## 2 Background
### Related Work
In that work, the authors defined a run-time approach to re-order the involved clusters in specific message streams, considering their priorities, in order to minimise traffic latency. Also, this approach provides a mechanism to increase the size of superframe durations (bandwidth) of the involved clusters, using the global inactive period or the active periods of non-involved clusters. [PERSON] and [PERSON] [PERSON] and [PERSON] (2017) proposed the Low-latency Two-way Beacon Scheduling (LTBS) approach for cluster-tree networks. In this approach, the authors modify the superframe structure to allow the broadcast of two beacons, defining one active part for the upstream traffic and another for downstream traffic. The authors also defined a set of algorithms to assign nodes to upstream and downstream slots in order to reduce the network latency, avoiding interferences among them. In turn, [PERSON] et al. [PERSON] et al. (2017) provided a Superframe Duration Adjustment Scheme (SUDAS) based on Markov chains, which analyses both the contention and contention-free periods, allocating GTS slots for devices based on the packet sizes. The underlying idea of SUDAS is to adequately allocate GTS for a set of requested devices, improving the bandwidth of the contention-free period. [PERSON] et al. [PERSON] et al. (2017) proposed an algorithm for the adjustment of the superframe duration and the CSMA Backoff Exponent (BE) parameter according to the network traffic, in order to decrease energy consumption and to improve the network throughput. However, these schemes just consider star topologies. [PERSON] et al. [PERSON] et al. (2017) provided algorithms to define the superframe durations for all clusters in a cluster-tree network, following a time-division approach. The main idea is to maximise the use of the beacon interval and to avoid any inactive period. For this, the authors proposed different allocating schemes, such as: the same SO for all clusters, highest SO for the PAN coordinator and a scheme that allocates a SO for the coordinator based on the traffic generated in its cluster. However, the authors just present simple schemes and do not consider important protocol constraints of cluster-tree networks, for instance, buffer constraints and timing constraints of messages. Finally, [PERSON] et al. [PERSON] et al. (2017) proposed the Time Division Beacon Frame Scheduling (TDBS) approach, which defines a Superframe Duration Scheduling (SDS) algorithm for cluster-tree networks, considering a set of clusters with different superframe durations and beacon intervals. In this approach, clusters are organised within a defined major cycle, based on the Least Common Multiple (LCM) of the beacon periodicities for all clusters. The major cycle is divided in minor cycles, which are used to sequentially schedule all clusters. TDBS defines the start time for all clusters in a collision-free scheduling scheme. Also, it provides a set of rules to adequately assign duty-cycles for each cluster-head, based on the following constraints: (1) equal duty-cycles for leaf cluster-heads; (2) duty-cycles of parent cluster-heads must be greater or equal to the sum of duty-cycles of their child cluster-heads; and (3) the sum of duty-cycles must be smaller or equal to one. This scheme is adequate to schedule cluster-tree networks, where clusters have a similar number of child nodes and similar traffic load. Its main advantage is that it allows setting different beacon periodicities for the different sets of clusters. Within this context, we can easily observe the shortage of mechanisms to properly allocate active communication periods within the CAP, in order to improve the throughput in cluster-tree networks avoiding common problems that can lead to undesirable network states (e.g., buffer overflows). This paper aims to provide a set of guidelines that enable network designers to efficiently define some of the most relevant operational parameters and message flow configurations for wide-scale cluster-tree networks.