At busy terminal taxi stands, passengers and taxi drivers frequently experience prolonged waiting times due to congestion and inefficient matching processes. This study develops micro-level analytical models specifically tailored to capture the stochastic passenger boarding process and on-site operational controls, including passenger admission batch sizes and taxi stop-line positioning, using Markov chain and probability theory. We primarily analyze two representative operational scenarios: one characterized by a single long queue (typically of taxis) and another involving simultaneous congestion in both taxi and passenger queues. Both analytical and numerical results indicate that simple changes can result in substantial reductions in passenger waiting times and improvements in taxi outflow. The analytical framework is further extended to scenarios permitting spatial redesign or new boarding points, thereby broadening its applicability to diverse operating conditions. We further conduct time-of-day simulations with time-varying passenger and taxi arrivals to examine how the proposed strategies enhance the experiences of both passengers and taxi drivers in more realistic operating environments. The proposed strategies are rigorously validated through extensive numerical simulations and calibration with empirical data, highlighting significant real-world efficiency improvements and practical viability.
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