Source-Aware Redundant Packet Forwarding Scheme for Emergency Information Delivery in Chain-Typed Multihop Wireless Sensor Networks

Abstract

For emergency information delivery of chain-typed multihop wireless sensor networks in closed long tunnel (CWSN-C), the scheme of sending the same packet multiple times is a good choice. In this paper, taking the application of rigid sliding guide obliquity monitoring in deep shaft as background, the source-aware redundant packet forwarding scheme for emergency information delivery in CWSN-C (SRPFEC) is proposed firstly. Secondly, more of comprehensive factors including application QoS and energy efficiency are considered for determining the number of redundant packets. Then, a method of solving for the number of redundant packets is proposed. Finally, Monte Carlo method and network simulation are employed to study the performances of proposed SRPFEC. The results show that (1) non-ACK scheme is highly suitable for the condition of large network size and hazardous wireless communication environment; (2) the non-source-aware solution is easy to use and is suitable for the occasion where the node could be replaced on demand expediently; (3) the source-aware solution has the better performance in energy efficiency and is suitable for the occasion where the network lifetime needs to be determined before deployment, and the node could not be replaced easily.

1. Introduction

Chain-typed wireless sensor network (CWSN) [1] is a special class of WSNs. It is proposed for a class of applications, which are often limited by the natural formation of landscape or manmade infrastructures of long ranges, such as rivers, coastal lines, highways, and national land borders. Chain-typed wireless sensor networks used in Closed long tunnel (CWSN-C) is the special case of CWSNs, such as CWSN in coal mine laneway [2], city subway [3], and long-distance tunnel [4]. CWSNs in these regions only can be deployed with chain-type topology by the geographical conditions. The classic hierarchy scheme cannot be adopted in these networks for the same reason. Therefore, the packets are usually delivered by a single path.

Taking all the single-hop physical-layer mechanisms like FEC or transmit power variation for granted, the prime mechanisms to improve packet delivery probability are retransmissions and usage of multiple packets [5]. Retransmission schemes are used to ensure the regular packets delivered correctly by adopting ARQ methods. However, they are not suitable for emergency packet delivery due to two reasons: $(1)$ the packet carrying emergency information should both have higher reliability and lower delay in delivery; $(2)$ the newest emergency information should have the highest priority. Thus, the scheme of sending the same packet multiple times turns to be a good choice in the emergency packet delivery.

Deb et al. [6] have proposed a scheme without acknowledgment information for packet delivery at a desired reliability using hop-by-hop broadcast. The scheme is called hop-by-hop reliability (HHR), which does not use MAC-layer acknowledgments but sends the same packet to the next forwarder (or upstream node) multiple times. The number of redundant packets is only determined by the desired end-to-end delivery probability. However, the number of redundant packets also affects performances and lifetime of the CWSN-C in practical applications.

2. Related Work

Due to the particularity of application environments, current researches on CWSN are mainly focused on application layer. Chen et al. [7] found out that adding a few mobile nodes can further extend the network survival time by balancing the energy consumption of nodes. Xijun et al. [8] proposed a node deployment method of double-chain structure with multisinks. The method is suitable for long-distance transmission and can solve the problem that sensor nodes closer to the sink node exhaust their energy earlier. Menon et al. [9] and Zhu et al. [10] built gas monitoring system using CWSN in underground coal mine separately. These works give impetus to the technology of CWSN. However, emergency information has not been considered in these CWSNs specially.

Recently, there are some progresses on emergency information delivery in wireless sensor networks. Cha et al. [11] provided a reliable data delivery scheme for mobile sensor networks with an enhanced delaying technique. The proposed protocol deals well with network partitioning and indefinite link disconnection, which often arises in mobile sensor networks and satisfies the requirement for delivery latency. Zhang and Luo [12] proposed reliability-guaranteed data forwarding protocol of correlated data in wireless sensor networks. It uses combined methods of multipoint coverage and multipath forwarding but not doing in-network data aggregation. Naveen and Kumar [13] proposed a relay selection scheme for geographical forwarding in sleep-wake cycling wireless sensor networks. The local forwarding problem has been formulated as a partially observable Markov decision process in their work. Dubey and Sahu [14] developed a fault tolerant packet forwarding scheme to control redundancy in wireless sensor networks. The proposed algorithm infuses the aspects of the gossip protocol for forwarding packets. Bader et al. [15] proposed an efficient multicarrier position-based packet forwarding protocol for wireless sensor networks. The key of this protocol is eliminating the need for potential relays to undergo a relay selection process. Even though these schemes can not be adopted in CWSN directly, they have laid a great foundation for emergency information delivery in CWSN.

In this paper, we build mathematical models to discuss how to ensure the network application QoS by properly arranging the number of redundant packets based on energy efficiency consideration when the source-aware redundant packet forwarding scheme for emergency information delivery in chain-type multihop wireless sensor networks (SRPFEC) is adopted.

The rest of the paper is organized as follows. In Section 2, the SRPFEC is proposed. The mathematical models for the number of redundant packets based on the application QoS and energy efficiency are discussed in Sections 3 and 4. Section 5 proposes a method of solving for the number of redundant packets. The performances of the proposed SRPFEC are evaluated by simulation in Section 6. Finally, Section 7 concludes the paper.

3. SRPEEC

In this paper, the CWSN-C is considered to be used to monitor the obliquity of rigid sliding guide in deep shaft of coal mine. In this CWSN-C, sensor nodes are used to collect and process the obliquity information periodically but not to forward the information to Sink node unless the obliquity is greater than a certain threshold; thus, all data transmitted over this CWSN-C are urgent.

As shown in Figure 1, sensor nodes $S_i$ are deployed in a closed deep shaft of coal mine, where $i=\mathrm{1,2},\dots ,N$ . $S_{\mathrm{0}}$ is used to denote sink node for the sake of discussion. The node which has collected emergency information generates the original packet and then forwards the packet and copies to its exclusive lower neighbor node without acknowledgment information. The relay nodes will generate new packets and copies based on packet copies received from the exclusive upper neighbor nodes and then forward the copies to their exclusive lower neighbor nodes.

Figure 1

Sketch map of SRPFEC.

Due to the limits of geographical conditions, $S_i$ can only communicate with $S_{i-\mathrm{1}}$ and $S_{i+\mathrm{1}}$ . $d_i$ denotes the distance between $S_i$ and $S_{i-\mathrm{1}}$ . ${\text{PER}}_i$ denotes the average local packet error rate when $S_i$ communicates with $S_{i-\mathrm{1}}$ ( $d_i$ and ${\text{PER}}_i$ could be deduced after the network deployment). $h\left(i,j\right)$ denotes the number of redundant packets forwarded from $S_i$ to $S_{i-\mathrm{1}}$ when the packet was originally generated by node $S_j$ . Obviously, we have $N>j>i>\mathrm{1}$ . An upper triangular square matrix H is used to store the $h\left(i,j\right)$ for discussion purposes:

$$\begin{array}{cc}& {\mathbf{H}}_{N\times N}=\left[\begin{array}{cccc}h\left(\mathrm{1,1}\right)& h\left(\mathrm{1,2}\right)& \cdots & h\left(\mathrm{1},N\right)\\ & h\left(\mathrm{2,2}\right)& \cdots & h\left(\mathrm{2},N\right)\\ & & \ddots & ⋮\\ & & & h\left(N,N\right)\end{array}\right].\end{array}$$

(1)

It is obviously true that only the number of forwarded redundant packets H affects the network performances if the network has been deployed. Therefore, in the following part, we discuss how to achieve the desired network performances by properly arranging the number of redundant packets H.

4. Application QoS of SRPFEC

Reaching probability and end to end delay are the key factors of application in CWSN-C, especially for emergency information delivery. As described above, this CWSN-C is used to transmit the alarm data. Meanwhile, the reaching probability and delay of the delivery should be guaranteed.

4.1. Reaching Probability

$p_{\text{reach}\_n}$ denotes the probability of a packet (originally generated by $S_n$ ) reached the sink node correctly. Then,

$$\begin{array}{cc}& p_{\text{reach}\_n}={\displaystyle \prod }_{x=\mathrm{1}}^n\left(\mathrm{1}-{{\text{PER}}_x}^{h\left(x,n\right)}\right)\ge p_{\text{demand}},\end{array}$$

(2)

where $p_{\text{demand}}$ denotes the desired reaching probability.

Taking logarithm of (2), we have

$$\begin{array}{cc}& \ln p_{\text{reach}\_n}={\displaystyle \sum }_{x=\mathrm{1}}^n\ln \left(\mathrm{1}-{{\text{PER}}_x}^{h\left(x,n\right)}\right)\ge \ln p_{\text{demand}}.\end{array}$$

(3)

Then, using differential principle,

$$\begin{array}{cc}& \ln p_{\text{reach}\_n}\approx -{\displaystyle \sum }_{x=\mathrm{1}}^n\hspace{0.17em}{{\text{PER}}_x}^{h\left(x,n\right)}\ge \ln p_{\text{demand}}.\end{array}$$

(4)

Further, using Taylor mean value theorem,

$$\begin{array}{cc}& \ln p_{\text{reach}\_n}\approx -{\displaystyle \sum }_{x=\mathrm{1}}^n\left(\mathrm{1}+h\left(x,n\right)\times \ln {\text{PER}}_x\right)\ge \ln p_{\text{demand}}.\end{array}$$

(5)

Taking all nodes into account, inequation (2) should be expressed as follows.

Feasibility Conditions 1. Defining matrix ${\mathbf{A}}_{N\times N}=\mathbf{G}\times {\mathbf{H}}^T+\ln p_{\text{demand}}\times \mathbf{I}+\mathbf{F}={\left[{\mathbf{a}}_{\mathrm{1}},{\mathbf{a}}_{\mathrm{2}},\dots ,{\mathbf{a}}_N\right]}^{\prime }$ . To achieve the desired reaching probability, the summation of each row vectors ${\mathbf{a}}_i$ should meet

$$\begin{array}{cc}& \text{sum}\left({\mathbf{a}}_i\right)\ge \mathrm{0},\hspace{1em}i=\mathrm{1,2},\dots ,N,\end{array}$$

(6)

where ${\mathbf{H}}^T$ is the transpose of matrix H,

$$\begin{array}{cc}& {\mathbf{G}}_{N\times N}=\left[\begin{array}{cccc}\ln {\text{PER}}_{\mathrm{1}}& & & \\ & \ln {\text{PER}}_{\mathrm{2}}& & \\ & & \ddots & \\ & & & \ln {\text{PER}}_N\end{array}\right],\\ {\mathbf{F}}_{N\times N}=\left[\begin{array}{cccc}\mathrm{1}& & & \\ & \mathrm{2}& & \\ & & \ddots & \\ & & & N\end{array}\right],\\ {\mathbf{I}}_{N\times N}=\left[\begin{array}{cccc}\mathrm{1}& & & \\ & \mathrm{1}& & \\ & & \ddots & \\ & & & \mathrm{1}\end{array}\right].\end{array}$$

(7)

4.2. End to End Delay

Usually, the end to end delay is composed of the network latency, $L_s$ , which is the transmission and retransmission time of the original packet across the network, and the queuing delay $L_w$ , which is the waiting time seen by packets at the interface queue [16]. Then, we have the delay of a packet (originally generated by $S_n$ ):

$$\begin{array}{cc}& L_{\text{delay}}=L_s+L_w.\end{array}$$

(8)

For $L_s$ , the transmission time includes the time of radio propagation and the time of channel contention. Generally, there are barely retransmission and channel contention in CWSN-C due to the network topology. Then, we have

$$\begin{array}{cc}& L_s={\displaystyle \sum }_{x=\mathrm{1}}^n\hspace{0.17em}t\left(d_x\right),\end{array}$$

(9)

where $t\left(d_x\right)$ is a function of transmission distance $d_x$ , which measures the transmission time of a packet from $S_x$ to $S_{x-\mathrm{1}}$ .

For $L_w$ , the queuing time is measured from the time the first packet is received to the time the last copy is received. It can be deduced by

$$\begin{array}{cc}& L_w={\displaystyle \sum }_{x=\mathrm{1}}^n\hspace{0.17em}h\left(x,n\right)\times t\left(d_x\right).\end{array}$$

(10)

Then, we have

$$\begin{array}{cc}& L_{\text{delay}}={\displaystyle \sum }_{x=\mathrm{1}}^n\hspace{0.17em}\left(h\left(x,n\right)+\mathrm{1}\right)\times t\left(d_x\right)\le L_{\text{demand}},\end{array}$$

(11)

where $L_{\text{demand}}$ denotes the desired end to end delay.

Taking all nodes into account, inequation (11) should be expressed as follows.

Feasibility Conditions 2. Defining matrix ${\mathbf{B}}_{N\times N}=t\left(\mathbf{D}\right)\times \left({\mathbf{H}}^T+\mathbf{M}\right)={\left[{\mathbf{b}}_{\mathrm{1}},{\mathbf{b}}_{\mathrm{2}},\dots ,{\mathbf{b}}_N\right]}^{\prime }$ . To achieve the desired end to end delay, the summation of each row vectors ${\mathbf{b}}_i$ should meet

$$\begin{array}{cc}& \text{sum}\left({\mathbf{b}}_i\right)\le L_{\text{demand}},\hspace{1em}i=\mathrm{1,2},\dots ,N,\end{array}$$

(12)

where ${\mathbf{H}}^T$ is the transpose of matrix H,

$$\begin{array}{cc}& {\mathbf{D}}_{N\times N}=\left[\begin{array}{cccc}{d}_{\mathrm{1}}& & & \\ & d_{\mathrm{2}}& & \\ & & \ddots & \\ & & & d_N\end{array}\right],\\ {\mathbf{M}}_{N\times N}=\left[\begin{array}{cccc}\mathrm{1}& & & \\ \mathrm{1}& \mathrm{1}& & \\ ⋮& & \ddots & \\ \mathrm{1}& \mathrm{1}& \cdots & \mathrm{1}\end{array}\right].\end{array}$$

(13)

5. Energy Efficiency of SRPFEC

In the proposed CWSN-C, sensor nodes are deployed along the deep shaft. It is difficult to replenish new nodes. Therefore, the energy efficiency should be considered.

5.1. Power Consumption Model

To evaluate the energy efficiency, a power consumption model of communication module including wireless transmitting and receiving is needed. It should to be pointed out that, to focus on the packet forwarding scheme, the energy cost of data processing is not considered. The actual power consumption is effected by many factors, such as deployment environment, node manufacture, and interference, so it is difficult to build a precise power consumption model. Without loss of generality, $E_r$ and $E_t\left(d\right)$ denote the receiving and transmission power consumption, respectively [17], where d is the transmission range. Since $E_r$ do not depend on the transmission range, it can be modeled as a constant. And apparently, the transmission range is equal to $d_i$ .

Assuming that the rigid sliding guide defeat happens at any location in monitoring area with the same probability, let P denote the number of times of the incident happened in unit time; then, the packet receiving and transmission power consumption of node $S_i$ can be expressed as

$$\begin{array}{cc}& E_{r\_\text{total}}\left(i\right)=\frac{P}{N}\times T_i\times E_r\times {\displaystyle \sum }_{x=\mathrm{1}}^{N-i}\hspace{0.17em}h\left(i,i+x\right),\\ E_{t\_\text{total}}\left(i\right)=\frac{P}{N}\times T_i\times E_t\left(d_i\right)\times {\displaystyle \sum }_{x=\mathrm{0}}^{N-i}\hspace{0.17em}h\left(i,i+x\right),\end{array}$$

(14)

where $T_i$ denotes the monitoring time of node $S_i$ .

Then, we have the total power consumption of node $S_i$ :

$$\begin{array}{ll}& E_{\text{total}}\left(i\right)=\frac{P}{N}\times T_i\times \left(E_r\times {\displaystyle \sum }_{x=\mathrm{1}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right.\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left.+E_t\left(d_i\right)\times {\displaystyle \sum }_{x=\mathrm{0}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right).\end{array}$$

(15)

As the wireless nodes are isomorphic, we have

$$\begin{array}{cc}& E_{\text{initial}}=E_{\text{total}}\left(i\right),\hspace{1em}\mathrm{1}\le i\le N,\end{array}$$

(16)

where $E_{\text{initial}}$ denotes the initial energy of each node.

5.2. Network Lifetime

According to (15) and (16), we have the lifetime of each node $S_i$ :

$$\begin{array}{ll}& T_i=\left(E_{\text{initial}}\times N\right)\left(P\times \left(E_r\times {\displaystyle \sum }_{x=\mathrm{1}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right.\right.\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}\hspace{0.5em}{\left.\left.+E_t\left(d_i\right)\times {\displaystyle \sum }_{x=\mathrm{0}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right)\right)}^{-1}.\end{array}$$

(17)

As described above, the energy exhausting of any node will cause the death of this CWSN-C. Then, we have the network lifetime T:

$$\begin{array}{ll}& T=\left(E_{\text{initial}}\times N\right)\left(P\times \max \left(E_r\times {\displaystyle \sum }_{x=\mathrm{1}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right.\right.\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}{\left.\left.+E_t\left(d_i\right)\times {{\displaystyle \sum }}_{x=\mathrm{0}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right)\right)}^{-1}.\end{array}$$

(18)

To simplify calculation and compensate preprocessing energy consumption of data collected by sensor, we have

$$\begin{array}{cc}& T=\frac{E_{\text{initial}}\times N}{P\times \max \left(\left(E_r+E_t\left(d_i\right)\right)\times {\sum }_{x=\mathrm{0}}^{N-i}\hspace{0.17em}h\left(i,i+x\right)\right)}.\end{array}$$

(19)

Taking all nodes into account, (19) should be expressed as follows.

Feasibility Conditions 3. Defining matrix ${\mathbf{C}}_{N\times N}=\left(E_t\left(\mathbf{D}\right)+E_r\right)\times \mathbf{H}={\left[{\mathbf{c}}_{\mathrm{1}},{\mathbf{c}}_{\mathrm{2}},\dots ,{\mathbf{c}}_N\right]}^{\prime }$ . To achieve the maximum network lifetime, the maximum value of the summation of each row vectors ${\mathbf{c}}_i$ should be as small as possible.

And the lifetime of the CWSN-C can be calculated by

$$\begin{array}{cc}& T=\frac{E_{\text{initial}}\times N}{P\times \max \left(\text{sum}\left({\mathbf{c}}_i\right)\right)},\hspace{1em}i=\mathrm{1,2},\dots ,N.\end{array}$$

(20)

6. Solution of Redundant Packets Arrangement

It seems that all inequalities in Feasibility Conditions 1, 2, and 3 are linearly independent, but Feasibility Conditions 3 is not easy to be expressed by a linear function, whose objective function is to find a minimum value in maximum set. Therefore, the Linear Programming method is not suitable to find H. In this section, we try to use exhaustive search method to find H.

6.1. Solution Analysis

As the solution matrix H is integer, the times of exhaustive search

$$\begin{array}{cc}& ST=S{L}^{(N\times \left(N+\mathrm{1}\right))/\mathrm{2}},\end{array}$$

(21)

where $SL$ is the length of search region. The algorithm complexity of searching solution matrix H is $O\left(S{L}^{N^{\mathrm{2}}}\right)$ .

6.2. Solution Based on Engineering Practice

6.2.1. Search Region

Supporting the application QoS is the primary goal of SRPFEC; thus, the limits of search region are determined by Feasibility Conditions 1 and 2.

Lower Limit   α. It is obviously true that the requirement of end to end delay does not affect the lower limit of search region. Therefore, only Feasibility Conditions 1 needs to be considered. As $\mathrm{0}\le p_{\text{demand}}\le \mathrm{1}$ and $\mathrm{0}\le {{\text{PER}}_x}^{h\left(x,n\right)}\le \mathrm{1}$ , according to (2), we have $\forall x,n$ , $\mathrm{1}-{{\text{PER}}_x}^{h\left(x,n\right)}\ge p_{\text{demand}}$ . Then,

$$\begin{array}{cc}& h\left(x,n\right)\ge \frac{\ln \left(\mathrm{1}-p_{\text{demand}}\right)}{\ln {\text{PER}}_x}={\log }_{{\text{PER}}_x}\left(\mathrm{1}-p_{\text{demand}}\right).\end{array}$$

(22)

Therefore, the lower limit

$$\begin{array}{cc}& \alpha ={\log }_{\max \left({\text{PER}}_x\right)}\left(\mathrm{1}-p_{\text{demand}}\right),\hspace{1em}x=\mathrm{1,2},\dots ,N.\end{array}$$

(23)

Upper Limit   β. It is obviously true that improving the reaching probability of 1-hop will exert a limited influence of global reaching probability in multihop network. It means that increasing the number of redundant packets is meaningless when it exceeds a threshold. Assuming that the accuracy of reaching probability is $\mathrm{1}{\mathrm{0}}^{-\lambda }$ , the upper limit β can be calculated by

$$\begin{array}{cc}& {\left(\mathrm{1}-{\text{PER}}^{\beta +\mathrm{1}}\right)}^N-{\left(\mathrm{1}-{\text{PER}}^{\beta }\right)}^N=\mathrm{1}{\mathrm{0}}^{-\lambda }.\end{array}$$

(24)

Then, we have

$$\begin{array}{cc}& SL=\beta -\alpha .\end{array}$$

(25)

6.2.2. Parameters Adjustment

In the proposed CWSN-C, all nodes are deployed with nearly equal interval. That means

$$\begin{array}{cc}& d=d_i,\hspace{1em}i=\mathrm{1,2},\dots ,N.\end{array}$$

(26)

Furthermore, in closed deep shaft, the geological structures of all nodes positions are the same. Therefore, they have the same characteristic of electromagnetic wave attenuation approximately. That means

$$\begin{array}{cc}& \text{PER}={\text{PER}}_i,\hspace{1em}i=\mathrm{1,2},\dots ,N.\end{array}$$

(27)

Then, the matrix A, B, and C can be expressed as

$$\begin{array}{cc}& {\mathbf{A}}_{N\times N}=\text{lnPER}\times {\mathbf{H}}^T+\ln p_{\text{demand}}\times \mathbf{I}+\mathbf{F}\mathbf{,}\\ {\mathbf{B}}_{N\times N}=t\left(d\right)\times \left({\mathbf{H}}^T+\mathbf{M}\right),\\ {\mathbf{C}}_{N\times N}=\left(E_t\left(d\right)+E_r\right)\times \mathbf{H}\mathbf{.}\end{array}$$

(28)

In addition, as the lower neighbor node has the heavier network load than the upper neighbor node, it is obviously true that, $h\left(i,j\right)\ge h\left(i-\mathrm{1},j\right)$ . Therefore, the algorithm complexity of searching solution decreases to $O\left(S{L}^N\right)$ .

The searched solution is named as source-aware solution ${\mathbf{H}}_{\text{source}}$ for discussion.

7. Performances

In this section, two methods are adopted to study the performances of SRPFEC, which are Monte Carlo simulation with Matlab and network simulation with OPNET Modeler. Rated models and parameters are as follows.

$(1)$ The desired reaching probability $p_{\text{demand}}=\mathrm{0.95}$ ; the desired end to end delay $L_{\text{demand}}=\mathrm{0.2}$  s; node spacing $d=\mathrm{80}$  m; packet size set as 1024 bits; transmission band $f=\mathrm{2.4}$  GHz; data rate set as Auto Calculate; simulation time set as 3600 s. The incident happens at 500 s.

$(2)$ The initial energy of each node is $E_{\text{initial}}=\mathrm{5400}$  J (two batteries with 2 × 1.5 V, 500 mAh). The transmitting and receiving energy cost [18] are given by

$$\begin{array}{cc}& E_{Tx}=E_{\text{elec}}\times k+{\epsilon }_{\text{amp}}\times k\times d^{\beta },\\ E_{Rx}=E_{\text{elec}}\times k,\end{array}$$

(29)

where k is data bits, d is transmission distance, $E_{\text{elec}}$ is transmitter and receiver electronics, and ${\epsilon }_{\text{amp}}$ is transmit amplifier. β is path loss exponent. Related typical values are $E_{\text{elec}}=\mathrm{50}$  nJ/bit and ${\epsilon }_{\text{amp}}=\mathrm{0.0013}$  pJ/bit/m⁴. Wireless network in closed deep shaft is a typical indoor network. According to the research report of COST 231, the path loss is β = 2–4 when the frequency of short-range low-power wireless communication is between 800 MHz and 2.4 GHz in Densely Furnished Rooms. Therefore, $\beta =\mathrm{4}$ is adopted in this work to evaluate the energy efficiency.

In addition, to evaluate the performances of SRPFEC intuitively, a solution without source awareness is also needed to compare with ${\mathbf{H}}_{\text{source}}$ . According to (28), the non-source-aware solution ${\mathbf{H}}_{\text{non}}$ can be easily obtained by using recurrence method and ceiling function.

7.1. Evaluation with an Instance

We take the proposed CWSN-C as an instance to evaluate the performances firstly. The related parameters are as follows. $(1)$ The number of nodes $N=\mathrm{15}$ ; $(2)$ the average packet error rate $\text{PER}=\mathrm{0.2}$ .

Figure 2 shows the source-aware solution ${\mathbf{H}}_{\text{source}}$ and non-source-aware solution ${\mathbf{H}}_{\text{non}}$ of redundant packets arrangement. It shows that the range of matrix element in ${\mathbf{H}}_{\text{source}}$ is smaller than that in ${\mathbf{H}}_{\text{non}}$ .

Figure 2

Solution of redundant packets arrangement.

It is obviously true that the network will face the biggest challenge when the incident happened at the sensing area of node $S_N$ . Figure 3 shows the network performances when the original packet generated by node $S_{\mathrm{15}}$ . It shows that ${\mathbf{H}}_{\text{source}}$ tends to consume more resources than ${\mathbf{H}}_{\text{non}}$ . However, they both have the better network performances than ACK scheme apparently.

Figure 3

Network performances.

The application QoS is most concerned about in the CWSN-C. Figure 4 shows the application QoS when the incident happened at the sensing area of each node. It shows that, the end to end delay with non-ACK scheme is only 29.2% of its with ACK scheme, and the difference of end to end delay between non-ACK and ACK increases from 0.08 s to 0.22 s with the routing hops growth. In addition, the end to end delay of ${\mathbf{H}}_{\text{source}}$ is a litter larger than that of ${\mathbf{H}}_{\text{non}}$ , but the reaching probability of ${\mathbf{H}}_{\text{source}}$ is better than that of ${\mathbf{H}}_{\text{non}}$ .

Figure 4

Application QoS.

Figure 5 shows the lifetime of each node in the CWSN-C where the incident happened at the sensing area of each node with equal probability. It shows that the average lifetime of nodes increases from 222.5 days to 246.4 days, and the lifetime of the network extends from 141.1 days to 146 days when the SRPFEC is adopted. Meanwhile, the standard deviation of the average lifetime decreases from 204.2 to 125.2, which means that ${\mathbf{H}}_{\text{source}}$ can balance the energy consumption of the CWSN-C.

Figure 5

Nodes lifetime.

7.2. Further Evaluation

To fully understand the SRPFEC, the performances of CWSN-C in different network environments need to be evaluated. Generally, the main influencing factors of CWSN-C performances are network size and channel quality. Therefore, the performances of SRPFEC with different number of nodes and different PER are discussed.

7.2.1. Number of Nodes

Figures 6–8 show the performances of SRPFEC with different number of nodes when the average packet error rate $\text{PER}=\mathrm{0.2}$ .

Figure 6

Network performances with different number of nodes.

Figure 7

Application QoS with different number of nodes.

Figure 8

Network lifetime with different number of nodes.

$(1)$ As the load is in the range of network capacity, the network performances with both non-ACK and ACK remain broadly flat as the network size growth. In addition, the overall number of dropping packets keeps growing in SRPFEC scheme, which caused the decreasing of throughput.

$(2)$ SRPFEC scheme presents significant advantages in ensuring application QoS with the network size growth. It shows that the difference of average end to end delay between non-ACK and ACK increases from 0.21 s to 0.48 s. In addition, the reaching probability has a great increase when ${\mathbf{H}}_{\text{source}}$ is adopted.

$(3)$ It shows that the extension network lifetime increases from 0 days to 20.7 days with the increasing network size from 5 to 30 when ${\mathbf{H}}_{\text{source}}$ is adopted. Moreover, the extension network lifetime will be longer with the network size growth.

7.2.2. PER

Figures 9–11 show the performances of SRPFEC with different PER when the number of nodes $N=\mathrm{15}$ .

Figure 9

Network performances with different PER.

Figure 10

Application QoS with different PER.

Figure 11

Network lifetime with different PER.

$(1)$ With the gradual deterioration of communication environment, the congestion of the CWSN-C with ACK scheme becomes more and more serious. Fortunately, the network performances with non-ACK scheme remain stable. However, the overall number of dropping packets keeps growing in SRPFEC scheme with PER increasing.

$(2)$ The ability of SRPFEC scheme for ensuring the required application QoS with the deterioration of communication environment is better than that of ACK scheme. In addition, there is a great increase of the reaching probability when ${\mathbf{H}}_{\text{source}}$ is adopted.

$(3)$ It shows that the extension network lifetime increases from 0 days to 6.8 days with the increasing PER from 0 to 0.4 when ${\mathbf{H}}_{\text{source}}$ is adopted.

8. Conclusions

$(1)$ In CWSN-C, non-ACK scheme is highly suitable for the condition of large network size and hazardous wireless communication environment. There are two advantages of this scheme. Firstly, the one directional data flow could improve the network usage. Secondly, the newest data would not be affected by the acknowledgement information of last packet.

$(2)$ As the number of redundant packets of each node can be set proactively, it is easy to adopt ${\mathbf{H}}_{\text{source}}$ of SRPFEC in CWSN-C. And it can present great network performances and can ensure the application QoS. The scheme is suitable for the occasion where the node could be replaced on demand expediently.

$(3)$ The network performances and application QoS of ${\mathbf{H}}_{\text{source}}$ are similar to those of ${\mathbf{H}}_{\text{non}}$ . Moreover, ${\mathbf{H}}_{\text{source}}$ has better performance than ${\mathbf{H}}_{\text{non}}$ in energy efficiency, such as network lifetime and energy balance. The scheme is suitable for the occasion where the network lifetime needs to be determined before deployment and the node could not be replaced easily.