Staffing Large Service Systems Under Arrival-rate Uncertainty

2013/04/24 by Jing Zan, Zan, Jing, John J. Hasenbein +3
Business, Management and Accounting · Health Professions · Social Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Healthcare Operations and Scheduling Optimization #Probability (math.PR) #Transportation Planning and Optimization

paper · pdf · doi:10.48550/arxiv.1304.6701

openalex publication_date 2013/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen-Van Leeuwaarden-Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the deterministic arrivals case.

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