Balancing Herding And Congestion In Service Systems: A Queueing Perspective

In service industries such as restaurants and tourism, empirical findings show that uninformed customers may consider queues as a signal of service quality and choose to join a longer queue. Service managers become aware of this phenomenon and stimulate customer purchase by maintaining a queue. In this paper, we explore issues related to the balance between herding and congestion for service systems using a state-dependent queue. In our model, the herding effect is represented by system idle probability (as opposed to system busy probability) and the congestion is represented by a non-decreasing function of queue length. An optimization problem with the objective of minimizing the long-run average cost and constraints on traffic intensities is formulated, and the structure of its optimal solution is characterized. Further, we find closed-form solutions of the optimal state-dependent traffic intensity and the optimal service rate switching state, and characterize the relationship between the optimal solution and system parameters. Through a series of propositions and numerical examples, we gain insight into the balance between stimulation of herding effect and reduction of customer waiting, and propose that service managers should intentionally slow down when the queue is short and operate at their full speed when the queue is long.