Information Technology Reference
In-Depth Information
3.2
Action Space
The production price selection problem that each agent is aiming to solve consists in
setting a price
p ∈P
that equals the experienced cost. Given that the price
p
is part of
the state space, the action space
A
is then defined as:
A
=
{⊕, , }
(14)
where
⊕
corresponds to the action of increasing the current price,
corresponds to the
action of decreasing the current price, while
corresponds to the action of leaving the
price unchanged.
3.3
Setting the Production Price
From the analysis conducted in section 2, we derived that the social transportation cost
is minimised when each market agent sets a price
p
that is equal to the production cost
c
. If we consider only congestion, the cost function is proportional to the delay caused
by a certain quantity of road users in a given time window
w ∈W
, and therefore the
cost
c
can be approximated as:
u
−
u
ff
)
c
=
v
(
(15)
where
v
is the value of time (assumed to be constant among road users),
is the length
of the link,
u
is the average speed detected over the time window
w
,and
u
ff
is the speed
at free flow on the link, i.e., the speed of a single road user travelling on the link.
Given that the agent is producing mobility at price
p
, we can compute the absolute
difference between the price
p
and the cost
c
:
u
−
u
ff
)
|
ω
=
|p − v
(
(16)
The value
ω
can be used by the market agent as feedback information to adjust
p
and
approximate it to the cost
c
, by using some learning algorithm.
4
Experimental Evaluation: Two Congestible Links in Parallel
The aim of this experimental evaluation is replicating the situation depicted in figure 1,
to evaluate whether the two market agents are able to minimise the social transportation
cost as in the analysis derived in section 2.
Let's assume that the speed at free flow on the two links is
50 km
/
h
and
30 km
/
h
respectively, and that both links are
long. Let's also assume that for both links
each additional road user causes a travel time increase of
1km
1sec
. Therefore, the travel
time (expressed in hours) on link 1 and 2 respectively is:
z
1
(
q
1
)=
1
z
2
(
q
2
)=
1
50
+0
.
0003
q
1
30
+0
.
0003
q
2
(17)
