Waiting for public transport services: Queueing analysis with balking and reneging behaviors of impatient passengers

• Queueing problems of bulk arrival and service with the balking and reneging behavior of customers.
• Compound Poisson processes.
• Analytical analysis of probabilistic characteristics of bulk queues.
• Large-scale Monte-Carlo simulations in the context of public transport services.

Queues of batch arrivals and bulk service including balking and reneging behaviors of customers are commonly observed in real life. This study formulates queues of this type using compound Poisson processes and determines some key probabilistic measures. Analytical investigation is undertaken yielding a range of mathematical results. The developed mathematical model and approaches apply to a variety of practical queueing processes that are featured with bulk queues, balking, and reneging. A bus bridging response to rail disruption is considered as an application example. And large-scale Monte-Carlo simulations are conducted to demonstrate the mathematical results.