Performance estimation of an email contact center by a finite source discrete time Geo/Geo/1 queue with disasters F. Jolai a, * , S.M. Asadzadeh a , M.R. Taghizadeh b a Department of Industrial Engineering, Faculty of Engineering, University of Tehran, Jalal Al Ahmad-karegar Cross, P.O. Box 11365-4563, Iran b Department of Industrial Management, Faculty of Management, University of Tehran, P.O. Box 14155-6311, Iran Received 7 June 2006; received in revised form 16 January 2008; accepted 16 January 2008 Available online 26 January 2008 Abstract In this paper, we model and analyze an email contact center as a queuing system. This queue system is a finite source discrete time Geo/Geo/1/1/N queue with disasters. The arrival process of ordinary customers (OCs) and disasters and service process are mutually independent and geometrically distributed. Disasters in this system cause the system to be empty at once. The main contribution of the paper is to model a clearing mechanism in a real finite source system with the aid of disasters. The system states are a Markov chain and we develop a numerical scheme to compute the steady state probabilities of the system. Some of the performance measures of the system are calculated. At the end numerical illustra- tions show how sensitive the system performance measures are when parameters of the system change. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Queue; Discrete time; Finite source; Disasters; Contact centers 1. Introduction In recent years, great attention has been paid to discrete time systems because of their ample application in communications. A fundamental motivation for the study of discrete-time queues is that these models are appropriate for modeling computer and telecommunications systems since the basic units are digital. In this sense, we refer to the books by Bruneel and Kim (1993) and Woodward (1994). Besides the communications applications of discrete time systems, these systems can be used in many cases such as traffic transportation, production and other stochastic systems. In Takagi (1993), discrete-time Geo/G/1/K/N systems are analyzed. To the best knowledge of the authors, this book is the most comprehensive one on this special topic in the existing literature. The assumption of geometric arrival and especially service time is a simplification of the system. Some of discrete time works that benefit this simplification are Artalejo and Herna ´ndez-Lerma 0360-8352/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2008.01.009 * Corresponding author. E-mail address: fjolai@ut.ac.ir (F. Jolai). Available online at www.sciencedirect.com Computers & Industrial Engineering 55 (2008) 543–556 www.elsevier.com/locate/caie