# Enabling Green Wireless Sensor Networks: Energy Efficient T-MAC Using Markov Chain Based Optimization

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## Abstract

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## 1. Introduction

- We derive an analytical model for T-MAC, applying a discrete-time Markov chain focussing on throughput, energy consumption, power efficiency and service energy under unsaturated traffic conditions.
- A node behaviour model is presented with a transmission probability, which reviews the back-off mechanism in the T-MAC protocol using the Markov chain. Moreover, the probabilities of a successful transmission, collision, and idle state of a node are computed in a cycle probability model, which is also illustrated.
- A system model, based on the M/M/1/∞ queuing model, is presented to analyse the throughput under unsaturated traffic conditions, and a service delay model is illustrated to calculate the average service delay using the adaptive sleep wakeup schedules.
- A comparative performance analysis is done with the aid of a simulation to assess the energy efficiency of the suggested model, as compared to the state-of-the-art S-MAC and X-MAC based techniques, in view of various metrics.

## 2. Related Works

#### 2.1. MAC Orientated Green Communication

#### 2.2. Routing Orientated Green Communication

## 3. Analytical Model of T-MAC Protocol

#### 3.1. Node Behaviour Model

#### 3.2. Cycle Probability Model

#### 3.3. Throughput Analysis

#### 3.4. Service Delay Analysis

#### 3.5. Energy Consumption and Power Efficiency

## 4. Experimental Results and Analysis

^{2}. The number of sensors deployed for this simulation is 50. The radio range of the sensor is assumed to be 50 m. The data packet size is taken to be 512 bits. The packet arrival rate follows the Poison process. The results provide an analysis for the probabilities of a successful transmission cycle, energy consumption, idle cycle, average service delay, throughput, collision cycle, and power efficiency for the different packet arrival rates ⋋. It is assumed that there are $n$ = 4 sensors, contending for the channel access, with a contention window size of $\mathrm{W}=16$. The energy consumed per unit of time for a successful transmission, idle state, collision, and sleep state is assumed to be ${E}_{ST}$ = 5 mJ, ${E}_{ID}$ = 0.2 mJ, ${E}_{COL}$ = 7 mJ and ${E}_{SL}$ = 0.04 mJ, respectively. The time is divided into a number of slots of length $\mathsf{\tau}$ = 10 s. The cycle length is assumed to be ${\mathrm{T}}_{\mathrm{cl}}$ = 30 µs. The sensor goes into sleep mode if no event occurred for a certain time of idle listening that assumed to be ${\mathrm{T}}_{\mathrm{A}}$ = 1 µs. The average transmission time of the sensors is assumed to be ${\mathrm{T}}_{\mathrm{s}}$ = 5 µs. The signal sampling time and rate are assumed to be ${\mathrm{T}}_{\mathrm{sam}}$ = 5 µs and ${\mathrm{R}}_{\mathrm{sam}}$ = 2 µs.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The idle probability ${P}_{ID}$ in a cycle versus the packet arrival rate ⋋ for the T-MAC, S-MAC and X-MAC protocols.

**Figure 3.**The collision probability ${P}_{COL}$ in a cycle versus the packet arrival rate ⋋ for the T-MAC, S-MAC and X-MAC protocols.

**Figure 4.**The successful transmission probability, ${P}_{ST},$ in a cycle versus different packet arrival rates ⋋, for the T-MAC, S-MAC and X-MAC protocols.

**Figure 5.**The average service delay with respect to the packet arrival rate ⋋ for the T-MAC, S-MAC and X-MAC protocols.

**Figure 7.**The average energy consumption versus packet arrival rate for the T-MAC, S-MAC and X-MAC protocols.

Notation | Description | Notation | Description |
---|---|---|---|

n | Number of sensor nodes | ${E}_{SL}$ | Sleeping energy |

W | Contention window size | ${P}_{SL}$ | Probability of sleeping |

p | Probability | ${T}_{COL}$ | Collision time |

${\mathsf{\Pi}}_{(.)}$ | State probability | ${T}_{ID}$ | Idle time |

$k$ | Positive integer | ${T}_{SL}$ | Sleep time |

${P}_{TR}$ | Probability of transmission | ${T}_{ST}$ | Successful transmission time |

${P}_{ST}$ | Probability of successful transmission | ${\mathrm{T}}_{1}$ | Missing transmission time |

${P}_{COL}$ | Probability of collision | ${\mathrm{T}}_{2}$ | Time taken by the node for not capturing the channel |

${P}_{ID}$ | Probability of idle | ${\mathrm{T}}_{3}$ | Time taken due to the back off procedure |

$\mathsf{\tau}$ | Time slot | ${\mathrm{T}}_{4}$ | Transmission time |

${E}_{ST}$ | Energy consumption in successful transmission | ${\mathrm{T}}_{\mathrm{CL}}$ | Duration of a cycle |

${E}_{ID}$ | Idle energy | ${\mathrm{T}}_{\mathrm{A}}$ | Threshold |

${E}_{COL}$ | Collision energy | $\mathrm{E}$ | Whole network energy |

${\mathrm{T}}_{\mathrm{sam}}$ | Sampling time in µs | S | Throughput |

${\mathrm{T}}_{\mathrm{s}}$ | Average transmission time | ${\mathrm{R}}_{\mathrm{sam}}$ | Sampling rate in µs |

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**MDPI and ACS Style**

Ram, M.; Kumar, S.; Kumar, V.; Sikandar, A.; Kharel, R. Enabling Green Wireless Sensor Networks: Energy Efficient T-MAC Using Markov Chain Based Optimization. *Electronics* **2019**, *8*, 534.
https://doi.org/10.3390/electronics8050534

**AMA Style**

Ram M, Kumar S, Kumar V, Sikandar A, Kharel R. Enabling Green Wireless Sensor Networks: Energy Efficient T-MAC Using Markov Chain Based Optimization. *Electronics*. 2019; 8(5):534.
https://doi.org/10.3390/electronics8050534

**Chicago/Turabian Style**

Ram, Mahendra, Sushil Kumar, Vinod Kumar, Ajay Sikandar, and Rupak Kharel. 2019. "Enabling Green Wireless Sensor Networks: Energy Efficient T-MAC Using Markov Chain Based Optimization" *Electronics* 8, no. 5: 534.
https://doi.org/10.3390/electronics8050534