Queueing analysis of internet-based call centers with interactive voice response and redial

Recently, call centers are important from a customer service point of view because they have a significant impact on customer satisfaction. In general, most of the management cost for call centers is labor cost for Customer Service Representatives (CSRs), and it is important for companies to manage CSRs in a cost-effective manner, keeping a high quality of customer service. Therefore, most of companies install Interactive Voice Response systems (IVRs) in order to not only reduce CSR management cost, but also to provide high-quality customer service. In this paper, focusing on call centers with IVRs, we investigate the impact of the service time at IVRs and number of IVRs on the utilization of a CSR. To this end, we model the call center with IVRs by a queueing system with retrials, analyzing the steady state probability by a continuous-time Markov chain. We derive performance measures such as the mean number of redialing customers, the blocking probability and the mean sojourn time. Numerical results show that under a low arrival rate of new calls, the utilization of a CSR is insensitive to the IVR service time as well as to the number of IVRs, and that the utilization grows proportionally with the increase in the probability that a customer in an IVR leaves for the CSR service.