A passenger distribution analysis model for the perceived time of airplane boarding/deboarding, utilizing an ex-Gaussian distribution
Introduction
Airplane movements at airports worldwide have been on an increasing trend lately, and airline companies are implementing various measures to reduce the time between flight arrival and departure to ensure timeliness. Within the flow of events from the time the airplane reaches the airport, the passengers disembark, the airplane's interior is cleaned and prepared, supplies are replenished, the next passengers board, to when the airplane departs again, boarding and deboarding take a long time, mainly because the passenger aisle is narrow and gets congested. Therefore, airline companies must reduce passenger boarding time for timely departure of flights. Consequently, airlines have developed various passenger boarding methods, such as boarding by row or giving priority boarding for passengers seated from back to front (Marelli et al., 1998, Van Landeghem and Beuselinck, 2002). Modifying the boarding time using boarding methods has been modeled in computer simulations in the past (Marelli et al., 1998, Van Landeghem and Beuselinck, 2002, Briel et al., 2003, Ferrari and Nagel, 2005, Bachmat et al., 2006; and Steffen, 2008). These methods have also been confirmed through experiments that used a mock-up of airplanes (Steffen, 2012). These studies confirm that the back-to-front boarding method does not necessarily minimize airplane boarding time.
On the other hand, in recent years, research related to perceived time is attracting attention in the field of travel behavior research. For example, a study on public transportation travel time found that the perceived time for traveling is longer for car drivers with regard to public transportation than the actual public transportation travel time, which explains why the modal shift from cars to public transportation has been difficult (Van Exel and Rietveld, 2010). Also, if the waiting time at the station was long, the perceived travel time of public transportation became longer, which again impacted the choice of public transport (González et al., 2015). Because the level of satisfaction greatly impacts airline selection, reducing actual boarding and deboarding times is critical for the airlines to increase passenger satisfaction. In addition to shortening the physical boarding time, shortening perceived time is also effective in improving passenger satisfaction.
This study focused on modeling the perceived time of boarding/deboarding, a topic presently unexplored in the literature. Moreover, it attempted to understand how passengers evaluate boarding and deboarding times, using an ex-Gaussian distribution enabled to determine the proportion of passengers whose perceived time was longer than the actual physical time it took for them to board and deboard. This will be useful in developing measures to improve passengers' level of satisfaction.
Section snippets
Experiments
We conducted an experiment that compared perceived time with measured time, where the latter is the physical time taken to board and deboard. The experiment was conducted using tables and chairs placed in a room and were made to resemble the interior of an airplane. Participants acting as passengers were handed boarding passes and instructed to go to their allotted seats. A stopwatch was used to measure the duration from the time the first passenger entered the airplane to the time that the
The model
In Fig. 2, the passenger distribution that takes Tp/Tm as the variable is positively skewed. With respect to constructing the passenger distribution model, positively skewed distributions, such as a log-normal distribution, an ex-Gaussian distribution, a Weibull distribution, and a Gumbel distribution, are considered appropriate. As is clear from the results of the experiment, there is a difference with respect to the proportion of Tp/Tm > 1 for each case. Therefore, formulating a model using
Discussion
In the field of experimental psychology, time perception refers to the time interval that is estimated by one's own perception. Numerous studies have been conducted in this field, and several models have been constructed and proposed on the basis of the experimental results. For example, in the change model, a participant's internal clock changes depending on their metabolism (Hoagland, 1933, Hoagland, 1981); in the storage size model, perceived time changes depending on the amount of
Conclusion
This study showed that in airplane boarding and deboarding, the proportion of passengers for whom perceived time was longer than measured time can be expressed through the τ parameter of an ex-Gaussian distribution. This is possible by modeling passenger distribution using an ex-Gaussian distribution with the ratio of perceived time and measured time taken as the variable. Further, differences in the load factor, seat pitch, and boarding/deboarding methods are considered as the factors to
Acknowledgements
We sincerely appreciate the valuable discussions held with Professor Makoto Ichikawa from Chiba University, Special Associate Professor Satoru Nakajo from The University of Tokyo, and Associate Professor Daichi Yanagisawa from The University of Tokyo. This work was supported by JSPS KAKENHI Grant Number 25287026.
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