a 2 GHz core.

The PMs used as the local resources are shown in Table \[PM\]. In public cloud, we use a compute optimized instance type, c3.large in EC2 [@EC2], because it has the best cost-performance ratio for CPU-intensive applications, compared with other instances provisioned by EC2. Each VM instance has 2 vCPUs with 2.7GHz. The price of a VM instance is \$0.105 per hour (in US east (N. Virginia)).

We use three performance metrics to evaluate task management algorithms:

-   ***rent cost***: the cost for leasing VMs from the public cloud;

-   ***makespan***: the latest finish time of tasks;

-   ***resource utilization***: the overall utilization of used PMs and rented VMs.

Comparison of Task Management Algorithms {#Comparison}
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In this section, we compare our Heuristic Algorithm (HA) with First Fit Decreasing (FFD) [@FFD] in both performance and overhead. FFD is assigning the longest task to the first core on which it will fit. The time complexity of FFD is $O(T\cdot(P+N_{RV}))$ [@FFD] if the tasks have been sorted in their sizes. Before running FFD, we sort PMs on their capacities in descending order in advanced.

### Performance Comparison {#PC}

Figures \[rentcost\], \[makespan\], and \[utilization\] show the rent costs, the makespans 