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Table 1 Notation

From: An IoT-based task scheduling optimization scheme considering the deadline and cost-aware scientific workflow for cloud computing

G = (T, E)G is the directed acyclic graph representing a scientific workflow, T = { t1, t2, t3, …, tn } is a set of tasks, and E = { eijti, tjT } is a set of edges, where n is the number of tasks in the workflow
DThe deadline of the workflow
wiThe computation workload of task ti
dataijThe transfer data between task ti and tj
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 vmk
time_intervalMinimum time interval for billing when leasing a VM
bandwidthThe average bandwidth between VMs
init_timeThe acquisition delay of a VM
processorkThe CPU processing performance of VM type vmk
per_varyPercentage of performance variation of a VM
pred(ti)List of all immediate predecessors of task ti
succ(ti)List of all immediate successors of task ti
ET(ti, vmk)Estimated execution time of task ti scheduled on a VM of type vmk
TT(epi)Data transfer time between task tp and ti
LST(ti)Latest start time of task ti
LFT(ti)Latest finish time of task ti
ST(ti)Start time of task ti on a VM
FT(ti)Finish time of task ti on a VM
LV(ti)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 \( {vm}_m^k \)
TECTotal execution cost of a workflow
TETTotal execution time of a workflow