Interactive Localisation System for Urban Planning Issues - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 462

The proposed model allows urban operators to retrieve a significant number of related
results, such as the influence area of each service site, the degree of utilization of each
service, the induced traffic flow increment on each road, the total cost of any given service
location. Moreover, other relevant information can be obtained: the minimum path matrix
for all the nodes of the network; the distribution of traffic due to a given origin-destination
matrix. For these reasons, the proposed model can be the basis of an interactive software
tool to be used as a decision support system, for instance, by Urban Planning Experts or
Public Administrators.

3.1 The model
- In order to define the model (Biancardi, De Lotto and Ferrara, 2000), the problem is to
consider M facilities Sj, 1≤j≤M of a certain nature to be located in a urban context under
the following assumptions:
- each facility has the assigned capacity to serve Cj clients per hour;
- the spatial distribution of the potential clients over the urban territory is known (more
precisely, the spatial distribution is discretized into elementary units called “cells”);
- each cell i, 1≤i≤N , contains p i (t) potential clients (time function valued in number of
clients per hour);
- the i-th cell is centred in the i-th road intersection, 1≤i≤N, N being the total number of
roads intersections of the urban transportation network considered.
The p i -th client's choice of the facility to reach is dictated by the cost to access the facility. In
the case of transportation by means of private vehicles, such a cost can be modelled as
directly proportional to the vehicle travel time t(i,j) from the i-th road intersection, from
which the p i -th client starts, to the j-th road intersection, where the facility is located. The
global vehicle travel time is obviously the sum of the travel times associated with the links
of the transportation network through which the client moves to reach the facility.
The urban transportation network can be represented by a graph with N nodes and a set of
oriented branches l(i,j), i≤N, j≤N, connecting the i-th node with the j-th node, with the travel
direction from i to j. Each link is marked by a label which defines the time-varying travel
time law on the link itself as a function of the traffic volume n ij (t) . To further refine the
model of the access to a facility the following aspects should be determinable:
- for any node, the time to access the nearest facility;

- the nodes “captured” by a facility, and the corresponding burden in terms of clients.

This, in turn, allows one to identify the influence area of each facility delimited, on the
nodes map, by the border lines connecting the nodes with associated longer access time;

- the number of clients reaching each facility;

- the induced traffic variation in each branch of the transportation network;

- the total cost for the users which is implied by the selected facility location: this quantity

can be computed by summing up all the access times associated with the nodes
multiplied for the number of clients arriving from each node.

3.2 The access time computation
To determine the quantities indicated above, it is necessary to compute the travel time
corresponding to each link of the considered transportation network, making reference to
the particular traffic conditions in the time interval of interest. The travel time is provided as
a function of the traffic intensity, of the parameters which determine the traffic fluidity, and