Database Reference
In-Depth Information
18.3.4.1 Warm PM CTMC
Warm PM CTMC is shown in Figure 18.5. Although warm PM CTMC is similar
to hot PM CTMC, there are few differences that set them apart. Jobs arrive to the
warm PM pool only if they are not provisioned on any of the hot PMs. Thus, effec-
tive arrival rate (λ
w
) to each warm PM is
λ
(
1
−
P
)(
1
−
P
)
λ
=
block
h
(18.28)
w
n
w
Initially, (state (0,0,0) in Figure 18.5), it is turned on but not ready for use. When
a job arrives, the warm PM requires some additional startup delay to be able to start
provisioning and the CTMC submodel goes from state (0,0,0) to state (0,1*,0). We
assume that (i) time to make a warm PM ready for use is exponentially distributed
with mean 1/γ
w
, (ii) provisioning delay of the first VM on a warm PM is 1/β
w
, and
(iii) provisioning delay for subsequent VMs is the same as that for a hot PM, that is,
1/β
h
. The buffer length of each warm PM is assumed to be
L
w
.
λ
w
λ
w
λ
w
0,0,0
0,1*,0
L
w
,1*,0
…
γ
w
γ
w
λ
w
λ
w
µ
0,1,0
L
w
,1,0
λ
w
…
λ
w
0,1**,0
L
w
,1**,0
β
w
µ
β
h
µ
β
w
µ
β
h
…
0,0,1
0,1,1
(
L
w
− 1),1,1
L
w
,1,1
λ
w
λ
w
λ
w
β
h
β
h
2µ
2µ
2µ
(
m
- 1)µ
β
h
β
h
(
m
- 1)µ
β
h
(
m
- 1)µ
(
m
- 1)µ
…
λ
w
0,0,(
m
− 1)
0,1,(
m
− 1)
(
L
w
−
1),1,(
m
−
1)
L
w
,1,(
m
−
1)
λ
w
λ
w
λ
w
m
µ
β
h
β
h
β
h
β
h
m
µ
m
µ
…
0,0,
m
1,0,
m
L
w
,0,
m
λ
w
λ
w
λ
w
FIGURE 18.5
VM provisioning submodel for each warm PM.
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