Asymptotically optimal staffing of service systems with joint QoS constraints

Jing Zan, John J. Hasenbein*, David P. Morton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 case of deterministic arrivals.

Original languageEnglish (US)
Pages (from-to)359-386
Number of pages28
JournalQueueing Systems
Issue number4
StatePublished - Oct 16 2014


  • Erlang-C formula
  • Halfin–Whitt regime
  • Parameter uncertainty

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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