W. Zhang, B. Derudder, J. Wang, F. Witlox / Bulletin of Geography. Socio-economic Series / 31 (2016): 145–160
149
and time) can also be used as an indicator of mea-
suring the possibility of inter-city journeys (see for
example, Wang et al., 2009; Spence, Linneker, 1994).
A major obstacle to using this proxy of interaction
potential is that infrastructures merely enable the
‘potential’ of inter-city interactions; actual passenger
volumes are co-determined by the ‘demand’ for
inter-city interactions and this ‘supply’ of transport
infrastructures. The ‘demand’ for inter-city travel
can be attributed to the socio-economic attributes
of cities and the distance between cities (Davies,
1979; Krings et al., 2009). Even having convenient
and efficient transport infrastructures linking to
each other does not guarantee that two (social or
economic) proximate cities will also exchange a lot
of passengers.
A related approach for assessing the potential
is using a range of combined measures that not
only reflect the quality of infrastructure networks,
but also the demand for inter-city linkages. For in-
stance, the indicator of weighted travel time sug-
gested by Gutiérrez (1996; 2001) consists of travel
times and urban mass which refers to, for example,
gross domestic product or population. However, the
‘demand’ for inter-city linkages is using simulation
approaches rather than more direct measures. Taken
together, these indices expressing the potential of
inter-city interaction by train mirror the quality or
efficiency of train transport infrastructures itself.
2.2. A proxy based on infrastructure volumes
The number of daily or weekly trains has been used
as a proxy (Derudder et al., 2014; Hall et al., 2006).
Using this proxy instead of the measurements
outlined in the previous section has two advantages.
As the volume of carriages contains more direct
information of inter-city flows, it seems to be a more
suitable measure of passenger flows. In addition, the
information on train numbers can be collected via
open information platforms of transport companies
much easier than through other ways such as
surveys. This proxy also can be viewed as the as-
sessment of transport infrastructures per se, which
indicates the traffic supply of infrastructure net-
works at the level of carriages.
Using the volume of carriages assumes that
every train holds similar passenger volumes, which
is of course is problematic. More importantly, this
proxy also assumes that the number of trains is
proportional to the volume of inter-city passengers
between any pair of cities. This is problematic
assumption because operationally, train networks
are organized by chain structures, unlike air travel
or bus trips where direct non-stop services are
main organizational forms. A link from an origin
to a destination produces n(n-1)/2n(n-1)/2 links
between any pair of stations if there are n stations
en route. In this case, the most important cities hold
similar positions with smaller cities that can be found
on same railway line, although this obviously does
not conform to the actual distribution of inter-city
flows of passengers. As a corollary, the volumes of
passengers of ‘major cities’ tend to be underestimat-
ed, while the roles of ‘small cities’ located on major
traffic arteries tend to be overstated. Consequently,
this proxy structurally predetermines a flatter
structure in the urban hierarchy than warranted.
3. An alternative approach
to approximating passenger flows
in railway networks
3.1. Dwell time
Dwell time, the time a train remains in a given
station, is primarily determined by the number of
boarding and alighting passengers, as well as some
extra factors such as passenger behavior, platform
and vehicle characteristics, and dispatching rules
(Lin, Wilson, 1992; Wiggenraad, 2001; Jong, Chang,
2011). It is a key parameter of the capacity and
performance of operation of trains as insufficient
dwell time would lead to train delays, while exces-
sive dwell time would result in inefficient operations
(Jong, Chang, 2011). Dwell time, therefore, is set by
scientific and efficient principles, which mainly fol-
low the experience of the length of boarding and
alighting processes from the past. A normal dwell
time lasts between 2 and 5 minutes, with a dwell
time of over 5 minutes often implying extraordinary
dispatching such as coupling, decoupling, and
meeting occurs in that station.
These underlying principles suggest that there is
a potential for modelling passenger flows based on
the corresponding dwell time in a certain station.
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150
However, eliminating the influence of extraordinary
dispatching rules on dwell time is needed: special
dispatching (e.g. overtaking, meeting, insufficient
headway) clearly biases the interpretation of dwell
times, and thus represent outliers. In our research,
we will adopt the strategy of replacing outliers with
mean values. This is mainly based upon two con-
siderations: (i) simply deleting outliers would be
equal to suggesting that trains did not stop in these
stations, which is obviously unreasonable; and (ii)
as the cause of producing outliers is known in our
case, it is possible to replace these outliers using
reasonable values to eliminate the effect of abnor-
mal dispatching.
After dealing with outliers, the adjusted dwell
times thus correspond with the time of boarding
and alighting. According to Jong and Chang’s re-
search (2011), the linear relation between the time
of passenger flows and the volume of passenger
flows is statistically significant. We thus introduce
a dummy parameter ‘r’, which refers to the correla-
tion coefficient between passenger volumes and the
boarding and alighting time, to simulate the vol-
ume of passenger flows. That is, the volume of pas-
senger flows ‘v’ is dependent on its adjusted dwell
time ‘t’, so that:
v = t × r
(1)
The stations of origin and destination do not
have dwell times, albeit that they are often the main
sources of passengers. To this end, we impose an as-
signed value by setting a relatively reliable boarding
and alighting time in starting and terminal stations
for empirical regions. In our case, the HSR net-
work within the Yangtze River Delta region, most
maximal dwell times (after replacing outliers) are
around 5 minutes . We posit that the passenger vol-
ume from original or to terminal station resemble
(or slight exceed) the passenger volume in the larg-
est transit station as a general rule. Thus, we assign
the dummy dwell time as 3 minutes.
3.2. Approximating passenger flows
between city-pairs
As our object of research is cities rather than train
stations, we combine multiple stations into one city
through summing adjusted dwell times in the case
of there being multiple stations in a single city.
From an operational perspective, the distribution
of passenger flows for a given train that passes ‘n’
cities can be summarized by means of an upper tri-
angular matrix as shown in table 1, where ‘v
ij
’ is the
number of passengers boarding in city ‘i’ and alight-
ing in city ‘j’. In table 1, each row indicates the dis-
tribution of alighting for passengers boarding in city
‘i’; each column indicates the distribution of board-
ing for passengers alighting in city ‘j’. As a conse-
quence, the sum of each row (V
ix
) is the number of
boarding passengers in city ‘i’, and the sum of each
column (V
xj
) is the number of alighting passengers
in city ‘j’.
Table 1. The distribution of passenger flows for a certain train
Alighting city
Boarding city
City
1
City
2
…
City
j
…
City
(n-1)
City
n
City
1
0
v
1,2
…
v
1,j
…
v
1,n-1
v
1,n
City
2
0
0
…
v
2,j
…
v
2,n-1
v
2,n
…
…
…
…
…
…
…
…
City
i
0
0
…
v
i,j
…
v
i,n-1
v
i,n
…
…
…
…
…
…
…
…
City
(n-1)
0
0
…
0
…
0
v
n-1,n
City
n
0
0
…
0
…
0
0
Source: Own studies
Following equation (1), passenger volumes in
city ‘i’ and ‘j’ can be obtained by:
v
ix
+ v
xi
= v
i
= t
i
× r
(2)
v
jx
+ v
xj
= v
j
= t
j
×r (3)
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