Fluid models for call centers with delay announcement and retrials

This paper models a call center as a multi-server queue where anticipated delays are announced to customers upon arrival, and customer balking, reneging and retrials are modeled explicitly. The resulting queue with delay announcement is modeled in a stationary setting. We propose a fluid approximation to estimate the possibility of announcing the mean delay distribution and the retrials in the system. This approximation method can overcome some of the computational issues involved with a continuous time Markov chain analysis. The fluid approximation is also validated that it can work well in overloaded systems by performing a comparison between the fluid model and the stochastic model with delay information, and by performing the other comparison between the fluid model and the simulation model. Through a numerical study, this paper demonstrates the significance of delay information in a call center with retrials. In particular, delay announcement is more important in the system with a high retrial probability. Thus, we show how a delay announcement greatly reduces customer reneging and thereby improves customer satisfaction. It is shown that disregarding retrials in call centers with delay information may result in large distortions in the management of call centers.