Bulletin of geography. Socio–economic series
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- 2.2. A proxy based on infrastructure volumes
- 3. An alternative approach to approximating passenger flows in railway networks 3.1. Dwell time
- 3.2. Approximating passenger flows between city-pairs
- Table 1.
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.
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.
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. - 10.1515/bog-2016-0010 Downloaded from De Gruyter Online at 09/23/2016 11:26:34AM via Universiteit Antwerpen
W. Zhang, B. Derudder, J. Wang, F. Witlox / Bulletin of Geography. Socio-economic Series / 31 (2016): 145–160 150
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)
- 10.1515/bog-2016-0010 Downloaded from De Gruyter Online at 09/23/2016 11:26:34AM via Universiteit Antwerpen
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