Help desk center operating model as a two-phase queueing system

We consider a two-phase queueing system with a Markovian arrival flow as an operating model for a help desk center. The first phase is a multiserver system with a finite buffer and impatient customers. After getting service in the first phase, a customer either enters the second phase with an infinite buffer or quits the system. Service times at the first and second stages have phase-type distributions with different parameters. We obtain an existence condition for a stationary regime of the system. An algorithm for computing stationary probabilities and basic performance characteristics of the system is presented. Laplace-Stieltjes transforms for the distributions of sojourn and waiting times in the first and second phases are found. Results of numerical experiments are presented. Optimization problem for the system operation is solved numerically.