resources increases. From Fig. \[scale1\], we can see that HA costs less 24.1%-75.1% and about 20% than FFD for Gaia and NASA traces, respectively, for any scale of local cloud, i.e., HA always consumes less cost than FFD. As shown in Fig. \[scale2\], the times consumed by FFD and HA both are stable as the increase of PM number. The reason is that the increase of PM number results in the decreasing of rented VM number, leading to the total number of the PMs and rented VMs ($P+N_{RV}$) having almost no change as the PM number increases.

![[The variations of rented costs and consumed times by task assignments with increasing the task number.]{}[]{data-label="scaleTask"}](scaleTask.pdf){width="0.8\columnwidth"}

Now, we examine the scalabilities of HA and FFD on the number of tasks by changing the task scale from 1000 to 35000 in number using Gaia trace. Figure \[scaleTask\] presents the result of the case of $\alpha=1$. Other cases have similar results. As shown in the figure, the consumed times of HA and FFD both are quadratically increasing with the task number, which is consistent with their respective time complexities. Figure \[scaleTask\] shows that the costs have nearly linear increases with the increase of task number 