The objective function in (8) deals with the network lifetime T, maximization. Eq. (9) defines T as the summation of rounds during which the normal and parent nodes perform their operations before their energies Ei and Ep are depleted. Eq. (10) calculates the received energy of the parent node. Where  is data aggregation factor, N is the total number of nodes, l is the size of the packet, i represents normal node, p denotes parent node. If the per bit sensing, processing and transmission energy of normal nodes is represented as  respectively and if the per bit transmission, dissipation and reception energy of parent node is represented as  respectively. Then Eq.13 provides details about the per round energy consumption cost of the network. In constraint (8.1 and 8.2), the initial energy E0 should always be greater than the current energy Ei and Ep because in every passage of time the current energies decreases. A node ceases to function when Ei and Ep <=ETX. Constraints in Eq.(8.3) considers sensing, processing and transmission of data by normal node and ensures that these event respect their initial energy level (q =). It is important to point out that there is no energy cost of   and  in normal node. They are only present at the parent node leading to minimizing and balancing of the energy consumption. Eq. (8.4) on the other hand does not consider  and  which are only present in normal nodes. This further minimizes and balances the energy consumption. Constraints in Eq. (8.5 and 8.6) ensure flow conservation when data is routed from i to p and from p to s with their physical link capacities; Cip and Cps, respectively. Violation of these two constraints leads to increased congestion which causes increased delay and eventually to packets being dropped. In order to retransmit the dropped packets, additional energy is consumed which result in decreased network lifetime. Constraint in Eq. (8.7 and 8.8) means that the routing protocol should be capable minimize the communication distance dip and dps to its minimum possible value dmin 


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