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amongst sinks and sources. The latter, depending on the network type,
can be interpreted as the reduction in the ability of sinks to receive fl ow
from sources (e.g. for EPN or GAS), or the average increase of the
path amongst sinks and sources (e.g. for RDN). The simple connectivity
loss (SCL) is defi ned as
SCL
=−
(
)
∑
1
N
N
n
where
N
i
,0
and
is
,
i
,
0
N
i
∑
,
0
N
are the number of sources connected to the
i
th sink in
undamaged and damaged conditions, respectively. The weighted con-
nectivity loss (WCL) is defi ned as
WCL
=
I
is
,
ijs
,
j
=
1
∑
(
)
=−
1
⎣
N
W
N
W
⎦
n
,
is
,
is
,
i
,
0
i
,
0
∑
N
i
∑
N
i
,
0
,
0
where the weights are defi ned as
W
,
as a function of other weights
W
j
,
s
assigned to the sources connected to
each node. The choice of the latter weights depends on the network type.
For some networks (e.g. EPN or GAS) setting the weight
W
j
,
s
=
W
and
W
=
I
W
i
,
0
j
,
0
is
,
ijs
,
js
,
j
=
1
j
=
1
Q
j
,
s
equal
to the fl ow from the sources is meaningful, for others (e.g. RDN) it
makes more sense to use as weight the inverse number of edges from
the source to the node of interest
W
j
,
s
=
1/
N
ij
,
s
. Figure 18.8 shows an
example of computation of the SCL and WCL measures for a simple
network with three nodes (one source and two sinks) and three edges.
Notice how the fact that, even if connectivity is maintained in the third
run, the path from sink 2 to source 3 is longer and penalised by a value
of WCL > SCL.
Flow-related measures, such as the system serviceability index
SSI
,
defi ned as the ratio of the sum of satisfi ed demands in the post-earth-
quake damaged conditions to the sum in the reference undamaged
pre-earthquake conditions. Usually its defi nition assumes that the
demand remains fi xed before and after the earthquake. Note that the
index looks only at a single system, without considering its interactions
with other infrastructural systems. It can be enhanced (enhanced system
serviceability index,
ESSI
) to account for demand variation. It can take
the form of a difference of weighted fl ows, as for instance in the Driver's
Delay metric (Shinozuka
et
al.
, 2003).
=
Examples of type 1 metrics include, with reference to an EPN, the Power
Loss
PL
=−
(
)
∑
, ,
, which corrects the connectivity loss with the
size of the power plants (real power
P
in MW) to which load buses are still
connected to. Another metric is focused on the Impact on the Population
IP
1
P
P
n
is
i
0
=−
(
)
∑
∑
, ,
, where the summation extends to the
number of load buses in the EPN, and
POP
i
is the population fed by the
i
th load bus (Poljanšek
et
al.
, 2010).
Examples of type 2 metrics include the
SSI
, which can be defi ned, e.g. for
an EPN, as the ratio of the real power delivered at load buses after an
earthquake to that before the earthquake. The SSI is given by
SSI
1
POP P
P
POP
iis
i
0
i
∑
∑
(
)
=
100
⎣
P
1
−
R
w
P
⎦
, where
P
i,
0
is the delivered power at
i
,
0
i
i
i
,
0
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