## 3 System Model
### Intra-Cluster Communication Session
The network is simulated for 100 immobile sensor nodes randomly distributed over a 2-dimensional geographical network area of 500 m \(\times\) 500 m. Each node has two properties, namely their location coordinates and the energy level used to determine their cluster membership. The nodes with the highest energy level are determined and then clusters are formed using the Voronoi algorithm. The inter-arrival of packets on each node in the network is exponentially distributed, following a Poisson process and independent per sensor node. The simulation results are obtained from an event driven custom built Visual C\(++\) simulator. The simulation parameters are shown in Table 2 similar to the parameters used in [10]. Some parameters are varied in the simulations to depict different scenarios as indicated on the results. The performance of the proposed EEMACCSN protocol is first compared to the BMA-RR [10], a MAC protocol for cluster based sensor networks. Figure 9 presents the results of energy consumption per node during intra-cluster communication round for variable arrival rates. The proposed MAC framework intra-cluster communication is compared with BMA-RR [10] energy consumption. The intra-cluster communication involves the communication of the normal cluster member nodes with their cluster head node, within a cluster. The energy consumption in the network increases with the increase in the arrival rate, this is due to the fact that at high arrival rates the network spends most of its time in the transmitting the packets which contributes to the high energy consumption. It is also observed that the energy consumption is high when the number of sessions is increased as more communication slots are assigned to nodes in a round. The energy consumption at arrival rates \(\lambda>0.04\) also reach a steady point due to the fact that the slots in each session are fixed, and only maximum available slots can be allocated just as in [10]. From the results we can deduce that EEMACCSN protocol improves the network energy consumption. This is due to the following; firstly the adaptive energy efficient cross-layer schedule for the medium access utilized by EEMACCSN. Secondly idle time is reduced during the sensor nodes contention period as only nodes that have data contend in EEMACCSN, unlike BMA-RR where all nodes are active during the contention period. Lastly the clustering algorithm of EEMACCSN allows nodes to defer transmission of announcements if a message from a higher energy node is heard leading to energy saving on such nodes. Figure 10 presents the performance of the proposed EEMACCSN protocol in direct and cooperative communication inter-cluster communication and the modified BMA-RR with direct inter-cluster communication. The results are for the complete protocol communication including communication within a cluster and between clusters and the base station. As observed, the energy consumption in the network increases with an increase in the arrival rate. The lowest energy consumer is the cooperative EEMACCSN, then direct EEMACCSN and lastly the modified BMA-RR for direct communication. EEMACCSN protocol improves the network energy consumption. This is due to the improved reliability by cooperative communication which reduces the probability of error occurrence in transmission reducing the need for packet retransmissions. The reduced number of retransmission means node spends little time in the active state leading to energy conservation. The analytical models are closely verified by the results as both the analytical and the simulation results are in agreement.