## 4 WirelessHART Scheduling Schemes
### Non-WirelessHART Scheduling Algorithms  
As we did in Section 3.4 for the routing algorithms, in this subsection, we will present some of the newest scheduling algorithms for WSN in order to provide some ideas for developers that intend to build new scheduling algorithms for the WirelessHART technology. The work in [85] presents the D-MSR (distributed network management scheme for real-time applications), a network management system that provides real-time, reliable communications and fulfills the throughput requirements of industrial control applications. For scheduling purposes, the system adopts the distributed scheduling algorithms for real-time applications (D-SAR; see [47]). It is worth noting that the D-SAR use concepts based on the ATMnetworks [86]. D-SAR uses a set of messages that traverses from the source to the destination based on the routes from the routing setup. Each device includes parameters, such as a list of suggested common unused timeslot-channel cells for further communication with the next hop, a destination address, traffic ID and the timeslot-channel cell selected on the previous hop. With this information, the devices organize their own schedule matrix and pass the message forward to the destination. It is also important to point out that D-MSR uses the virtual circuit technique in order to provide real-time communication. The work in [87] proposes a service-oriented and Markov random field (MRF)-based scheduling algorithm for WSN, called MRF-based multi-service node scheduling (MMNS). It is worth noting that the proposed algorithm is a heuristic solution. Its objective is to manage devices that are equipped with multiple sensors (for example, sound, motion and temperature), thus providing various sensing services from the same node. The proposal intends to arrange resource sharing among multiple services in an energy-efficient way. The MMNS algorithm is based on two other algorithms developed in [87]: the multi-service data denoising (MDD) algorithm and the representative node selection and service determination (RSD). The first one has the objective of minimizing the noise level of the sensed data. The later intends to detect representative nodes of the network and the services that they provide. The work in [88] differs from the other papers in this area since it presents two scheduling methods for shared timeslots in ISA100.11a networks. The first one, traffic-aware message scheduling (TAMS), uses traffic information to define groups of devices and decides in which cycles the groups will attempt to transmit in order to use the bandwidth wisely by avoiding collisions in every cycle. The second algorithm is the contention window size adjustment (CWSA) algorithm, which also uses traffic information to adjust the size of the contention window (fixed at 192 microseconds by the ISA100.11a specification, regardless of the traffic) when the probability of a collision in a timeslot exceeds a threshold. The algorithm developed by [76] has the objective of reducing the jitter provoked mainly by multiple arrivals of each packet through different paths and by the drift of the starting/ending slot position in a superframe. In order to do this, the algorithm classifies the transmissions into tasks that group the transmissions so as to take the data from the source to the destination. After the tasks are defined so as to avoid conflicts, the schedulability is guaranteed by giving priority to tasks based on the information about their deadline and the number of hops. The work in [75] describes a method that finds conflict-free TDMA schedules and minimizes scheduling delay in multi-hop TDMA wireless networks. The solution is divided into two parts. The first one consists of finding a transmission order that satisfies the precedence requirements for the communication. This solution uses integer programing in order to find the transmission order that minimizes the maximum scheduling delay.