Loss systems with slow retrials in the halfin-whitt regime

Florin Avram (1) , A.J.E.M. Janssen , J.S.H. van Leeuwaarden (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Department of mathematics and computing science [Eindhoven]

The Halfin-Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with theQEDregime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohenś equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohenś equation and Mills' ratio for the Gaussian and Poisson distributions. © 2013 Applied Probability Trust.

Domaines: Probabilités [math.PR]

Florin Avram, A.J.E.M. Janssen, J.S.H. van Leeuwaarden. Loss systems with slow retrials in the halfin-whitt regime. Advances in Applied Probability, 2013, 45 (1), pp.274-294. ⟨10.1239/aap/1363354111⟩. ⟨hal-00867035⟩