Cost-Effective Resource Provisioning for Real-Time Workflow in Cloud

Table 1

List of symbols.

Symbol	Meaning
	A workflow represented by DAG
T{t1, t2, …, tn}	A set of n tasks
	The related workloads of n tasks in T
E{eij}	A set of directed edges between two tasks in
D	The deadline of workflow
Parent(ti)	Parent task of ti
Child(ti)	Child task of ti
	Total cost of workflow
	Total workload of workflow
	Total execution time of workflow
	Execution time of task ti on VMj
RT	Resource occupation time
BT	Resource initial booting time
Ci	Cost of task ti
TT	Data transfer time
BL(d)	A set of tasks in layer d
BD(ti)	The longest path of ti to texit
LMET(d)	The minimum execution time of layer d
CSW	Sub-workflow containing all of critical tasks
NSW	Sub-workflow not containing any of critical tasks
	A set of m types of
VMj(MFLOPSj, PRICEj)	A type of
MFLOPSj	Mega-floating point operations per second of
PRICEj	Price of
τ	Billing cycle defined by VMS provider
Pj	Computational performance of
Cj	Cost of resource
X{x1, x2, …, xm}	VMs vector of provisioning results
xj	Number of billing cycles of
fk(W)	First k types of VMs satisfying the workload