Geoscience Reference
In-Depth Information
However, the estimation of future ridership cannot only be based on line coverage
since it depends not only on the location of the stations of the line, but also on
the overall location of the network. In their paper, De Cea et al. (
1986
) use origin-
destination pairs for computing the total population affected by an improvement of a
transportation network. In Laporte et al. (
2005
), trip coverage is analytically defined
and used to compute the network coverage as a good estimate of future ridership.
The objective of minimizing the total travel time of passengers was introduced
in Vuchic and Newell (
1968
). These authors considered the case of a population
concentrated in a specified area and commuting to a central point. Their aim was to
determine an optimal interstation spacing, while taking access time, kinematics of
trains, dwell times and intermodal transfer times into account.
There exist a number of papers dealing with the location of new stations on
general railway lines. Here we will highlight some of them. Hamacher et al.
(
2001
) studied a problem in which the objective is to maximize the saving in
passenger travel time when introducing new stations. Schöbel (
2005
) considered
the maximization of coverage and the minimization of the number of new stations
as bicriteria problems. Gross et al. (
2009
) presented two models combining the
number of stations and the distances to them. In the first one, the objective is to
minimize the number of new stations assuming that the demand is covered within a
predefined distance. The second problem is NP-hard and consists of minimizing the
sum of distances from the demand points to the closest (old or new) station under the
constraint that the number of new stations is bounded above. They have considered
two environments for each problem (a planar space with an `
1
metric, and a network)
thus giving rise to four cases. For each case, they have identified a polynomial
complexity dominating set for the new stations. Körner et al. (
2012
) have dealt
with the problem of locating two new facilities in a mixed planar-network space so
that the number of trips between each pair of demand points is maximized. In this
paper it is assumed that an alternative mode of transportation exists. The authors
have analyzed the cases of segments and tree-networks and have also designed
polynomial time algorithms. For the case of more than two facilities to be located
on a segment, the big-cube-small-cube method has been shown to be efficient. In a
very recent paper by Carrizosa et al. (
2013
), the kinematics of the trains are taken
into account in order to minimize the total travel time when a given number of new
stops are located, as well as the total travel time of traversing all edges, subject to
the coverage of all demand points.
22.5
Conclusions
The design of rapid transit systems is a complex process which involves the
participation of many players. These projects are fraught with high costs and
uncertainty. Formulating models and designing algorithms for such problems is
difficult since the objectives and constraints are not as well defined as in many
operational research problems. Analytical techniques can be employed to assist
