# A Comprehensive Worst Case Bounds Analysis of IEEE 802.15.7
## 5 Numerical Analysis
### Scalability Analysis  
The IEEE 802.15.7 provides a rigid superframe structure in regard to its GTS mechanism, to support time-critical traffic. For contention free communication the standard supports seven guaranteed timeslots in every superframe. If more nodes need to use the service, they must wait for the adjacent superframe for an opportunity to transmit the data. This creates an increase in delay due to unavailability of bandwidth. Our model enables us to compute these delay bounds as we will show next. For this experiment, each transmission corresponds to a unique node, thus in this experiment we showcase the impact of the addition of multiple nodes into the network. To showcase this phenomena, we take a fixed superframe order of six and vary the number of transmissions, analyzing its delay and bandwidth utilization. As the value of SO is six, we have a timeslot length of 960 optical clocks and a CFP length of 6720 optical clocks. In Figure 11, it can be noticed that until the seventh transmission, the delay increases linearly and the total available bandwidth keeps on decreasing. At the seventh transmission there is no more bandwidth in the current superframe and any other transmissions by other nodes must wait until the adjacent superframe to transmit the data, hence a steep increase in delay is visible. Figure 10: Delay bound (optical clocks). Scalability is increasingly a major IoT requirement to carry out fine grained monitoring of physical properties such as in ref. [32]. In such application domains, it is expected to find a hundred nodes relaying time-critical data to a sink. A rigid GTS structure will be a deterrent to such scenarios. Interestingly, as already mentioned, the IEEE 802.15.4 supports a quite similar GTS communication service, which also supports seven GTS. Having scalability in mind, the IEEE 802.15.4 introduced a technique called CAP reduction by which one can replace the CAP region of the adjacent superframe with additional GTS. In some of our previous works, we explored the CAP reduction functionality of IEEE 802.15.4 and carried out a detailed performance analysis [33]. Additionally, we proposed a dynamic switching of CAP reduction for better performance [34]. In this work, we now propose to briefly analyze the impact of such a CAP reduction technique for IEEE 802.15.7 networks. With this mechanism, the CAP region of the adjacent superframe will be replaced with seven GTS as shown in Figure 12b making an extended CFP region with 14 GTSs. Importantly, the implementation of this mechanism imposes the design of additional complexity into the protocol. For supporting CAP reduction, one must include in the Beacon payload a primitive to announce the triggering of the CAP reduction mechanism to all the nodes in the network. It is also important to set up a concept similar to what is know as mutisuperframe (in IEEE 802.15.4) into this protocol. However, the actual implementation of the technique goes beyond the scope of this paper and is to be addressed in future work. To carry out what we propose, it suffices to introduce the necessary changes into the theoretical model. Figure 11: GTS scalability analysis of IEEE 802.15.7. We take the architecture in Figure 12b to analyze the impact of CAP reduction on IEEE 802.15.7 networks. We redo the same scalability test but with CAP reduction enabled. It is very evident that the delay is reduced as the transmissions at the end of the first superframe need not wait 6720 optical clocks to get accommodated in the adjacent superframe. Due to the addition of 14 additional GTS slots, there is a significant increase in the available bandwidth and results show a steady increase of its usage as expected. As much as the CAP reduction technique increases the available bandwidth of the network, it must be noted that having a static CAP reduction technique can also have some adverse results. For instance, we took a data set with a burst of 10 Mb and an arrival rate of 100 Mbps and verified the delay over the network.