Information Technology Reference
In-Depth Information
It is interesting to notice that if
π
1
=
π
2
=0
, the number of road users that will choose
link 1 and 2 respectively is:
β
1
+
β
2
+
1
β
2
Q
α
2
− α
1
β
1
+
β
2
=
q
1
β
1
+
β
2
−
1
β
1
Q
α
2
− α
1
β
1
+
β
2
=
q
2
q
1
=
q
2
=
(12)
2
2
Setting a price that simply covers productions costs induce a user equilibrium that is
equivalent to the system optimum. In this way, the social transportation cost is min-
imised by two independent market agents that compete in the market to accommodate
the road users, rather than by a centralised regulator with full knowledge. Indeed, for the
two links in parallel, the selected price is equivalent to the social welfare maximising
toll that derives from a first-best marginal external cost analysis [4].
3
Beyond Economic Analysis
In the previous section we analytically demonstrated how the collective behaviour of
well-designed market agents minimises the social transportation cost. This fact vali-
dates the artificial market as an allocation technique for a road transport system with
many advantages over centralised control, such as the complete distribution and the
computational tractability. However, in general it is not always possible to have per-
fect knowledge of the demand functions (i.e., the quantity
Q
in the previous example)
or the cost function
c
(
q
)
. For this reason, it is necessary to go beyond static economic
analysis, and using AI techniques to compensate the impossibility of deriving analytical
solutions. In this section we extend the artificial market notion for a more realistic road
transport network. We identify an approximation of the cost function, based on realis-
tic assumptions and minimal
apriori
knowledge. We then define the state and action
space of each agent that operates in the market. Finally we outline possible learning
algorithms that are suitable for the production price selection problem that each agent
faces.
3.1
State Space
Let
W
=
{w
1
,w
2
,..., w
m
}
be a set of
m
=24
/τ
time windows that composes a day,
each of them of
τ
hours. Let
be the set of
n
possible prices applied by the agent that governs the link, where
p
min
and
p
max
are the
minimum and maximum price respectively. Let
u
in
(
t
)
P
=
{p
1
=
p
min
,p
2
,..., p
n
=
p
max
}
be the average speed of the road
users that enter the link at time
t
,and
u
out
(
t
)
be the average speed of the road users that
exit the link at time
t
.Let
u
(
t
)=(
u
in
(
t
)+
u
out
(
t
))
/
2
be the average of the two speeds
at time
t
.Let
u
be the average speed over a time window
w
j
∈W
, calculated as:
w
j
u
(
t
)
dt
w
j
−
1
u
=
(13)
w
j
− w
j−
1
Finally, let
be a discretisation of the image of the function
u
.
The state space is therefore defined as
U
=
{u
1
, u
2
,..., u
r
}
S
=
W×P×U
