Improving Link Reliability of IEEE 802.15.4g SUN with Re-Transmission Shaping

Packet re-transmissions are a common technique to improve link reliability in low-power wireless networks. However, since packet re-transmissions increase the end-device energy consumption and the network load, a maximum number of re-transmissions per packet is typically set, also considering the duty-cycle limitations imposed by radio-frequency regulations. Moreover, the number of re-transmissions per packet is typically set to a constant value, meaning that all packet re-transmissions are treated the same regardless of actual channel conditions (i.e., multi-path propagation or internal/external interference effects). Taking that into account, in this paper we propose and evaluate the concept of re-transmission shaping, a mechanism that manages packet re-transmissions to maximize link reliability, while minimizing energy consumption and meeting radio-frequency regulation constraints. The proposed re-transmission shaping mechanism operates by keeping track of unused packet re-transmissions and allocating additional re-transmission when the instantaneous link quality decreases due to channel impairments. To evaluate the re-transmission shaping mechanism we use trace-based simulations using a IEEE~802.15.4g SUN data-set and two widely used metrics, the PDR (Packet Delivery Ratio) and the RNP (Required Number of Packets). The obtained results show that re-transmission shaping is a useful mechanism to improve link reliability of low-power wireless communications, as it can increase PDR from 77.9% to 99.2% while sustaining a RNP of 2.35 re-transmissions per packet, when compared to using a single re-transmission per packet.


INTRODUCTION
Achieving link reliability in low-power wireless networks has been a quest for the past decades. Various authors have proposed different strategies at the physical, data-link and network layers to cope with the intrinsic problems of the wireless channel (i.e., multipath propagation and internal/external interference effects), while keeping a low-power consumption profile that allows devices to operate using batteries for multiple years and meeting the dutycycle limitations imposed by radio-frequency regulations.
Given the rising interest in reliability for low-power wireless communications, the IETF (Internet Engineering Task Force) has recently chartered the RAW (Reliable and Available Wireless) group [9]. The aim of RAW is to achieve deterministic performance metrics [4], such as low packet error rate, bounded consecutive packet losses and bounded latency, over wireless links to provide high reliability and availability for IP (Internet Protocol) communications. These performance metrics are known as PAREO [8] and are key to enable the convergence between OT (Operational Technologies) and IT (Information Technologies), as demanded by the Industrial Internet.
To provide high reliability for low-power wireless communications, in this article we propose re-transmission shaping, a mechanism that keeps track of unused packet re-transmissions (i.e., packets that have been successfully received without using all the possible re-transmissions), and allows to use them in the future to maintain link reliability under adverse channel conditions caused by multi-path propagation or internal/external interference effects.
To evaluate the proposed re-transmission shaping mechanism we use simulations based on a IEEE 802. 15.4g [1,2] SUN (Smart Utility Network) data-set [12], obtained through a real-world deployment of 11 devices in a large industrial scenario, using two widely used metrics: the PDR (Packet Delivery Ratio) and the RNP (Required Number of Packets). In addition to having a low implementation complexity, the results show that the re-transmission shaping mechanism can improve PDR significantly (i.e., from 77.4% to 99.2%) while keeping the RNP within bounds (i.e., 2.35 re-transmissions per packet) compared to single re-transmission per packet.
The remainder of this article is organized as follows. Section 2 presents the previous works related to reliability of packet delivery in low-power wireless networks. Section 3 introduces the concept of re-transmission shaping and describes a mechanism to implement it. Section 4 presents the methodology that we have used to validate the proposed re-transmission shaping mechanism. Section 5 presents and discusses the performance evaluation results obtained through simulation. Finally, Section 6 concludes the paper.

RELATED WORK
As introduced earlier, over the past decades various authors have studied the issues of reliability in low-power wireless communications and have proposed different strategies to cope with the intrinsic problems of the wireless channel (i.e., multi-path propagation and internal/external interference effects), while keeping a low-power profile that allows devices to operate using batteries for multiple years. In this section we briefly present various of these techniques that are implemented either at the physical, data-link or network layers, respectively.
Regarding the physical layer, in [5] the authors proposed to exploit constructive interference as a means to increase link reliability of time-synchronized IEEE 802.15.4 networks using the OQPSK-DSSK (Offset Quadrature Phase-Shift Keying -Direct Sequence Spread Spectrum) modulation. The results show that using an algorithm named Flashflood, 94.88% end-to-end reliability can be achieved in a time-synchronized mesh network with 4 hops deployed in an environment with a high level of radio-frequency interference in the 2.4 GHz band.
Also at the physical layer, the authors of [13] evaluated the robustness of the BPSK (Binary Phase Shift Keying), OQPSK (Offset Quadrature Phase-Shift Keying) and 16-QAM (Quadrature Amplitude Modulation) modulations with OFDM (Orthogonal Frequency Division Multiplexing), which were introduced in IEEE 802.15.4g [1] SUN (Smart Utility Network) in 2015. The results show that using these modulations with OFDM provides a link robustness that is at least 6 dB better than DSSS-OPQSK, which was introduced in the original IEEE 802.15.4 [2] standard.
At the data-link layer, the authors of [14] experimentally demonstrate that channel hopping can be used to mitigate the effects of multi-path fading in low-power wireless networks based on the IEEE 802.15.4 standard. Based on these results, the authors of [15] evaluated to which extent can channel hopping mitigate the effects of multi-path propagation and internal/external interference and improve link reliability. The results show that channel hopping can reduce the number of re-transmissions by 56% compared to a single-channel approach.
Also at the data-link layer, the authors of [11] introduced and validated the concept of modulation diversity, which exploits the robustness properties of different modulations to increase link reliability. In [7] the authors evaluated an adaptive modulation selection strategy for packet re-transmissions, showing that with up to 2 re-transmissions per packet link reliability can increase from 93.8% to 94.6% when compared to always using the same modulation for packet re-transmissions.
Finally, regarding the network layer, the authors of [6] studied the use of packet replication at the network layer to improve the end-to-end reliability by exploiting the disjoint paths available in a time-synchronized mesh network. The results show that packet replication improves the network reliability by a factor of 18×, while reducing the end-to-end latency by 40%.
In summary, the results show that constructive interference and channel hopping mechanisms can help coping with multi-path propagation and external interference. However, both techniques require network-wide time synchronization, which increases system complexity and impacts battery duration. In contrast, the results show that modulation diversity allows to improve link robustness, but it still cannot meet the target PDR requirements of industrial applications (i.e., PDR>99%). Finally, packet replication at the network layer can meet the PDR requirements of industrial applications. However, packet replication also requires a mesh network with time-synchronized nodes, increasing the deployment complexity and cost. Taking all this into account, in this paper we propose re-transmission shaping as a mechanism to improve link reliability in star networks without time synchronization requirements. However, please take into account that re-transmission shaping can also be used in mesh networks, or in conjunction with the other link reliability mechanisms presented earlier.

OVERVIEW OF THE RE-TRANSMISSION SHAPING MECHANISM
As introduced earlier, re-transmissions are a common mechanism used at the data-link layer to guarantee the delivery of data packets between an end-device and a gateway using a wireless communication technology. Whenever the acknowledgment packet from the gateway is not received at the end-device due to physical layer effects (i.e., multi-path propagation or internal/external interference), the end-device will re-transmit the original data packet again to provide another opportunity for the packet to be successfully received at the gateway. However, since physical layer effects are not deterministic and packet re-transmission increases end-device energy consumption and network load, a maximum number of retransmissions per data packet is typically set. But assigning a fixed number of re-transmissions per packet may not be optimal, as if channel conditions are too adverse, the originating end-device could need more than the fixed number of re-transmissions to deliver a data packet and, hence, this would be lost. Taking that into account, the aim of the re-transmission shaping mechanism that we present in this section is to dynamically adapt the number of maximum re-transmissions per packet according to channel conditions in order to meet both the data delivery requirements of the application and the target battery lifetime of end-devices. That is, given the average number of re-transmissions per data packet, the re-transmission shaping mechanism keeps track of the number of re-transmissions that have not been used to transmit previous data packets (i.e., if packets have been received by the gateway at the first transmission attempt). These unused re-transmission attempts are accumulated and can be used in the future when channel conditions are bad and the average number of re-transmissions per data packet is not sufficient to guarantee successful delivery.
Considering this high-level description, we now focus on presenting the system model that defines how re-transmission shaping operates. For that, we assume that we have a network with end-devices, with a battery of capacity (mAh) that transmit a data packet with length (bytes) and period (seconds), and one gateway that receives the packets transmitted by end-devices. Upon successfully receiving a data packet from any end-device the gateway transmits an acknowledgment packet (ACK) back to the originating end-device. If the originating end-device does not receive the acknowledgment packet, either because the original data packet is not successfully received or the acknowledgment packet is lost, then the originating end-device re-transmits the data packet.
Considering the values of , and , the average number of re-transmissions per data packet is AVERAGE and we assume that it is set to a value that allows to meet the battery lifetime of the device. That is, if AVERAGE =3 the device is allowed to perform 3 re-transmissions per data packet while operating for 1 year 1 . Then, when the source end-device succeeds in transmitting a data packet with a number of re-transmissions, being 0 ≤ < AVERAGE , the number = AVERAGE − of unused re-transmissions can be accumulated for the re-transmission of subsequent data packets.
Hence, as depicted in Figure 1, the model of the re-transmission shaping mechanism is based on 5 variables AVERAGE , MAXIMUM , ALLOWED , USED and AVAILABLE , as described next: • AVERAGE is an input value that represents the average number of re-transmissions per data packet that are allowed while ensuring the lifetime of the end-device. It is not required to be an integer, it can be directly derived from the device power constraint. • MAXIMUM is an input value that represents the number of extra re-transmissions per packet that are allowed in addition to AVERAGE . • ALLOWED is an output value that represents the maximum number of re-transmissions that are allowed for the current data packet being transmitted. • USED is an input value that represents the number of retransmissions that have been required to successfully deliver the previous data packet to the gateway. • AVAILABLE is an internal state variable that accumulates the number of re-transmissions that have not been spent in previous data packet transmissions and, hence, can be used in the future. It is initialized to zero.
Regarding MAXIMUM , notice that its value is set to avoid a given packet transmission that experiences bad instantaneous channel conditions to deplete all the ALLOWED re-transmissions available. Hence, its value has to be set depending on the context of each deployment. For environments presenting short deep drops in the link reliability it can be set to a high value, allowing to strongly increase the number of re-transmissions for short periods of time. Figure 1: Diagram of the re-transmission shaping mechanism with the input ( AVERAGE , MAXIMUM and USED ), output ( ALLOWED ) and the internal state ( AVAILABLE ) variables, and its relationship with the data-link layer.
In contrast, for environments with long shallow drops in link reliability it can be set to a low value, allowing to extend the effects of re-transmission shaping for a longer period of time.
Using these variables, the operating principle of the re-transmission shaping mechanism is the following. Before a data packet transmission starts, the re-transmission shaping mechanism calculates the ALLOWED of re-transmissions available as ALLOWED ( ) = floor( AVERAGE + min{ AVAILABLE ( ), so that, if unused re-transmissions are available, they are added to AVERAGE without exceeding the threshold set by MAXIMUM . The ALLOWED value is then used by the physical layer to perform re-transmissions until the data packet is either successfully received (i.e., including the acknowledgment) or the number of re-transmissions becomes zero and no more re-transmissions can be performed. In either case, the re-transmission shaping module receives the number USED of re-transmissions used for that particular data packet and performs the following operation to update the internal AVAILABLE variable: Notice that it cannot be negative because USED is always lower than ALLOWED , which depends on AVAILABLE as in Equation 1.
Since in the first iteration AVAILABLE = 0, the formula that expresses AVAILABLE for a generic time step is Notice that using these variables, the re-transmission shaping mechanism can emulate the usual re-transmissions strategy where AVERAGE is set to a constant value per data packet. This behavior can be achieved by setting AVERAGE to an integer value and making MAXIMUM equal to zero. In that case, for every data packet transmission the maximum number of re-transmission attempts is constantly equal to AVERAGE . In this case, the re-transmission shaping mechanism does not perform any additional task to the basic fixed number of re-transmissions case. In fact, as it can be noticed from Equation 1, despite AVAILABLE increases, the value of ALLOWED is always upper bounded by AVERAGE . Hereinafter, we will refer to the particular case in which MAXIMUM is set to zero as no re-transmission shaping (i.e., noRS), as this represents the

EVALUATION METHODOLOGY
In this section, we present an overview of the data-set and a description of the simulator that we use to evaluate the re-transmission shaping mechanism presented in Section 3. Throughout this section we use two performance metrics, the PDR (Packet Delivery Ratio) and the RNP (Required Number of Packets), that are widely used in low-power wireless communications [3]. On one hand, the PDR is defined as the ratio between the received and transmitted packets. On the other hand, the RNP is defined as the average number of re-transmissions required before a data packet is successfully received.

Data-set overview
To evaluate the re-transmission shaping mechanism we use a dataset of measurements obtained from a low-power wireless network deployed in an industrial warehouse to collected temperature, humidity, pressure and illumination measurements to monitor an HVAC (Heating, Ventilation and Air Conditioning) system. The network uses a star topology and consists of 11 OpenMote-B devices [10] Table 1: Unique identifier (last 2 bytes of EUI-64), total received packets, and average RSSI (dBm), CCA (dBm) and PDR (%) values of the devices used in the deployment.
To simulate the data-link layer for the specific environment under analysis, a trace file for each end-device has been created from the original data-set. Each trace file contains PDR values for each IEEE 802.15.4g SUN modulation over time, which have been calculated by computing the frequency of successful transmissions over a window of minutes ( = 5 was used in our analysis). Notice that these windows do not overlap (i.e., each window starts where the previous one ends), and we have removed windows with PDR=0% if no successful transmission has been found within 75 minutes of the window center. Hence, for each minute in the original data-set time range, the trace file keeps a PDR value that is an estimate of the probability of a successful transmission for each IEEE 802.15.4g SUN modulation. Figure 2 depicts calculated PDR values of the SUN-FSK, SUN-OQPSK and SUN-OFDM modulations for all devices present in the experiment. The solid lines represent the median, whereas the colored shadows represent the inter-quartile range computed over the accumulated PDR in one hour. On average, the PDR for the SUN-FSK, SUN-OQPSK and SUN-OFDM modulations is 81.3%, 80.7% and 65.7%, respectively. Notice that SUN-FSK and SUN-OQPSK provide substantially better PDR, but this can be explained by the fact that the radio transceiver used (i.e., Atmel AT86RF215) has a transmit power for the SUN-OFDM signal that is 6 dB lower. Regardless, it is important to notice that the instantaneous PDR values for individual devices and modulations can be 100% at given times or drop to values below 20% at other times. This is caused by the multi-path propagation and internal/external interference effects at the physical layer, and has a large impact on the target application.

Trace-based simulation
To evaluate the performance of the re-transmission shaping mechanism presented earlier we have developed a Python simulator 2 that implements the re-transmission shaping mechanism and uses the trace files presented earlier to simulate channel conditions.
To simulate the transmission of a given data packet the simulator first determines the value of ALLOWED based on the values of AVERAGE , MAXIMUM and AVAILABLE of the re-transmissions shaping mechanism, as described in Section 3. Then, for each ALLOWED the simulator determines which IEEE 802.15.4g SUN modulation to use using one of the two simple strategies available: RANDOM and BEST. In the RANDOM strategy the transmitting device randomly selects one of the three IEEE 802.15.4g SUN modulations available by sampling from a uniform distribution. In contrast, when using the BEST strategy the transmitting end-device always selects the modulation that has the best instantaneous PDR. Of course, the BEST strategy is an ideal scenario, as the instantaneous PDR value cannot be predicted in advance. However, using this strategy allows us to have an upper performance bound that allows to compare the performance of the RANDOM strategy to.
Once the modulation is selected, the channel simulator uses the PDR values for the given IEEE 802.15.4g SUN modulation and enddevice, which have been obtained from the data-set, to determine if a the data packet transmission and its acknowledgment are successfully received or not. It does so by comparing a randomly generated number using a uniform distribution with the computed PDR value for the current data packet transmission. If the random value is below the computed PDR value the data packet is considered as successfully received. Otherwise, the data packet is considered as not successfully received. If the data packet is successfully received, the process is then repeated for the acknowledgment packet using the same PDR value and procedure. That is, the simulator assumes that links are symmetric and data packets are received according to a Bernoulli trial with probability equal to the computed PDR value.
The process is repeated until the data packet and the acknowledgment are successfully received or the number of transmissions for the current data packet reaches ALLOWED . If the data packet and the acknowledgment are successfully received, the channel simulator returns the number of transmissions used ( USED ) for the current packet to the re-transmission shaping module. On the contrary, if the data packet has not been successfully received the simulator returns 0 to the re-transmission shaping module, indicating that all transmission attempts have been used.
Finally, upon receiving USED value the re-transmission shaping mechanism updates the AVAILABLE value according to Equation 2 and the process is repeated for the remaining data packet transmissions.

RESULTS AND DISCUSSION
This section presents and discusses the results obtained using the data-set and the channel simulator described in Section 4 using the values = 9 and = {1, 2, 3, 6, 9} presented in Section 3. We have selected these values experimentally, knowing that = 9 re-transmissions per packet allows to reach a PDR>99%, as required by our application, and setting = {1, 2, 3, 6, 9} allows to explore the solution space that allows to reach the target PDR while minimizing the energy consumption.

Re-transmission shaping operation
As introduced in Section 3, the re-transmission shaping mechanism uses the average number of packets ( ), the maximum number of packets ( ), the number of packets available ( ), the number of packets allowed ( ALLOWED ) and the number of packets transmitted ( USED ) to operate. Figure 3 shows the evolution of the number of packets allowed ( ALLOWED ) and the number of packets transmitted ( USED ) for every packet number in the simulation using the RANDOM strategy. The solid line represents the median and the shaded area represents the inter-quartile range of the two metrics, which have been computed using one hour-wide windows.
As it can be observed, for the device with low average transmit probability error values (i.e., EUI-16=55-AD depicted in Figure 3(a)) the variable ALLOWED remains constant at = 9, whereas the variable USED fluctuates between 1 and 9 + AVERAGE depending on the number of packet re-transmissions required for a given data packet. This indicates that the instantaneous transmit probability is good most of the times, allowing unused retransmissions (i.e., ALLOWED − USED ) to be accumulated for future use in AVAILABLE , as well as allowing the device to transmit more packets than defined by AVERAGE to compensate for poor channel conditions.
In contrast, for the device with high average transmit probability error values (i.e., EUI-16=56-0B depicted in Figure 3(b)) the variable ALLOWED drops to AVERAGE = 3 between packets 25000 and 45000, indicating that there are no additional re-transmissions to be used to compensate for the high average transmit probability error values. However, as channel conditions improve USED drops below 3 again, allowing AVAILABLE to grow again and compensate for future channel impairments.
Last but not least, for the average of all devices (i.e., Figure 3(c)) notice how the USED average value is below 3 most of the times. This indicates that on average devices will be using less than 3 re-transmissions per data packet and, hence, the number of packets available in ALLOWED will grow, allowing to compensate for future propagation or interference effects that cause high instantaneous transmit probability errors.

Evolution of performance metrics
As introduced in Section 4, we use the PDR and the RNP as the performance metrics to evaluate the re-transmissions shaping mechanism presented in Section 3. Figure 4 presents the evolution of the PDR (a) and RNP (b) metrics for the RANDOM and BEST strategies with and without retransmission shaping for AVERAGE = 3. The results are the average of all the devices present in the deployment.
As it can be observed, re-transmission shaping allows to increase the PDR for both the RANDOM and the BEST strategies. In particular, re-transmission shaping increases the PDR by 4.92% (from 0.935 to 0.981) for the RANDOM strategy and by 2.17% (from 0.969 to 0.990) for the BEST strategy. Regarding RNP, re-transmission shaping increases the average RNP for both the RANDOM and the BEST strategies. Specifically, re-transmission shaping increases the RNP by 40% (from 1.50 to 2.10) for the RANDOM strategy and by 27% (from 1.26 to 1.6) for the BEST strategy.
In turn, Figure 5 and Table 2 show the relation between the PDR and the RNP metrics for different values of average re-transmissions per packet (i.e., AVG = {2, 3, 6, 9}) and maximum re-transmissions per packet (i.e., MAXIMUM = 9). For AVERAGE = 1 we can observe that PDR is 77.4% and 88.9% for the BEST and RANDOM strategies regardless of whether re-transmission shaping is enabled or not.  Also, for AVERAGE = 1 we have that = 1 for all cases. Both results are expected, as we only allow one packet re-transmission per packet and, hence, the re-transmission shaping does not make any effect.
It is interesting to notice that for the RANDOM strategy with AVERAGE = 2 using re-transmission shaping the PDR improves by 6.9% (from 89.3% to 96.2%) while the RNP increases 35.9% (from 1.31 to 1.78). In contrast, adding another transmission attempt to the RANDOM strategy without re-transmission shaping would increase PDR by 4.6% (from 89.3% to 93.4%) while the RNP would increase by 13.7% (from 1.31 to 1.49). Of course, increasing the PDR is more difficult as its value approaches 100%, but the mean RNP value is still below the target (i.e., AVERAGE = 2). Adding more retransmissions per packet allows to further increase the PDR at the expense of increasing the RNP and, hence, the energy consumption. With AVERAGE = 6 and re-transmission shaping the PDR reaches 98.8%, whereas with AVERAGE = 9 the PDR reaches 99.2%. Of course, the RNP raises to 2.20 and 2.35 respectively, indicating that more packets are required on average.

Discussion
In the previous subsections we have shown how the modulation shaping mechanism operates and how it can improve the PDR and RNP metrics compared to not using it.
As a summary of our findings, Figure 6 shows the percentage increment of the PDR (left) and RNP (right) performance metrics for the different AVERAGE values (i.e., AVERAGE = {2, 3, 6, 9}) with respect to AVERAGE = 1 using the RANDOM strategy and with MAXIMUM = 9. As it can be observed, the benefits of using re-transmission shaping ranges from 24% to 28% in terms of PDR, whereas without re-transmission shaping the benefit of packet retransmissions ranges from 15% to 26.5%. In contrast, in terms of RNP the energy overhead of using re-transmissions shaping ranges from 80% to 135%, whereas without re-transmission shaping the energy overhead is between 35% to 100%. Of course, the relative benefit of re-transmission shaping decreases as the PDR approaches 100%, whereas the RNP increases as more packets are required to sustain the PDR values.   If we compare the results presented using the RANDOM strategy for AVERAGE = 1 and AVERAGE = 9 without using the retransmission shaping mechanism, we observe that the PDR increases by 26.9% (i.e., from 77.4% to 98.2%) and the RNP increases by 98% (i.e., from 1.00 to 1.98). Yet, the PDR does not reach the target value of our application (i.e., 98.2% instead of 99%) and the RNP is well below the AVERAGE value (i.e., 1.98 instead of 9). In contrast, using the re-transmission shaping mechanism allows to further increase the PDR by 28% (i.e., from 77.4% to 99.2%) while increasing the RNP by 135% (i.e., from 1.00 to 2.35).
In summary, the proposed re-transmission shaping mechanism allows to increase the average PDR by better distributing data packet re-transmissions according to instantaneous channel conditions caused by multi-path propagation or internal/external interference. Of course, this may increase the average RNP compared to not using the re-transmission shaping mechanism, but the mechanism design ensures that the RNP is always kept below AVERAGE . Hence, an end-device with a battery designed to operate for 1 year with AVERAGE = 9 will increase its PDR while minimizing its RNP.
Based on these results, we can state that re-transmission shaping proves to be an interesting mechanism to increase the link reliability for low-power wireless networks, while allowing devices to operate for extended periods of time using batteries. In addition to that, we want to remark two aspects regarding the implementation of the re-transmission shaping mechanism. First, implementing the re-transmission shaping mechanism is feasible in terms of the computational complexity and the memory capacity required considering the capabilities of the embedded micro-controllers that are typically used to implement low-power wireless networks. Second, implementing the re-transmission shaping mechanism is independent of the physical and data-link layers and, hence, it can be used to improve the reliability of wireless technologies other than IEEE 802.15.4g SUN. Figure 6: PDR (left) and RNP (right) percentage increment with respect to AVERAGE = 1 for the RANDOM strategy with MAXIMUM = 9. RS indicates using the re-transmission shaping mechanism, whereas noRS indicates not using the retransmission shaping mechanism (as described in Section 3).

CONCLUSIONS
This paper has presented and evaluated the concept of re-transmission shaping as a means to increase the link reliability of low-power wireless communications. In summary, re-transmission shaping operates by keeping track of unused re-transmissions of data packets when wireless channel conditions are good, and allows additional re-transmissions of data packets when the channel conditions are bad, either due to multi-path propagation or internal/external interference effects. To evaluate the re-transmissions shaping mechanism we use trace-based simulations with the IEEE 802.15.4g SUN standard, and we use the PDR (Packet Delivery Ratio) and the RNP (Required Number of Packets) as the performance metrics to assess its suitability. The results presented show that setting AVERAGE = 9 allows to reach a PDR of 99.2% with an RNP of 2.35. Compared to AVERAGE = 1, the PDR has increased by 27.34% (from 77.9% to 99.2%) and the RNP has increased by 235% (from 1.0 to 2.35). Yet, the average RNP does not reach 3 even for AVERAGE = 9, meaning that an end device designed to support AVERAGE = 3 for one year would still be able to operate after that period. Based on these results, we can conclude that re-transmission shaping is a useful tool to improve the link reliability of low-power wireless networks, as it can significantly improve PDR while sustaining a RNP below the target AVERAGE .
Given the potential of re-transmission shaping as a tool to increase link reliability for low-power wireless communications, in the future we will explore more advanced mechanisms to determine the number of re-transmissions that can be made available per data packet in order to further increase the PDR, while trying to maintain or reduce the RNP. In addition, we will also study the suitability of combining re-transmission shaping with other mechanisms targeted at improving link reliability of low-power wireless networks, such as adaptive modulation selection techniques, which have also demonstrated their potential in that regard.