Performance analysis of call centers with abandonment, retrial and after-call work

This paper considers a multiserver queueing model with abandonment, retrial and after-call work for call centers. Upon a phone call, customers that find a free call line occupy the line immediately while those who see all the call lines busy are blocked and join an orbit. Customers holding a call line are served according to the first-come first-served discipline. After completing a call, the customer leaves the system while the server must start an after-call work and the call line is released for a newly arrived customer. Waiting customers may abandon after some waiting time and then either join the orbit or leave forever. Customers in the orbit retry to hold a free call line after some time. We formulate the queueing system using a continuous-time level-dependent quasi-birth-and-death process for which a sufficient condition for the ergodicity is derived. We obtain a numerical solution for the stationary distribution based on which performance measures such as the waiting time distribution and the blocking probability are derived. Using Little’s law, we obtain explicit formulae which verify the accuracy of the numerical solution. We compare our model with some simpler models which do not fully take into account some human behaviors. The comparison shows significant differences implying the importance of our model. Numerical results show various insights into the performance of call centers.