Performance estimation of an email contact center by a finite source discrete time Geo/Geo/1 queue with disasters

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/∞/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 illustrations show how sensitive the system performance measures are when parameters of the system change.