288% more than that by HA and is larger than the number of tasks for both Gaia and NASA traces, and thus the time consumed by FFD is more than HA. When $\alpha\geq 3$, rented VM numbers are smaller than task numbers, therefore, FFD consumes less time than HA.

![[The rent costs decreasing with increasing of PM numbers.]{}[]{data-label="scale1"}](scale1.pdf){width="0.8\columnwidth"}

![[The times consumed by task assignments, stable when the local PM number is increasing.]{}[]{data-label="scale2"}](scale2.pdf){width="0.8\columnwidth"}

Next, we examine the scalabilities of HA and FFD on the number of local PMs. We scale the PM resources by a factor ranging from 1 to 10. For example, when the scale factor is 1, 15 PMs described in Table \[PM\] are used for running tasks, while there would be 150 PMs when the scale factor is 10. Figures \[scale1\] and \[scale2\] show the changes of costs and time consumed by HA and FFD with the scale factor, respectively. We present the results of the case of $\alpha=4$ here. Other cases have similar results. As shown in Fig. \[scale1\], the cost is decreased with increasing of PM numbers because the resources should be leased from the public cloud are reduced in amount as the amount of local 