sensors Article

An Energy-Aware Hybrid ARQ Scheme with Multi-ACKs for Data Sensing Wireless Sensor Networks Jinhuan Zhang and Jun Long * School of Information Science and Engineering, Central South University, Changsha 410083, China; [email protected] * Correspondence: [email protected]; Tel.: +86-0731-8253-9926 Received: 30 April 2017; Accepted: 9 June 2017; Published: 12 June 2017

Abstract: Wireless sensor networks (WSNs) are one of the important supporting technologies of edge computing. In WSNs, reliable communications are essential for most applications due to the unreliability of wireless links. In addition, network lifetime is also an important performance metric and needs to be considered in many WSN studies. In the paper, an energy-aware hybrid Automatic Repeat-reQuest protocol (ARQ) scheme is proposed to ensure energy efficiency under the guarantee of network transmission reliability. In the scheme, the source node sends data packets continuously with the correct window size and it does not need to wait for the acknowledgement (ACK) confirmation for each data packet. When the destination receives K data packets, it will return multiple copies of one ACK for confirmation to avoid ACK packet loss. The energy consumption of each node in flat circle network applying the proposed scheme is statistical analyzed and the cases under which it is more energy efficiency than the original scheme is discussed. Moreover, how to select parameters of the scheme is addressed to extend the network lifetime under the constraint of the network reliability. In addition, the energy efficiency of the proposed schemes is evaluated. Simulation results are presented to demonstrate that a node energy consumption reduction could be gained and the network lifetime is prolonged. Keywords: wireless sensor networks; energy efficiency; reliable communication; energy consumption; multiple ACK copies

1. Introduction Edge computing covers a wide range of technologies and wireless sensor networks (WSNs) are one of its important supporting technologies. WSNs are widely applied in more and more fields, such as the Internet of Things, Cyber Physical Systems, Vehicle Systems and Smart Cities [1–7]. Because sensor nodes have limited batteries and these are hard to replace, the network lifetime is an important performance metric that needs to be considered in any WSN study [8–12]. In addition, due to transmission interference, obstacles and intrusions, wireless links are unreliable. Thus, many errors occur in the data packet transmission process. To ensure the transmission reliability is a key issue for successful application of WSNs. However, ensuring 100% reliable transmission is costly and unnecessary in some wireless communication cases. For example, many applications such as environment (temperature, humidity), or agriculture (water tank, irrigation) monitoring require that each data packet be successfully delivered to the sink with a statistical probability δ < 1, such as 60%–95% [13]. Moreover, how to prolong the network lifetime with the assurance of transmission reliability is a challenging issue. Among the two reliable transmission schemes—packet-loss avoidance and packet-loss recovery [13]—since the packet-loss avoidance is costly, reliable protocols based on packet-loss recovery are more widely applied in WSNs [14–16]. However, in a typical packet-loss recovery scheme (e.g., Sensors 2017, 17, 1366; doi:10.3390/s17061366

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Automatic Repeat-reQuest (ARQ)), when any one packet runs into a transmission error, it is recovered by retransmitting the packet. To reduce the number of retransmissions for packet loss recovery and improve the energy efficiency, the idea of using multiple acknowledgements (ACKs) is proposed. Nguyen et al. [17] proposed a multi-ACK data forwarding scheme to improve the reliability and energy efficiency of WSNs. However, this work just gave a simple analysis of energy consumption and transmission delay for individual nodes. Liu et al. [18] proposed the protocol named send and wait one data multi-ACK (SW-ODMA) ARQ protocol to improve the energy efficiency and statistical reliability. In the scheme, the transmitter just sends one data packet and multiple ACKs are returned from the receiver after receiving the data packet. Dong et al. [19] proposed a novel data gathering protocol named Broadcasting Combined with Multi-Negative Acknowledgement (NACK)/Acknowledgement (ACK) (BCMN/A) based on the analysis strategy to meet requirements of a sensing application through trade-offs between the energy consumption and source-to-sink transport delay under the reliability constraint of wireless sensor networks. In the scheme, the data gathering deploys the send and wait hop-by-hop automatic repeat-reQuest (SW HBH ARQ) protocol. Accordingly, the data load analysis and energy consumption are also under SW HBH ARQ protocol control. To ensure the data packets are transmitted continuously without waiting for confirming messages, the hybrid ARQ scheme to enable source nodes to send data packets continuously with the window size of W is considered [20]. Accordingly, an energy-aware hybrid ARQ scheme for unicast is proposed to ensure energy efficiency and transmission reliability in this paper. Compared with the previous study, we make the following contributions: (1)

(2)

(3)

The energy-aware hybrid ARQ scheme for unicast is proposed to ensure the energy efficiency under the guarantee of network transmission reliability. In the scheme, the source node sends data packets continuously with the window size of W and it is not necessary to wait for the confirming ACK of each packet. When the sink receives K data packets, it will return multiple copies of one ACK for confirmation. After the source node has received ACK packets with some statistical success probability satisfying the transmission constraint, it would send the subsequent packets the window size of W. Otherwise, the source node would retransmit the data packets in the same window. The energy cost of the proposed scheme is statistically analyzed for each node in a flat circle network. Under the typical reliable data transmission model and applying the statistical theory, the theoretical analysis on data load of each node in the flat circle network is presented to ensure the constraint of network transmission reliability is met. Furthermore, the energy cost of each node in one round of data gathering is statistically analyzed based on the classical energy consumption model. The conditions under which the proposed energy-aware hybrid ARQ can be more effective than the original ARQ scheme are discussed. In addition, based on the analysis of the trade-off between node data load and the network statistical reliability, how to select parameters including the transmission range r, the number of returned copies of ACK n for K packets received is described considering the constraint of required reliability δ to prolong the network lifetime.

The rest of this paper is organized as follows: Section 2 reviews related works. The system model is described in Section 3. The energy-aware hybrid ARQ scheme and its theoretical energy cost analysis are demonstrated in Section 4, including the analysis and discussions on energy-efficiency conditions and how to select the optimized parameters to achieve the optimal goal of prolonging the network service lifetime. Section 5 presents the simulation results to evaluate the efficiency of the proposed ARQ scheme. We conclude in Section 6. 2. Related Work There are a great deal of research work on WSNs, including reducing end-to-end delay [21–24], improving energy efficiency and transmission reliability [4,8–14], and other aspects [3,5–7,25]. Focusing

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on the transmission characteristics of WSN, the research on energy-efficient and reliable data transmission theory and application technology is of great significance [19,20]. However how to reduce the energy cost with the guarantee of the transmission reliability is a challenging issue. To ensure reliable communication is essential for most wireless sensor network applications. Due to the unreliability of links, a great deal of research efforts have been devoted to this field to provide reliable transmission service in WSNs. Liu et al. [13] pointed out that the existing works mainly fall into two categories: packet-loss avoidance and packet-loss recovery. The packet-loss avoidance approach (e.g., [26,27]) attempts to reduce the occurrence of packet loss and the packet-loss recovery (e.g., [8,15,16,28]) tries to recover from packet loss when it happens. Because packet-loss avoidance methods are costly, due to cost considerations the most widely used mechanisms in networks are based on packet-loss recovery. One type of reliable protocol based on packet-loss recovery is the retransmission after packet loss and its representative protocol is Automatic Repeat-reQuest (ARQ). Rosberg et al. [20] introduced a new notion of statistical reliability to achieve a balance between data reliability and energy consumption. Based on this, the energy efficiency of a comprehensive set of statistically reliable data delivery protocols are analyzed for linear networks. Liu et al. [18] studied the protocol named send and wait one data multi-ACK (SW-ODMA) ARQ protocol to improve the energy efficiency and statistical reliability. In the protocol, the transmitter sends one data packet at a time and multiple ACKs are returned after receiving the data packet at the receiver. When the returned ACKs are received, the transmitter will send the next data packet. Through reducing the returned ACKs loss, this achieves the goal of reducing retransmission times for sending data packets that consumes more energy. However, in the SW-ODMA scheme, the transmitter will not send the next packet until it receives ACK confirming package or it will resend the last packet when there is a timeout. For coping with the harsh conditions where link packet error rate may be as high as 70% and path length could be up to tens of hops, Jung et al. [29] proposed the hybrid automatic repeat request (HARQ) scheme for wireless sensor network multicast services. In the proposed algorithm, the HARQ operation is combined with an autonomous retransmission method that ensures a data packet is transmitted irrespective of whether or not the packet is successfully decoded at the receiver. However, the traditional per-hop and end-to-end (E2E) recovery schemes suffer from low E2E success rate and poor energy efficiency in large-scale real environments. To address these problems, Liu et al. [13] introduced a novel in-middle recovery scheme and realize it by designing and implementing a proliferation routing, which integrates three core technologies, namely, capability-based path finder, a randomized dispersity, and reproduction. Proliferation routing (PR) offers great flexibilities for transmissions. It can not only be applied with any Medium Access Control (MAC) protocol and routing metric, but also obtains a desired service quality (i.e., transmission success rate, energy cost, etc.) by controlling the system parameters. Although a PR scheme ensures transmission success by packet reproduction in the transmission process to the destination, it cannot necessarily improve the network lifetime effectively. More reproduced data packets will lead to more energy cost for transmission to the destination. The sensors close to the sink deplete their energy faster than other sensors because these sensors have to relay many more data packets for a large part of the network. Therefore, to reduce the number of retransmissions for packet loss recovery is a more effective approach to decrease the network energy consumption and extend the network lifetime for ARQ. Moreover, in order to ensure the data packets are transmitted continuously and without waiting for the confirmation messages of each successful transmitted data packet, an energy-aware hybrid ARQ scheme for unicast is proposed in the paper to address these issues. 3. The System Model and Problem Statement 3.1. The System Model Consider a wireless sensor network consisting of sensor nodes that are randomly scattered in a flat region with the radius of R (m). Nodes do not move after being deployed to detect the event.

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Sensors 2017, 17, 1366periodically generates a message contained in multi-packets, and forwards the packets 4 of 29 The sensor node

with a window size of W to a special destination node, called the sink. The sink is located at the center point network. Assume Assume the the information informationgenerated generatedatateach eachsensor sensornode nodeisisexact. exact.InIn one round point of of the the network. one round of of data gathering, each sensor node not only generates and transmits its own sensed data packets, data gathering, each sensor node not only generates and transmits its own sensed data packets, but also but alsomessages relays messages from other to via the multi-hop sink via multi-hop wireless communications. The relays from other nodes tonodes the sink wireless communications. The message message routing is fixed and the time is slotted. All sensor nodes are assumed to be synchronized. routing is fixed and the time is slotted. All sensor nodes are assumed to be synchronized. Moreover, Moreover, node has antransmission identical transmission range of r (m). each node each has an identical range of r (m). The wireless channel channelisisassumed assumed with nonzero packet loss reliability. A packet can be The wireless with nonzero packet loss reliability. A packet loss canloss be restored restored by retransmitting the lost packet, which, however, results in additional energy cost. by retransmitting the lost packet, which, however, results in additional energy cost. Assuming a node Assuming a node n l has the distance l = ir + x (m) to the sink, then the probability of a data packet nl has the distance l = ir + x (m) to the sink, then the probability of a data packet being successfully being successfully transmitted from nodeon nl the to other nodes routing denoted 1 − pi, transmitted from node nl to other nodes routing pathon is the denoted as 1path − piis , and 1 − qiasdenotes and 1 − q i denotes the successful transmission probability of the returned ACK packet. The reliable the successful transmission probability of the returned ACK packet. The reliable transmission model transmission model 1is[20]. shown Figure 1 [20]. For probability ̅ denotes 1 − p1i − and is shown in Figure Forinsimplification, thesimplification, probability pi the denotes 1 − pi and qi denotes qi . denotes 1 − q i. Besides, the system model assumes that the successful transmission probabilities of Besides, the system model assumes that the successful transmission probabilities of data or ACK in data or ACK in one hopare transmission areallthe sameBecause for all links. of the unreliable links, some one hop transmission the same for links. of theBecause unreliable links, some packets may packets may need to be retransmitted to ensure the network reliability. In our application, the need to be retransmitted to ensure the network reliability. In our application, the network statistical network statistical reliability is set to be δ (0 < δ < 1) from one source node to the sink. reliability is set to be δ (0 < δ < 1) from one source node to the sink. 1  ph

1  ph 1 nl 1

nl

1  qh

1  qh 1 Figure 1. 1. Reliable Reliabletransmission transmission model. model. Figure

3.2. 3.2. Energy Energy Consumption Consumption Model Model Following thetypical typical energy consumption model the expected cost for Following the energy consumption model in [30],inthe[30], expected energy costenergy for transmitting transmitting and receiving a packet is computed by: and receiving a packet is computed by:  ET  l p Eelec  l p fs d 2 2 if (d  d0 )  i f ( d < d0 )  ET= l p Eelec + l p ε f s d4 ) d ) ET l E l p Eelec+  llpεamp d d4 if (di f(dd0> ET= p elec p amp 0   E (E (l p ) l plE pE elec R elec  l pR) =

(1)(1)

where, denotes the transmitting circuit loss energy and d0 denotes the threshold. The parameters where, Eelec elec denotes the transmitting circuit loss energy and d0 denotes the threshold. The parameters εεfsfs and and εεamp respectivelyrepresent representthe the energy energy required required by by the the power power amplifier amplifier and and llpp indicates indicates the the amp respectively packet packet length length (bits). (bits). Following Following the the parameters parameters in in [30], [30], the the network network energy energy consumption consumption parameters parameters and 1. and the the corresponding corresponding values values are are shown shown in in Table Table 1. Table Table 1. 1. Parameters Parameters and and corresponding corresponding values. values. Parameter (units) Parameter (units) Threshold distance (d0) (m) Threshold distance (d0 ) (m) Sensing range r (m) Sensing range r (m) Eelec (nJ/bit) Eelec (nJ/bit) 2) εfsε (pJ/bit/m 2 fs (pJ/bit/m ) 4) (pJ/bit/m εamp ε (pJ/bit/m4 ) amp

Value Value 87 87 15 15 50 50 10 10 0.0013 0.0013

3.3. Problem Statement Network reliability represents the statistical probability of a packet being successfully forwarded from one node to the sink. Assume δ denotes the QoS level probability that each sensed data packet

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3.3. Problem Statement SensorsNetwork 2017, 17, 1366 reliability

5 of 29 represents the statistical probability of a packet being successfully forwarded from one node to the sink. Assume δ denotes the QoS level probability that each sensed data packet is is successfully received by sink the sink a probability less Let δthe i denote the network successfully received by the with with a probability not lessnot than δ. than Let δi δ. denote network reliability reliability packets successfully transmitted from a node l with the of packetsof successfully transmitted from a node nl with the ndistance of distance i hops to of thei hops sink. to the sink. In In the the paper, paper, we we consider consider the the hybrid hybrid ARQ ARQ scheme scheme for for unicast unicast and and its its operation operation is is as as shown shown in in Figure 2. In the scheme, a source node sends data packets continuously with the window size of W Figure 2. In the scheme, a source node sends data packets continuously with the window size of and it waits for for the the confirming of ACK of each data.data. When the sink receives K data packets, it willit W and it waits confirming of ACK of each When the sink receives K data packets, send K ACKs for confirmation. After the sending node has received ACKs with thewith statistical success will send K ACKs for confirmation. After the sending node has received ACKs the statistical probability satisfying the transmission constraint δ i , it would send the subsequent W packets. success probability satisfying the transmission constraint δi , it would send the subsequent W packets. Otherwise, Otherwise, the the sending sending node node would would retransmit retransmit the the data data packets packets in in the the origin origin window. window. As As shown shown in in Figure 2, the source node first continuously sends three data packets including packet 1, packet 2 and Figure 2, the source node first continuously sends three data packets including packet 1, packet 2 and packet inthe thesame samewindow, window, however, in the transmission process, two packets (packet 2 and packet 33 in however, in the transmission process, two packets (packet 2 and packet packet 3) are lost. thenode source node would thenthe transmit the same three but in the 3) are lost. Then theThen source would then transmit same three packets, butpackets, in the transmission transmission process, packet 2 and ACK 3 are lost. Under this condition, the packet success process, packet 2 and ACK 3 are lost. Under this condition, the packet success transmission probability transmission probability δ i = 2/3 is also not satisfied. Therefore, the source node transmits the same δi = 2/3 is also not satisfied. Therefore, the source node transmits the same three packets again. In this three packets process, again. Inthe this transmission third ACK just lost success and accordingly the transmission third ACK is justprocess, lost andthe accordingly theisstatistical transmission statistical success transmission probability is 2/3, satisfying the transmission reliability. Then, the probability is 2/3, satisfying the transmission reliability. Then, the source node would send the next source node would send the next three packets three packets (packet 4, packet 5 and packet 6). (packet 4, packet 5 and packet 6).

Figure with the the transmission transmission success success probability probability δδii == 2/3 2/3 Figure 2. 2. An An example example of one type of ARQ scheme with under under KK ==11and andW W==3.3.

As limited byby thethe node with thethe maximum energy cost, so As we weknow knowthat thatthe thenetwork networklifetime lifetimeis is limited node with maximum energy cost, we focus on on thethe minimization of of the maximum so we focus minimization the maximumenergy energyconsumption consumptionamong amongthe thenodes nodesas aswell well as as ensuring the reliability requirements. Consequently, the issue studied in this paper can be abstracted ensuring the reliability requirements. Consequently, the issue studied in this paper can be abstracted as the following expression: as the following expression:   max ( T ) = min maxE( E  i)   0< i ≤ n i )   max(T )  min max( 0i n Ei = S1 Et1 + S2 E2r (2) (1)  E i i S i E t  iS i E r    s.t. δ = β > δ  ∏ i j  s.t .      



ji∈ Pi j P

j

i

The subscripts j represent the hops of nodes to the sink in the Si1 and Si2 respectively The subscriptsi iand and j represent the hops of nodes to the sinknetwork. in the network. and represent therepresent amount of receivingand data (bits) ofdata node(bits) nl with i hopsnto the sink. Et and Er respectively thesending amountand of sending receiving of node with i hops to the l denote the energy cost for sending and receiving one bit data. Ei denotes the total energy consumption sink. Et and Er denote the energy cost for sending and receiving one bit data. Ei denotes the total of sensor nl Pi represents the nodes set contained in the routing path from node nl to the destination. energy consumption of sensor n l Pi represents the nodes set contained in the routing path from node βj indicates the reliability of one hop of the path. n l to the destination. βj indicates the reliability of one hop of the path.

4. An Energy-Aware Hybrid ARQ Scheme In this section, the overall approach of the proposed energy-aware hybrid ARQ scheme for unicast is presented firstly. Then, the statistical analysis of energy cost of the energy-aware hybrid ARQ scheme operating end-to-end (E2E) and hop-by-hop (HBH) are respectively demonstrated. At the end, we give discussions and analysis on the proposed scheme, including the theory analysis on

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4. An Energy-Aware Hybrid ARQ Scheme In this section, the overall approach of the proposed energy-aware hybrid ARQ scheme for unicast 2017, 17, 1366 Then, the statistical analysis of energy cost of the energy-aware hybrid ARQ scheme 6 of 29 isSensors presented firstly. operating end-to-end (E2E) and hop-by-hop (HBH) are respectively demonstrated. At the end, we the discussions energy efficiency and how parameters achieve the goal give and analysis on to theselect proposed scheme,toincluding the optimization theory analysis ondescribed the energyby Equation (2). efficiency and how to select parameters to achieve the optimization goal described by Equation (2).

4.1.The TheOverall OverallApproach Approach 4.1. thescheme, scheme, the source node sends data packets continuously with a window W and InInthe the source node sends data packets continuously with a window sizesize of Wofand it is it is necessary not necessary to for wait the confirming each data.the When the receives receiver Kreceives K data not to wait thefor confirming ACK ofACK eachof data. When receiver data packets, packets, it will return multiple copies of one confirming ACK to avoid unnecessary data packet it will return multiple copies of one confirming ACK to avoid unnecessary data packet retransmissions retransmissions causedloss, by ACK packet loss, because the ACK packet marks the sequence caused by ACK packet because the ACK packet merely marks the merely sequence number and its number and its size is much smaller than that of the data packets. When the source node has received size is much smaller than that of the data packets. When the source node has received ACK packets, ACK packets, it calculates the statistical probability of successful transmission. If the transmission it calculates the statistical probability of successful transmission. If the transmission constraint δ is constraint δ is satisfied, would sendpackets the subsequent packets with theW. window size the of W. Otherwise, satisfied, it would send theit subsequent with the window size of Otherwise, source node the source node would retransmit the data packets in the window. would retransmit the data packets in the window. paper, operation the proposed energy-aware hybrid ARQ isscheme shown3,in InInthethe paper, the the operation of theofproposed energy-aware hybrid ARQ scheme shown is in Figure Figure wherenode the source node continuously sends three including data packets including packet packet3 2 where the3,source continuously sends three data packets packet 1, packet 2 and1,packet and packet 3 in the same window firstly. However, in the transmission process, two packets in the same window firstly. However, in the transmission process, two packets (packet 2 and packet 3) (packet 2 and are lost. Then the source node three would retransmit the same three packets. But are lost. Then thepacket source3)node would retransmit the same packets. But in the transmission process, in packet the transmission process, the packetthe 1 packet is lost.successful Under this condition, probability the packet δsuccessful the 1 is lost. Under this condition, transmission = 2/3 is transmission probability δ = 2/3 is satisfied. Then, the source node would send the subsequent three satisfied. Then, the source node would send the subsequent three packets (packet 4, packet 5 and packets 4, packet and packet 6).inAs can see that the ACK losses inbecause the transmission packet 6). (packet As we can see that5the ACK losses thewe transmission process are reduced multiple process are reduced because multiple copies of ACK are returned for confirming K data packets. That copies of ACK are returned for confirming K data packets. That improves the ACK transmission improves the ACK transmission reliability and leads to the reduction of data packet retransmission. reliability and leads to the reduction of data packet retransmission. Thus, the transmission and energy Thus, theare transmission and energy efficiency are further improved by continuously transmitting data efficiency further improved by continuously transmitting data packets with a certain window size packets with a certain window size and returning multiple copies of one ACK for K received data and returning multiple copies of one ACK for K received data packets. The proposed scheme can packets. The proposed operate E2E and HBH. scheme can operate E2E and HBH.

Figure The energy-aware hybrid ARQ scheme with transmission success probability δi 2/3 = 2/3 Figure 3. 3. The energy-aware hybrid ARQ scheme with thethe transmission success probability δi = under andWW==3.3. under KK = =1 1and

4.2.Energy EnergyConsumption ConsumptionofofEnergy-Aware Energy-Aware Hybrid E2E ARQ 4.2. Hybrid E2E ARQ thissection, section,we weanalyze analyzethe theenergy energycost costwhen whenthe theenergy-aware energy-awarehybrid hybridARQ ARQscheme schemeoperates operates InInthis E2E. In order to do energy consumption analysis, the data load of each node is calculated firstly E2E. In order to do energy consumption analysis, the data load of each node is calculated firstly applyingthe thestatistical statisticalapproach. approach. applying e2er , e2e,t e2e,r Theorem respectively Dhe,2xet, and Dhx Theorem1.1.Assume Assumethat thatDh,x andDh,x respectivelydenote denotethetheamount amountofofdata datathat thatis istransmitted transmittedand and , received by node nl with h hop distance from sink (that is l = hr + x (x < r)).xMeanwhile, it is assumed that received by node n l with h hop distance from sink (that is l  hr  x ( r )). Meanwhile, it is assumed

that

Ahe,2xe,t

and

Ahe,2xe,r

denote the amount of ACK packet which is transmitted and received by node n l

respectively. In one round of data gathering, we obtain the following formulas:

Dhe,2xe,t  X hh ( )  X hh1 ( )

lr l  2r l  zr  X hh 2 ( )  ...  X hh z ( ) l l l

(2)

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e2e,r Ae2e,t h,x and A h,x denote the amount of ACK packet which is transmitted and received by node nl respectively. In one round of data gathering, we obtain the following formulas: e2e,t Dh,x = Xhh (δ) + Xhh+1 (δ)

l+r l + 2r l + zr + Xhh+2 (δ) + . . . + Xhh+z (δ) l l l

(3)

e2e,r e2e,t Dh,x = Dh,x − Xhh (δ) h h Ae2e,t h,x = Yh ( δ ) + Yh+1 ( δ )

(4)

l + 2r l + zr l+r + Yhh+2 (δ) + . . . + Yhh+z (δ) l l l

(5)

e2e,t −1 Ae2e,r h,x = A h,x + Yh ( δ )

(6)

where, W represents the window size, l = hr + x (x < r) and: e2e n W/K Lh (δ)

h −1

Xhh (δ)

1 − (1 − ∏ih=−01 pi W (1 − (1 − ∏ qi ) )

=W· ∏ih=−01

Xhh+ j (δ)

)

i =0

h + j −1 1 − (1 − ∏ i =0

p i (1 − (1 − ∏ q i ) ) i =0

e2e n W/K Lh+ j (δ)

h + j −1

p i W (1 − (1 − ∏ q i ) )

)

h+ j

∏

i =0

=W· h + j −1 ∏ i =0

(7)

n W/K

h −1

W

n W/K

h + j −1

pW k

(8)

k = h +1

p i W (1 − (1 − ∏ q i ) ) i =0

h+ j

h + j −1

Yhh+ j (δ) = nW · Xh+ j (δ)

∏

k =0

h −1

W/K pW /K k ∏ qk

(9)

k =0

Yhh (δ) = 0

(10)





    log(1 − δ)   Le2e ( δ ) = h  W/K  n h −1    log(1 − ∏h−1 p W (1 − (1 − ∏ q ) ) ) i i =0 i  

(11)

i =0

Proof. All packets in a window with size W are sent continuously and don’t need to wait for the confirmation of each ACK. In addition, in order to increase the successful probability of receiving ACK, the receiver responses n copies of one ACK for each K reception of data packet in the proposed protocol.  n W/K h −1 So the probability of all packets are sent successfully in a window is ∏ih−−01 pW 1 − ( 1 − q ) . ∏ i i =0 i Assuming all packets in the window are transmitted with the least attempts N, the probability with at  n W/K N h −1 least one successful transmission is 1 − (1 − ∏ih−−01 pW 1 − ( 1 − q ) ) . In order to ensure ∏ i i =0 i  n W/K N the statistical reliability of δ, we ensure 1 − (1 − ∏ih−−01 pW 1 − (1 − ∏ih=−01 qi ) ) ≥ δ is satisfied. i Hence, we can get:

log(1−δ) n W/K

≥ N For further processing this expression is

h −1 log (1−∏ih=−01 pW ) i (1−(1− ∏i =0 qi ) ) e2e rounded up to be an integer to obtain Lh (δ), which represents the least number of data packet sending

times from the source node nl to the sink to ensure the reliability of δ. That is:

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 Le2e h (δ)



    log(1 − δ)   = n W/K  h −1    log(1 − ∏h−1 p W (1 − (1 − ∏ q ) ) ) i i =0 i  

(12)

i =0

Assuming that Xh denotes the times of the window that all data in the window with size W are sent successfully with the reliability of δ, Xh obeys the upper bound of geometric distribution [20]. h −1

h −1

i =0

i =0

n W/K

W That is Xh ∼ G ( Le2e h ( δ ), ∏ p i (1 − (1 − ∏ q i ) )

E [ Xh ] =

Le2e h ( δ )−1

∑

k =1

h −1

n W/K

h −1

W

k ( ∏ p i (1 − (1 − ∏ q i ) ) i =0

h −1

h −1

i =0

i =0

h −1

n W/K k −1

h −1

W

)(1 − ∏ pi (1 − (1 − ∏ qi ) )

i =0 e2e n W/K Lh (δ)−1

W Le2e h ( δ )(1 − ∏ pi (1 − (1 − ∏ qi ) )

i =0

)

+...

i =0

)

(13)

e2e W/K L h (δ)

h −1

h −1

n

i =0

i =0

h −1

h −1

i n W/K

i =0

i =0

1−(1− ∏ pi W (1−(1− ∏ qi ) )

=

)). Therefore, we obtain the following formula:

)

∏ pi W (1−(1− ∏ qi ) )

Considering the window size of W and letting Xhh (δ) represent the statistical amount of data packet sending of the source node nl , it is obtained by the following formula:

Xhh (δ)

1 − (1 − ∏ih=−01

p i W (1 − (1 − ∏ q i ) )

)

i =0

=W· ∏ih=−01

e2e n W/K Lh (δ)

h −1

W

(14)

n W/K

h −1

p i (1 − (1 − ∏ q i ) ) i =0

As for node at (h + j)r + x from the sink, the least sending times of data packets and the sending data packet statistics of the node are calculated similarly by the following formulas:  Le2e h+ j (δ )



    log(1 − δ)   = W/K  n h + j −1     log(1 − ∏h+ j−1 p W (1 − (1 − ∏ q ) ) )   i i i =0

(15)

i =0

h + j −1

h+ j Xh+ j ( δ )

1 − (1 − ∏ i =0

h + j −1

p i W (1 − (1 − ∏ q i ) )

)

i =0

=W· h + j −1 ∏ i =0

e2e n W/K Lh+ j (δ)

h + j −1

(16)

n W/K

p i W (1 − (1 − ∏ q i ) ) i =0

As for node at (h + j)r + x from the sink, the data packets transmitted to the node at hr + x from the sink are: h + j −1

Xhh+ j (δ)

1 − (1 − ∏ i =0

=W· h + j −1 ∏ i =0

h + j −1

e2e n W/K Lh+ j (δ)

p i W (1 − (1 − ∏ q i ) ) i =0

h + j −1

n W/K

p i W (1 − (1 − ∏ q i ) ) i =0

)

h+ j

∏

k = h +1

pW k

(17)

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Since n copies of ACK are sent each time when the sink successfully received the K data packets, the ACK amount received by the sink from h hop is: h −1

Yh−1 (δ) = nW · Xhh (δ) ∏ pW j /K

(18)

j =0

At h hop, the number of ACK sent for nodes at h + j can be calculated as follows: h+ j

h + j −1

Yhh+ j (δ) = nW · Xh+ j (δ)

∏

k =0

h −1

W/K pW /K k ∏ qk

(19)

k =0

The nodes at h hop do not need to send an ACK confirmation for themselves, so: Yhh (δ) = 0

(20)

Because the nodes at h hop need to forward all packets and ACKs which arrive at the hth hop, as 9 of 29 shown in Figure 4, following [18], the total number of transmitted data packets and ACKs of node nl can be computed by: lr l  2r l  zr Dhe,2xe,t  X hh ( )  X hh1 ( )  X hh 2 ( )  ...  X hh z ( ) (20) l + lr l +l 2r l + zr e2e,t h h h h Dh,x = Xh (δ) + Xh+1 (δ) + X h +2 ( δ ) + . . . + Xh+z (δl) (21) l l l l r l  2r l  zr Ahe,2xe,t  Yhh ( )  Yhh1 (l )+ r  Yhh 2 ( ) l + 2r ...  Yhh z ( ) (21) h l l + zr h h l + Y h (δ) l + . . . + Y ( δ ) (22) Ae2e,t = Y ( δ ) + Y ( δ ) h +2 h+z h h +1 h,x l l l where the distance from the node n l to the sink is l = hr + x and z is the integer which makes zr + x where the distance from the node nl to the sink is l = hr + x and z is the integer which makes zr + x just just lessless thanthan R. R.

Sensors 2017, 17, 1366

dr

R

h l

r

x

r

r

dr

nl Al  r

Al  2 r

Al 3r

lr

l  2r

Figure 4. The sketch of data transmission of the node nl . Figure 4. The sketch of data transmission of the node nl.

Considering the process of data transmission without data aggregation, the number of receiving data Considering the process of data transmission without data aggregation, the number of receiving e2e,r packets Dh,x ofe2node nl is equal to the number of sending packets minus its own generated data packets. er , e2e,rpackets Dhx of the number ofnodes sending its own generated data n l is equal A equals the, sum ofnode the number of senttoACKs for other andpackets its ownminus returned ACKs.  h,x

e2e,r

data packets. Ah,x equals the sum of the number of sent ACKs for other nodes and its own returned According to the statistical data load of each node and following the typical energy consumption ACKs. model □described in Equation (1), the energy consumption for sending and receiving the data packet According tounder the statistical data loadthat of each node and theand typical can be calculated the assumption the number of following bits in ACK dataenergy packet consumption are λ1 and λ2 model described respectively and in λ2 Equation  λ1 : (1), the energy consumption for sending and receiving the data packet can be calculated under the assumption that number of bitsαin ACK and data packet are  1 and e2e,t e2e,t Eh,x = λthe (23) 2 Dh,x ( Eelec + ε ψ d )  2 respectively and 2 1 :

Ehe,2xe,t  2Dhe,2xe,t (Eelec  d )

(22)

Ehe,2xe,r  2 Dhe,2xe,r Eelec

(23)

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e2e,r e2e,r Eh,x = λ2 Dh,x Eelec

(24)

Similarly, the energy consumption for sending and receiving ACK are calculated by: e2e,t α eh,x = λ1 Ae2e,t h,x ( Eelec + ε ψ d )

(25)

e2e,r eh,x = λ1 Ae2e,r h,x Eelec

(26)

4.3. Energy Consumption of Energy-Aware Hybrid HBH ARQ In this part, we similarly analyze the energy consumption when the energy-aware hybrid ARQ scheme operates HBH. The data load of each node is analyzed firstly to do energy cost analysis. hbh,t hbh,r Theorem 2. Assume that Dh,x and Dh,x respectively denote the amount of data that is transmitted and hbh,r received by node nl at h hop from sink. Besides, it is assumed that Ahbh,t h,x and A h,x denote the amount of ACK data which is transmitted and received by node nl respectively. In one round of data gathering, the data load of nl is calculated by: hbh,r +1 W Dh,x = Xhh+ 1 ( δ ) p h +1

l+r l + 2r l + zr +1 +1 ( δ ) p h +1 W ( δ ) p h +1 W + Xhh+ + . . . + Xhh+ 2 z l l l l+r l + 2r l + zr + Xhh+2 (δ) + . . . + Xhh+z (δ) l l l

(28)

hbh,r Ahbh,t h,x = nDh,x /K

(29)

hbh,t W W/K /K Ahbh,r h,x = nDh,x p h q h−1

(30)

hbh,t Dh,x = Xhh (δ) + Xhh+1 (δ)

where: Xhh (δ)

(27)

=W·

Xhh+ j (δ) = W ·

1 − (1 − p h W (1 − (1 − q h ) n )

hbh W/K Lh (δ)

)

(31)

n W/K

p h W (1 − (1 − q h ) )

1 − (1 − p h + j W (1 − (1 − q h + j ) n )

hbh W/K Lh+ j (δ)

)

W/K

(32)

+1 W Xhh+ j (δ) = Xhh+ j ( δ ) p h+1 , j ∈ {1, 2, . . . , z }

(33)

p h + j W (1 − (1 − q h + j ) n )

Proof. In order to meet the hop transmission reliability δ1/h and combining theorem 1, the maximum number of the total transmission for nodes at h hop with distance l = hr + x to sink is: & Lhbh h (δ) =

'

log(1 − δ1/h ) log(1 − ph W (1 − (1 − qh )n )

W/K

(34)

)

Hence, to ensure the network reliability, the amount of data to be transmitted hop by hop for the nodes is statistically calculated by the following equation:

Xhh (δ) = W ·

1 − (1 − p h W (1 − (1 − q h ) n ) W

hbh W/K Lh (δ)

n W/K

p h (1 − (1 − q h ) )

)

(35)

For a data packet at (h + j)r + x transmitted to the next hop, the expected maximum retransmission number and the amount of data transmitted are respectively computed as follows:

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



log(1 − δ1/(h+ j) )

  Lhbh h+ j (δ ) =  W/K   log(1 − ph+ j W (1 − (1 − qh+ j )n ) )

h+ j Xh+ j

= Xhh+ j = W ·

1 − (1 − p h + j W (1 − (1 − q h + j ) n ) p h + j W (1 − (1 − q h + j ) n )

(36)

hbh W/K Lh+ j (δ)

)

W/K

(37)

Therefore, the data load transmitted by node at l = hr + x is calculated by: hbh,t Dh,x = Xhh (δ) + Xhh+1 (δ)

l + 2r l + zr l+r + Xhh+2 (δ) + . . . + Xhh+z (δ) l l l

(38)

In addition, considering the number of received data packets equals the number of data packets sent by the previous node multiplied by the packet loss rate, that is: hbh,r W Dh,x = Dhhbh,t +1,x p h+1 , j ∈ {1, 2, . . . , z }

(39)

According to the proposed energy-aware hybrid ARQ scheme, the number of the returned ACK equals the number of received data packets divided by K. Moreover, the node does not need to send ACK for its own generated packets, so the nodes at l = hr + x just need to receive data packets and ACKs returned from other nodes. Hence, we obtain the following equations: hbh,r W +1 Dh,x = Xhh+ 1 ( δ ) p h +1

l+r W l + 2r W l + zr +1 +1 + Xhh+ + . . . + Xhh+ 2 ( δ ) p h +1 z ( δ ) p h +1 l l l hbh,r Ahbh,t h,x = nDh,x /K

(40) (41)

hbh,t As mentioned above, the number of ACK sent for subsequent nodes by node nl is Dh,x . Considering the transmission probability ph and n copies of ACKs returned for each K data packets with probability qh−1 , we can get the amount of ACK data received by node nl : hbh,t W W/K /K Ahbh,r h,x = nDh,x p h q h−1

(42)

 According to the data load of each node and the typical energy consumption model, the energy consumption can be calculated as follows: hbh,t hbh,t Eh,x = λ2 Dh,x ( Eelec + ε ψ dα )

(43)

hbh,r hbh,r Eh,x = λ2 Dh,x Eelec

(44)

hbh,t α eh,x = λ1 Ahbh,t h,x ( Eelec + ε ψ d )

(45)

hbh,r eh,x = λ1 Ahbh,r h,x Eelec

(46)

4.4. Discussion on the Performance of Energy Efficiency 4.4.1. Performance of Energy Efficiency In this section, we discuss the conditions under which the proposed ARQ can be more energy efficient than the existing ARQ scheme. In the section, we just do analysis on the E2E operation because the analytical procedure of HBH is similar to that of the E2E operation. As can be seen from the previous sections, the SW-ODMA ARQ protocol is a special case of our proposed energy-aware hybrid ARQ scheme when W = 1 and K = 1. The biggest difference between the proposed energy-aware

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hybrid ARQ and the original hybrid ARQ scheme is that multiple ACK messages are sent for multiple messages rather than a single message. From the statistical point of view, we need to prove whether the proposed ARQ is more energy efficiency than the original ARQ in one round of data gathering, and the other conclusions are the same for the whole running time of the network. For the case that multiple ACK messages are sent for a single message, the probability of one h −1

returned ACK from the sink to the source node is ∏ qi . So the data load of each node is calculated by i =0

the following equations: e2e,t

h

h

D h,x = X h (δ) + X h+1 (δ)

l+r l + 2r l + zr h h + X h +2 ( δ ) + . . . + X h+z (δ ) l l l e2e,r

e2e,t

h

D h,x = D h,x − X h (δ) e2e,t

h

h

Ah,x = Y h (δ) + Y h+1 (δ)

(48)

l+r l + 2r l + zr h h + Y h +2 ( δ ) + . . . + Y h+z (δ ) l l l

e2e,r

−1

e2e,t

(47)

Ah,x = Ah,x + Y h (δ)

(49) (50)

where:

e2e

n W Lh (δ)

h −1

h X h (δ)

1 − (1 − ∏ih=−01 pi W (1 − (1 − ∏ qi ) ) ) i =0

=W· ∏ih=−01

(51)

n W

h −1

W

p i (1 − (1 − ∏ q i ) ) i =0

e2e

h + j −1

h X h+ j (δ )

1 − (1 − ∏ i =0

p i W (1 − (1 − ∏ q i ) ) )

h + j −1

∏

n W

h + j −1

pW k

(52)

k = h +1

p i W (1 − (1 − ∏ q i ) ) i =0

h

h+ j

h + j −1

Y h+ j (δ) = nW · X h+ j (δ)

∏

k =0

−1

h

h+ j

i =0

=W· ∏ i =0

n W L h+ j (δ)

h + j −1

h −1

W pW k ∏ qk

(53)

k =0

h

h −1

Y h (δ) = 0, Y h (δ) = nW · X h (δ) ∏ pW j

(54)

j =0

 e2e Lh (δ)



    log(1 − δ)   = W  n h −1    log(1 − ∏h−1 p W (1 − (1 − ∏ q ) ) )  i i =0 i  

(55)

i =0

Therefore, the energy cost is: e2e,t

e2e,t

Eh,x = λ2 D h,x ( Eelec + ε ψ dα ) e2e,r

e2e,r

Eh,x = λ2 D h,x Eelec e2e,t

α ee2e.t h,x = λ1 A h,x ( Eelec + ε ψ d ) e2e,r

ee2e,r h,x = λ1 A h,x Eelec

(56) (57) (58) (59)

When satisfying the following condition, the proposed energy-aware hybrid ARQ scheme is more energy efficiency than the typical hybrid ARQ scheme as described in Figure 2:

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e2e,t

e2e,r

e2e,r Eh,x + Eh,x + ee2e,t h,x + e h,x e2e,t e2e,r e2e,t e2e,r Eh,x + Eh,x + eh,x + eh,x

>1

(60)

After the concrete parameters are substituted and further simplified, we can get the following result:   z     h h Eelec h ( δ ) l +ir − h (δ) elec 1 + E E+ X ( δ ) − X X ( δ ) − X ∑ α α h +i h h +i h l Eelec +ε ψ d elec ε ψ d i =0     z   h + i −1 h − 1 h +i h +i W W/K l +ir + λλ21 1 + E E+elecε ψ dα W X ( δ ) − X ( δ ) p q /K ∑ ∏ k ∏ k h +i l h +i elec i =0 k =0 k =0   h −1 h + λλ12 E E+elecε ψ dα W X h (δ) − Xhh (δ) ∏ pW k /K > 0 

elec

(61)

k =0

Due to the complicated mathematical expressions, the final expression is hard to reduce to one containing parameters W, K, δ, λ1 , λ2 , n, r, pi and qi . However, from the mathematical expression, we know that the energy efficiency is related with the parameters r, n and K under the given pi , qi , δ and W. Following the similar process, we can discuss and analyze the conditions that the proposed hybrid ARQ scheme can be more effective than the original ARQ operating hop by hop. 4.4.2. Parameter Optimization According to the discussion above, the energy efficiency is related with the parameters r, n and K under the given pi , qi , δ and W. In this section, how to select parameters of the transmission range of r and the number of returned copies n ACKs for K(K ≤ W) packets successfully received to achieve the optimization goal of Equation (2) is discussed. It can be seen from the previous sections that the number of data load is different with the distance of source node to the sink, the transmission range of r and the number n of returned ACKs for K packets received considering the constraint of required reliability δ. Thus, the energy cost of each node is different with the different parameters. However, the maximum lifetime can be achieved by optimizing the parameters selection under the guarantee of network reliability. The detailed procedure applying the enumeration method to select the optimizing parameters is described in Algorithm 1. Algorithm 1: Parameter selection to maximize network lifetime under the required reliability Input: K set {1, . . . , w}, n set {1, . . . , m} and r = {r_set} Output: the optimized K _min, n _min and r _min 1: let globalE = ∞ 2: for each K in {1, . . . , w} 3: for each n in {1, . . . , m} 4: for each r = {r_set} 5: for each node with distance l to sink in the network topology 6: calculate the data load under the current r, n and K according to theorem; 7: calculate the energy consumption El according to Formula 1 and 2; 8: if El > e_r 9: e_r = El ; 10: end if 11: end for 12: if globalE > e_r 13: globalE = e_r; 14: r _min = r; 15: n _min = n; 16: K _min = K; 17: end if 18: end for 19: end for 20: end for 21: output K _min, n _min and r _min

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5. Performance Evaluation In this section, the simulation results are presented to evaluate the energy-aware hybrid ARQ scheme under different parameters. The simulation scenario is described firstly, focusing more on the network model and parameters applied in the simulation experiments. Then the evaluation and comparison are presented to reflect the impact of control parameters on the performance. Sensors 2017, 17,results 1366 14 of 29 5.1. Parameter Settings center point of the network. The data packet size is fixed  2 = 100 bits and the ACK packet size is circle network consisting of 600 sensor nodes that are randomly scattered 20 bits toa random ensure flat  1 =Consider 2 1 . The network reliability to be ensured in the following evaluation is in a flat network with the radius of 10 (m), which is shown in are Figure 5. The sink is located at the center randomly set as   0.70 . Other parameters of the network as shown in Table 1. Assuming the point of the network. The data packet size is fixed λ2 = 100 bits and the ACK packet size is λ1 = 20 bits window size is W  3 . For each node n l , the probability of a data and ACK packet successfully to ensure λ2  λ1 . The network reliability to be ensured in the following evaluation is randomly set 1qi = 0.8the as δ = 0.70.toOther parameters the networkassumed are as shown 1. Assuming window sizepis 0.8 and (the value of transmitted the next node areofrespectively 1  pi in=Table i W = q3. For each node selected, nl , the probability of a affect data and ACK packet successfully transmitted to the the and are randomly which do not the evaluation on the theoretical analysis on i next node are respectively assumed 1 − pi = 0.8 and 1 − qi = 0.8 (the value of pi and qi are randomly proposed energy-aware hybrid ARQ scheme). The simulation is conducted to evaluate the selected, which do not affect the evaluation on the theoretical analysis on the proposed energy-aware correctness and efficiency. hybrid ARQ scheme). The simulation is conducted to evaluate the correctness and efficiency. 10 8 6 4 2 0 -2 -4 -6 -8 -10 -10

-8

-6

-4

-2

0

2

4

6

8

10

Figure 5. The network topology.

Figure 5. The network topology.

5.2. Evaluation on the Energy-Aware Hybrid ARQ Scheme

5.2. Evaluation on the the Energy-Aware Hybridscheme ARQ Scheme In the section, proposed ARQ operating E2E and HBH is evaluated, respectively. In the following evaluations, the relations among energy cost and scheme parameters are described. In the section, the proposed ARQ scheme operating E2E and HBH is evaluated, respectively. In the following evaluations, the relations E2E among energy cost and scheme parameters are described. 5.2.1. Evaluation on the Energy-Aware ARQ the part, the on the proposed 5.2.1. In Evaluation on evaluation the Energy-Aware E2E ARQhybrid ARQ scheme E2E operation are demonstrated. Figure 6 shows the sending and receiving data load of each node when r = 2 m and n = 1 under In the part, the evaluation on the proposed hybrid ARQ scheme E2E operation are demonstrated. the assurance of the network reliability δ = 0.70. From the figure, it can be seen that the data load is rthe 2 energy n1 under Figure 6 shows sending andsink receiving loadFigures of each7 node m and consumption increasing as thethe distance to the gettingdata smaller, and 8 when describe  0.70the the assurance the forms. network . From the the figure, it can be to seen data load is of each node inoftwo Asreliability can be seen from figures, nodes closer thethat sinkthe bear more data increasing as the distance to the sink getting smaller, Figures 7 and 8 describe the energy consumption of each node in two forms. As can be seen from the figures, the nodes closer to the sink bear more data load and have more energy consumption because they not only need to transmit their own data but also forward the data packets from other nodes in the larger part of the network. This is in accordance with the actual analysis result.

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load and have more energy consumption because they not only need to transmit their own data but 15 15 of of 29 29 packets from other nodes in the larger part of the network. This is in accordance 15 of 29 with the actual analysis result.

Sensors Sensors 2017, 2017, 17, 17, 1366 1366 also forward the data Sensors 2017, 17, 1366

6000 6000 sending sending receiving receiving sending ACK ACK sending sending receiving ACK ACK receiving receiving ACK sending ACK receiving

6000 5000 5000

data data load load of each nodenode data load of each each node of

5000 4000 4000 4000 3000 3000 3000 2000 2000 2000 1000 1000 1000 00 0

00

11

22

33

0

1

2

3

44 55 66 distance distance to to sink sink 4 5 6 distance to sink

77

88

99

10 10

7

8

9

10

n11,, K1 and  0.70 0.70.. Figure Figure 6. 6. Data Data load load of of each each node node sending sending and and receiving receiving with with r2,, n and  Figure 6. Data load of each node sending and receiving withr r= n =1 ,1, K K =11 and and δ=0.70. 2,2,n 0.70 . Figure 6. Data load of each node sending and receiving with 0.06 0.06 0.06

Energy consumption of each nodenode Energy consumption of each each node Energy consumption of

0.05 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.01 00 0

00

11

22

33

0

1

2

3

44 55 66 distance distance to to sink sink 4 5 6 distance to sink

77

88

99

10 10

7

8

9

10

2,2,, n K 0.70 n 11, =0.70. 0.70.. Figure 7. Energy consumption of each node with ,, K Figure 7. 7. Energy consumption ofof each node with and δ Figure Energy consumption each node withr r= n =1 =11 and and Figure 7. Energy consumption of each node with r2, n1 , K1 and   0.70 . 0.06 0.06 0.06 0.05 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.0100 10 10 0 10

55 5

10 10 55

00 0

00

-5 -5 -5

-5 -5 -10 -10

-10 -10

10

5

0

-5

r2 , n 11,, KK 0.70 n =0.70. 0.70.. Figure 8. dimensional energy consumption diagram with Figure 8. Three Three dimensional energy consumption diagram with and δ Figure 8. Three dimensional energy consumption diagram with r = ,2, n = 1, =11 and and Figure 8. Three dimensional energy consumption diagram with r2, n1 , K1 and   0.70 . -10

-10

In In the the following, following, we we will will evaluate evaluate the the scheme scheme under under different different parameters parameters to to meet meet the the network network Inthe thefollowing, following,we wewill willevaluate evaluatethe thescheme schemeunder underdifferent differentparameters parametersto tomeet meetthe thenetwork network In n 0.70 0.70.. The reliability == {1, reliability   The randomly randomly selected selected parameters parameters sets sets are are K == {1, {1, 2, 2, 3}, 3}, {1, 2, 2, 3, 3, 4, 4, 5} 5} and and reliability δ = 0.70. The randomly selected parameters sets are KK = {1, 2, 3}, n = {1, 2, 3, 4, 5} and r = {4, n   0.70 reliability . The randomly selected parameters sets are = {1, 2, 3}, = {1, 2, 3, 4, 5} and n r5, =6,= {4, K (m). the ,, their values only the of and {4, 5, 6, 6, 7} 7} (m). For the parameters parameters their values can only be be integers. In W the=case case of and 7} 5, (m). For theFor parameters K and n, their values can only becan integers. Inintegers. the case In of 3, the n , their rW K22 or = {4, 5, 6, values 7} (m). of For the can parameters values can only be integers. In the case of and K K 3 W 1 W  3 W 1 , the only be 1, 3. When and = 1, the SW-ODMA in [18] , the values of can only be 1, or 3. When and = 1, the SW-ODMA in [18] is values of K can only be 1, 2 or 3. When W = 1 and K = 1, the SW-ODMA in [18] is the special case is of K K W  3 W 1 , the values of can only be 1, 2 or 3. When and = 1, the SW-ODMA in [18] is the the special special case case of of our our proposed proposed scheme. scheme. For For the the number number of of copies copies of of the the returned returned ACKs, ACKs, n is is also also n the special case of our proposed scheme. For the number of copies of the returned ACKs, is also n with is with integer integer values. values. Hence, Hence, in in the the evaluation evaluation is randomly randomly set set {1, {1, 2, 2, 3, 3, 4, 4, 5} 5} in in order order to to gain gain fully fully with integer results. values. and and reliable reliable results. Hence, in the evaluation n is randomly set {1, 2, 3, 4, 5} in order to gain fully and reliable results.

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our proposed For the number of copies of with the returned ACKs, n is also for with integer values. When nscheme. = 1, it is the original ARQ scheme one ACK confirmation one data packet. nevaluation When = 1, it is the original ARQ scheme with one ACK confirmation for one data packet. Hence, in the n is randomly set {1, 2, 3, 4, 5} in order to gain fully and reliable results. Besides, to study the influence of the transmission range in the evaluation, we let the transmission Besides, to study of theARQ transmission the evaluation, wefor let the When n = 1,the it influence is the original scheme range with onein ACK confirmation onetransmission data packet. range is changing and the experimental values are randomly set 4 (m), 5 (m), 6 (m) or 7 (m) range is study changing and the experimental valuesrange are randomly set 4 (m),we 5 (m), 6 (m) or 7 (m) Besides, to the influence of the transmission r in the evaluation, let the transmission according to the network range and assurance of node connectivity. Figure 9 shows the energy according to the network and assurance ofrandomly node connectivity. 9 shows energy range r is changing and the range experimental values are set 4 (m), 5 Figure (m), 6 (m) or 7 (m)the according consumption of each node with different when K1 and n1. From the figure, we can see that to the network and assurance of node when connectivity. Figure of K1 and n91shows consumption ofrange each node with different . Fromthe theenergy figure, consumption we can see that the overall trend of energy consumption is changing bigger for nodes closer to the sink than those eachoverall node with r when K = 1 andisnchanging = 1. Frombigger the figure, we can see that thesink overall trend of the trenddifferent of energy consumption for nodes closer to the than those nodes far from the sink. Moreover, the energy cost is different with different values. Especially energyfar consumption is changing bigger nodes closer to the sink than those nodesvalues. far from the sink. nodes from the sink. Moreover, the for energy cost is different with different Especially when =the 5 (m), the maximum nodewith energy consumption isEspecially minimized, which can be the seen from the Moreover, energy cost is different different r values. when r = 5 (m), maximum when = 5 (m), the maximum node energy consumption is minimized, which can be seen from the Figureenergy 10 obviously. It means that different transmission range leads to differentIt energy node consumption is minimized, which can be seen from the Figure 10 obviously. means Figure 10 obviously. It means that different transmission range leads to different energy that different transmission range leadsnot to different energy consumption consumption and the energy costr does have linear relation with . and the energy cost does not consumption and the energy have linear relation with r. cost does not have linear relation with .

rr

rr

rr

rr

rr

rr rr

0.014 0.014

r=4 r r==45 r r==56 r r==67 r=7

E nergy c ons umum ption of of eaceac h node E nergy c ons ption h node

0.012 0.012 0.01 0.01 0.008 0.008 0.006 0.006 0.004 0.004 0.002 0.002 0 0

0 0

1 1

2 2

3 3

4 5 6 4distance 5 to sink 6 distance to sink

7 7

8 8

9 9

10 10

rr

1, nn  0.70 . Figure 9. 9. Comparison of of energy consumption with different when KK andδ = Figure Comparison energy consumption with different r when = 1, = 11and 0.70. Figure 9. Comparison of energy consumption with different when K1, n1 and   0.70 .

rr

Figure different r when K = 1, n1 =, 1n and K 1 Figure 10. 10. Comparison Comparisonof ofthe themaximum maximumenergy energyconsumption consumptionwith with different when Figure 10. Comparison of the maximum energy consumption with different when K1, n1 δand = 0.70.   0.70 . and   0.70 .

When the returned returned ACK has the the different different number number of of copies, copies, the the data data and and ACK ACK load load under under the the When the returned ACK has the different number of copies, the data and ACK load under the condition that that all all nodes nodes generate generate data data for E2E ARQ protocol are different. different. Figure Figure 11 demonstrates demonstrates the condition condition that all nodes generate data for E2E ARQ protocol are different. Figure 11 demonstrates the n comparison of energy consumption with different n when K = 1 and r = 3. comparison of energy consumption with different when K1 and r  3. comparison of energy consumption with different n when K1 and r  3.

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0.03

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1729 of 28 17 of

Energy consumption of each node

0.025 0.03 n= n= n= n=

Energy consumption of each node

0.02 0.025

n= n= n= n= 1 2 3 5

1 2 3 5

0.015 0.02

0.01 0.015 0.005 0.01

0.005

0

0

1

2

3

4 5 6 distance to sink

7

0

1 2 3 4 5 6different 7 8 Figure 11. Comparison of 0energy consumption with distance to sink

  0.70 .

8

9

10

n 9 when 10 K1 , r  3

and

n

Figure 11. Comparison of energy consumption with different n when K = 1, K r = 13 and δ = 0.70. Figure 11. Comparison of energy consumption with different when , r  3 and

From the figure, we can see that the energy consumption can be decreased by reducing data   0.70 . packets retransmission through the number of returned copies. This thatdata the From the figure, we can seeincreasing that the energy consumption canACK be decreased by means reducing improvement of the successful reception ofthe ACK by increasing the ACK number of returned ACKthat copies packets through increasing number of returned copies. This means From retransmission the figure, we can see that the energy consumption can be decreased by reducing datathe can reduce the unnecessary retransmission of data packet which consumes more large energy than improvement of the successful receptionthe of ACK by of increasing number returned packets retransmission through increasing number returnedthe ACK copies.ofThis meansACK that copies the thatreduce of ACKthe packet. Hence, the total energy consumption each node is reduced, leads tothan the can unnecessary of data packetofwhich consumes more which large energy improvement of the successful retransmission reception of ACK by increasing the number of returned ACK copies reduction of the maximum energy cost in one data gathering round as shown in Figure 12. The of ACK packet. Hence, the total energy consumption each nodemore is reduced, which leads canthat reduce the unnecessary retransmission of data packet whichofconsumes large energy than number of returned ACK packets is not the more the data better. It needs round to satisfy the least number of to the reduction of the maximum energy cost in one gathering as shown in Figure that of ACK packet. Hence, the total energy consumption of each node is reduced, which leads to the 12. retransmission times which can be obtained from Theorem 1 for proposed E2E ARQ If The number of maximum returned ACK packets the more the better. It the needs satisfy leastprotocol. number reduction of the energy costisinnot one data gathering round as to shown inthe Figure 12. The of we continue to increase the value of returned ACK copies, more energy is cost for transmitting the retransmission times which can be from the Theorem forneeds the proposed number of returned ACK packets is obtained not the more better.1 It to satisfyE2E theARQ leastprotocol. number If ofwe ACKs. to increase the value of returned ACK copies, more energy is cost for transmitting the ACKs. continue retransmission times which can be obtained from Theorem 1 for the proposed E2E ARQ protocol. If we continue to increase the value of returned ACK copies, more energy is cost for transmitting the ACKs.

n

Figure K = K 1, r 1 =, 3rand 3 Figure 12. 12. Comparison of the maximum energy consumption with different n when when δand = 0.70.   0.70 .

Figure 12. Comparison of the maximum energy consumption with different

n

when

K1, r  3

Figure consumption with different K when n = 1 and 3. K when n1r = Figure 13 13shows showsthe thecomparison comparisonofofenergy energy consumption with different and and   0.70 . Figure 14 demonstrates the comparison of the maximum energy consumption in the same case. We r  3. Figure 14 demonstrates the comparison of the maximum energy consumption in the same case. can see the figure thatthat the energy consumption is smaller with bigger K under given given andnδ. We can from see thethe figure the energy consumption is smaller with bigger under K Kwhen nn,1 rand Figure 13from shows comparison of energy consumption with different This is because that the bigger K leads to smaller number of returned ACKs and so the energy cost K maximum and 14 .demonstrates This is because the bigger leads to smaller of returned and so r , 3. Figure thethat comparison of the energynumber consumption in the ACKs same case. is reduced. costthe is figure reduced. Wethe canenergy see from that the energy consumption is smaller with bigger K under given n

r

, r and  . This is because that the bigger the energy cost is reduced.

K

leads to smaller number of returned ACKs and so

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18 18 of of 29 28 0.03 K= 1 K=2 K =1 3 K=

Energy Energy consumption of eachofnode consumption each node

0.03 0.025

K=2 K=3

0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005 0.005 0 0

0 0

1 1

2 2

3 3

4 5 6 distance to sink 4

5

6

7 7

8 8

distance to sink Figure 13. Comparison of energy consumption with different

9 9

K

10 10

when

n1 , r  3

and

 Figure  0.70 .13. Comparison of energy consumption with different K when n = 1, r = 3 and δ = 0.70. Figure 13. Comparison of energy consumption with different K when n1 , r  3 and   0.70 .

3 Figure when n = n 1, r 1=, 3rand Figure 14. 14. Comparison of the maximum energy consumption with different KK when δand = 0.70.   0.70 . Figure 14. Comparison of the maximum energy consumption with different K when n1 , r  3

  0.70 .on the 5.2.2. Evaluation 5.2.2.and the Energy-Aware Energy-AwareHBH HBHARQ ARQ the the hybrid scheme operating HBH. Figure 15 presents the In thepart, part,we weevaluate evaluate theproposed proposed hybrid ARQ scheme operating HBH. Figure 15 presents 5.2.2.In Evaluation on the Energy-Aware HBH ARQARQ comparison of energy consumption withwith different r whenr Kwhen = 1 and 1, which the special case of Kn1=and n1,iswhich the comparison of energy consumption different is the special In the part, we evaluate the proposed hybrid ARQ scheme operating HBH. Figure 15 presents send one data packet and with one ACK packet reply. From the figure, we can see that different r case of send one data packet and with one ACK packet reply. From the figure, we can seeleads that r when K1 and reliability n1, which=is 0.70, the comparison of energy consumption with different of the special to different data load each node under the same which r different leads toofdifferent data loadtheofconstraint each node under thenetwork constraint of theδsame network case of different send onenode dataenergy packet consumption. and with one ACK packet From the 15 figure, we can different see that causes can be seen reply. from the Figure that there   0.70 , which reliability causes differentItnode energy consumption. It can be seenis from the r with different leadsdifferent to different load ofenergy each node under the constraint of the same network energy cost r. Thedata maximum cost in one round of data gathering is minimized Figure 15 that there is different energy cost with different r. The maximum energy cost in one round  0.70 reliability , which causes different energy consumption. It linear can berelation seen from the when r = 5  (m) as can be seen from the Figurenode 16. This means that there is no between r of data gathering is minimized when = 5 (m) as can be seen from the Figure 16. This means that the energy cost andisthe transmission When the returned has different of copies, r. TheACK Figure 15 that there different energyrange. cost with different maximum energy number cost in one round there is no consumption linear relationofbetween theisenergy cost and the transmission range. When the returned the energy each node shown in Figure 17. Figure 18 shows the maximum energy of data gathering is minimized when r = 5 (m) as can be seen from the Figure 16. This means that ACKcomparison. has different number of copies, theFigure energy of each the node is shown in Figure 17. cost can bebetween seen from 18,consumption if blindly increasing number of returned ACK there is no linear As relation thethe energy cost and the transmission range. When the returned Figure 18 shows the maximum energy cost comparison. As can be seen from the Figure 18, if blindly copies, it will causenumber the waste energy. is because the unnecessary increasing of the of ACK has different of of copies, theThis energy consumption of each node is shown in number Figure 17. increasing the number ofleads returned ACK copies, it will cause the waste of energy. This is becausewith the the returned ACK copies to more energy cost. Figure 19 shows the energy cost comparison Figure 18 shows the maximum energy cost comparison. As can be seen from the Figure 18, if blindly unnecessary increasing of the number ofconsumption the returnedchanges ACK copies leads to values more energy different K.the From the Figure 14, the energy with different when ncost. = increasing number of returned ACK copies, it will cause the waste of energy.K This is because the1 K Figure 19 shows the energy cost comparison with different . From the Figure 14, the energy and r = 3 (m). The ACK load is reduced when the K changes bigger, which can be seen obviously unnecessary increasing of the number of the returned ACK copies leads to more energy cost. from the Figure 20. Figure 19 shows the energy cost comparison with different K . From the Figure 14, the energy

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consumption changes Sensors 2017, 17, 1366 consumption changes consumption changes reduced when the K reduced when K reduced when the the K

19 of 29 19 19 of of 29 29

1 and rr 33 (m). with different K when n The ACK load is 19 of 28 with values is K values n11 and with different different K values when when n and r  3 (m). (m). The The ACK ACK load load is changes bigger, which can be seen obviously from the Figure 20. changes bigger, which can be seen obviously from the Figure 20. changes bigger, which can be seen obviously from the Figure 20. -3

x 10 -3 -3 3.5 xx 10 10 3.5 3.5

r=4 r=4 rr== 54 r=5 rr== 65 r=6 rr== 76 rr == 77

Energy consumption ofeach each node Energy consumption node Energy consumption ofofeach node

3 33 2.5 2.5 2.5 2 22 1.5 1.5 1.5 1 11 0.5 0.5 0.5 0 00

0 00

1 11

2 22

3 33

4 5 6 44 55 6 distance to sink6 distance to sink distance to sink

7 77

8 88

9 99

10 10 10

rr

K n 0.70. 0.70.. Figure 15. Comparison of energy consumption with different and Figure Comparison energy consumption with different r when =1 =1 11, 111and Figure 15. Comparison of energy consumption with different when and K 1,,, nn n  0.70 0.70. Figure 15.15. Comparison of of energy consumption with different when KK andδ =

rr

K 11 Figure 16. Comparison Comparison of of the the maximum maximumenergy energyconsumption consumptionwith withdifferent differentr when when Figure 16. K = 1, n1 and 11=,,, 1n n Figure when K n 1 Figure 16. 16. Comparison Comparison of of the the maximum maximum energy energy consumption consumption with with different different when K  0.70 and . δand = 0.70.  0.70 0.70 .. and  -3

Energy consumption ofeach each node Energy consumption node Energy consumption ofofeach node

x 10 -3 -3 6 xx 10 66 10

n=1 n=1 nn== 21 n=2 nn== 32 n=3 nn== 53 nn == 55

5 55 4 44 3 33 2 22 1 11 0 00

0 00

1 11

2 22

3 33

4 5 6 44 55 6 distance to sink6 distance to sink distance to sink

7 77

8 88

9 99

nn

10 10 10

Figure Comparison of of energy different n when K when = 1, r =K 3 and 1 δr= 30.70.and Figure 17.17.Comparison energyconsumption consumptionwith with different Figure when K11,,, rr 33 and Figure 17. 17. Comparison Comparison of of energy energy consumption consumption with with different different when K and  0.70 .  0.70 0.70 ..

The maximum energy consumption

20 of 28 20 20 of of 29 29

Themaximum maximumenergy energyconsumption consumption The

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n

Figure 18. Comparison of the maximum energy consumption with different and

  0.70 .

when

K1, r  3

-3

6

x 10

nn

33 Figure when Comparison of of the the maximum maximum energy energy consumption consumption with with different different nK= when K = K 1, r1 K 1=,, 3rrand Figure 18. 18. Comparison Comparison of the maximum energy consumption with different 1 when K = 2   0.70 and δ = 0.70.   0.70 .. and K=3

-3 10 -3

4

x 6 x 10 6

K= 1 K= 1 K=2 K=2 K=3 K=3

5 5 Energyconsumption consumptionofofeach eachnode node Energy

Energy consumption of each node

5

3

4 4

2

1

0

3 3

2 2

1 0 1

0 0

1

0 0

2

1 1

3

2 2

3 3

4 5 6 distance to sink 4 4

5 5

6 6

7

7 7

8

8 8

distance with to sink Figure 19. Comparison of energy consumption distance to sink different

9

9 9

K

10

10 10

when

n1 , r  3

and

  0.70 . Figure 19. Comparison of energy consumption with different K when n = 1, r = 3 and δ = 0.70. Figure 19. Comparison of energy consumption with different K when n1 , r  3 and Figure 19. Comparison of energy consumption with different  0.70 -3 0.70 .. 6

K

when

n1 , r  3

and

10

K=1

6 6

5

10 -3 10 -3

K=1 K=1

5 5

4

K=2 4 4

K=2 K=2

K=3 K=3 K=3

3 3 3

2

2 2

1

1 1

0

0 0

1

1 1

2 22

3 3

3

Figure 20. Comparison of the maximum energy consumption with different

K K

when

n n11, rr 33 r  3

20. of maximum energy consumption different when Figure 20. Comparison Comparison of the the maximumenergy energyconsumption consumption with with different K when = 1, r =, n 3 and K n when 1, FigureFigure 20. Comparison of the maximum with different

 0.70 and 0.70 .. and δ = 0.70.

and   0.70 . 5.3. 5.3. Evaluation Evaluation on on the the Parameters Parameters Optimization Optimization Selection Selection

5.3. Evaluation on the Parameters Optimization Selection

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21 of 29 21 of 28, parameters

r by the Section 5.2, the energy consumption is related with the r, n and As demonstrated the Section the consumption is so related with theselection parameters K under thebygiven  energy and W parameters, the optimal of the p i , q5.2, i , n Evaluation W optimal and K ofunder theand given , satisfy and the parameters, so efficiency the optimal selection of the pneeds K Optimization i , q i to parameters energy goal described by 5.3. onr,thenParameters Selection r K procedure Equation (2). of parameters optimization selection parameters of Following , n and the needs to satisfy the optimal energy efficiency goal applying described the by As demonstrated by the Section 5.2, the energy consumption is related with the parameters r, Equation (2). method, Followingwhen the procedure of parameters optimization selection K =applying enumeration the predetermined parameters sets are {1, 2, the 3}, n and K under the given pi , qi , δ and W parameters, so the optimal selection of the parameters of K enumeration method, when the predetermined parameters sets are {1, 2, 3}, n = r = {1, 2, 3, 4, 5, 6} and = {4, 5, 6, 7} (m), the optimized parameters are selected for E2E and HBH r, n and K needs to satisfy the optimal energy efficiency goal described by Equation (2). Following r

n procedure operation. = {1, 2, 3, 4,of 5, parameters 6} and = {4, 5, 6, 7} (m), selection the optimized parameters are selectedmethod, for E2E when and HBH the optimization applying the enumeration the n operation. predetermined parameters sets are K = {1, 2, 3}, n = {1, 2, 3, 4, 5, 6} and r = {4, 5, 6, 7} (m), the optimized Figures 21–23 show the comparison of maximum energy cost under different , and K parameters are for E2E andE2E HBH operation. K Figures 21–23 show the comparison of maximum energy cost under , n and in one round ofselected data gathering for operation. As can be seen from thedifferent figures, when = 5 (m), Figures 21–23 show the comparison of maximum energy cost under different r, n and K in one n one n = {1,when in of data gathering forfrom E2E the operation. be4,seen the figures, 5 (m), = 5round and K = 3 are selected set of As= can {2, 3, 5, 6,from 7} (m), 2, 3, 4, 5,=6} and round of dataKgathering for E2E operation. As can be seen from the figures, when r = 5 (m), n = 5 n n 5 and 3 are selected from the = {2, 3, 4, gathering 5, 6, 7} (m), = {1, 2, 3, 4, 5, 6} and K = {1, 2, 3}, the=maximum energy cost in set oneofround of data is minimized. and K = 3 are selected from the set of r = {2, 3, 4, 5, 6, 7} (m), n = {1, 2, 3, 4, 5, 6} and K = {1, 2, 3}, the K =Figures {1, 2, 3},24–26 the maximum cost in round ofenergy data gathering is different minimized., n and K show the energy comparison ofone maximum cost under maximum energy cost in one round of data gathering is minimized. n and K Figures 24–26 show the comparison of maximum energy cost under different in one round24–26 of datashow gathering for HBH operation. As can be seen thedifferent figures, when =in 5 (m), Figures the comparison of maximum energy costfrom under r, n, and K one n one n when in data forfrom HBHthe operation. As can the figures, 5n(m), Kgathering = 2round = 3 gathering are selected setAs of can =be {2,seen 3,be4,seen 5, 6,from 7} (m), = {1,when 2,r 3, 5,=6} and round ofand dataof for HBH operation. from the figures, = 54,(m), =2 n =K {1, n 6}=and 2=and 3 are selected from {2, 3, 4,ngathering 5,= 6, {1, 2, 3, {1, 4, 5, K and 32,are selected from the set ofcost r the =in {2,set 3, of 4,round 5, 6,= 7} {1,7}2,(m), 3, is 4,minimized. 5, K= 2, 6} 3},and the 3},K the=maximum energy one of(m), data maximum cost in one energy round of data gathering K = {1, 2,energy 3}, the maximum cost in one roundisofminimized. data gathering is minimized.

r r

r r

r r

the maximum the maximum nodenode energy energy cost(J) cost(J)

r r

r r

r r

0.06 0.06 0.04 0.04 0.02 0.02 0

0 1 2 nu 3 1 mb 4 er 2 the o f nu 3 co mb p i e 4 er so of fA co ck pie so fA ck the

5 5

6 6

1 1

2 2

3 3

6

7

ge r an7 i6o n s ge 5mis an 4 tr ans nr o i s the mis ns tr a e th

4

5

r r

n n

Figure 21. The comparison of maximum energy cost under different and when K = 1 and Figure 21. The comparison of maximum energy cost under different r and n when K = 1 and K δ ==10.70.   0.7021.. The comparison of maximum energy cost under different and Figure when and

the maximum the maximum nodenode energy energy cost(J) cost(J)

  0.70 .

0.015 0.015 0.01 0.01 0.005 0.005 0

0 1 2 nu 1 3 mb 2 e 4 the ro fc nu 3 op mb ies er 4 of of co Ac pie k so fA ck the

5 5

6 6

1 1

2 2

3 3

6

7

ge an7 4 6o n r i 5 mis s ge r an 4 r ans on t i s the mis ns tr a e th

5

n r r and n

Figure The comparison comparison of n when K = 2 and K δ ==20.70. Figure 22. 22. The of maximum maximum energy energy cost cost under underdifferent differentr andand when and

  0.7022.. The comparison of maximum energy cost under different Figure   0.70 .

when

K

= 2 and

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the maximum node node energy cost(J) the maximum the maximum node energy energy cost(J) cost(J)

x 10

-3

8 x 10

-3

8 x 10 6 8 6 4 6 4 2 4 2 0 2 0 1

2 nu 0 1 3 mb 2 er t he 4 of nu 3 1c o 5 mb pie e 2 6 s t he ro of 4 fc nu A 3 o ck 5 mb pie 6 er so 4 of fA co ck 5 pie 6 so fA ck t he

6

7

e n7g 6o n r a i s 3 5 is 7nge 2 4 ans m 6 n r a io tr 1 s 3 e is 5 ge th m 2 an 4 tr ans nr o 1 i s 3 t he mis 2 ns under different and tr a 1 e th

4

5

r r r

n n n

Figure 23. The comparison of maximum energy cost when K = 3 and Figure when K = 3 and   0.7023.. The comparison of maximum energy cost under different and Figure 23. The comparison of maximum energy cost under different r and n when K = 3 and   0.70 K δ==3 0.70. . Figure 23. The comparison of maximum energy cost under different and when and

  0.70 . -3

the maximum node node energy cost(J) the maximum the maximum node energy energy cost(J) cost(J)

x 10

-3

8 x 10

-3

8 x 10 6 8 6 4 6 4 2 4 2 0 2 0

1 2 nu 0 1 3 mb 2 er the 4 of nu 3 5 1c op mb i er 4 6 2es o the of f nu c A 3 ck 5 op mb ies 6 er 4 of of Ac co k 5 pie 6 so fA c k energy comparison of maximum the

6

7

ge an7 4 6 nr o i e 3 5 mis s 7ng 2 4 ans 6 n r a 1 3 the tr 5 is sio e g m 2 an 4 tr ans nr 1 sio 3 is the m 2 ns tr a under different and 1 the

5

n r n r r and n

Figure 24. The cost when K = 1 and Figure 24. n when K = 1 and K δ ==10.70. Figure 24.. The The comparison comparison of of maximum maximum energy energy cost costunder underdifferent differentr andand when and   0.70

  0.70 Figure 24.. The comparison of maximum energy cost under different   0.70 .

when

K

= 1 and

-3

the maximum node node energy cost(J) the maximum the maximum node energy energy cost(J) cost(J)

x 10

-3

5 x 10

-3

5 4 x 10 54 3 43 2 32 1 21 0 10

1

2 7 nu 0 1 3 mb 6 2 e the 4 5 ge ro n a7 nu f 1c 3 5 4 mb op 6nr i2es sio er e 4 6 3 the 5 is of of m 7ng 5 2 nu co 4 r ans 6o n r a mb pie 3 Ac k i t 1 s 6 3 e so 4 er 5s mis ge th of fA 2 r an co ck 5 4 tr an pie 1 io n e s 6 3 h so is t m fA 2 different arnsand comparison n when c k energy comparison of of maximum maximum energy cost costunder under different and tr 1 t he the

Figure Figure 25. 25. The The Figure   0.7025.. The comparison of maximum energy cost under different

  0.70 Figure 25.. The comparison of maximum energy cost under different   0.70 .

n r r and n r and n

K = 2 and K δ ==20.70. when and when K = 2 and

when

K

= 2 and

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-3

the

the node maximum node energy cost(J) the maximum energy cost(J)

x 10 4

-3

3 x 10 4 2 3 1 2 0 1 1

nu mb 0 er of c

the

nu mb er

2

3

o1p ies 2of

of c

4

A 3c k

4

op ies

5

6 1

5

6

of Figure energy cost Figure 26. 26. The The comparison comparison of of maximum maximum A

  0.70 .

ck

2

3

4 the 4

6

5 m ns tr a

io n is s

6

7 ge r an

7

ge r an on i s mis under2different different r and and when ns n when K = 3 and tr a 1 e h t

3

5

r

n

K δ==3 0.70. and

r

5.4. Evaluation on the Performance by Comparison with SW-ODMA ARQ Figure 26. The comparison of maximum energy cost under different and n when K = 3 and 5.4. Evaluation on the Performance by Comparison with SW-ODMA ARQ Our proposed scheme is a generalization of the original SW-ODMA ARQ protocol [18].   0.70 . Our proposed scheme generalization ofthe theproposed original scheme SW-ODMA protocolwidow [18]. The The SW-ODMA ARQ schemeisisathe special case of whenARQ the sending size SW-ODMA scheme is the case of the scheme wheninthe sending widow size 5.4.=Evaluation Performance by Comparison withproposed SW-ODMA ARQ W 1 and KARQ =on 1. the In this case, thespecial energy consumption is the same as shown Figures 27 and 28 when operating E2E thecase, assurance of the same network reliability δ= Forin E2E operation, when K and W 1 Our and proposed = 1.with In this energy consumption is the same as0.70. shown Figures and 28 scheme is athe generalization of the original SW-ODMA ARQ protocol27[18]. The the sending window size Wwith = 2 and the sendingofpackets in the windowreliability are transmitted continuously,   0.70 when operating E2E and the assurance the same network . For E2E SW-ODMA ARQ scheme is the special case of the proposed scheme when the sending widow size the comparison energy consumption between SW-ODMA with multiple of one W scheme 2 andfollowing operation, sizeconsumption in Figures the window K =of1.the W1 and when Insending this case,window the energy isthe thesending same aspackets shown in 27 andare 28 ACK for one receiving data packet and the proposed hybrid scheme when K = 2 is shown in Figure 29 transmitted continuously, the comparison of energy consumption between scheme following when operating E2E and with the assurance of the same network reliability   0.70 . For E2E for one round of data gathering. the for comparison, the parameters thethe number of thehybrid returned ACK SW-ODMA with multiple of oneIn ACK one receiving data packetofand proposed scheme W n2=and operation, when the range sending window size the sending packets in theofwindow are and the transmission are randomly selected 2 and r = 4 with the constraint the network K = continuously, when 2 is shown inthe Figure 29 for one round ofconsumption data gathering. In thescheme comparison, the transmitted comparison of energy between following reliability δ of = 0.70. parameters themultiple number ofone theACK returned ACK and thedata transmission are randomly selected SW-ODMA with for one receiving packet andrange theseen proposed scheme Figure 30 shows the of maximum energy cost comparison. As can be from hybrid the figure, the r 4 n 2   0.70 and with the constraint of the network reliability . K when = 2 is cost shown in Figure 29 for one round of datawindow gathering. the maximum energy is reduced by 25.60%. When the sending sizeIn W the = 3,comparison, the comparison parameters of the number of the returned ACK and the transmission range are randomly selected of energy consumption following SW-ODMA with multiple of one ACK for one receiving data packet

r4 with n 2the  in0.70 and thescheme constraint of the . 31. and proposed hybrid when K =network 2 and K reliability = 3 is shown Figure

Figure 27. Comparison of energy consumption with SW-ODMA under and

W1, K

= 1,

n 2, r  3

  0.70 .

1, KK= 1,=n1,= n 3 Figure 27. Comparison of energy consumption = 1, 2, r2=, 3rand consumption with with SW-ODMA SW-ODMAunder underWW δand = 0.70.   0.70 .

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Figure 28. Comparison of the maximum energy consumption with SW-ODMA under

K

= 1,

n 2, r  3

and

W1 ,

  0.70 .

Figure 28. 28.Comparison Comparisonofof maximum energy consumption SW-ODMA Figure thethe maximum energy consumption with with SW-ODMA underunder W = 1,W K =11,, nK= 2, r =n 3 and 2, rδ=3 0.70. = 1, and   0.70 .

Figure 29. Comparison of energy consumption between scheme following SW-ODMA and the proposed scheme when

W  2 , n 2, r4

and

  0.70 .

Figure 30 shows the maximum energy cost comparison. As can be seen from the figure, the maximum energy cost is reduced by 25.60%. When the sending window size W  3 , the comparison Figure 29. Comparison of energy consumption between scheme following SW-ODMA and the of energy following SW-ODMA with between multiplescheme of one ACK for one receivingand datathe packet Figureconsumption 29. Comparison of energy consumption following SW-ODMA proposed scheme when

W  2 , n 2, r4

and

  0.70 .

K4 and K = 3 is shown in Figure 31. proposed scheme whenscheme W = 2, nwhen = 2, r = δ = 0.70. and the proposed hybrid = 2 and

The consumption The maximum maximum energy energyThe consumption maximum energy consumption

Figure 30 shows the maximum energy cost comparison. As can be seen from the figure, the maximum energy cost is reduced by 25.60%. When the sending window size W  3 , the comparison of energy consumption following SW-ODMA with multiple of one ACK for one receiving data packet and the proposed hybrid scheme when K = 2 and K = 3 is shown in Figure 31.

Figure 30. Comparison of the maximum energy consumption between scheme following SW-ODMA Figure 30. Comparison of the maximum energy consumption between scheme following SW-ODMA and the proposed scheme when W  2 , n 2, r4 and   0.70 . and the proposed scheme when W = 2, n = 2, r = 4 and δ = 0.70.

Figure 30. Comparison of the maximum energy consumption between scheme following SW-ODMA and the proposed scheme when

W  2 , n 2, r4

and

  0.70 .

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Figure 31. 31. Comparison and the the Figure Comparison of of energy energy consumption consumption between between scheme scheme following following SW-ODMA SW-ODMA and 4 and n2,2r, =r  0.70 . proposed 4 and δ= 0.70. when WW=3,3n, = proposed scheme scheme when

Figure 32 32 shows shows the the maximum maximum energy energy cost cost comparison. comparison. As Figure As can can be be seen seen from from the the figure, figure, the the 2 and 38.99% when = 3 respectively. maximum energy cost is reduced by 30.85% maximum 30.85% when when KK= 2=and byby 38.99% when K =K3 respectively.

Figure 32. 32. Comparison Figure Comparison of of the the maximum maximum energy energy consumption consumption between between scheme scheme following following SW-ODMA SW-ODMA r 4 W  3 n 2   0.70 . and δ = 0.70. and the the proposed proposed scheme scheme when when W = 3, n, = 2, r, = 4 andand

Comparing the scheme following Comparing the proposed proposed scheme scheme with with the the scheme following SW-ODMA SW-ODMA operating operating HBH, HBH, Figures 33 and 34 respectively show the energy cost comparison of each node when the sending sending Figures 33 and 34 respectively show the energy cost comparison of each node when the rthe 4 and 3 under window size sizeWW randomly selected same reliability network window = 2 2andand W =W3 under randomly selected n = 2, rn = 24 ,and samethe network   0.70 . Figures 35 and demonstrate 36 respectively demonstrate thecost maximum energy δreliability = 0.70. Figures 35 and 36 respectively the maximum energy comparison undercost the comparison From Figure we can see that the energy cost isBesides, reducedthe by cases. From under Figurethe 35, cases. we can see that the35, maximum energy costmaximum is reduced by 17.30%. K K= 2=and maximum energythe cost is reducedenergy by 15.20% when K = 2by and by 18.67% 3 respectively can 17.30%. Besides, maximum cost is reduced 15.20% whenwhen by 18.67% as when be seen from the Figure 36. K = 3 respectively as can be seen from the Figure 36.

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Figure 33. Comparison energy of energy consumption between between scheme following SW-ODMA and the 33. Comparison Figure 33. Comparison of of energy consumption consumption between scheme scheme following following SW-ODMA and the r 4 W  2 n 2   0.70 proposed scheme when , , and . Figure scheme 33. Comparison energy between following SW-ODMA and the proposed when =2, 4 and δ= 4 and 2n, =n2,consumption 2r, =r 0.70.  0.70scheme when WWof . proposed scheme when W  2 10 , -3n 2, r4 and   0.70 . 2.5

10 -3

2.5 2.5

SW-ODMA The proposed scheme when K= 2 SW-ODMA The proposed scheme when K = 3

10 -3 2

The proposed scheme when K= 2

SW-ODMA The proposed proposedscheme schemewhen whenK= K 2= 3 The The proposed scheme when K = 3

2 2 1.5

1.5 1.5

1

1

0.5 0.5

1

0.5

0

0

1

2

3

4

5

6

7

8

9

10

distance to sink

Figure 34. Comparison of energy consumption between scheme following SW-ODMA and the 0 proposed scheme when

0

33 4 44 6 W0 0 3 1, 1 n222 , r 6 and 55  0.70 . 77

distance sink distance to to sink

8

8

9

9

10

10

Figure 34.34.Comparison scheme following SW-ODMA andthethe the Figure Comparisonof energy consumption consumption between between Figure 34. Comparison ofofenergy energy consumption between scheme schemefollowing followingSW-ODMA SW-ODMAand and 44 and 0.70.. r when 33n, ,=n n  0.70 proposed scheme when WWW =3, 2,2r2, = 4 and δ= 0.70. proposed scheme when , r and

Figure 35. Comparison of the maximum energy consumption between scheme following SW-ODMA and the proposed scheme when

W  2 , n 2, r4

and

  0.70 .

Figure Comparisonofofthe themaximum maximumenergy energy consumption consumption between SW-ODMA Figure 35.35. Comparison betweenscheme schemefollowing following SW-ODMA Figure 35. Comparison of the maximum energy consumption between scheme following SW-ODMA r 4 W  2 n 2   0.70 proposed schemewhen whenW = 2, n, = 2, r ,= 4 andand . andand thethe proposed scheme δ = 0.70. and the proposed scheme when W  2 , n 2, r4 and   0.70 .

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Figure 36. Comparison of the maximum energy consumption between scheme following SW-ODMA

Figure 36. Comparison of the maximum energy consumption between scheme following SW-ODMA and the proposed scheme when W  3 , n 2, r4 and   0.70 . and the proposed scheme when W = 3, n = 2, r = 4 and δ = 0.70.

6. Conclusions

6. Conclusions

In this paper, the problem of an effective data transmission scheme to reduce energy cost and

ensure reliabilityof with ARQ is studied. Data transmission reliability In this transmission paper, the problem an hybrid effective data transmission scheme toshould reducetake energy cost and as transmission well as energyreliability efficiency into an energy-aware ensure withconsideration. hybrid ARQTo is address studied.these Dataproblems, transmission should takehybrid reliability ARQ scheme is proposed to improve the energy efficiency with the assurance of network as well as energy efficiency into consideration. To address these problems, an energy-aware hybrid transmission reliability. The theoretical analysis of data load of each node with reliability constraint ARQ scheme is proposed to improve the energy efficiency with the assurance of network transmission for flat circle network is presented. Based on this, the energy efficiency is discussed. Because the reliability. The theoretical analysis of data load of each node with reliability constraint for flat circle energy efficiency is related with the parameters r, n and K under the given p , q i ,  and network is presented. Based on this, the energy efficiency is discussed. Because thei energy efficiency is W we study how to select parameters applying the enumeration method to obtain the optimal related with the parameters r, n and K under the given pi , qi , δ and W we study how to select parameters energy efficiency goal. The simulations are extensively done to evaluate the theoretical analysis and applying the enumeration method to obtain the optimal energy efficiency goal. The simulations are verify the effectiveness of the proposed ARQ scheme. extensively done to evaluate the theoretical analysis and verify the effectiveness of the proposed ARQ Acknowledgments: scheme. This work was supported in part by the Natural Science Foundation of Hunan Province (2017JJ3417 and 2016JC2011), the National Natural Science Foundation of China (61272150, 61379110, 61472450, M1450004), Ministry Foundation of in China MCM20121031), theof National Acknowledgments: ThisEducation work was supported part(20130162110079 by the Naturaland Science Foundation HunanHigh Province (2017JJ3417 and 2016JC2011), National Natural of China (61272150,and 61379110, 61472450, Technology Research and the Development Program Science of ChinaFoundation (863 Program) (2012AA010105) the National M1450004), Ministry Education Foundation of China (20130162110079 and MCM20121031), the National High Basic Research Program of China (973 Program) (2014CB046305). Technology Research and Development Program of China (863 Program) (2012AA010105) and the National Basic Author Contributions: Zhang conceived the method idea, designed and performed the experiments, Research Program of ChinaJinhuan (973 Program) (2014CB046305). analyzed the data, and wrote the paper. Jun Long commented on the work.

Author Contributions: Jinhuan Zhang conceived the method idea, designed and performed the experiments, Conflicts of Interest: The authors declare conflict of interest.on the work. analyzed the data, and wrote the paper. Jun no Long commented Conflicts of Interest: The authors declare no conflict of interest. References 1. Yick, J.; Mukherjee, B.; Ghosal, D. Wireless Sensor Network Survey. Comput. Netw. 2008, 52, 2292–2330, References doi:10.1016/j.comnet.2008.04.002.

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