Abstract: There are many factors that affect the performance of a queuing system. Under certain assumptions, the number of waiters determines the service efficiency while the presence of impatient customers will affect the service earnings. Traditional queuing theory primarily analyzes queuing models with different time distribution types, while a Monte Carlo simulation model can adapt to the queuing processes of different time distribution types simultaneously. In this paper, several queuing models under common conditions were constructed and simulated by a Monte Carlo simulation; in particular, some commonly used indicators were analyzed. Through a comparison and analysis of the simulation results from these models, it is shown that if the number of waiters is adjusted based on the customer queuing circumstances, it can not only improve service efficiency, but also avoid excessive waste of idle resources and loss of customers. Meanwhile, the simulation results can be used as the basis for setting up queue types and model parameters, as well as a reference for decision making.

Key words: queuing theory, Monte Carlo simulation, backup waiters, impatient customers, customer loss