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In-Depth Information
3.2 Notations
We use the following notations in this paper:
vm
i
:The
i
th
virtual machine to be scheduled.
j
th
physical server.
M
j
:The
S
: A feasible schedule.
P
idle
j
: Idle power consumption of the
M
j
.
P
max
j
: Maximum power consumption of the
M
j
.
P
j
(
t
): Power consumption of a single physical server (
M
j
) at a time point
t
.
U
j
(
t
): CPU utilization of the
M
j
at a time point
t
.
ts
i
: Fixed starting time of
vm
i
.
dur
i
: Duration time of
vm
i
.
T
: The maximum time of the scheduling problem.
r
j
(
t
): Set of indexes of all VMs that are assigned to the physical machine
M
j
at time
t
.
3.3 Power Consumption Model
In this paper, we use the following energy consumption model proposed in [
10
]
for a physical server
M
j
. The power consumption of each physical server, denoted
P
j
(
.
as
), is formulated as:
P
idle
j
P
max
j
− P
idle
j
P
j
(
t
)=
+(
)
× U
j
(
t
)
(1)
The CPU utilization, denoted as
U
j
(
t
), of the physical server at time
t
is
formulated as:
)=
PE
j
mips
i,c
MIPS
j,c
U
j
(
t
(2)
c
=1
i∈r
j
(
t
)
The energy consumption of the server at time
t
is formulated as:
E
j
=
T
j
0
P
j
(
U
j
(
t
))
dt
(3)
where:
U
j
(
t
M
j
t
≤ U
j
(
t
≤
) : CPU utilization of the server
at time
and 0
)
1.
PE
j
: Number of processing elements (i.e. cores) of the physical server
M
j
.
mips
i,c
: Allocated MIPS of the c
th
processing element to the
vm
i
by
M
j
.
MIPS
j,c
: Total MIPS of the c
th
processing element on the
M
j
.
T
j
: Working time of a physical server
T
j
is defined as union of time
intervals of all VMs that are allocated to a physical machine
M
j
.The
j
th
at time
t
.
T
j
=
[
ts
i
;
ts
i
+
dur
i
]
(4)
vm
i
∈r
j,t
The union of two time intervals [a;b] and [c;d] is defined as: [
a
;
b
]
∪
[
c
;
d
]=
{x ∈
R
| x ∈
[
a
;
b
]
or x ∈
[
c, d
]
}
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