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Energy-efficient analysis of an IEEE 802.11 PCF MAC protocol based on WLAN

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Abstract

The point coordination function (PCF) of the IEEE 802.11 standard represents a well-known medium access control (MAC) protocol providing quality-of-service guarantees in wireless local area networks (WLANs). However, few papers theoretically analyze energy efficiency. This paper presents a Parallel Gated Poll (PGP) access mechanism that exploits the PCF defined in the IEEE 802.11. The basic idea is, during the contention free period, idle stations can save energy by turning into sleep and active stations exchange data packet under a gated service polling scheme to improve the energy efficiency. Besides, the mean cycle analysis model is setup to evaluate the energy efficiency of a typically PCF protocol and PGP protocol. By applying the classic 1-limited and parallel gated polling model, the closed expressions of energy efficiency of PCF and PGP are formulated respectively. Simulations show that our analytical results are very accurate with the simulation results. Both analytical and simulation results show the high energy efficiency of PGP.

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Acknowledgements

This work was supported by a Grant from the National Science Foundation of China (No. 61463051, No.61761045, No.61463049 and No.61461054), and the National Science Foundation of Yunnan Province (No.2017FB100).

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Yunnan University, Kunming, 650091, China

    Guan Zheng, Yang Zhi-Jun, He Min & Qian Wen-Hua

  2. Educational and Scientific Institute, Educational Department of Yunnan Province, Kunming, 650223, China

    Yang Zhi-Jun

Authors
  1. Guan Zheng
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  2. Yang Zhi-Jun
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  3. He Min
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  4. Qian Wen-Hua
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Corresponding author

Correspondence to Qian Wen-Hua.

Appendix: stepwise derivation of Lemma 1

Appendix: stepwise derivation of Lemma 1

In this section we use the definition of \({{\text{G}}_i}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)\) discussed in Sect. 3.2.3 to get \({{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right),~\) the generation function of STA i at the time tn+1.

\({{\text{G}}_i}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)\) is defined as follow,

$${{\text{G}}_i}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)=\mathop \sum \limits_{{{x_1}=0}}^{\infty } \mathop \sum \limits_{{{x_2}=0}}^{\infty } \cdots \mathop \sum \limits_{{{x_i}=0}}^{\infty } \cdots \mathop \sum \limits_{{{x_N}=0}}^{\infty } z_{1}^{{{x_1}}}z_{2}^{{{x_2}}} \cdots z_{i}^{{{x_i}}} \cdots z_{N}^{{{x_N}}}{\pi _i}\left( {{x_1}, \cdots ,{x_i}, \cdots ,{x_N}} \right)$$
$$i=1,2, \cdots ,N$$

As \({\pi _i}\left( {{x_1}, \cdots ,{x_i}, \cdots ,{x_N}} \right)=\mathop {\lim }\nolimits_{{n \to \infty }} {\mathbb{P}}\left[ {{\xi _j}\left( n \right)={x_j};\, j=1,2, \cdots ,N} \right]\) is the stationary distribution of the system queue length at the polling time of STA i. We have

$${{\text{G}}_i}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)=\mathop {\lim }\limits_{{n \to \infty }} {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\xi _j}\left( n \right)}}} \right]$$

By analogy, we could calculate \({{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right),~\)the generation function of STA i at the time tn+1 as follow:

$${{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)=\mathop {\lim }\limits_{{n \to \infty }} {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right]$$
(24)

Note here \({\xi _j}\left( {n+1} \right)\) is conditional in PGP, so we rewrite (24) in a conditional probability form following

$${\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right]={\mathbb{E}}\left[ {{\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} \left. {z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right|{\xi _j}\left( n \right)} \right]} \right]=\mathop \sum \limits_{{k=0}}^{\infty } {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} \left. {z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right|{\xi _j}\left( n \right)=k} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=k} \right\}$$
(25)

Take (3) into (25). As the timing variables for AP switch from each STA to the next are independent of each other, the \({{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)\) can be expressed as follow:

$${{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)=\mathop {\lim }\limits_{{n \to \infty }} {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right]$$
$$=\mathop {\lim }\limits_{{n \to \infty }} \mathop \sum \limits_{{k=0}}^{\infty } {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} \left. {z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right|{\xi _j}\left( n \right)=k} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=k} \right\}$$
$$=\mathop {\lim }\limits_{{n \to \infty }} {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} \left. {z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right|{\xi _j}\left( n \right)=0} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=0} \right\}+\mathop {\lim }\limits_{{n \to \infty }} \mathop \sum \limits_{{k=1}}^{\infty } {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} \left. {z_{j}^{{{\xi _j}\left( {n+1} \right)}}} \right|{\xi _j}\left( n \right)=k} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=k} \right\}$$
$$=\mathop {{\text{lim}}}\limits_{{n \to \infty }} {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\mu _j}\left( {{u_i}} \right)}}} \right]{\mathbb{E}}\left[ {\mathop \prod \limits_{{j \ne i}}^{N} \left. {z_{j}^{{{\xi _j}\left( n \right)}}z_{j}^{0}} \right|{\xi _j}\left( n \right)=0} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=0} \right\}+\mathop {\lim }\limits_{{n \to \infty }} \mathop \sum \limits_{{k=1}}^{\infty } {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\eta _j}\left( {{\nu _i}} \right)}}\mathop \prod \limits_{{j \ne i}}^{N} \left. {z_{j}^{{{\xi _j}\left( n \right)}}} \right|{\xi _j}\left( n \right)=k} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=k} \right\}$$
(26)

Considering the property of \({\left. {{{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)} \right|_{{z_i}=0}}={\mathbb{E}}\left[ {\mathop \prod \limits_{{\begin{array}{*{20}{c}} {j=1} \\ {j \ne i} \end{array}}}^{N} z_{j}^{{{\xi _j}\left( n \right)}}\left| {{\xi _j}\left( n \right)=k} \right.} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=0} \right\}\), for the first part of the summation (26), we can transform it as,

$$\mathop {\lim }\limits_{{n \to \infty }} {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\mu _j}\left( {{u_i}} \right)}}} \right]{\mathbb{E}}\left[ {\mathop \prod \limits_{{\begin{array}{*{20}{c}} {j=1} \\ {j \ne i} \end{array}}}^{N} z_{j}^{{{\xi _j}\left( n \right)}}\left| {{\xi _j}\left( n \right)=k} \right.} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=0} \right\}$$
$$={R_i}{\left. {\left( {\mathop \prod \limits_{{j=1}}^{N} {A_j}\left( {{z_j}} \right)} \right){{\text{G}}_{i+1}}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)} \right|_{{z_i}=0}}$$
(27)

For the second part of (26), we have,

$$\mathop {\lim }\limits_{{n \to \infty }} \mathop \sum \limits_{{k=1}}^{\infty } {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\eta _j}\left( {{\nu _i}} \right)}}\mathop \prod \limits_{{j \ne i}}^{N} \left. {z_{j}^{{{\xi _j}\left( n \right)}}} \right|{\xi _j}\left( n \right)=k} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=k} \right\}$$
$$\mathop {=\lim }\limits_{{n \to \infty }} \mathop \sum \limits_{{k=0}}^{\infty } {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\eta _j}\left( {{\nu _i}} \right)}}\mathop \prod \limits_{{j \ne i}}^{N} \left. {z_{j}^{{{\xi _j}\left( n \right)}}} \right|{\xi _j}\left( n \right)=k} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=k} \right\} - ~~~~{\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\eta _j}\left( {{\nu _i}} \right)}}\mathop \prod \limits_{{j \ne i}}^{N} \left. {z_{j}^{{{\xi _j}\left( n \right)}}} \right|{\xi _j}\left( n \right)=0} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=0} \right\}$$
$$=\mathop {\lim }\limits_{{n \to \infty }} \left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\eta _j}\left( {{\nu _i}} \right)}}\mathop \prod \limits_{{j \ne i}}^{N} z_{j}^{{{\xi _j}\left( n \right)}}} \right] - {\mathbb{E}}\left[ {\mathop \prod \limits_{{j=1}}^{N} z_{j}^{{{\eta _j}\left( {{\nu _i}} \right)}}\mathop \prod \limits_{{j \ne i}}^{N} \left. {z_{j}^{{{\xi _j}\left( n \right)}}} \right|{\xi _j}\left( n \right)=0} \right]{\mathbb{P}}\left\{ {{\xi _j}\left( n \right)=0} \right\}$$
$$={{\text{G}}_i}\left( {{z_1}, \cdots ,{z_{i - 1}},{\text{B}}\left( {\mathop \prod \limits_{{j=1}}^{N} {{\text{A}}_j}\left( {{z_j}} \right)} \right),{z_{i+1}}, \cdots ,{z_N}} \right) - {\left. {{{\text{G}}_i}\left( {{z_1}, \cdots ,{z_i}, \cdots ,{z_N}} \right)} \right|_{{z_i}=0}}$$
(28)

Combining (27) and (28), this completes the derivation of function (4).

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Zheng, G., Zhi-Jun, Y., Min, H. et al. Energy-efficient analysis of an IEEE 802.11 PCF MAC protocol based on WLAN. J Ambient Intell Human Comput 10, 1727–1737 (2019). https://doi.org/10.1007/s12652-018-0684-8

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