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**Staffing many-server systems with admission control and retrials.**
*(English)*
Zbl 1318.60091

Summary: In many-server systems it is crucial to staff the right number of servers so that targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are difficult to solve. During the last decade, a powerful many-server asymptotic theory has been developed to solve such problems and optimal staffing rules are known to obey the square-root staffing principle. In this paper we develop many-server asymptotics in the so-called quality and efficiency driven regime, and present refinements to many-server asymptotics and square-root staffing for a Markovian queueing model with admission control and retrials.

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

### Keywords:

many-server systems; QED regime; Halfin-Whitt regime; Markovian queueing model; heavy traffic; diffusion limits; admission control; retrials; square-root staffing; optimality gap
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\textit{A. J. E. M. Janssen} and \textit{J. S. H. van Leeuwaarden}, Adv. Appl. Probab. 47, No. 2, 450--475 (2015; Zbl 1318.60091)

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