## 9 Conclusions  
The IEEE 802.15.4/ZigBee cluster-tree topology is one of the most suitable topologies to build wide-scale wireless sensor networks. However, these standards do not define mechanisms to adequately allocate communication resources to the cluster-heads (active communication periods and buffer sizes). Therefore, some well-known data communication problems may arise, such as: network congestion near the PAN coordinator, discarded messages due to buffer overflows and high end-to-end communication delays. In this paper, we present a set of boundary equations for IEEE 802.15.4/ZigBee cluster-tree networks (protocol, buffer and timing constraints), which provide a set of guidelines for the proper allocation of such communication resources. Within this context, we propose the use of two different proportional _Superframe Duration Allocation_ (SDA) schemes: _Load-SDA_ and _Nodes-SDA_ schemes. The main target of these allocation schemes is to define adequate active communication periods and buffer sizes for the cluster-heads of the cluster-tree network. The Load-SDA scheme considers the message load imposed by descendant nodes to allocate superframe durations for cluster-heads, whereas the Nodes-SDA scheme considers only the number of descendant nodes of the cluster-heads.  
Simulation results show that the use of adequate superframe duration allocations and buffer sizes can improve several communication metrics, such as the reduction of both the number of discarded messages due to buffer overflows and the end-to-end message communication delays. Thus, the proposed schemes can be used by network designers to build efficient cluster-tree networks in what concerns the definition of network parameters and the configuration of message streams.  
As future work, we intend to add new mechanisms for the allocation schemes, such as: (a) configuration of CSMA-CA parameters to improve the message throughput; and (b) aggregation or information fusion mechanisms in order to decrease the number of messages to be transferred in congested areas of the network. Also, we intend to implement the proposed superframe allocation schemes using a real hardware testbed and to design an approach to dynamic environments (with mobile nodes).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Load-SDA Scheme**} & \multicolumn{3}{c}{**Nodes-SDA Scheme**} \\ \hline
**Depths** & **High Load Branch** & **Low Load Branch** & **High Load Branch** & **Low Load Branch** \\ \hline Depth 1 & 6 & 4 & 6 & 6 \\ Depth 2 & 4 & 2 & 4 & 4 \\ Depth 3 & 3 & 1 & 3 & 3 \\ Depth 4 & 3 & 1 & 3 & 2 \\ Depth 5 & 3 & 1 & 3 & 2 \\ Depth 6 & 2 & 1 & 2 & 2 \\ Depth 7 & 2 & 1 & 2 & 1 \\ Depth 8 & 1 & 1 & 1 & 1 \\ Depth 9 & 1 & - & 1 & - \\ Depth 10 & 1 & - & 1 &  
**Acknowledgments:** The authors would like to acknowledge the support from CNPq-Brazil (projects 400508/2014-1; 445700/2014-9 and grant GDE-201373/2012-2) and FCT-Portugal (project UID/EMS/50022/2013) funding agencies.  
**Author Contributions:** [PERSON] and [PERSON] proposed the Superframe Duration Allocation Schemes; [PERSON] designed the simulation models; [PERSON], [PERSON] and [PERSON] proposed the assessment framework; [PERSON] performed the simulation assessments and analysed the resulting data; All the authors contributed to the writing of this document; [PERSON] and [PERSON] revised its final version.  
**Conflicts of Interest:** The authors declare no conflict of interest.