Performance analysis of the unslotted IEEE 802.15.4k MAC protocols under saturated traffic and fading channel conditions

Abstract

The IEEE 802.15.4 standard is known as the most used technology for Wireless Sensor Networks (WSNs) because of their low rate and especially their energy efficiency. To better support the requirements of Low Energy Critical Infrastructure Monitoring (LECIM) applications, the IEEE 802.15.4k is approved. This amendment is intended for critical packets transmission using the Priority Channel Access (PCA) that has become a real issue in infrastructures applications. The analysis presented in this paper investigates, for the first time in the literature, the performance analysis of the IEEE 802.15.4k in non beacon-enabled mode assuming star topology, saturated traffic and fading channel conditions. Where fading channel is a very important factor in the network as it affects its performance. We emphasize that this is an original work that has never been treated in literature. In this paper, we have developed a two dimensional Markov chain model for the IEEE 802.15.4k unslotted Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) with PCA backoff mechanism, and, a three dimensional Markov chain model for the IEEE 802.15.4k unslotted CSMA/CA mechanism. Furthermore, to test the efficiency of the proposed model, we have analyzed the impact of variation of network size, probability that the available packet is critical, Bit Error Rate (BER), and packet length on the reliability, power consumption and throughput in order to compare the performance of both mechanisms. With the increase of network size and packet length, it is observed that PCA achieves a reduction in energy, a higher throughput and a lower reliability compared to CSMA/CA. The obtained results are satisfactory because packet length and network size are the most important parameters in industrial applications especially in critical systems. Finally, a comparative table was given to compare the behavior of the IEEE 802.15.4k network in terms of performance metrics.

Appendices

Appendix A: Derivation of Eq. (49)

$$\begin{aligned} E_{PCA}^{U}= & {} P_{sense}\Bigg ( \sum _{i=0}^{W-1}\sum _{k=1}^{d}p_{i,k}\Bigg )+P_{tm}\sum _{k=0}^{L_{p}-1}(p_{-2,k}+p_{-3,k})+P_{i}(p_{-2,L_{p}}+p_{-3,L_{p}})\nonumber \\&+ \sum _{k=L_{p}+1}^{L_{p}+L_{ack}+1}(P_{rm}~p_{-2,k}+P_{i}~p_{-3,k})\nonumber \\= & {} P_{sense}\Bigg (\frac{P_{Q}~h_{p}}{W}\sum _{k=1}^{d}\sum _{j=0}^{min(W-1-i,k-1)}C_{k-1}^{j}~(1-\alpha )^{j} ~\alpha ^{k-j-1}\Bigg )\nonumber \\&+ P_{tm}\Bigg (L_{p}(1-\alpha )(1-P_{f})~\frac{P_{Q}h_{p}}{W} \nonumber \\&\times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j} \alpha ^{k-j-1}+L_{p}(1-\alpha )P_{f}~\frac{P_{Q}h_{p}}{W} \nonumber \\&\times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j} \alpha ^{k-j-1} \Bigg )\nonumber \\&+P_{i}\Bigg (\frac{P_{Q}~h_{p}}{W}(1-\alpha )(1-Pf)\sum _{k=1}^{d}\sum _{j=0}^{min(W-1-i,k-1)}C_{k-1}^{j}~(1-\alpha )^{j} ~\alpha ^{k-j-1}\nonumber \\&+\frac{P_{Q}~h_{p}}{W}(1-\alpha )P_{f} \times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1-i,k-1)}C_{k-1}^{j}~(1-\alpha )^{j} ~\alpha ^{k-j-1}\Bigg )\nonumber \\&+\Bigg (P_{rm}(L_{ack}+1)(1-\alpha )(1-P_{f})~\frac{P_{Q}h_{p}}{W} \nonumber \\&\times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j}\alpha ^{k-j-1}+(L_{ack}+1)(1-\alpha )(1-P_{f})~\frac{P_{Q}h_{p}}{W} \nonumber \\&\times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j} \alpha ^{k-j-1}\Bigg )\nonumber \\ \end{aligned}$$

$$\begin{aligned}= & {} P_{sense}\Bigg (\sum _{k=1}^{d}\sum _{j=0}^{min(W-1-i,k-1)}C_{k-1}^{j}~(1-\alpha )^{j} ~\alpha ^{k-j-1}\frac{P_{Q}~h_{p}}{W}\Bigg )\nonumber \\&+P_{tm}\Bigg (L_{p}(1-\alpha )~\frac{h_{p}}{W} \times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j} \alpha ^{k-j-1}\times P_{Q})\Bigg )\nonumber \\&+P_{i}\Bigg ((1-\alpha )~\frac{h_{p}}{W} \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j} \alpha ^{k-j-1} \times P_{Q}\Bigg )\nonumber \\&+\Bigg ((1-\alpha )~\frac{h_{p}}{W} \times \sum _{k=1}^{d}\sum _{j=0}^{min(W-1,k-1)} C_{j}^{k-1} (1-\alpha )^{j} \alpha ^{k-j-1}\times P_{Q}\Bigg )\nonumber \\&\Big [P_{rm}(1-P_{f})+P_{i}P_{f}\Big ]\nonumber \\= & {} \sum _{k=1}^{d}\sum _{j=0}^{min(W-1-i,k-1)}C_{k-1}^{j}~(1-\alpha )^{j} ~\alpha ^{k-j-1} \frac{P_{Q}~h_{p}}{W} \Bigg [P_{sense}{+}(1{-}\alpha )\Bigg (L_{p}P_{tm}{+}P_{i}\nonumber \\&+(1-P_{f})(L_{ack}+1)P_{rm}+ P_{f}(L_{ack}+1)P_{i}\Bigg )\Bigg ]. \end{aligned}$$

(A.1)

Appendix B: Derivation of Eq. (50)

$$\begin{aligned} E_{CSMA}^{U}&=P_{i}\sum _{i=0}^{m}\sum _{k=1}^{W_{i}-1}\sum _{j=0}^{n}b_{i,k,j}+P_{sense}\sum _{i=0}^{m}\sum _{j=0}^{n}b_{i,0,j}\\&\quad +P_{tm}\sum _{k=0}^{L_{p}-1}\sum _{j=0}^{n}(b_{-1,k,j}+b_{-2,k,j}) +P_{i}\sum _{j=0}^{n}(b_{-1,L_{p},j}\\&\quad +b_{-2,L_{p},j})+\sum _{j=0}^{n}\sum _{k=L_{p}+1}^{L_{p}+L_{ack}+1}(P_{rm}~b_{-2,k,j}+P_{i}~b_{-1,k,j})\\&=P_{i}\Bigg (\frac{(1-h_{p})P_{Q}}{2}\Bigg [\frac{1-(2x)^{m+1}}{1-2x}W_{0}+\frac{1-x^{m+1}}{1-x}\Bigg ]\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg )\\&\quad + P_{sense}\Bigg (~P_{Q}(1-h_{p})\frac{1-y_{p}^{n+1}}{1-y_{p}}\frac{1-\alpha ^{m+1}}{1-\alpha }\Bigg ) \\&\quad +P_{tm} \Bigg (L_{p}P_{Q}P_{f}(1-h_{p})(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\\&\quad +L_{p}P_{Q}(1-P_{f})(1-h_{p})(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg )\\&\quad +P_{i}\Bigg (P_{f}P_{Q}(1-h_{p})(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\\&\quad +(1-P_{f})P_{Q}(1-h_{p})\times (1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg )\\&\quad +\Bigg (P_{Q}(1-h_{p})(L_{ack}+1)(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\bigg [P_{rm}(1-P_{f})+P_{i}P_{f}\bigg ]\Bigg )\\&=P_{i}\Bigg (\frac{(1-h_{p})P_{Q}}{2}\Bigg [\frac{1-(2x)^{m+1}}{1-2x}W_{0}+\frac{1-x^{m+1}}{1-x}\Bigg ]\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg )\\&\quad + P_{sense}\Bigg (~P_{Q}(1-h_{p})\frac{1-y_{p}^{n+1}}{1-y_{p}}\frac{1-\alpha ^{m+1}}{1-\alpha }\Bigg ) \\&\quad +P_{tm} \Bigg (L_{p}P_{Q}(1-h_{p})(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg ) \end{aligned}$$

$$\begin{aligned}&\qquad \qquad +P_{i}\Bigg (P_{Q}(1-h_{p})(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}+P_{Q}(1-h_{p}) \nonumber \\&\qquad \qquad \times (1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg )+\Bigg (P_{Q}(1-h_{p})(L_{ack}+1)(1-\alpha ^{m+1})\frac{1-y_{p}^{n+1}}{1-y_{p}} \nonumber \\&\qquad \qquad \bigg [P_{rm}(1-P_{f})+P_{i}P_{f}\bigg ]\Bigg ) \nonumber \\&=(1-h_{p})P_{Q}\frac{1-y_{p}^{n+1}}{1-y_{p}}\Bigg [\dfrac{P_{i}}{2}\bigg (\frac{1-(2x)^{m+1}}{1-2x}W_{0}+\frac{1-x^{m+1}}{1-x}\bigg ) \nonumber \\&\quad +\frac{1-x^{m+1}}{1-x}P_{sense}+P_{tm}L_{p}(1-\alpha ^{m+1}) \nonumber \\&\quad +P_{i}(1-\alpha ^{m+1})+(L_{ack}+1)(1-\alpha ^{m+1})\bigg ((P_{rm}1-P_{f})+P_{i}P_{f}\bigg )\Bigg ]. \end{aligned}$$

(B.1)