Joint Service Depth and Priority Design in Queueing Systems

In AI-assisted service systems, the server can choose how much processing effort to spend on each job, which we call the service depth. Deeper reasoning improves output quality but occupies the server longer and increases congestion, and the realized processing time remains random because AI models are probabilistic and tasks vary in complexity. We study the joint design of service depth and priority in a single-server queue whose customers differ in delay sensitivity, with the goal of maximizing social welfare. For each customer type, the decision maker chooses a priority level and a service depth, and service times are exponential with mean equal to the chosen depth. With two customer types and linear service values, we characterize the centralized optimum. Counterintuitively, it prioritizes the patient type and gives it a smaller service depth when patient customers are sufficiently prevalent. When delay sensitivity is private, however, incentive compatibility requires the impatient type to receive a weakly shorter sojourn time, so the optimal price menu never prioritizes the patient type. Consequently, there can be a welfare gap between the centralized decision maker's optimal control policy and the optimal decentralized pricing mechanism. With a continuum of types, the centralized optimum is monotone: more delay-sensitive customers receive weakly smaller depth and higher priority, so the optimum can be implemented by a price menu with no welfare loss. Allowing randomized depths similarly closes the gap in the two-type model. Finally, we calibrate an agentic AI service system using published coding-agent trials from DeepSWE and numerically examine priority inversion, the value of joint design, and the welfare gain from personalization.