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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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