Airline and high-speed rail collaboration and competition under travel time variability

With the expansion of high-speed rail (HSR) service in many countries, competition between HSR and regional air transport has become increasingly fierce. However, HSR can also serve as a collaborator to connect passengers from hubs to smaller cities, potentially benefiting both modes of transportation. This paper presents a stochastic equilibrium model of transportation mode choices for intercity travelers, considering both flight and HSR options under travel time variability and the possibility of missing flights. HSR is assumed to provide fixed travel time and highfrequency service, while airlines ' flight times and security delays are subject to variability expressed as probability distributions. In addition, the study proposes an optimization model for operators to determine the optimal route frequency and itinerary fare, and investigates the fare equilibrium condition under competition, with or without modal collaboration. In the numerical exercises, the impact of introducing HSR and its service frequency on airline ridership, as well as the effect of customs control time variance and flight time variance on pricing, are investigated. The findings reveal the potential impacts of HSR on airline ridership, and suggest the importance of considering differences in travel time and security delay variabilities between HSR and airlines. Furthermore, the frequency optimization result shows the benefit of collaboration between airline and HSR, where hub -to -hub routes are emphasized and some passengers are split to transfer to HSR.