The Important Role of Time Limits when Consumers Choose their Time in Service

A main challenge that service providers face when managing service systems is how to generate value and regulate congestion at the same time. To this end, classical queueing models suggest managers charge per-use fees and invest in capacity to speed up the service. However, in discretionary services, in which consumers value time in service and choose how long to stay, per-use fees result in suboptimal performance and speeding-up does not apply. We study a queueing model of a service provider and rational consumers who are heterogenous in their requirements for service duration. Consumers incur disutility from waiting and choose whether to join and how long to stay in service. We consider time limits as a novel mechanism that may help in controlling congestion. Time limits put a cap on the maximum time that customers can spend in service. We analyze their effectiveness when combined with two price schemes: per-use fees and price rates. Time limits are effective because they reduce time in service and impact waiting times and joining behavior. Revenue maximizing firms and social planners who maximize social welfare benefit from implementing time limits in addition to price rates. Social planners who seek to maximize consumer welfare, however, should focus on regulating congestion and should therefore offer the service for free, but implement time limits, if congestion levels are high. The attractiveness of time limits goes further. We show that time limits are not only a useful lever that works well when combined with simple price mechanisms, but they are in fact optimal when congestion is high. Service providers can achieve the first-best outcome and extract all customer surplus by coupling a time limit with an optimal price mechanism. Thus, we conclude that providers of discretionary services should set time limits when congestion is an issue