Database Reference
In-Depth Information
Equation 18.18 can be explained in the following way. In states, π
(
i
,
c
)
, jobs
can be rejected if there is no cold PM is available for provisioning. To com-
pute the job rejection probability, we use a Markov reward approach [19].
A reward rate of δ
c
(1 −
P
c
)/λ is assigned to each state and the overall prob-
ability is computed as expected steady-state reward rate.
(ii) Mean number of jobs in the RPDE queue
([
EN
R
PDE
])
. We can compute the
RPDE queue length as
−
∑
(
N
1
=
EN
i
π
+
π
+
π
)
(18.19)
(, )
ih
( ,)
iw
(, )
ic
PDE
R
i
=
0
(iii) Mean queuing delay
(
E
[
T
q_dec
]). Conditioned upon the job not being
rejected, we can compute mean queuing delay using Little's law [21]:
−
∑
π
N
1
i
(
+
π
+
π
)
(, )
ih
()
iw
,
(
ic
,)
=
i
=
0
ET
(18.20)
qdec
_
λ
(
1
−
P
−
P
)
block
drop
(iv) Mean decision delay
(
E
[
T
decision
]). Conditioned upon the job not being
rejected, this is given by
1
/
δ
+− +−
−
(
1
P
)(
1
/
δ
(
1
P
)/
δ
)
=
h
h
w
w
c
ET
(18.21)
(
)
decision
1
P
−
P
bl
ock
drop
18.3.2 sharPe C
oDe
For
the
rPDe s
ubmoDel
The RPDE submodel can be implemented using SHARPE software package, as
shown below.
format 8
* Markov model for RPDE; all rates are in jobs/hr
bind
lambda 1000
delta_h 20*60
delta_w 20*60
delta_c 20*60
N 100
* Dummy values for P_h, P_w, and P_c
* These values will be computed from VM provisioning sub-model
P_h
0.8
P_w
0.9
P_c
1.0
end
Search WWH ::
Custom Search