Table 1 Notation

G = (T, E)

G is the directed acyclic graph representing a scientific workflow, T = { t₁, t₂, t₃, …, t_n } is a set of tasks, and E = { e_ij ∣ t_i, t_j ∈ T } is a set of edges, where n is the number of tasks in the workflow

D

The deadline of the workflow

w_i

The computation workload of task t_i

data_ij

The transfer data between task t_i and t_j

VM = \( \left\{{vm}_1^2,{vm}_2^3,\dots, {vm}_m^k\right\} \)

VM is the set of VMs in the cloud, where m is the identifier of the VM and k is the VM type

\( {cost}_{vm^k} \)

The cost of VM type vm^k

time_interval

Minimum time interval for billing when leasing a VM

bandwidth

The average bandwidth between VMs

init_time

The acquisition delay of a VM

processor_k

The CPU processing performance of VM type vm^k

per_vary

Percentage of performance variation of a VM

pred(t_i)

List of all immediate predecessors of task t_i

succ(t_i)

List of all immediate successors of task t_i

ET(t_i, vm^k)

Estimated execution time of task t_i scheduled on a VM of type vm^k

TT(e_pi)

Data transfer time between task t_p and t_i

LST(t_i)

Latest start time of task t_i

LFT(t_i)

Latest finish time of task t_i

ST(t_i)

Start time of task t_i on a VM

FT(t_i)

Finish time of task t_i on a VM

LV(t_i)

The level number l associates a task to a BoT

BoT(l)

A set of tasks that have the same level number l

\( Avail\left({vm}_m^k\right) \)

The ready time of VM \( {vm}_m^k \) to execute a new task

\( VLST\left({vm}_m^k\right) \)

Lease start time of VM \( {vm}_m^k \)

\( VLFT\left({vm}_m^k\right) \)

Lease finish time of VM \( {vm}_m^k \)

TEC

Total execution cost of a workflow

TET

Total execution time of a workflow