# A Multi-Service Adaptive Semi-Persistent LTE Uplink Scheduler for Low Power M2M Devices
## 6 Results  
### Multi-Service Adaptive SPS Algorithm  
Figure 10 compares the Cumulative Distribution Functions (CDF) for the different runs for traffic class A which is the most delay sensitive class with a PDB of 50 ms where the request inter-arrival gap is exponentially distributed with the mean \(\mathcal{V}\lambda_{S}\) equal to the PDB. From Figure 9, it is observed that increasing the value of \(f_{S}\) increases the service capacity \(N_{S}\). However, in Figure 10, it is obvious that the capacity increment comes at a cost of increase in delay. Since we are interested in keeping the delay only under the class-specific PDB, not decreasing the overall delay, the value of \(f_{S}\) can be maximized as \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Traffic Class**} & \multirow{2}{*}{**Burst Size (Packets)**} &
\begin{tabular}{c} **Mean Arrival Rate** \\ **(Bursts/s)** \\ \end{tabular} & **PDB (ms)** \\ \hline A & & 40 & 50 \\ \hline B & & 20 & 100 \\ \hline C & & 13.33 & 150 \\ \hline D & & 10 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Traffic Model for Power Saving with DRX. Figure 9: Service capacity \(N_{S}\) of 5 traffic classes in single-class environment. long as the target percentage of packets meet their delay budgets. It can be deduced that, \(f_{S}=0.4\), which indicates an SPS period \(T_{SPS,A}=20\) ms is the optimum configuration with 100% class A packets meeting their delay constraints and also supports more capacity (6 class A UEs) than \(f_{S}=0.2\) (3 class A UEs). Larger values of \(f_{S}=0.6\) and 0.8 are not satisfactory with only 77% and 39.5% class A packets meeting their delay budgets. The dynamic scheduler serves 95% class A packets within their delay budgets. Figure 11 again compares the uplink delay CDFs for class A traffic where the request inter-arrival gap is exponentially distributed with the mean \(\mathcal{V}\Lambda_{S}\) equal to 20% of the PDB i.e., 10 ms. For high request arrival rates, the control channel constraints for the dynamic scheduler comes into play and the peaks in requests often causes PDCCH saturation momentarily. This saturation points builds up queues at the UEs which may be observed in some dynamically scheduled packets experiencing very high delays. Figure 11 shows the delay values in logarithmic scale due to such large variations in delay. The higher request arrival rate requires more PRBs per SPS allocation. The higher the value of \(f_{S}\), also more packets are accumulated in the device buffers. If the required resources are higher than the adaptive PRB ceiling, then all the buffered packets cannot be served at one go and some packets need to wait/be discarded. This causes the adaptive SPS algorithm to fail to meet the PDB in some cases with high request arrival rate, especially for \(f_{S}=0.6\) and 0.8. However, it is still possible to satisfy 99% class A packets' delay constraints with \(f_{S}=0.4\)  
Figure 10: Delay CDF for traffic class A (\(\frac{1}{\Lambda_{S}}=T_{PDB,S}\)). Again, Figure 12 compares the Cumulative Distribution Functions (CDF) for the different scheduling schemes for traffic class E which has the longest PDB value of 250 ms where the request inter-arrival gap is exponentially distributed with the mean \(1/\lambda_{S}\) equal to the PDB. For class E traffic as well, \(f_{S}=0.4\) offers optimum results with 100% packets meeting their delay constraints and also more capacity (30 class E nodes) than \(f_{S}=0.2\) (15 class E nodes). We further notice that, for \(f_{S}=0.6\), the performance of the adaptive SPS for class E traffic is better (90% meeting PDB) than that for class A (77% meeting PDB in Figure 10).