Analysis of a busy period queuing system with balking, reneging and motivating

Queuing model is widely applied in production, inventory and service industries. It is fundamental to improve the performance of queuing model by characterizing the practical queuing characteristics. In this paper, we consider impatient behaviors of customers who possibly balk and renege in a multi-server busy period queuing system, and study strategic behavior of the service provider who attempts to improve service rate when the system is busy. The piecewise curves with threshold structure are used to construct the dynamic inputting probability, dynamic service degree and dynamic reneging rate, and they are introduced to model the balking, motivating and reneging behaviors of the busy queue. The steady-state probabilities and the performance measures of the proposed model are derived. Finally, an empirical example is given to show the effectiveness of the proposed model by comparing it with the queuing model in literature.