## 2 Related Work  
The main characteristics of the network considered in this work are random topology, multi-hop relay, and single gateway. Regarding the second one, the work in [5] proposes multi hop transmission protocol in which the packets are sent from one hop to another hop and finally to the sink. The packets from source node to sink are selected via cluster head using fuzzy logic. This approach uses three input parameters, current energy, trust factor, and distance from base station are calculated to the selected cluster. If the cluster head has a greater number of cluster heads between sink and itself, it employs the fuzzy logic to choose the preferred cluster head to reach the data. The neighbor node, nearer to sink can be elected by the best forwarding node. The best forwarding node is selected based on high trust factor and distance to sink node. The protocol results in increased lifetime and reduces overhead in the network. A multi-hop network is also considered in [6]. These authors propose a location-free single copy protocol (RECRP); no extra hardware is needed to determine the location, parameters like received signal strength indicator (RSSI) and Doppler scale shift measurement (relative speed) are used for estimation of distance. Transmission power and channel frequency parameters are dynamically controlled by optimal min-max technique. It uses two-hop forwarding capabilities to achieve energy efficiency. Another benefit of the protocol is that it can prevent communication voids. The protocol results in decreased energy per node per message and end-to-end delay compared to other techniques, while keeping an increased packet delivery ratio. The energy efficiency issue has been addressed in SOSRP [7], where a decentralized self-organizable scalable routing protocol is proposed, where a node failure does not affect the communication in the network. It is a hop-by-hop-based communication protocol where messages are forwarded to the gateway by the relay nodes. The scenario considers nodes deployed randomly at different depths. Initialization of the network is done by means of HELLO packets; the gateway broadcasts this packet among nodes within its transmission range. After the packet is received, a node increments a counter, stores the hop count and re-broadcasts the packet. A temporary failure is introduced to further test the system and identify fault tolerance. This scheme is based on 3D distance between source and destination and hop count. The work in [8] also addresses the energy efficiency issue. The routing protocol EECOR (Energy Efficient Cooperative Opportunistic Routing) is proposed to forward the packets towards the sink. The source node determines the forwarding relay set based on local information of the forwarding node. To select the best relay, fuzzy logic is used considering two input parameters, i.e., energy consumption ratio and packet delivery probability. The output value is described by a figure of merit called Chance; a high value of Chance in the proposed scheme indicates that the neighbor node in the forwarding relay has the opportunity to be selected as best relay. In addition, to avoid packet collision, holding time is introduced for each forwarder to schedule packet transmission towards the sink. The protocol results in better end-to-end delay due to avoidance of packet collision and achieves lower energy consumption. However, the drawback is that parameters such as distance, transmission range, and hop count are not considered while designing the protocol. Fuzzy logic is used in this work to improve energy efficiency. Nevertheless, fuzzy logic had been previously used in [9] BHUSHAN for parent node selection and also for scheduling and tree formation. The selection of the forwarding node is made based on the minimum number of dynamic neighbors. Another common approach is clustering, also used in a work already presented [5]. In FBECS [10], the protocol is cluster based in which sensor nodes send or forward the data to their respective cluster heads.