# An Efficient Hybrid Data Gathering Scheme in Wireless Sensor Networks

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4 An Efficient Hybrid Data Gathering Scheme in Wireless Sensor Networks 101 gathering in each cluster is lower bounded by log 2 N max, where N max = max of (N 1, N 2 N M ). So overall delay will be, ceil( log 2 N max ) + ceil( log 2 M ) + 1 ceil( log 2 (N max M ) ) = ceil( log 2 N ) + k (3) k is a constant which decreases as the distribution of the sensor nodes is more uniform, and becomes zero when N 1 = N 2 =.. = N M = N max.. Here ceil(x) is the ceiling of x, denoting the least integer, greater than or equal to x. So, we see the delay to have a complexity be O(logN). ii) Message Complexity: In the HDS scheme, in each round, there is a single cluster and group formation phase and a single leader and super leader election phase. Assuming, each node has a packet to send in every round, total number of messages passed is N. Thus message passing complexity is linear, i.e. O(N). iii) Energy Delay product: As we can, reasonably say that the radio transmission and reception energy is greater than CPU or processing energy by several orders of magnitude, we take message passing as a rough measure of energy consumption in the nodes. Thus energy x delay product have a complexity of O(N logn). iv) Mean Delay: We define the mean delay as the average of the delay to the BS from each of the nodes. The network has a total of N 1 +N N M (=N) nodes. In the first slot they are divided in (N 1 /2 + N 2 /2 + + N M /2) groups. Now each of the (N 1 /2 + N 2 /2 + + N M /2) transmitter nodes in the first slot ( 1 from each group) will have a delay of (log(mn i ) + 1) time slots to the base station, where N i denotes the nodes in the i th cluster. Similarly calculating for the t th slot each of the (N 1 /2 t + N 2 /2 t + + N M /2 t ) transmitter nodes have a delay of (log(mn i ) t + 1) time slots to the base station. So, for calculating the mean delay, we go for the weighted mean, MD = log N log M i { ( Nj[log Ni i+ 2]/ 2 )} i= 1 j= 1 N (4) 5 Simulation Results Our proposed scheme is validated by extensive computer simulations. A network consisting of 100 homogeneous sensor nodes deployed randomly in a field of size 50m x 50m is considered for the simulation model. The BS is fixed and located x=50m and y=150m. The network is geographically divided into 5 equal sized clusters. HDS is compared with the classical data gathering schemes in literature like the PEGASIS, LBERRA, SHORT and BINARY. It not only shows a very good network lifetime as compared to these schemes but also has a better energy-delay product. The simulation results are as follows.

5 102 A. Chakraborty, S.K. Mitra, and M.K. Naskar Fig. 1. Comparison of Network Lifetime and Energy-Delay Product vs Number of Nodes From Figure 1, we see that as the number of nodes increases the network lifetime falls. But among others HDS shows the best performance. So it is energy efficient. The better performance in the Energy-delay product signifies better throughput on top of energy efficiency. The detailed results about the simulation are given in Table 1. Fig. 2. Fraction of Packets successfully reaching the base station with retransmission Attempts the upper dark portion of the bar shows the range of the fraction, the tips indicating maximum and minimum fractions (simulated in TOSSIM) The packet reception ratio is calculated as the ratio of the packets received successfully to the total packets transmitted. In HDS we calculated the fraction of packets reaching the BS successfully, by varying the number of retransmission attempts. As the number of retransmission attempts increase the packet reception ratio also increases. The Figure 2 depicts the packet loss in HDS. This simulation introduces the interference model in our simulation making it more realistic.

6 An Efficient Hybrid Data Gathering Scheme in Wireless Sensor Networks Performance Comparison Table 1. Comparison of the various schemes FND: First Node Dies, HND: Half Nodes Die, LND: Last Node Dies, Delay calculated in average slots per round Performance Metrics PEGASIS BINARY SHORT LBEERA HDS Network Lifetime (rounds) Energy Consumption (mj) FND HND LND Delay Mean Conclusions Our proposed algorithm overcomes the losses incurred from all other data gathering schemes proposed in literature. HDS makes a good harmony among network lifetime, energy costs and network throughput. It not only reduces the network lifetime but also guarantees the best energy-delay product. The coding of HDS in nesc deserves a special mention as it proves the scheme to be feasible on real hardware platforms. Also the radio interference model used for simulation purposes helped us to study the problem from the perspective of a more realistic physical layer. References 1. Lindsey, S., Raghavendra, C.S.: PEGASIS: Power Efficient Gathering in Sensor Information Systems. In: Proceedings of IEEE ICC 2001, pp (2001) 2. Yang, Y., Wu, H.H., Chen, H.H.: SHORT: Shortest Hop Routing Tree for Wireless Sensor Networks. In: IEEE ICC 2006 proceedings (2006) 3. Levis, P.: TinyOS Programming (2006) 4. Lindsey, S., Raghavendra, C.S., Sivalingam, K.: Data Gathering in Sensor Networks using energy*delay metric. In: Proceedings of the 15th International Parallel and Distributed Processing Symposium, pp (2001) 5. Yu1, Y., Wei, G.: Energy Aware Routing Algorithm Based on Layered Chain in Wireless Sensor Network, /07/\$ IEEE (2007) 6. Heinzelman, W., Chandrakasan, A., Balakrishnan, H.: Energy- Efficient Communication Protocol for Wireless Microsensor Networks. In: IEEE Proceedings of the Hawaii International Conference on System Sciences (2000)

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