Quantitative and Qualitative Analysis of Aircraft Round-Trip Times Using Phase Type Distributions

One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make.