# Performance Analysis of On-Demand Scheduling with and without Network Coding in Wireless Broadcast
## 6 Performance Evaluation
### Simulation Results in Real-Time Models
#### 6.1.1 Impact of Workload  
Figure 2a shows the impact of workload under different number of clients. When the number of clients increases, the system workload becomes heavier. As a result, more requests miss their deadlines and the algorithms' performances decline (Figure 2a). In the non-coding versions of the real-time algorithms, SIN outperforms EDF, because EDF only considers the request urgency. On the contrary, SIN considers both the request urgency and the item popularity, and hence SIN satisfies more requests than EDF (Figure 2b). The performance difference between EDF and SIN becomes more significant with an increase workload. The observations are consistent with the results reported in previous studies [9; 50].  
The network coding versions of EDF and SIN, namely EDF_N and SIN_N, outperform their respective non-coding versions notably in terms of achieving the lower deadline miss ratio (DMR). For instance, with the moderate system workload (default setting) this performance improvement is 28% and 19%, respectively for EDF_N and SIN_N. The main reason of this performance improvement is that the coding version achieves a higher average broadcast productivity (ABP) than the corresponding non-coding version (Figure 2b). This result shows that more requests can be satisfied by a single broadcast with network coding.  
Figure 3: Impact of deadline range on the real-time model.  
Figure 2: Impact of workload on the real-time model.  
Figure 2b shows that with an increase number of clients, the ABP of both the coding and non-coding version increases. With the growing number of requests, the popularity of data items increases. Therefore, for the non-coding version, despite a heavier system workload, the ABP increases. For the coding version, more requests provide more coding opportunities (Figure 2c), thereby yielding a higher ABP (Figure 2b). Please note that the amount of performance improvement of using network coding for EDF is larger than SIN and the amount of performance improvement of SIN_N over SIN diminishes when the number of clients is large. This is because network coding indirectly endows the item popularity attribute to EDF when it chooses the largest clique that contains the data item with the earliest deadline. Therefore, the performance improvement of EDF_N is more significant, and it increases with the item popularity. However, since SIN has already considered the item popularity, the performance gain due to network coding in SIN_N is less significant. On the whole, SIN_N achieves the highest ABP and the lowest DMR (Figure 2a).  
Figure 2c shows that SIN_N consistently achieves a higher average encode length (AEL) than EDF_N. The result shown in Figure 2d explores the reason. In particular, it shows the percentage distribution of number of items in an encoded packet under the default setting. Most of the encoded packets consist of two items, while the rest packets consist of one or three items. Specifically, SIN_N gives a higher chance of encoding more than one data items in a packet than EDF_N. For instance, 77.2% of the packets encoded by SIN_N consist of two data items, while 74.8% of the packets encoded by EDF_N consist of two data items. On the other hand, the number of items which are not encoded in SIN_N is less than that of EDF_N. Specifically, 11% of the items are not encoded in SIN_N, while 14.2% of the items are not encoded in EDF_N. In general, a higher ABP and AEL can be achieved if there are more encoded packets which consists of more data items. This has been demonstrated in Figure 2b,c, respectively.