The aim of the objective function in Eq.16 is to minimize the EED whenever a source node s attempt to send a data to the destination node d. Eq. 17 calculates the over all delay from s to d via p (parent node). is the nodal delay at s and is the delay from p to d. For high-emergency data, where the communication is direct therefore EEDsp = ,we have low EED. However, in the first part of Eq.17, high delay is experienced and our aim is to minimize it.
Eq. 18 defines the nodal delay as summation of transmission delay ,queuing delay, processing delay , and channel capture delay . In Eq.19, is defined as the summation of parent node transmission delay ,aggregation delay, reception delay . Constraint 16.
1 provides the lower and upper bounds for N (network size in terms of the number of nodes). If N is very large then more nodes will compete for channel access. This leads to increased and ultimately increased EED. In order to cope with this issue, the proposed protocol considers proper number of nodes (8). Constraint 16.2 declares that the number of packets sent by the transmitter is should not surpass the handling capacity of the receiver . Violation of the constraints means congestion at the receiver end, causing the queue Dqueue size to grow.
Similarly, constraint in Eq.16.3 and 16.4 means that the packet arrival rate ?arr should not surpass the packet departure rate ?dep at a node i and node p. Violation of the equations lead to increased Dqueue . If the packets are dropped due to violation of equations 16.
1, 16.2, 16.3 or 16.4 then these packets must be retransmitted because every data is critical in WBSNs. As a result, excess energy is consumed (i.e., network lifetime decreases) and EED is increased. As a solution for such situation, constraint in equation 16.
5 emphasizes on the minimization of packet retransmissions . Lastly, constraint in Eq. 16.6 bounds the bit level errors at any node ni to an acceptable level nth, else more erroneous packets leads to increased Dpr