The principal-agent problem for service rate event-dependency

Abstract

This study aims to determine the cost of letting an agent adjust the service rate to the last realized event, being a customer arrival or a service completion. We study this question in a single-server queue under a principal-agent framework. The principal seeks to reduce the expected waiting time by incentivizing the agent to modify the service rate through a performance-based payout. We show that a large range of improvement is achievable by selecting event-dependent service rates. However, the agent’s payout can grow high in the realized improvement, suggesting to limit the use of incentives for event-dependent service rates to a bounded waiting time improvement. When the service rate after an arrival is contractible, the agent should be paid more in contexts with a low variability inter-arrival time. The opposite conclusion holds when the average service rate is contractible. Further, we provide a criterion to determine when it is optimal for the agent to accelerate after an arrival or after a service completion. Finally, we investigate the effect of event-dependency on customers’ fairness and abandonment.