MMAP|M|N queueing system with impatient heterogeneous customers as a model of a contact center

A multi-server queueing system with infinite buffer and impatient heterogeneous customers as a model of a contact center that processes incoming calls (priority customers) and e-mail requests (non-priority customers) is investigated. The arrival flow is described by a Marked Markovian Arrival Process (MMAP). The service time of priority and non-priority customers by a server has an exponential distribution with different parameters. The steady state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace–Stieltjes transforms of the sojourn and waiting time distribution are derived. The problem of optimal choice of the number of contact center agents under the constraint that the average waiting time of e-mail requests does not exceed a predefined value is numerically solved.