The Impact of Inspection Cost on Equilibrium, Revenue, and Social Welfare in a Single-Server Queue
研究顾客在可付费获取队列长度信息时的决策均衡，发现检查成本高低决定队列信息应完全公开、完全不公开还是按需公开，且社会福利最大化要求检查成本为零。
Classical models of customer decision making in unobservable queues assume acquiring queue length information is too costly. However, due to recent advancements in communication technology, various services now make this kind of information accessible to customers at a reasonable cost. In our model, which reflects this new opportunity, customers choose among three options: join the queue, balk, or inspect the queue length before deciding whether to join. Inspection is associated with a cost. We compute the equilibrium in this model and prove its existence and uniqueness. Based on two normalized parameters—congestion and service valuation—we map all possible input parameter sets into three scenarios. Each scenario is characterized by a different impact of inspection cost on equilibrium and revenue-maximization queue disclosure policy: fully observable (when inspection cost is very low), fully unobservable (when inspection cost is too high), or observable by demand (when inspection cost is at an intermediate level). We show that when maximizing social welfare, the optimal disclosure policy is zero inspection cost. We show the structure remains the same when a fraction of the customers are considered urgent, that is, they always join, whereas the others are nonurgent and therefore join according to their equilibrium strategy.