Abstract
The paper develops a model to examine how different factors influence ferry users’ waiting time at the terminals. The estimations are based on interviews of 10,952 Norwegian ferry travellers just after they boarded the ferries. The interviews were conducted in 2013 at 16 of the most important ferry connections in Norway. The average headway and waiting time at the terminals were 52 and 15 min, respectively. By comparison, average sailing time at the services in question was 38 min, indicating that waiting-time costs at the terminals make up a large proportion of ferry users’ time costs. The model’s results show that the users’ waiting time at the terminals increases concavely with the ferries’ headway and distance travelled to the terminals, that is, the marginal effects of these factors diminish when their values increase. The first result indicates that the proportion of ferry users arriving randomly at the terminals decreases with the ferries’ headway. The model also reveals that a large proportion (20%) of the waiting times at the terminals is due to the travellers being unable to board their desired departure because of the ferries’ capacity restrictions. Other variables, like the mode of transport travellers’ used to get to the terminals, their income, and how often they used the service, influence waiting time significantly in the hypothesised directions, even though some (e.g. income and trip frequency) have very moderate influences on waiting time.
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Notes
\(\frac{18.7 \cdot 1.2 \cdot TK}{38.1 \cdot TK} \cdot 100\%\) = 0.59 in which TK are passengers’ time cost per unit of time in the ferries. The results in Wardman et al. (2016) indicate that our multiplier of 1.2 is a conservative estimate.
Suppose \(ET_{i}\) is the expected driving time for kilometer i to the ferry quay and \(ET = ET_{1} + ET_{2} + \cdots + ET_{n}\) is total expected driving time and n is total trip length in kilometer to the ferry quay. When we assume the Ti values are independent with identical distributions, we obtain \(\sigma_{T} = \sigma_{{T_{1} }} \cdot \sqrt n\), where \(\sigma_{{T_{1} }}\) and σT are standard deviations of driving time per kilometer and driving time for the total trip to the ferry port, respectively.
For high-frequency ferry services (headway less than 30 min), a large proportion of travellers will arrive randomly to the terminals, and DT will have little influence on waiting time.
If the headway between the departures is longer than, for example, 45 min, a large proportion of frequent travellers will not arrive randomly to the ferry quays.
When most travelers arrive randomly at the terminals (headway less than 30 minutes), their expected waiting time is (fairly) independent of the ferries’ punctuality but will increase with the rate of cancelled departures.
This service level is far lower than the stated goal from the Norwegian authorities of 98%.
From formula (1) follows \(\frac{\partial WT}{\partial Z} = c\alpha_{Z} Z^{c - 1} > 0, \frac{{\partial^{2} WT}}{{\partial Z^{2} }} \ge \left( { < 0} \right)\; {\text{when}}\; c \ge \left( < \right)1,c=a,b, Z = HE, DT\).
AIC is Akaike information criterion, see Fox (2016).
In our dataset approximately 7%.
Let headway, HE\(= \frac{O}{F}\) where O are opening hours and F frequency. Using the power relationship between waiting time (WT) and headway in formula (1) it can be deduced that \(\frac{dWT}{dF } \ < {0\; {\text{and}}\; \frac{{d^{2} WT}}{{dF^{2} }}} \ > 0\). Hence, WT deceases convexly with F meaning that the marginal effect of F on WT diminishes. The same is true for hidden waiting time (HT). The above implies that the marginal benefits for the users of increasing frequency decline.
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Appendix: The Questionnaire
Appendix: The Questionnaire
Only questions applied in this study are included. The complete questionnaire can be observed in Denstadli et al. (2013).
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Hanssen, TE.S., Jørgensen, F. & Larsen, B. Determinants affecting ferry users’ waiting time at ferry terminals. Transportation 47, 1711–1732 (2020). https://doi.org/10.1007/s11116-019-09979-5
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DOI: https://doi.org/10.1007/s11116-019-09979-5