## 4 WirelessHART Scheduling Schemes
### Non-WirelessHART Scheduling Algorithms
The hypernodes consist of a set of devices that connect directly among each other, thus forming a complete graph. The logical organization of a set of hypernodes forms a hypergraph. Finally, in terms of scheduling, the paper proposes the division of the scheduling into two parts. The first one is the dedicated scheduling, which decides the quantity of slots that should be allocated to each hypernode in order to fit the periodic packet transmissions between the devices and the respective destination. The second scheduling scheme, called the \"shared slot scheme\", allows the hypernodes to use remaining time slots from successfully delivered transmissions in order to enhance the flexibility and reliability of the communications. It is worth noting that the proposed scheme supports both single-path and the any path routing introduced in [97]. Although the work presented in [98] is not a scheduling algorithm, it deals with the flow priority assignment issue in WirelessHART networks. This issue consists of assigning priorities for real-time flows, so that those flows can meet their deadlines, and also works in alignment with schedulability tests, so that the networks can support effective network capacity planning and efficient admission control of devices and topology adaptations. As the optimal priority assignment is the NP-hard problem, the paper first proposes an optimal priority-assigning algorithm based on local search for any given worst-case delay analysis. However, for the sake of efficiency, the paper proposes a heuristic search algorithm for priority assignment. The paper in [99] addresses the problem of single-hop networks with heterogeneous traffic with packet delay constraints. The objective of the paper is to provide optimal time slot allocation and to schedule the packet transmission. The author divides the solution for this problem into two parts. The first part is called the \"subperiod slot allocation problem\", which consists of defining how many slots each device will have available for transmission/retransmission based on the success probability of each link. This part of the problem is NP-hard and was modeled as a nonlinear integer programming problem. Thus, the authors propose converting the problem into a linear integer programming problem and then present a polynomial time algorithm to compute the optimal solution for it. The second part of the problem is a matter of allocating which slots are allocated to each device in order to deal with the delay restriction defined by the publish rate of each device and how those transmissions relate to other transmissions from different devices. This is accomplished by allocating the number of slots defined for each device in a time subperiod defined by the report period for that device and then combining those subperiods into a hyperperiod. This hyperperiod has the duration of the least common multiple of the report rates present in the network in order to accommodate multiple subperiods without fractionating. However, the technique is not suitable for WirelessHART, because it focuses on single-hop wireless networks and, thus, differs from the multi-hop nature of the WirelessHART network. Although the system model proposed is compliant with the WirelessHART specification, it could also be applied in the WIA-PA and ISA100.11a single-hop cluster structures.