Copyright © 2018Rakesh Kumar Sahu, Narendra S. Chaudhari. This is an open access article distributed under the Creative Commons Attribu- tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. International Journal of Engineering & Technology, 7 (2) (2018) 674-677 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET doi: 10.14419/ijet.v7i2.10740 Research paper Mathematical formulation of energy efficient routing with constraint in mobile ad hoc network Rakesh Kumar Sahu 1 *, Narendra S. Chaudhari 1, 2 1 Department of Computer Science & Engineering, Indian Institute of Technology, Indore, India 2 Department of Computer Science & Engineering, Visvesvaraya National Institute of Technology (VNIT), Nagpur (M.S.), 440010, INDIA *Corresponding author E-mail:rakeshsahubl@yahoo.co.in Abstract Energy consumption of nodes during the transmission is an important factor for the efficiency and lifetime of a mobile ad hoc network. The reduction in consumption of energy can be achieved, only when its consumption at each step is known. The purpose of this paper is to formulate the mathematical model of energy consumption of network on the basis on links and available nodes in order to formulate the energy optimization function. The probability of link failure in route and innetwork have been taken into consideration as constraints while formulating the objective function of estimated energy consumption, as the low connectivity is one of the challenges due to mobili- ty in ad hoc network. Keywords:Ad Hoc Network; Dynamic Topology; Energy Aware; Link Failure; Routing Protocol. 1. Introduction Energy efficient routing is an effective technique for reducing the energy consumption during the transmission in Mobile Ad hoc Network (MANET). In general, link failure in the network leads to unsuccessful transmission and causes retransmission of packet from one node to another. This amounts to the wastage of energy of the nodes in the path.Hence, energy efficient routing in ad hoc networks is neither complete nor efficient without the considera- tion of link assessment prior to the transmission. Transmission on healthy linked path enhances the reliability and quality of the ser- vice. It is desirable for a routing protocol to cope up with undesir- able situation like link failure and link breakdown situation. This paper estimates energy requirement for the successful transmis- sion of packet in the network. It considers possible consumption of energy of all three kinds of node in the network. 2. Literature survey In order to reduce the energy consumption in transmission, the vital role is being played by the routing mechanism employed in the network. There are several scientists and researcher contribut- ed in this area but it still demands the focus to reduce power con- sumption. In [1] author applied technique to reduce the number of transmission and decreases the energy consumption by using the network coding for head of the cluster and furthermore improve the coding opportunities while employing the queue management process. The work in paper [2], expresses the power saving proto- col based on MAC in mobile ad hoc network. The protocol is used a technique which allows the host to sleep for a given interval of time and wake up as soon as its assigned time is over in order to minimize the power consumption. The work by author [3] on en- ergy efficiency based on combination of node’s lifetime and dis- tance-based power metrics and investigates some properties of power adjusted transmissions and demonstrates the power is the function of linear equation. The transmission decision is made as per the location of neighbors and the destination nodes in the net- work and optimizes the power between two nodes. In paper [4] discussed the power requirement of nodes in the network by using the two techniques namely carrier-sense multiple-access/collision- avoidance (CSMA/CS) and request-to-send (RTS)/clear-to-send (CTS). The work proposed in paper [5], focuses to minimize the energy by utilizing the combination of two concepts that are mul- tipath routing and energy reservation mechanism. In paper [6] focuses on reducing the energy consumption while avoiding the packet loss of wireless sensor network. The paper [7] aimed the energy consumption optimization in mobile ad hoc network for ad hoc on demand multipath distance vector (AOMDV) by employ- ing the fitness function technique in routing protocol. On the basis of this fitness function it obtained the multipath which reduces the energy consumption in the transmission. The work in paper [8] discussed the cluster based scheme which improves the scalability and stability of the given network. The articulated algorithm treat- ed the cluster of nodes the bird’s flock with dynamic formation. Furthermore a mechanism based dynamic topology is proposed to reduce the congestion in the network in order to enhance the per- formance of the network. In work [9], the author proposes a rout- ing protocol, which is based on dynamic connectivity without the any intervention and maintain connectivity metric and reduces the overhead of RREQ and RREP messages in the network. The work [10] illustrates a protocol which optimizes the transmission over- head while utilizing prediction of node mobility in combination with cluster formation. The paper [11] uses the greedy algorithm for the formation of cluster of nodes. The paper is based on the theoretical analysis of decision making problem based on coopera- tive game analysis theory. The research work expressed [12] is simulate the urban scenario for the large network for the quality of services along with the scalability. The protocol uses a technique which utilizes node clustering along with the virtual backbone. The author proposed an algorithm [13] which uses the genetic