## 6 Evaluation
### Simulations
#### 6.1.2 Simulation Results  
In this section, we changed the parameters initial load, load skewness, network conditions, and the number of tasks in order to evaluate the scheduling algorithms' effects on makespan and data locality. We also changed the number of tasks, servers, and cores to evaluate the offline algorithms' scalability. **Effects of initial loads. ** In these simulations, we set \(|T|\) to 100, \(|S|\) to 50, \(core\_num\) to 40, \(\alpha\) to 0, \(\theta\) to 1, and changed the ranges of initial loads \([0,\beta]\). A larger \(\beta\) indicates that fewer cores will be free soon, so the makespan will be longer. Figure 5a shows how the initial loads affect the makespans. When \(\beta\) reached 100, 1000, and 10,000, the makespans computed by DynDLOn were 4, 15, and 78, respectively, and the makespans computed by DynDLOff were 3, 13, and 73, respectively. We observed that when \(\beta\) was small (\(\beta=100\) or \(\beta=1000\)), DynDLOff's makespan was at most 20% lower than other offline algorithms'. However, when \(\beta\) was large (\(\beta=10\),000), DynDLOff's makespans were at least 30% lower than other offline algorithms'. For all \(\beta\) settings, in terms of makespans, DynDLOn was slightly better than other online algorithms. Regarding data locality, a data-local task must wait for its preferred cores to be free. When \(\beta\) is large, the waiting costs cannot be ignored, so for a larger \(\beta\), the schedulers assign more data-remote tasks. Figure 5b shows that DynDLOn's data locality was better than other online algorithms'. We also can see that BAR's data locality was better than other offline algorithms', because BAR's data-remote costs increased with the total number of data-remote tasks. However, BAR's makespan was twice as large as DynDLOff's when \(\beta=10\),000. Because BAR's data-remote cost function overestimated these costs, it had to assign more data-local tasks to high-load servers. Thus, although DynDLOff's data locality was worse than BAR's, its makespan was better. **Effects of load skewness. ** In these simulations, we set \(|T|\) to 100, \(|S|\) to 50, \(core\_num\) to 40, \(\beta\) to 100, \(\theta\) to 1, and changed the load-skewness factor \(\alpha\) to 10, 20, and 40. A larger \(\alpha\) indicates that the servers' initial loads are more imbalanced (i.e., some servers' loads are much smaller than others), so data-remote tasks are more likely to be assigned to the same low-load server. Figure 6 shows how load skewness affected makespans and data localities. DynDLOn's and DynDLOff's makespans were far smaller than other algorithms' makespans when the initial loads were skewed. Although DynDLOn's and DELAY's data localities were similar, DynDLOn's makespan was 30% smaller  
Figure 5: Effects of initial loads. LIST: list scheduling; LTFPA: Local-Tasks-First Priority Algorithm; HTA: Algorithm for Hadoop Task Assignment Problem. \begin{table}
\begin{tabular}{l l r} \hline \hline
**Parameter** & **Description** & **Default Value** \\ \hline \(|T|\) & Number of tasks & 100 \\ \(|S|\) & Number of servers & 50 \\ \(core\_num\) & Number of cores in a server & 40 \\ \(\alpha\) & Load skewness factor & 0 \\ \(\beta\) & Range of initial load & 100 \\ \(\theta\) & Network factor & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Key parameters. than DELAY's. This is because DELAY assigned more data-remote tasks to the same servers than DynDLOn did. When \(\alpha\) was larger, DynDLOff assigned more data-remote tasks. Because we set \(\beta\) to 100, a larger \(\alpha\) led to larger initial loads. DynDLOff does not wait for data-local cores to be free, so although it assigned more data-remote tasks, its makespan was better. **Effects of network conditions. ** In these simulations, we set \(|T|\) to 100, \(|S|\) to 50, _core_num_ to 40, \(\beta\) to 1000, and \(\alpha\) to 0, and changed the network factor \(\theta\) to 1, 2, and 4. A larger \(\theta\) indicates the network conditions are worse, so a data-remote task needs more time to transfer data.