The objective function in (8) deals with the network lifetime T, maximization. Eq.

(9) describes T as the addition of rounds through which the normal and parent nodes execute their operations before their energies Ei and Ep are depleted. Eq. (10) computes the received energy of the parent node. Where is data aggregation factor, N is the aggregate number of nodes, l is the packet size, i represents normal node, p denotes parent node. If the per bit processing, transmission energy and sensing 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 gives full info about the per round energy depletion 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 as time passes 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 management when data is sent from i to p and from p to s with their physical link capacities; Cip and Cps, respectively. When these two constraints are violated this leads to rise in congestion which causes rise delay and eventually lead to high packets dropped rate. Additional energy is consumed when retransmission is done which result in decreased network lifetime. Constraint in Eq.

(8.7 and 8.8) means that the routing protocol has to be capable enough to minimize the communication distance dip and dps to its barest minimum value dmin