The Modeling of Call Center Functioning in Case of Overload

Abstract

The mathematical model of call center functioning in case of overload is constructed and analyzed. In the model multi-skilled routing based on usage of one group of operators capable of serving simple requests and several groups of experts (consultants) handling more advanced topics is taken into account together with the possibility of request repetition in case of blocking or unsuccessful waiting time. Markov process that describes model functioning is constructed. Main performance measures of interest are defined through the values of stationary probabilities of model’s states. Algorithm of characteristics estimation is suggested based on solving the system of state equations. Expressions that relates introduced performance measures in form of conservation laws are derived. It is shown how to use found relations for quantitative and qualitative analysis of the model functioning. The usage of the model for elimination of call center overload based on reducing of the input flow is considered.