# End to End Delay and Energy Consumption in a Two Tier Cluster Hierarchical Wireless Sensor Networks
## 10 Conclusions and Further Work  
In this paper, the end-to-end (E2E) delay and the energy consumption of a two tier Wireless Sensor Network (WSN) has been studied. In the WSN, sensors transmit the sensed information to their cluster head (CH) by using some simple random access protocol (RAP) such as the Frame-Slotted ALOHA (FSA). In a second action, the information received by the CHs is transferred in hop by hop, ring by ring mode to the sink, by using a TDMA protocol. A Markovian model and a simple propagation-attenuation model have been formulated to evaluate, respectively the E2E delay and the energy consumption. The numerical results show that from the point of view of energy consumption  
Figure 11: End to end delay (in mini-slots), from sensor to the sink, for \(r_{\max}=5\), \(p_{act}=0.001\) and \((N_{msC},N_{intra};N_{msT},N_{inter})=(2,3;1,7)\).  
Figure 12: Energy consumption for several radius of the WSN, with \(N_{s}=364\) sensors, \(p_{act}=0.001\) and \(r_{\max}=5\).  
and for small coverage areas, a very low number of clusters is convenient, perhaps a single one in which the sink acts as the single CH. On the other hand, when the coverage area is big, it becomes convenient to use several clusters grouped in concentric rings around the sink. From the point of view of the E2E delay, it is important to note that the more CHs the WSN has the less contention delay the data packets will experience, but the information coming from the limits far from the sink will suffer more delay. This is due to the increase in the number of jumps to reach the sink, although the increase in the delay is not as high as might be expected.  
Several objectives are planned for the near future, some of them are already in progress. First is to consider that clusters near to the sink are smaller in size than clusters far from the sink [38]. This fact would increase the density of CHs per ring near the sink in such a way that, on the one hand, it would collect less local traffic for CH and on the other hand the retransmission of exogenous traffic would be reduced. This strategy would reduce the frequency of CH rotation, which tends to add an excessive communication overhead to the WSN, resulting in high energy consumption. Second, in order to avoid that CHs close to the sink carry all the traffic coming from outer rings, to address analytical models with mixed-routing schemes, i.e., to combine direct transmission mode with hop-by-hop transmission mode as has been pointed out in [5]. Third, the study of a comparative analysis of the previous architectures, taking into account key performance indicators such as flow, delay and lifetime of the resulting wireless sensor networks.  
**Author Contributions:** [PERSON], along with co-authors of [24; 33] conceived the scenario; [PERSON] suggested the FSA protocol, the queue model and wrote the document; [PERSON], [PERSON] and [PERSON], conceived the model of energy consumption, analyzed the data and helped to write the paper.  
**Funding:** This research received no external funding.  
**Acknowledgments:** The work of [PERSON] (ITACA research institute) is partly supported by the Spanish national projects TIN2013-47272-C2-1-R and TEC2015-71932-REDT. The work of [PERSON], [PERSON], and [PERSON], and the collaboration between the two institutions, is supported by the Universidad Santo Tomas under Master Degree's research and academic projects.  
**Conflicts of Interest:** The authors declare no conflict of interest.