Computers & Operations Research 34 (2007) 983 – 996 www.elsevier.com/locate/cor Applications of maximum queue lengths to call center management J.R. Artalejo a , ∗ , A. Economou b , A. Gómez-Corral a a Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain b Department of Mathematics, University of Athens, Panepistemiopolis, Athens 15784, Greece Available online 29 June 2005 Abstract This paper deals with the distribution of the maximum queue length in two-dimensional Markov models. In this framework, two typical assumptions are: (1) the stationary regime, and (2) the system homogeneity (i.e., homogeneity of the underlying infinitesimal generator). In the absence of these assumptions, the computation of the stationary queue length distribution becomes extremely intricate or, even, intractable. The use of maximum queue lengths provides an alternative queueing measure overcoming these problems. We apply our results to some problems arising from call center management.  2005 Elsevier Ltd. All rights reserved. Keywords: Call center; Maximum queue length; Level dependent quasi-birth-and-death processes; Customer behavior; Routing rules 1. Introduction In recent years, there has been a rapidly growing interest on call centers making emphasis on design and management problems. A comprehensive review of the existing literature can be found in the survey papers by Gans et al. [1], and Koole and Mandelbaum [2]. ∗ Corresponding author. Fax: +34 913944606. E-mail addresses: jesus_artalejo@mat.ucm.es (J.R. Artalejo), aeconom@math.uoa.gr (A. Economou), antonio_gomez@mat.ucm.es (A. Gómez-Corral). 0305-0548/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2005.05.020