Chat Based Contact Center Modeling System Modeling, Parameter Estimation and Missing Data Sampling

A Markovian system model for a contact center chat function is considered and partially validated. A hypothesis test on real chat data shows that it is reasonable to model the arrival process as a Poisson process. The arrival rate can be estimated using Maximum likelihood. The service process is more involved and the estimation of the service rate depends on the number of simultaneous chats handled by an agent. The estimation is made more difficult by the low level of detail in the given data-sets. A missing data approach with Gibbs sampling is used to obtain estimates for the service rates. Finally, we try to capture the generalized behaviour of the service-process and propose to use generalized functions to describe it when little information is available about the system at hand.