Download Closed Charging Cordon Design Problem

Bk ,1 =
Bk , 2
Bk ,3
Bk , 4
Bk ,5
Bk , 6
( A1(1) k + A2(1,4,5) k + A3(1,2,5) k + A4(1,2,4,5,8) k + A5(1,2,3,5) k )
5
( A3(1,2,5) k + A4(1,2,4,5,8) k + A5(1,2,3,5) k )
=
3
( A5(1,2,3,5) k )
=
1
( A2(1,4,5) k + A4(1,2,4,5,8) k )
=
2
( A2(1,4,5) k + A3(1,2,5) k + A4(1,2,4,5,8) k + A5(1,2,3,5) k )
=
4
( A4(1,2,4,5,8) k )
=
1
Note that the above formulas are only correct for each link k if the values in at
least 95% of the A vectors are all greater then zero or are all less then zero. If
this is not the case then the value entered in the B matrix must be zero for that
link and node. Using the values in the example above the B matrix becomes:
Bk ,i
M
M
M
M
M 
 M


 − 6.2 − 6 − 5 − 7.5 − 6.5 − 7 
 M
M
M
M
M
M 


= 0
0
4
−2
0
−1
 M
M
M
M
M
M 

 0
0 −3
0
0
0 


M
M
M
M
M 
 M
The idea behind the B matrix is to show how any one node that has been inside a
cordon will affect the traffic behaviour on some link or links in a certain way until
proven otherwise.
In the example it can be seen that by placing any of the nodes 1, 2, 3, 4, 5 or 8 in
the cordon a decrease in the traffic behaviour will occur on link X. This is not
however true on links Y and Z. Placing node 3 in the cordon will lead to an
increase of traffic behaviour on link Y by 4 units. This is obviously not an accurate
representation of what happens but the thought is that it will give a starting point
in helping to predict what the next cordon should look like and it will also become
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