# Opportunistic Multipath Routing in Long-Hop Wireless Sensor Networks
## 1 Introduction  
Most existing routing protocols in Wireless Sensor Networks (WSNs) are designed based on the single-path routing protocol. The single-path routing protocols could discovery the route with minimal computational complexity, resource utilization, and achievable network throughput. However, due to the unreliability of wireless links, single-path routing protocols cannot be considered effective techniques to meet the requirement like packet delivery ratio. Also, when the path fails to transmit a packet, extra overhead and delay occur to recover the path to deliver the packet continuously. Multipath routing protocols have the opposite advantages and disadvantages of single-path routing [1]. Both single-path and multipath protocols have their advantages and disadvantages; many studies have been proposed to satisfy the packet delivery ratio that is one of the important metric in WSNs. Multipath routing protocols are exploited to various objectives such as load balancing [2; 3] and quality of service (QoS) supporting [4; 5]. These multipath focus on prolonging the network life time and qualified services. However, if a packet transmission failure occurs, it is not much different from a single-path because a packet is transmitted over only one path among the multiple paths. Thus, multipath routing protocols [6; 7; 8; 9; 10] could achieve the required packet delivery ratio by creating multiple paths to the destination and simultaneously transmitting the packet on the paths. In this paper, we focus on the last design issue to improve packet delivery ratio. In addition to multipath routing, the opportunistic routing protocols [11; 12; 13] are exploited to improve link reliability. As the opportunistic routing is a receiver-based transmission, an intermediate node not only selects oneneighbor node to transmit data but also provides the transmission opportunity to all neighbor nodes. It could maximize a link reliability. The maximized link reliability could have a positive effect on the packet delivery ratio. However, the packet delivery ratio would be degraded in a long-hop sensor network since packet or bit errors accumulate and the packet delivery ratio is the product of the link success ratio (assuming no retransmission) [14; 15]. Thus, multipath routing requires larger numbers of paths to prevent the degradation of the packet delivery ratio of each path where the long-hop path is assumed in WSNs. That is, the existing multipath routing could satisfy the required packet delivery ratio by increasing the number of paths. However, the approach should accompany excessive energy consumption. In addition, sufficient numbers of paths are not feasible when the network is narrow. On the other hand, opportunistic routing cannot guarantee the required packet delivery ratio and requires more energy than single path routing because an intermediate node broadcasts the packet to all of its neighbors. Thus, opportunistic routing, in particular, suffers from packet delivery ratio degradation under long-hop WSNs. Based on the deficiency of high-energy consumption in the abovementioned routing protocols, a sleep scheduling approach based on learning automata [16] has been proposed to solve the partial coverage problem, in which monitoring only a limited percentage of it is enough instead of monitoring the full coverage of WSNs. In other words, the proposed approach finds a minimal set of nodes to cover the demand portion based on learning automata with preservation of the connectivity among the nodes. As the number of participating nodes for monitoring is reduced, the energy consumption is reduced and the network lifetime is prolonged. However, since the multipath routing and opportunistic routing exploit a large number of nodes to improve packet delivery ratio, the decrease of participating nodes might degrade the performance of them. To improve reliability, reliable routing based on a learning algorithms [17; 18] have been recently proposed.