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(iii) initial VM provisioning rates (β
w
vs. β
c
) and buffer sizes (
L
w
vs.
L
c
). Effective
arrival rate (λ
c
) to each cold PM is given by
λ
(
1
−
P
)(
1
−
P
)(
1
−
P
)
λ
=
block
h
w
(18.31)
c
n
c
18.3.4.4 Cold PM Submodel Outputs
The steady-state probability (
B
c
) that a cold PM cannot accept a job is given by
−
∑
m
1
()
c
()
c
()
c
()
c
()
c
B
c
=
φ
+
φ
+
φ
+
φ
+
φ
(18.32)
(, *, )
L
10
(, ,)
L
10
(, **,)
L
10
(
LLi
,,)
1
(, ,)
Lm
0
c
c
c
c
c
i
=
1
Thus, the probability (
P
c
) that at least one PM in a cold pool can accept a job is
given by
n
c
P
=1( )
B
(18.33)
c
c
SHARPE codes for the warm and cold PM submodels can be developed in a simi-
lar manner [7] as shown in Section 18.3.4. From the VM provisioning submodels, we
can also compute mean queuing delay (E[
T
q_vm
]) and conditional mean provisioning
delay (E[
T
prov
]) [8]. The mean response delay is then given by
E
[
T
resp
] =
E
[
T
q_dec
] +
E
[
T
decision
] +
E
[
T
q_vm
] +
E
[
T
prov
]
(18.34)
18.3.5 s
ubmoDel
i
nteraCtions
Figure 18.7 shows the interactions among the submodels as an import graph [5].
Steady-state probabilities (
P
h
,
P
w
, and
P
c
) that at least one PM in a pool (hot, warm,
Job rejection probability and mean response delay
Outputs from
performance model
E
[
T
resp
]=
E
[
T
q_dec
]+
E
[
T
decision
]+
E
[
T
q_vm
]+
E
[
T
prov
]
P
reject
=
P
block
+
P
drop
RPDE
submodel
P
block
P
block
P
h
P
block
P
c
P
w
VM
provisioning
submodels
P
h
P
w
Cold pool
submodel
Hot pool
submodel
Warm pool
submodel
P
h
FIGURE 18.7
Interactions among the submodels.
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