## 6 Performance Evaluation of the Proposed Topology  
Several simulation experiments were carried out to evaluate the performance of the logical topology. The proposed logical topology was used for data collection, and its performance was measured against existing data collection protocols, namely LEACH [41], PEGASIS [40], and COSEN [43]. The simulation program was written in object oriented programming language C++. One hundred sensor nodes were assumed to be randomly distributed in the target field of 100 m \(\times\) 100 m, and the BS was located at (25, 150). Cartesian coordinates were used to locate the sensor nodes. It was further assumed that each sensor starts with one Joule of initial energy. In practice it is difficult to model energy expenditure in radio wave propagation. Therefore, in order to measure the energy expenditure in the network, the same simplified radio model used in LEACH and PEGASIS was used. The value of the radio parameters of transmitter and receiver electronics that were used in the simulation are \(E_{tx-elec}=E_{Rx-elec}=E_{elec}=50\) nJ/bit. The value of transmit amplifier was assumed to be 100 pJ/bit/\(m^{2}\). It was further assumed that a computation cost of 5 nJ/bit/message would be required to fuse 2000-bit messages. The bandwidth of the channel was set to 1 Mb/s. Thus the total transmission cost for a \(k\)-bit message is given by the following equation:  
\[E_{tx}(k,d)=E_{elec}k+kd^{2}\]  
where \(d\) is the distance between sender and receiver measured in meters. In the case of receiving a message, the energy consumption equation is given by the following equation:  
\[E_{rx}(k)=E_{elec}\]  
Multiple runs of the simulation for each protocol were performed and the average value was taken. The metrics that were considered to measure the performance of each protocol were (i) overall energy expenditure in the network; (ii) lifetime of the network; (iii) time to complete a fixed number of operational rounds. The first experiment measured the total energy consumption by the system varying the number of operational rounds. We measured the total energy consumption in the system after 100, 200, 300, 400 and 500 rounds of operation. As most of the nodes were dying after 500 rounds of operations, we stopped measuring the total energy spent in the system after 500 operation rounds. The total energy spent by the system was calculated by summing up the energy spent by each individual sensor node. Figure 22 shows the results. It is notable that all the chain-based protocols outperform the cluster-based protocol LEACH. PEGASIS was found to be more energy conservative than LEACH and COSEN, however, the proposed topology outperformed PEGASIS by saving more than 10% of total energy for 500 data collection rounds. This is because of the optimal chain creation by the proposed algorithm and the efficient leader selection processes. While the proposed topology was the most efficient in total energy consumed, the main success of the proposed topology is the even distribution of energy consumption. Uneven energy consumption by the sensor nodes adversely affects the system lifetime. Figure 23 demonstrates the lifetime comparisons  
Figure 22: Total energy consumption comparison among LEACH, PEGASIS, COSEN, EEPB, ICCASM and the proposed topology. between the proposed topology and the protocols PEGASIS, COSEN, EEPB and ICCASM. The figure shows that the death of the first node in PEGASIS occurs at an early stage compared with COSEN and the proposed topology. For PEGASIS, 10% of the nodes die at around 400 operational rounds, whereas for the proposed topology, 10% of the nodes die at around 550 rounds. Although the final node expiration time is impressive for EEPB, the protocol suffers from uneven energy dissipation. The first node of the protocol EEPB dies only after 410 operational rounds. The protocol ICCASM shows almost similar lifetime patters with the protocol PEGASIS.