|
λ
|
The number of arrival customer per (unit time) UT |
j
|
Task execution demand |
|
m
|
Server size |
s
|
Server speed |
| µ |
The number of completed service per UT |
ρ
|
The utilization factor of servers |
|
P
k
|
The probability that k service requests in system |
P
q
|
The probability to wait |
|
W
|
Waiting time of customers |
fw(t) |
The pdf of waiting time |
|
u(t) |
Unit impulse function |
T
|
The expectation of waiting time |
|
ɛ
|
Revenue |
C
|
Cost |
|
G
|
Profit of cloud service providers |
a
|
Fees per one billion instructions |
|
D
|
Maximum tolerable time that customers can wait |
β
|
Rental price of a server per UT |
|
N
sw
|
Average gate switching factor per clock cycle |
C
l
|
Load capacitance |
|
V
|
Supply voltage |
f
|
Lock frequency |
|
ϕ
|
A positive constant |
b
|
A positive proportional coefficient |
|
P
d
|
Dynamic power consumption |
P
∗
|
Static power consumption |
|
δ
|
Electricity price of energy |
H
∗
|
A working point in feasibel region
|
|
H
|
A point on boundary |
r
|
Shortest robustness radius |
|
θ
|
Polar angle in vector form |
r
1
|
Step length of neighborhood search |
| 11
|
Indicator function 1 |
s
z
|
optimal server size |
| 12
|
Indicator function 2 |
m
z
|
optimal server speed |
