Analysis Of Customers’ Optimal Strategies In Continuous-Time Queueing Systems

Due to broad applications for management in service systems, it has brought a research boom to study customer behavior in queueing systems from an economic viewpoint at home and abroad recently. By using the knowledge of game theory, this paper analyzes customer behavior in two types of classical queueing model and obtains the customers’ optimal policy in both types of queues on the basis of predecessors’ work.Firstly, this paper investigates the equilibrium balking strategies of customers in M/M/1 queueing system subject to Poisson generated partial failures and repairs. That is, whenever a partial failure occurs, customers are not allowed to enter and the server undertakes the present workload with a lower-rate service rather than completely stops to work. When the system becomes empty, the server is rendered inoperative and an exponential repair time is set on. Upon arrival, the customers make their decisions whether to join or balk based on different precision levels of system information, along with the natural reward-cost structure. This paper discusses the fully observable and fully unobservable queues respectively. For each type of queue, the corresponding Nash equilibrium balking strategies of customers and the expected social benefits per time unit are derived.Secondly, this paper studies the optimal balking strategies of customers with a higher priority in the preemptive M/G/1 queue, where there are two classes of customers who have different priorities. When a low-priority customer is being served, the arriving high-priority customer preempts the server while the low-priority customer will go back to the head of the queue of its class. The preempted customer resumes service at the point of interruption upon reentering the service facility. Upon arrival, the high-priority customers that aiming to maximizing their own benefits decide for themselves whether to join or balk based on a natural reward-cost structure. This paper derives the individual optimal strategy(equilibrium strategy) and social optimal strategy for the high-priority customers in the unobservable case.Finally, this paper considers the strategic behavior of customers with a lower priority in the preemptive M/G/1 queue, where there are two classes of customers who have different priorities. Different from the high-priority customers, the low-priority customers may be preempted in their service process, thus it is necessary to analyze their decision problem. This paper deals with the strategic behavior of the low-priority customers in the unobservable cases and derives the corresponding equilibrium and optimal balking strategies in the end.