Hyper-geometric energy factor based semi-Markov prediction mechanism for effective cluster head election in WSNs

Abstract

The lifetime of a Wireless Sensor Network (WSN) depends on the efficiency of the Cluster Head (CH) selection techniques that address most of the significant issues related to network management. The existing energy based CH selection mechanisms consider that all the participating sensors are trustworthy. Conversely, the trust-based CH selection schemes assume that the sensor nodes are energy efficient. But, these assumptions of energy factor or trust assessment made by the CH selection mechanisms may not be true and the Residual Energy (RE) of the sensors may not be the sole factor to identify an effective CH in a WSN. Hence, this paper presents hybrid integrated energy and trust assessment based forecasting model known as Hyper-geometric Energy Factor based Semi-Markov Prediction Mechanism (HEFSPM) for effective CH election so as to improve the lifetime of the network. From the simulation results, it is inferred that HEFSPM is superior in improving the lifetime of the network to a maximum extent of 22% than the existing CH election mechanisms considered for investigation.

Keywords

Semi-markov process Cluster Head Hyper-geometric distribution energy trust assessment prediction probability

1 Introduction

In the recent past, considerable amount of research and contribution has been attributed for investigating the role and deployment of sensors that are significant for enabling co-operative information processing and distribution management [1 –3].

Wireless Sensor Networks (WSNs) have the potential of integrating embedded computing, sensor and distributed information processing technologies into a single entity for observing and gathering information in a collaborative way. The objective of collaborative information processing in WSNs depends on energy, which is the key factor for improving the lifetime of the network [4 , 20].

Further, sensors with limited energy cannot contribute to data processing as they are not capable of co-operating in data collection process independent of the kind of data monitored, collected and gathered [6]. Thus, the Residual Energy (RE) possessed by individual sensors is analyzed by most of the researchers. Most of the existing Cluster Head (CH) election algorithms either concentrate on energy consumption or the trust of the sensors in forwarding packets [7, 18].

In this paper, the core objective of collaborative information processing for improving the lifetime of the network is achieved by computing a hybrid energy-trust assessment parameter called Hyper-geometric trust factor (HG_TRUST). This hybrid energy-trust assessment parameter is computed through a Semi-Markov prediction mechanism that targets on improving the network lifetime.

2 Related works

Organization of nodes in the form of clusters in order to achieve energy efficient data transmission and improve the scalability and stability of the network is one of the most prominent solutions for collaborative data processing in WSNs [8, 19].

Initially, Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol was proposed for resolving the challenging issue that lies behind the formation of clusters [9, 17]. It uses a random selection method that uses stochastic values to select the CH. The selected CH then gathers data from its members and then transfers it to the Base Station (BS). The main role of CH in LEACH is to act as a communication link between nodes and the BS.

Thein et al. [10] has modified LEACH-C protocol based on the stochastic CH selection algorithm by considering two more additional parameters like RE of a sensor relative to the RE of the network, and distributing the roles of CH evenly so as to balance the energy load among all the nodes.

Further, Younis and Fahmy [11] have proposed a Hybrid Energy-Efficient Distributed clustering (HEED) which periodically selects CHs based on the sensors’ RE and their proximity to their neighbors or sensors’ degree. They have developed an evolutionary based routing protocol for clustering heterogeneous nodes in the WSNs.

In addition, a novel CH election scheme called Cluster Head Selection approach for Collaborative Data Processing (CHSCDP) proposed by Qiang et al. [12] is implemented using a hierarchical parameter that organizes the set of sensors in the form of clusters. Each CH performs three different tasks viz.,

Periodical updation of the nodes’ energy information and aggregation of the collected information to remove redundancy.

Secondly, sending of time slot to each sensor for transmission based on the Time Division Multiple Access (TDMA) scheme.

Finally, transmission of collected data to the nearby CH either directly or indirectly to the BS.

From the review conducted, it is inferred that most of the CH election algorithms have not employed both energy and trust factor for selection. Further, Semi-Markov based CH prediction mechanism for sending the aggregated data to the BS is not available in the existing literature. Hence, in this paper, a Semi-Markov prediction mechanism is proposed for improving the lifetime of the network through integrated energy-trust prediction.

3 Hyper-Geometric Energy Factor based Semi-Markov Prediction Mechanism (HEFSPM)

Hyper-Geometric Energy Factor based Semi-Markov Prediction Mechanism (HEFSPM) aims at improving the lifetime of the network through effective CH election. In this mechanism, the election of CH is based on a hybrid energy-trust forecasting parameter called Hyper-geometric trust factor which is predicted in three steps.

Initially, a threshold energy parameter which pertains to the availability rate of sensor nodes is computed.

Secondly, a trust assessment factor is manipulated based on Hyper-geometric distribution when the node’s energy stability is within the estimated threshold energy parameter.

Thirdly, a sensor node is elected as the CH when the predicted Hyper-geometric trust factor is more than the optimal value of CH election as identified by HEFSPM.

Thus, “Given a sensor network ‘N’ which contains sensor nodes ‘M’ with adequate RE ‘E’ and Trust Factor ‘T’, the problem is defined as a CH election mechanism ‘CE(M,T)’ that quantifies the possibility of a sensor being elected as the CH using a Hyper-geometric distribution based decision parameter, that integrates energy and trust of each participating sensors as a single entity for improving the network lifetime”.

3.1 Computation of threshold energy parameter

Generally, uniform distribution of CH roles to sensors aids in balancing the energy drain of the network, as CHs are phenomenal in performing data collection and forwarding. Thus, the node elected as the CH must be investigated for its stability based on an energy parameter as they drain out maximum amount of RE at a rapid rate.

In HEFSPM, a threshold energy parameter is computed for analyzing the stability of the sensor which has the probability of being elected as the CH. According to the definitions of the utilized energy model [13], the drain rate of sensors, ‘E_CP’ is directly proportional to the square of the distance between the sources and the sink as given by Equation (1) $E_{CP} = \frac{d_{i, s}}{d_{i, k} + d_{k, s}}$ (1) where, ‘i’ and ‘k’ represent the source and the co-operative intermediate sensor whose inter-distance to the destination is less than ‘m’ paths.

The energy consumption of sensors is optimal only when ‘E_CP’ reaches its maximum at ‘k = 1’ and when ‘k’ exists in the shortest routing path from ‘i’ to ‘s’. This consideration of shortest path is mainly for enabling a reliable shortest path between the source and sink. The proposed HEFSPM mechanism uses an energy model which is similar to the one contributed by Heinzelman that is used for calculating the amount of energy utilized by the sensors as given in [14].

HEFSPM uses the exhaustive set of possible channel models that belong to the category of multipath fading. This energy model possesses an inter-cluster node distance of d⁴ (d-distance between sensors) and they suffer from d² power loss. The incorporation of multipath or free space model is triggered based on the distance between the inter-cluster nodes that is dynamically identified with the help of threshold parameter. The transmission and receiver costs for transmitting m-bit of information are given by Equations (2) and (3). $\begin{matrix} E_{TC} (m, d) = f (x) \\ = {\begin{matrix} E_{ec} + m + {8 f}_{sd} * m * d^{2}, if (d < d_{t}) \\ E_{ec} + m + {8 t}_{mp} * m * d^{4}, if (d \geq d_{t}) \end{matrix} \end{matrix}$ (2) where, $Threshold parameter, d_{t} = \sqrt{\frac{8 f_{sd}}{{8 t}_{mp}}}$ (3)

The energy used by the amplifier for enabling a longer distance transmission in HEFSPM is equal to 0.0018pJ/bit/m⁴. In contrast, the energy utilized for shorter distance transmission is equal to10J/bit/m². E_ec, m,f_sd, t_mp represents the energy required for packet generation, number of bits of data transmitted, frequency for establishing connectivity between source and destination, and transmission rate respectively. Similarly, the transmission of data from the source and the sink is achieved either through single hop or multi-hop data transfer when they are within the same communication range. The amount of energy consumed for single and multi-hop data transfer used in this mechanism is similar to that of CHSCDP. In HEFSPM, the threshold energy parameter is elucidated exhaustively from the probe parameters that are included in the packets relayed between the source and destination. Further, the threshold energy parameter in each sensor node is calculated through Equation (4). $E_{TEP} = {mE}_{select} + m (\frac{1}{c} - 1) E_{drain}$ (4)

where, ‘c’ is the compression constant and ‘ $m (\frac{1}{c} - 1) E_{drain}$ ’ is defined as the energy required by a sensor nodes for aggregating ‘m’ bits of data.

3.2 Determination of transition probabilities for HEFSPM

In this step, when the calculated energy parameter is found to be greater than the expected optimal energy parameter threshold of 0.6 as defined in [15, 16], the trust assessment factor is predicted based on the following transition probabilities.

α_p – Transition probability for a co-operative sensor to turn into selfish

λ₂ – Behavioural probability for a mobile sensor to become a failure

λ_p – Behavioural probability for a co-operative node to turn into selfish

μ_p – Behavioural probability for a selfish node to turn into co-operative

γμ – Behavioural probability for a failure or senode to recover into co-operative node

μ – Behavioural Probability for a failure node to become co-operative

These probabilities are obtained from probe packets that extract information associated to nodes’ link stability in terms of energy, nodes’ mobility rate and nodes’ radius of communication. The elucidated behavioral properties present the complete transition of all possible behaviors that a sensor could exhibit.

3.3 Computation of Hyper-Geometric Trust Factor and Cluster Head Election

The RE of the sensors aids in estimating their trust and stability to enable them in maintaining the lifetime of the network. The drain rate of the RE of the sensors is always two-stage hyper-exponentially distributed with parameters α₁ (co-operative role) and α₂ (selfish behaviour). This two-stage hyper-exponential distribution based drain rate of sensors supports energy balancing by providing flexibility in the rate of energy consumption, depending on the state of the sensors participating in the data dissemination process.

The state of the sensors participating in routing can be co-operative, selfish or failed. Hence, the lifetime that depends on the drain rate of the sensor network solely depends on the kind of role played by the nodes. Therefore, a continuous semi-Markov chain based node behavior prediction process is incorporated for identifying the trust parameter that integrates the energy factor estimated previously based on fuzzy probability.

In this Markov chain, the following parameters are taken into consideration.

β – Time required by a selfish sensor to become co-operative

$\frac{1}{α_{p}}$ – Mean time taken for identifying the sensors as selfish

$\frac{1}{β_{p}}$ – Average transition time essential for rehabilitating the sensors into co-operative

From Fig. 1, the balance equations which are used for deriving the steady state probabilities of HEFSPM are derived as shown in Equations (5), (6), (7), (8) and (9) respectively. $(α_{1} + α_{p}) π_{CR} = γ μ π_{SF} + β π_{F} + β_{P} π_{C}$ (5) $(α_{1} + α_{p}) π_{SC} = α_{1} π_{CR}$ (6) $γ μ π_{SF} = β_{P} π_{SS}$ (7) $β_{P} π_{SS} = α_{P} π_{SC}$ (8) $π_{F} = α_{2} π_{SC}$ (9)

From Equation (5), the steady state probability which quantifies the expected probability of a co-operative sensor to exhibit selfish behaviour ‘π_CS’ is derived as shown in Equations (10) and (11). $β_{P} π_{CS} = α_{P} π_{CR}$ (10) $π_{CS} = \frac{α_{p}}{β_{P}} π_{CR}$ (11)

Likewise, the steady state probability for a selfish sensor node to recuperate into a co-operative node ‘π_SC’ is given by Equation (12), $π_{SC} = \frac{α_{1}}{α_{2} + α_{P}} π_{CR}$ (12)

Then, the product co-efficient ‘γμ’ which quantifies the expected probability of a failed sensor to recover into a co-operative node and the steady state probability for a selfish node to become a failure node ‘π_SF’ is given by Equation (13). $π_{SF} = \frac{μ_{in}}{γ μ} π_{SS}$ (13)

Similarly, the expected steady state probability for a selfish sensor to retain its own state ‘π_SS’ is given by Equation (14). $π_{SS} = \frac{α_{P}}{β_{P}} π_{SC}$ (14)

Finally, the steady state probability for a failure node that cannot be rehabilitated ‘π_F’ is given by Equations (15) and (16) respectively. $π_{F} = \frac{λ_{2}}{μ} π_{SC}$ (15) $π_{F} = \frac{λ_{2}}{μ} \frac{λ_{1}}{λ_{2} + λ_{P}} π_{CR}$ (16)

Therefore the steady state probability vectors used for modeling the nodes’ behavior obtained through hyper-geometric distribution is shown in Equations (17), (18) and (19). $π_{AA} = \frac{λ_{P}}{μ_{P}} \frac{λ_{1}}{λ_{2} + λ_{P}} π_{CC}$ (17) $π_{AF} = \frac{μ_{P}}{γ μ} \frac{λ_{P}}{μ_{P}} \frac{λ_{1}}{λ_{2} + λ_{P}} π_{CC}$ (18) $π_{CC} = \frac{1}{1 + (1 + \frac{λ_{2}}{μ} + \frac{λ_{P}}{μ_{P}} + \frac{λ_{P}}{γ μ}) \frac{λ_{1}}{λ_{2} + λ_{P}} + \frac{λ_{P}}{μ_{P}}}$ (19)

Therefore, the hyper-geometrical trust factor that quantifies the total reliability of a sensor is given by Equation (20).

$\begin{matrix} {HG}_{TRUST} \\ = \frac{1 + \frac{λ_{1}}{λ_{2} + λ_{P}}}{1 + \frac{λ_{1}}{λ_{2} + λ_{P}} + \frac{λ_{1} λ_{2}}{μ (λ_{2} + λ_{P})} + \frac{λ_{P}}{μ_{P}} + \frac{λ_{P}}{μ_{P}} \frac{λ_{1}}{λ_{2} + λ_{P}} + \frac{λ_{P}}{γ μ} \frac{λ_{1}}{λ_{2} + λ_{P}}} \end{matrix}$ (20)

The CH election is initiated only when the value of ‘HG_TRUST’ is found to be above the threshold of 0.45 (as obtained through simulations) under the availability of expected optimal energy parameterthreshold.

4 Simulation experiments and analysis

In this section, the performance evaluation of HEFSPM is carried out using ns-2.25. A maximum of 100 sensors are simulated in an environment with an area of 100*100 m. Packet size of 500 bytes is taken into consideration. IEEE 802.11 is used as the MAC protocol. The simulation is carried over a period of 300 sec.

The results are compared with the baseline CH selection mechanisms like CHSCDP, HEED and LEACH-C. Generally, the reliability in data transfer of the sensor network solely depends on the CH of each cluster formed through local clustering. Hence, the technique used for CH election may increase the packet delivery rate and throughput. But it may decrease the total energy consumption and packet drop rate.

Hence, HEFSPM is evaluated based on the following performance metrics. Table 1 illustrates the simulation parameters that are set for the study.

4.1 Type performance analysis for HEFSPM

The performance investigation of HEFSPM is achieved by carrying out four experiments.

Experiment 1 – Performance evaluation of HEFSPM based on RE and percentage of alive nodes

Experiment 2 – Performance evaluation of HEFSPM based on varying clustering co-efficient

Experiment 3 – Performance evaluation based on varying number of sensors

Experiment 4 – Performance evaluation based on varying transmission range

a) Experiment 1 – Performance Evaluation of HEFSPM Based on Residual Energy and Percentage of Alive Nodes

In Experiment 1, the performance of HEFSPM is compared with CHSCDP, HEED and LEACH-C based on the RE and percentage of alive nodes of the whole network evaluated in various rounds.

Figure 2 clearly shows that the energy stability of HEFSPM has only meager fluctuations in contrast to CHSCDP, HEED and LEACH-C. The energy stability of HEFSPM in terms of mean RE is also comparatively superior to the considered baseline CH selection schemes.

This energy balancing nature of HEFSPM is mainly due to the incorporation of degree of closeness to sink and degree of closeness to shortest path. HEFSPM also alternates between single-hop and multi-hop communication depending on the inter-distance between the source and the sink. It yields 12%, 16%, 19% and 37% better energy stability compared to CHSCDP, HEED and LEACH-C respectively.

Similarly, Fig. 3 shows the performance of HEFSPM based on the percentage of alive nodes, as the lifetime of the sensors is an important parameter for evaluating the performance of the sensor network.

In this simulation, lifetime refers to the cumulative amount of time a network survives before the death of its sensors due to total energy drain. HEFSPM distinctively enhances the lifetime of the network when compared to CHSCDP, HEED and LEACH-C. It is also transparent that the death time of CHs in CHSCDP, HEED and LEACH-C are 295, 289 and 282 respectively.

It is obvious that HEFSPM possesses maximum capability in converging when the network fails in contrast to the baseline CH election schemes. They perform better energy balancing, thus, improving the lifetime of the network.

b) Experiment 2 – Performance Evaluation of HEFSPM Based on Varying Clustering Co-Efficient

In Experiment 2, as shown in Figs. 4, 5 and 6, HEFSPM is evaluated based on the average delay observed by varying the clustering co-efficient (P = 0.6, 0.4 and 0.2) respectively.

HEFSPM is found to be better than CHSCDP, HEED and LEACH-C in terms of energy consumption and lifetime. This improvement of HEFSPM is due to the utilization of hyper geometric parameter that elects CH based on energy andtrust.

Figure 4 confirms that the average delay of HEFSPM is reduced to a maximum extent of 14%, 18%, 22% and 25% when compared to CHSCDP, HEED and LEACH-C when the clustering co-efficient is 0.60.

Likewise, from Fig. 5, it can be inferred that the average delay of HEFSPM is reduced to a maximum extent of 16%, 21%, 25% and 28% in contrast to CHSCDP, HEED and LEACH-C when the clustering co-efficient is 0.40.

From Fig. 6, it is evident that the average delay of HEFSPM is reduced to a maximum extent of 19%, 24%, 28% and 32% when compared to CHSCDP, HEED and LEACH-C when the clustering co-efficient is 0.20.

This experiment also proves that the clustering co-efficient of HEFSPM is inversely proportional to the inter-distance of nodes under communication.

c) Experiment 3-Performance Evaluation of HEFSPM Based on Varying Number of Sensor Nodes

In Experiment 3, the performance of HEFSPM is analyzed based on packet delivery ratio, throughput, energy consumption, packet drop rate and average delay by varying the number of sensors.

Figures 7 and 8 highlight the superior performance of HEFSPM with respect to the packet delivery ratio and throughput compared with the existing CH selection approaches like CHSCDP, HEED and LEACH-C.

HEFSPM exhibits an improvement of 15% to 18% when compared to CHSCDP, 21% to 23% in contrast to HEED and 25% to 28% superior to LEACH-C in terms of packet delivery ratio.

Similarly, HEFSPM shows 17% to 24%, 26% to 28%, and 31% to 34% better throughput in contrast to CHSCDP, HEED and LEACH-C.

It is inferred from the comparative analysis that HEFSPM is a reliable CH election scheme as it improves the packet delivery ratio and throughput of the network by employing Hyper-geometric trust factor for CH reliability and selection.

Thus, HEFSPM on an average increases the packet delivery rate and throughput to a maximum extent of 25% and 32% respectively.

Likewise, Figs. 9 and 10 show the performance of HEFSPM when compared to CHSCDP, HEED and LEACH-C analyzed in terms of total energy consumption and packet drop rate. HEFSPM involves less energy and packet drop rate as it elects a reliable and optimal CH by considering each sensors’ packet forwarding rate and available energy.

Thus HEFSPM reduces the total energy consumption to a maximum extent of 18% to 21%, 23% to 25% and 27% to 33% in contrast to CHSCDP, HEED and LEACH-C respectively. HEFSPM also minimizes the packet drop to a considerable level of 16% to 18%, 20% to 23% and 25% to 31% when compared to CHSCDP, HEED and LEACH-C respectively. It is also inferred that PEFCHSS is capable of reducing the total energy consumption and packet drop rate on an average by 25% and 27% respectively.

In addition, from Fig. 11, it is evident that HEFSPM involves of 9% to 12%, 14% to 17% and 18% to 21% lesser average delay when compared to CHSCDP, HEED and LEACH-C respectively. It is also inferred that HEFSPM reduces the average delay on an average by 18%.

d) Experiment 4-Performance Evaluation of HEFSPM by Varying Transmission Range

In Experiment 4, the performance of HEFSPM is analyzed based on packet delivery ratio, throughput, energy consumptions, packet drop rate and average delay by varying the transmission range of sensors. Figures 12 and 13 highlight the superior performance of HEFSPM with respect to the packet delivery ratio and throughput in contrast to the existing CH selection approaches like CHSCDP, HEED and LEACH-C. It is inferred from the comparative analysis that HEFSPM yields better packet delivery ratio and throughput as it uses integrates energy and trust related parameter elucidated through probe packets.

HEFSPM yields 12% to 15%, 17% to 19% and 22% to 24% better packet delivery ratio in contrast to CHSCDP, HEED and LEACH-C respectively. Similarly, HEFSPM offers an increased throughput of 14% to 18%, 20% to 24% and 26% to 29% when compared to CHSCDP, HEED and LEACH-C respectively.

Thus HEFSPM on an average increases the packet delivery rate and throughput to a maximum extent of 17% and 25% respectively.

Likewise, Figs. 14 and 15 present the performance of HEFSPM in comparison with CHSCDP, HEED and LEACH-C analyzed in terms of total energy consumption and packet drop rate. HEFSPM decreases the total energy consumed and the packet drop rate as it elects a reliable and optimal CH by considering unequal balancing clustering scheme. Thus, HEFSPM reduces the total energy consumption to a maximum extent of 13% to 16%, 18% to 21% and 23% to 26% in contrast to CHSCDP, HEED and LEACH-C respectively. It also reduces the packet drop rate to a considerable level of 14% to 16%, 18% to 21% and 23% to 26% when compared to CHSCDP, HEED and LEACH-C respectively.

It is also inferred that HEFSPM is capable of reducing the total energy consumption and packet drop rate on an average by 22% and 15% respectively.

Finally, Fig. 16 shows the performance of HEFSPM based on average delay. HEFSPM involves 13% to 15%, 17% to 19% and 22% to 25% lesser average delay in contrast to CHSCDP, HEED and LEACH-C.

It is also inferred that HEFSPM is efficient in reducing the average delay on an average by 23%.

Finally, the percentage improvement of HEFSPM is compared with the predominant CH election mechanisms like CHSCDP, HEED and LEACH-C and shown in Table 2.

5 Conclusions

In this paper, Hyper-geometric Energy Factor based Semi-Markov Prediction Mechanism has been proposed for effective CH election in order to improve the lifetime of network. Simulation results of HEFSPM show that the average delay is 9% to 12%, 14% to 17%, and 18% to 21% lesser than CHSCDP, HEED and LEACH-C respectively. HEFSPM reduces the total energy consumption to a maximum extent of 13% to 16%, 18% to 21% and 23% to 26% in contrast to CHSCDP, HEED and LEACH-C respectively. HEFSPM is also effective in reducing the total energy consumption and packet drop rate on an average by 22% and 15% respectively.

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