## 3 Efficient Superframe Structures with Adaptive Duty Cycle \((Ess_{ADC})\)
### \(Ess_{ADC}\) Algorithm  
PAN coordinator applies \(ESS_{ADC}\) algorithm by adjusting the values of SO and BO as shown in Figure 4.  
After receiving all the \(GTS_{req}^{ESS_{ADC}}\), PAN coordinator calculates the fractional slot requests for each node. Suppose node \(S\) requested \(k\) slots. It needs to compute the percentage of available GTS being utilized by all nodes. This will help the PAN coordinator to determine the slot usage in fractions. PAN coordinator accumulates all these slots (K) requested by all nodes \(S\). The coordinator computes the ratio (A) between total available slots as compared to the GTS requested by all nodes. The proposed scheme offers 14 GTS in a superframe, so A = 14/K. PAN coordinator after computing the value of A, needs to compare it with the total number of available GTS. In case, the value of A is greater than the available GTS, then it needs to increase the duty cycle by increasing the value of SO. At the same time, the duty cycle should not increase from 50%. This increase in the duty cycle depends on the value of C calculated as:  
\[C=\lceil(\left|log_{2}A\right|,1)\rceil \tag{13}\]  
If A is less than the available GTS limit, then the duty cycle may be reduced. This decrease in duty cycle should not violate the SO and BO limits as defined in the standard. At the same time, the PAN coordinator should be precise about the reduction in the duty cycle. The reduced parameters of SO and BO depends upon the value of \(B\), which is determined as:  
\[B=\lfloor(log_{2}A,1)\rfloor \tag{14}\]  
This algorithm helps the PAN coordinator to adapt the duty cycle of the next superframe without violating the standard limits, such as the difference between BO and SO should not increase from 9 and values of SO and BO should remain in their boundary limits.  
Figure 5 shows that \(ESS_{ADC}\) algorithm adjusts SO according to the data requests generated by the nodes for three different data ranges. The SO trend is observed for five different beacon intervals. In each beacon interval, 15 nodes send their data requests to PAN coordinator. The nodes increase their data requests with an increment of 15 bytes in the next beacon interval. It is evident from the results that, SO value becomes 0,1,2 and 3, when data requests of nodes are less than 16 bytes, 16-30 bytes, 31-60 bytes and 61-120 bytes respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline
**b0 – b3 (GTS Req)** & **Value of X** & **b6, b7 (Reserved Bit)** & **Description** \\ \hline
0001 & 0 & 00 & More than 50\% slot is occupied \\
0001 & 1 & 01 & GTS between 25\% to 50\% is occupied \\
0001 & 2 & 10 & GTS between 12.5\% to 25\% is occupied \\
0001 & 3 & 11 & GTS between 6.25\% to 12.5\% is occupied \\
1110 & 4 & 00 & No more additional GTS required \\
1110 & 5 & 01 & 1 to 15 more GTS required \\
1110 & 6 & 10 & 16 to 31 more GTS required \\
1110 & 7 & 11 & 32 to 63 more GTS required \\ \hline \end{tabular}
\end{table}
Table 1: Parameter values describing slot utilization.  
Figure 4: Proposed \(ESS_{ADC}\) algorithm.  
Figure 5: \(ESS_{ADC}\) adjusting its SO against transmitted data.