Joint Admission and Aggregate Service Rate Control of an Unobservable Queue

We consider a joint admission and aggregate service rate control problem in a service system. Admission control involves deciding which arriving customers to admit and which to reject. Aggregate service rate control focuses on determining the staffing level and/or service rate for the system. We consider a general reward structure and a convex service cost structure to capture many variations that arise in practice. We show that, under specific structural properties of the revenue and cost functions, the joint optimization of admission and aggregate service rate decisions can be analyzed to produce interesting and implementable policies. Specifically, for systems with a linear service cost structure, we identify a critical operational threshold for the arrival rate. For arrival rates below this threshold, the optimal policy is to close the system and reject all customers. Above this threshold, the optimal policy is to admit all customers and choose an aggregate service rate that depends on the actual arrival rate. In contrast, for systems with a strictly convex service cost structure, under certain conditions, we identify two operational thresholds for the arrival rate. When the arrival rate is below the lower threshold, it is optimal to close the system. It is optimal to admit all customers and choose an arrival-rate-dependent aggregate service rate for arrival rates between the two thresholds. Above the higher threshold, the optimal admission rate and the optimal aggregate service rate do not change any further. We further demonstrate the value of joint optimization by comparing it with two natural benchmarks—optimizing admission rate alone and optimizing aggregate service alone. In stationary arrival settings, we show that joint optimization not only informs the critical decision of whether to operate but also shows that optimizing admission rate or aggregate service rate alone can lead to significant profit losses. We then extend the analysis to nonstationary arrivals with real-world call center data, which further demonstrates the practical value of joint optimization.

• 저널Production and Operations Management
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1177/10591478261471260
• 저자Wei Liu, Vidyadhar G. Kulkarni