Wireless sensor and actuator networks (WSANs) are wireless networks in which two types of devices can be found, namely, sensors and actuators .
The sensor nodes are normally responsible for sensing the environment in which the nodes are deployed, whereas the actuator nodes act as the sink gathering all the data from the sensor nodes. WSANs can be seen as collaborative systems since the nodes exchange data in an ad hoc manner to achieve a common goal . Moreover, the actuators can influence on the behavior of sensors, so the dataflow in those networks is bidirectional. Several limitations influence the performance of WSANs such as limited transmission range of nodes, energy consumption, bandwidth, size, and cost and thus affect their deployment . These limitations coupled with the highly dense and mobile nature of the nodes pose a great challenge to the design and management of WSANs . Due to the limited coverage area of nodes in WSANs communications are likely to be multi-hop in such networks. There could be three types of data communications in WSANs in terms of the direction of the data flow : First, Single-sink single-hop communications, where an actuator communicates with a sensor or vice versa using only one hop; second, single-sink multi-hop communications, where a high density of nodes is assumed so that the sensors can communicate with the sink through multiple hops, and finally, multi-sink multi-hop communications, this is a general scenario where multiple sinks are included. Whenever a source node wants to establish a communication path with a destination node, it must start a discovery route procedure. This discovery procedure depends on the routing protocol used. According to the management of the routing tables, the routing protocols are normally categorized as reactive routing protocols, proactive routing protocols, and hybrid routing protocols . The reactive routing protocols are more suitable for high mobile and high-density scenarios due to the required low maintenance for their routing table. Their maintenance requires smaller amount of dataflow among nodes than in proactive routing protocols. As a consequence, reactive protocols incur lower overheads [6–8]. Another classification of routing protocols can be found in , where the routing protocols for wireless sensors networks are categorized as data-centric, hierarchical, or location based . Data-centric routing protocols are focused on the interest of the measured information so they work on demand in a reactive way. In hierarchical routing protocols, the nodes are divided into clusters in order to save energy and reduce the overheads. The use of clusters is common in WSANs since the communications are centralized at the actuators which make decisions based on the collected information. The location-based routing protocols get the positioning information either by Global Positioning System (GPS) or by Received Signal Strength (RSS) . The positioning information is usually used to reduce the overheads by forwarding the data packets directly to the destination nodes, decreasing the number of useless communications . Furthermore, positioning information can also be used to improve the reliability of route selection using GPS , or RSS .
The routing protocols are normally evaluated in terms of throughput, delay, overhead, delivery ratio, and path duration among others [7, 14, 15]. Although some terms are related to each other, i.e., a high overhead in the network worsens the throughput, the primary objective of designing routing protocols is to improve one of the above-mentioned features . This article is focused on path duration. The path duration in wireless networks gets its importance due to the following reasons:
Whenever an established route is broken a repair procedure must be carried out in order to re-establish the broken route. Although the recovery procedure depends on the routing protocol used, it normally requires an extra dataflow and consequently extra energy consumption.
Some applications may require minimum path duration in order to exchange the whole information so the quality of service can be guaranteed .
There are some solutions to solve the problem of the time consumed to repair a broken path [14, 17]. In multipath routing techniques , the routing protocols store more than one route per destination so that alternative routes can be used whenever a breakage of a route occurs. In , a bypass mechanism was presented to act against individual broken links along the whole communication path. However, these mentioned solutions do not guarantee path duration since they do not prevent links from being broken in the first place. The breakage of a route can be caused by multiple factors. The main factors which affect the path duration are
Mobility factors: The relative speed between two nodes, the nodes' directions, and the relative angle between two nodes determine how the overlapping area of the nodes' transmission areas varies and, as a consequence, they have a significant impact on the duration of the links. Additionally, the mobility models also play an important role in path duration since they determine the nodes' movements in the deployed scenario [17, 18].
Positioning factor: The point at which two nodes start communicating with each other influences the link duration and as a result, affects the path duration .
Power factors: The transmission power determines the coverage area of nodes. Notice that the power consumption is a limiting factor in WSANs, and consequently the transmission power is also limited. Besides, if a node with low battery takes part in a communication path, it will put at risk the duration of the path .
Link quality factors: If a noisy environment is considered and a multipath propagation model is used, the path duration can be determined by link quality metrics such as Signal-Noise-Ratio  or Bit Error Rate . In high-density scenarios, the interferences among nodes can also affect the performance of the network . The problems in wireless networks related to interference are pointed out and solved in  by using a cross-layer design of AODV which selects the best path in terms of signal quality.
Length of the path: The number of hops also affects the path lifetime. It has been shown that the path duration decreased exponentially with the number of hops .
The power transmission of devices is usually fixed by designing factors so the network designer does not have any control over it. It depends on the wireless technology used . On other hand, the link quality factors depend on the environment and it can be unpredictable or changeable. As a consequence, making use of mobility and positioning factors is the easiest way to estimate path duration. In this article, a novel approach for improving path selection based on mobility and positioning factors is proposed. It is aimed at reactive routing protocols. A decision tree has been included into a reactive routing like Ad Hoc On-Demand Distance Vector (AODV)  in order to accomplish the proposed approach. Additionally, an improved discovery procedure of routes is proposed. It is based on mobility and the number of hops forming the communication routes. The objectives of this discovery procedure are (1) to help to increment the path duration and (2) to reduce the number of control packets used during the discovery procedure.
The remainder of this article is presented as follows: Section 2 details the related study while the definitions of path and link duration in terms of mobility parameters are provided in Section 3. A description of the proposed decision tree is presented in Section 4 and its implementation over AODV routing protocol in Section 5. The optimized discovery procedure is described in detail in Section 6. The experimentation and performance evaluation based on the simulation results of the proposed approaches and their comparisons to AODV are presented in Section 7. Finally, the conclusions of this article can be found in Section 8.