Equilibrium Queueing Strategies in M/G/1 Queues with the Reference Time Effect

Waiting is a major factor influencing the perception of delay-sensitive customers in the service industry. In the process of queueing, some customers often have a psychological expectation of waiting time in the face of uncertain delay information, so that customer service utility depends not only on the actual waiting time, but also on the relative amount of the actual waiting time and the psychological expectation of waiting time. Therefore, this paper investigates how the reference time effect affects heterogeneous customers' queueing decisions and service system efficiency measures (system throughput and social welfare) in an M/G/1 queue with limited service resources and capacity. The results show that the equilibrium joining probability of customers, the system throughput and social welfare are relatively higher as the proportion of customers with high tolerance levels in the queue increases. In addition, the maintenance of customer homogeneity is better for the improvement of service resource utilization, while the maintenance of customer heterogeneity is better for social welfare. As the psychological expected waiting time increases, the equilibrium joining probability of potential customers and the system throughput increase, while the equilibrium joining probability of existing customers decreases, and the social welfare shows a non-monotonic trend of first decreasing and then increasing. The equilibrium queueing strategies for each type of customer and the service system efficiency measures are not monotonic with the change of the reference time effect parameter. Finally, the optimal social welfare is increasing with respect to the degree of reference time effect and the psychological expectation of waiting time.