=0.8,{q}_i^a=0.8 \). As can be seen from Fig. 3, the ARM-DDS protocol delay is less than the SW-ARQ delay. And the further away from the sink, the greater the delay is reduced. When applications require different delays, the ARM-DDS policy can change the value of c to cause the data to be sent with the expected delay.

Regarding the loss of energy, the energy consumption of the ARM-DDS protocol proposed in this paper will be even larger. Because the ARM-DDS protocol increases the number of data transmissions compared to the SW-ARQ protocol, energy consumption is greater. Studies have shown that in a traditional flat network, when the lifetime of a network is exhausted, the energy remaining in the entire network is still as high as 90% [51]. Therefore, the ARM-DDS strategy can make full use of the remaining energy and increase the number of transmission groups at the far-sink without losing the network lifetime. Use this method to increase the energy utilization of the entire network [52, 53]. Therefore, adopting the above method does not affect the lifetime and can reduce the delay. Under the optimization of the differentiated service, the energy utilization of the entire network can also be increased.

In the previous section, we mainly studied the transmission algorithm and c value algorithm of ARM-DDS scheme. This section mainly discusses two other important parameters of the differentiated service: the data volume ξ_i and the maximum number of retransmissions\( {\upgamma}_h^{\mathrm{ARM}}\left(\delta \right) \). Among them, \( {\upgamma}_h^{\mathrm{ARM}}\left(\delta \right) \) is the main parameter affecting network delay, and the data quantity ξ_i is the main parameter affecting energy consumption.

When studying the difference in data volume between the ARM-DDS scheme and the traditional protocol, first analyze the data situation of the nodes in the network under the assumption that the data between the nodes is not lost, to provide a calculation for the case where the data loss rate between nodes is > 0, the basics.

According to the reference [16], when the node transmits data with the transmission radius r, if the data transmission between the nodes is not lost, the distance of the node i from the sink is d,d = hr + ∆ (where ∆ is a less than r Constant), then the amount of data borne by the node ξ_i is shown as equation (7).

In a planar wireless sensor network, all data must have certain reliability requirements when it reaches the sink [54]. The statistical reliability required for transmission to the sink is represented by δ. The maximum number of retransmissions of the ARM-DDS scheme \( {\gamma}_h^{\mathrm{ARM}}\left(\delta \right) \) is different from the maximum number of retransmissions in the legacy protocol. In the SW-ARQ protocol, when applications with different reliability δ requirements are simultaneously transmitted since the service cannot be distinguished, all data can be transmitted only according to the maximum δ. This will cause the data that has already met δ to be retransmitted, the excess energy is wasted, and the delay is added. ARM-DDS scheme was proposed to optimize the above situation. The protocol can reasonably distinguish between applications with different δ requirements and set the appropriate number of retransmissions for each application.

For any node i in the planar network, the success rate of the node per-hop transmission is \( {p}_i^s \). According to the reference, in the planar wireless sensor network, the SW-hop-by-hop ARQ protocol is used, and the node with the hop count h is used. When the maximum number of retransmissions is as follows, the reliability is guaranteed to be δ:

The biggest difference between the ARM-DDS protocol and the SW-ARQ protocol is the maximum number of retransmissions. Under the differentiated service, the maximum number of retransmissions of the ARM-DDS protocol must be less than or equal to the SW-ARQ protocol. Theorem 1 gives the maximum number of retransmissions \( {\upgamma}_h^{\mathrm{ARM}}\left(\delta \right) \) of the ARM-DDS protocol.

Theorem 1: In the ARM-DDS protocol, it is assumed that there are m kinds of data packets with different reliability requirements δ^k in the data stream to be transmitted, each ratio ϱ_k% (where k is the number of different data streams, 0 ≤ k ≤ m), the maximum number of retransmissions under different data reliability requirements is \( {\upgamma}_h^k\left({\delta}^k\right) \), so the maximum number of retransmissions under the

Proof In the SW-hop-by-hop ARQ transmission mode, the maximum number of retransmissions of a hop is γ_h(δ). Based on this, the ARM-DDS protocol differentiates the data streams with different reliability requirements. When the reliability requirement is δ^k, \( {\upgamma}_h^k\left({\delta}^k\right) \) times need to be retransmitted, and the data stream is the proportion of the overall data stream which is ϱ_k%, so we can conclude that the maximum retransmission number of the data stream with the reliability requirement of δ^k is \( {\gamma}_h^k\left({\delta}^k\right){\varrho}_k \). Similarly, all the different reliability requirements data will be obtained. The flow is weighted and calculated:

In the previous, the retransmission times and data amount parameters of the ARM-DDS protocol are proposed. To get the influence of these parameters on the whole network, it is necessary to calculate the amount of data and the amount of ACK when transmitting data and analyze the difference between the ARM-DDS scheme and the SW-ARQ protocol data transmission.

In the SW-ARQ protocol, the number of data packets and the amount of information that each node bears are as follows:

Let the distance of the node i from the sink be d; then, we know that d = r × h + ∆ if the transmission and reception (SW-ARQ) mode are used. Considering that the reliability required for transmission is δ, the data commitment amount \( {D}_{\xi, i}^{h,t} \) of the node i, and the ACK amount \( {X}_{\xi, i}^{h,t} \) are

Theorem 2: When multiple sets of data of ARM-DDS protocol are transmitted simultaneously, the amount of data is given as follows: According to Theorem 1, it is assumed that the hop count of node i ish, considering the reliability requirement is δ^k, and the maximum number of retransmissions is \( {\gamma}_h^k\left({\delta}^k\right) \). Therefore, the expected number of transmissions per hop \( {S}_h^{\mathrm{send}} \), the amount of reception \( {S}_h^{\mathrm{rec}} \), and the amount of ACK \( {S}_h^{AR} \) and the number of transmission \( {S}_h^{AS} \) are as follows:

Among them,

Proof Because the ARM-DDS strategy is used, the node’s data needs to be sent at least c_h times. Therefore, the probability that the transmitted data has at least c_h times is 1. If at least one of the transmitted data is successfully transmitted, the data transmission will stop. Only when this c_h data transmission fails will c_h packets be sent again. The probability of successful transmission within 2c_h times is \( \left(1-{\left(1-{p}_i^s{q}_i^a\right)}^{c_h}\right){\left(1-{p}_i^s{q}_i^a\right)}^{c_h} \).This means the first set of data transfers failed, but the second set of c_h data transfers was successful. And sender also successfully received the ACK from the next hop. The probability that the second group c_h transmission is successful is the probability that all the first c_h group data transmission failures \( {\left(1-{p}_i^s{q}_i^a\right)}^{c_h} \) are multiplied by the probability that the second group data is successfully sent to receive. And the probability that sender successfully receives the ACK is \( 1-{\left(1-{p}_i^s{q}_i^a\right)}^{c_h} \). By analogy, the probability of successful transmission in the first vc_h is \( \left(1-{\left(1-{p}_i^s{q}_i^a\right)}^{c_h}\right){\left(1-{p}_i^s{q}_i^a\right)}^{\left(v-1\right){c}_h} \). Until (v + 1)c_h is greater than \( {\gamma}_h^k\left({\delta}^k\right) \), the \( {\gamma}_h^k\left({\delta}^k\right)-\left\lfloor {\gamma}_h^k\left({\delta}^k\right)/{c}_h\right\rfloor \) group data is continuously transmitted. Therefore, the expected value sent by the node is

When a packet from an h + j hop node is sent to a node with a hop count of h, the amount of data that the node needs to bear is: \( \frac{\left(d+ jr\right)}{d} \). Therefore, the number of packets sent from the node of h + j hop to h hop is \( {E}_{h+j}^h\left({\delta}^k\right)\frac{\left(d+ jr\right)}{d} \). The probability of sending to h hop is \( {p_i^s}^j \). Therefore, the number of packets sent by the node with the hop count is

The number of ACKs that need to be sent is as follows: Each node receives an ACK and sends an ACK. Therefore, the number of ACKs sent is equal to the number of received packets. The number of received packets is the number of data sent by the previous node multiplied by \( {p}_i^s \) (because there is a packet loss). Therefore, there is the following formula:

Considering that the number of packets sent by the node i with the hop count h to the next hop is \( {S}_h^{\mathrm{send}} \), the packets arriving at the next hop are \( {p}_i^s \). Each packet is received by the receive and returns an ACK. The probability that the return ACK is successfully received by sender is \( {q}_i^a \). Therefore, the number of ACKs received by the node is

As can be seen from Section 5.2, the larger the c value, the smaller the transmission delay. In the ARM-DDS scheme, if the c value is greater than 1, the transmission delay compared to the SW-ARQ protocol will be reduced. In the ARM-DDS protocol, since the non-hotspots area has more energy remaining, we can set the non-hotspots area to have a larger c value. This reduces transmission delays, ensures network lifetime, and increases energy utilization.

Theorem 3: In the ARM-DDS protocol, the node i of any h hop and its distance to the sink is d, d = hr + ∆. The end-to-end delay ω_h is as follows when transmitting data with different delay requirements:

Proof According to Theorem 1, under the delay required by the application, the maximum number of retransmissions of the node of the h hop is \( {\gamma}_h^k\left({\delta}^k\right) \). The transmission delay can be expressed as \( {w}_h=\sum \limits_{v=0}^{\gamma_h^k\left({\delta}^k\right)}{p}_v{P}_v \), where p_v is the probability of successfully transmitting a packet for the v time, and P_v is the delay of the vth successful transmission. When the node sends data to the next hop, all packets need to arrive: \( s\left({c}_h-1\right)+\frac{1}{2}{\tau}_{\mathrm{round}} \). Where c_h is the number of consecutively transmitted packets for the h hop, and s is the data sent each time interval between. If the first set of c_h data transmission fails, the sender will transmit the second set of data of c_h until the maximum number of retransmissions is less than c_h times.

Therefore, we can conclude that the probability of successful arrival at the vth (v ≤ γ_h(δ)) transmission is \( {p}_i^s\prod \limits_{m=1}^v\left(1-{p}_i^s\right) \). The maximum expected delay after receive processing the data packet is \( \frac{1}{2}{\tau}_{\mathrm{round}}+\mu +\left({c}_h-1\right)\left(s+b\right)+{\tau}_{\mathrm{rtto}}\left(v-{c}_h-1\right) \).

In summary, the delay for h hop to jump to j is as follows:

The end-to-end delay of the h-th hop is

Theorem 4: In a planar wireless sensor network with radius R, the known transmission radius is r and the node distribution density is ρ. The average end-to-end delay per hop is ω_h. The average weighted delay for the entire network is as follows:

Proof Suppose the radius of the planar network is R, the radius per hop is r, the density of nodes is ρ, and the end-to-end delay per hop is ω_h. Since each hop of the planar network can be approximated as a ring shape, the area of the hth hop can be found as π(hr)² − π((h − 1)r)². Therefore, the node of the hth jump has a total of ρ[π(hr)² − π((h − 1)r)²], and the average weighted delay of the entire planar network is

which is

This paper uses the above formula theorem to calculate the performance of the ARM-DDS protocol in terms of network transmission delay.

In WSNs, nodes in the non-hotspots area still have a lot of energy left when the network life expires, causing waste. Therefore, the remaining energy of the non-hotspots region node can be fully utilized to set a larger c value and reduce the transmission delay. The nodes of hotspots need not lose excess energy. Therefore, setting c = 1 does not reduce the network lifetime. The following is the theorem about network energy consumption.

Theorem 5: In the ARM-DDS protocol, considering that the energy consumption of nodes transmitting and receiving data packets is \( {e}_p^t \) and \( {e}_p^r \), respectively, the energy consumption of transmitting and receiving ACKs by nodes is \( {e}_A^t \) and \( {e}_A^t \), respectively. Then the energy consumption of the h-th hop node is as follows:

Proof From Theorem 2, the transmission received data packet \( {S}_h^{\mathrm{send}} \) and the reception amount \( {S}_h^{\mathrm{rec}} \) and the ACK bearer \( {S}_h^{AR} \) and the transmission amount \( {S}_h^{AS} \) are obtained.

So the energy consumption of a node is the product of the number of transmissions and the energy required to transmit each packet:

Theorem 5 is given to provide a theoretical basis for network lifetime. Investigating the energy consumption of hotspot nodes helps determine network lifetime.

This article does not consider low probability burst situations. Assume that all nodes consume the same amount of energy per round. After deriving the energy consumption of all nodes in the network, the network lifetime can be given.

Theorem 6: Assuming that the lifetime of a planar network is \( \mathcal{L} \), the total energy of the nodes in the hotspots region \( {\mathcal{O}}_1^{\mathrm{all}} \) is related to the energy consumption \( {o}_1^i \). We can get the following formula:

The subscript refers to the hotspot area node closest to the sink. The average lifetime of these nodes determines the lifetime of the entire network.

Proof Because in a flat network, we can know from the energy consumption formula that the energy consumption of the near-sink node is the largest. Once the network has energy-saving exhaustion, it means that the planar network is exhausted. Assume that in one cycle, the energy consumption of the near-sink node is \( {o}_1^i={\mathrm{S}}_1^{\mathrm{send}}{e}_p^t+{\mathrm{S}}_1^{\mathrm{rec}}{e}_p^r+{\mathrm{S}}_1^{AS}{e}_A^t+{\mathrm{S}}_1^{AR}{e}_A^r \), the total energy of the node is \( {\mathcal{O}}_1^{\mathrm{all}} \). Therefore, in the case of constant physical conditions, the node near the sink can run the \( \mathcal{L}=\frac{{\mathcal{O}}_1^{\mathrm{all}}}{o_1^i} \) period, after which the node will run out of energy, so define it as the lifetime of the entire network.

This paper uses the above formula theorem to calculate the performance of the ARM-DDS protocol in terms of network energy consumption.

Algorithm 2 gives the value of c in different network environments, as shown in Fig. 4. The end-to-end delay at different c values is given in Fig. 5. Combined with Figs. 4 and 5, the following conclusions are given: (1) The lower the data transmission delay, the larger the value of c. The reason is that the larger the number of simultaneous transmission groups c, the smaller the expected time required for successful transmission. Therefore, when transmitting time-sensitive data, the value of c will be larger. (2) The reduced delay of the ARM-DDS protocol is limited. This is because if the c-group data is sent at the same time, and the transmission time is increased by (c − 1)s. When the value of c is too large, an increase in the transmission time causes an increase in delay.

Figures 6 and 7 show the one-hop delay of the ARM-DDS protocol and the SW-ARQ protocol under different data streams with different delay requirements. From Fig. 6, the following conclusions can be drawn:

Figures 8 and 9 are end-to-end (E2E) delays at different success rates p. The following can be seen from the figures:

Therefore, the worse the network environment the ARM-DDS protocol works in, the more the transmission delay is reduced.

Figure 10 is the E2E delay of the ARM-DDS protocol and the SW-ARQ protocol under the comprehensive reliability change of the data stream. The following can be seen from Figs. 10 and 11:

However, when the reliability requirement is low, the c value near the sink is close to 1, and the delay reduction rate becomes smaller.

Figure 12 illustrates the average weighted delay of the ARM-DDS protocol and the SW-ARQ protocol for different reliability requirements. It can be seen from Fig. 12:

Figure 13 shows the delay reduction rate of the ARM-DDS protocol and the SW-ARQ protocol under the different reliability requirements δ. It is obviously to optimize the transmission delay when the reliability δ is between 0.80 and 0.96, the ARM-DDS protocol can reduce the delay by 12–14% in compare with the traditional SW-ARQ protocol. As the reliability requirements increase, the rate of delay reduction increases. Explain that the ARM-DDS strategy performs better under high-reliability requirements.

Thus, the ARM-DDS protocol can be used to transport data streams that require more timeliness.

Figures 14 and 15 show the delay comparison of the ARM-DDS protocol with the traditional SW-ARQ protocol under different τ_round. The following conclusions can be drawn:

However, if SW-ARQ sends c packets, it will consume the time associated with cτ_round. So when τ_round increases, the delay of SW-ARQ is bigger than that of ARM-DDS.

Figure 16 is intended to examine the delay reduction of the ARM-DDS protocol that is influenced by the different transmission radii r. The conclusion is given by the information from Fig. 16: With the transmission radius changes, it causes the number of hops of the node changes as following. But the delay did not change significantly. So we conclude that the variation of the transmission radius does not significantly affect the ARM-DDS reduction delay.

Figures 17, 18, and 19 show the results of the comparison of data reception and transmission amount between the legacy protocol and the ARM-DDS protocol. The information can be obtained from Figs. 17, 18, and 19:

Hence, it is found that the energy consumption of ARM-DDS which is far from the sink protocol is larger than the energy consumption of the SW-ARQ protocol, and the ARM-DDS protocol could effectively improve the energy usage rate of the network.

Figure 20 emphasis that the maximum number of c value retransmissions times of the ARM-DDS protocol interactive with the SW-ARQ protocol under different \( {p}_i^s \). As shown in Fig. 20: With the ARM-DDS protocol reducing the delay as much as possible, its c value is under the maximum number of retransmissions. The ARM-DDS protocol does not affect the network lifetime due to the value of c selected by the near-sink node that does not exceed the maximum number of retransmissions. On the other hand, the ARM-DDS protocol can increase the node energy consumption in the far-sink area. Thus, the ARM-DDS protocol can increase the energy utilization of the entire network without reducing network lifetime.

From the system model given in Section 4, the network lifetime is defined as the death time of the first node in the network. In a flat network, the nodes near the sink not only need to undertake the energy of data transmitting that was created by themselves but also the amount of data transferred from the far-sink nodes due to the “many to one” data collective models throughout the centralization of the sink. Hence, the node near the sink will have the largest energy consumption in the entire network. So the first dead node in the network is usually one of the nodes close to sink. Figures 21 and 22 show the total energy consumption of a node in one cycle according to Theorem 2. Figures 21 is a comparison diagram of the SW-ARQ protocol and ARM-DDS energy consumption. The conclusions are as follows:

Therefore, the SW-ARQ protocol at the near-sink nodes expects the number of retransmissions to be higher than the ARM-DDS protocol. If the network transmission environment deteriorates, the transmission success rate will become lower. As can be seen from the figure, the energy consumption of the ARM-DDS protocol is smaller than the SW-ARQ protocol. And it is more obvious when it is higher than the \( {p}_i^s \) value.

Figure 23 illustrates the energy utilization rate under different strategies. Energy utilization rate refers to the ratio of the remaining energy of the network to the initial total energy of the network when the network dies. From the experimental results of Fig. 23, the energy utilization rate of ARM-DDS is about 65%, and the energy utilization rate of SW-ARQ is about 37%. It can be seen that the ARM-DDS proposed in this paper significantly improves network energy utilization.

From Fig. 24, it can be shown that: ARM-DDS increases almost 28% of energy utilization in compare with the SW-ARQ protocol. Moreover, energy utilization has a minimal effect on both the transmission and reliability requirements of the network. All of these indicate that the ARM-DDS protocol proposed in this paper has a positive influence on energy utilization compared to the SW-ARQ protocol.