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.

在餐饮业和旅游业等服务行业中，经验发现表明，不知情的客户可能将排队视为服务质量的信号，并选择加入更长的排队。服务经理意识到这种现象，并通过排队来刺激客户购买。在本文中，我们使用状态依赖队列探索与服务系统的从众和拥塞之间的平衡有关的问题。在我们的模型中，羊群效应由系统空闲概率（而不是系统繁忙概率）表示，拥塞由队列长度的非递减函数表示。提出了以长期平均成本最小化和交通强度约束为目标的优化问题，并对其优化解决方案的结构进行了表征。进一步，我们找到了最佳状态依赖业务强度和最佳服务速率切换状态的闭式解，并刻画了最佳解与系统参数之间的关系。通过一系列命题和数值示例，我们深入了解了羊群效应的刺激与减少客户等待之间的平衡，并建议服务管理者在队列较短时应有意放慢速度，而在队列不足时应全速运行。长。