## 5 Experiments and Analyses
### Video Delivery Experiment
#### 5.1.4 Ratios of the Three Types of Requests: 2:1:1 and 1:1:2 on the SPA-WP and Random  
In the fourth part of this experiment, we redid the second and third parts, _i.e._, with the SPA-WP and Random, but 300 type-1, 150 type-2 and 150 type-3 requests were submitted, _i.e._, the ratio of the three types is 2:1:1. Table 15 shows the experimental results. Lastly, 150 type-1, 150 type-2 and 300 type-3 requests were submitted, _i.e._, the ratio is 1:1:2. Table 16 shows the results. By comparing Tables 14 and 15 we can see that when the SPA-WP is employed, the average turnaround time of type-\(i\) requests in Table 15 is longer than that of type-\(i\) in Table 14, \(i=1\), 2 and 3, _i.e._, 153.58 \(>\) 146.27 (type-1), 178.81 \(>\) 174.41 (type-2), and 180.48 \(>\) 173.81 (type-3), because when many more type-1 requests are submitted, their waiting delays in type-1 global queue will be consequently longer (but not significantly), and the execution of the other two types of requests may be preempted, no matter whether the requests are now being executed by level-1, level-2 or level-3 \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Items**} & **Type-1** & **Type-2** & **Type-3** & **Total No.** & **Percentage of** & **Average** \\  & **requests** & **requests** & **requests** & **of requests** & **requests** & **turnaround time** \\ \hline Node 1 & 96/35 & 60/36 & 60/35 & 216/106 & 36/18(\%) & 157.47/159.63 \\ Node 2 & 5/36 & 36/37 & 44/35 & 85/108 & 14/18(\%) & 168.90/168.92 \\ Node 3 & 2/31 & 32/33 & 22/32 & 56/96 & 9/16 (\%) & 169.03/178.34 \\ Node 4 & 94/33 & 59/31 & 57/32 & 210/96 & 36/16(\%) & 157.36/159.95 \\ Node 5 & 2/31 & 8/29 & 9/34 & 19/94 & 3/15 (\%) & 167.46/178.30 \\ Node 6 & 1/34 & 5/34 & 8/32 & 14/100 & 2/17 (\%) & 168.77/178.36 \\ No. of preemptions & 0/0 & 46/0 & 69/0 & - & - & - \\ Total & 200 & 200 & 200 & 600 & 100\% & 164.83/170.58 \\ Turnaround & (146.27/34.44)/ & (174.41/31.04)/ & (173.81/31.05)/ & & 164.83/170.58 & - & - \\ time/SD & (172.49/31.14) & (172.98/31.16) & (166.28/31.03) & & & \\ \hline \end{tabular}
\end{table} 
Table 14: The numbers of requests allocated and their turnaround times when 200 type-\(i\) requests were submitted, \(i=1\), 2, 3, and SPA-WP and Random algorithms were employed. resource nodes. The latter is also the reason why the numbers of preempted type-2 and type-3 requests are higher than those listed in Table 14, _i.e._, 59 \(>\) 46 (type-2) and 75 \(>\) 69 (type-3). For the same reasons, the average turnaround time of the 600 requests shown in Table 15, _i.e._, 166.61 s, is also longer than that illustrated in Table 14, _i.e._, 164.83 s.  
The turnaround time of type-2 requests shown in Table 16 (X portion of X/Y) is shorter than those listed in Tables 14 and 15, _i.e._, 161.55 \(<\) 174.41 (Table 14) and 161.55 \(<\) 178.81 (Table 15), because when the number of type-1 requests is smaller, the type-2 requests have lower probability of being preempted (no. of preemptions in the column of type-2 request in Table 16 is 10), consequently shortening type-2 requests' average turnaround time. When many more type-3 requests were submitted, their queuing delays in the type-3 global queue were longer, and the probability that their execution is preempted was also higher. That is why the number of preemption of type-3 requests was