Bayesian analysis of Markov modulated queues with abandonment

We consider a Markovian queueing model with abandonment where customer arrival, service and abandonment processes are all modulated by an external environmental process. The environmental process depicts all factors that affect the exponential arrival, service, and abandonment rates. Moreover, the environmental process is a hidden Markov process whose true state is not observable. Instead, our observations consist only of customer arrival, service, and departure times during some period of time. The main objective is to conduct Bayesian analysis in order to infer the parameters of the stochastic system, as well as some important queueing performance measures. This also includes the unknown dimension of the environmental process. We illustrate the implementation of our model and the Bayesian approach by using simulated and actual data on call centers.