Two-Heterogeneous Server Markovian Queueing Model with Discouraged Arrivals, Reneging and Retention of Reneged Customers

 Customer impatience (reneging) has negative impact on the performance of queueing systems. If we talk from business point of view, firms lose their potential customers due to customer impatience which affects their business as a whole. It is envisaged that if the firms employ certain customer retention strategies then there are chances that a certain fraction of impatient customers can be retained in the queueing system for their further service. Recently, Kumar and Sharma (2012c) study a finite capacity multi-server Markovian queueing system with discouraged arrivals, reneging and retention of reneged customers. They consider homogeneous servers. In real life, the servers that are not mechanically controlled may not possess same service rates. Thus, it is more appropriate to consider heterogeneous servers. In this paper, we extend the work of Kumar and Sharma (2012c) by considering heterogeneous servers. We consider a two-heterogeneous servers’ finite capacity Markovian queueing system with discouraged arrivals, reneging and retention of reneged customers. The steady-state probabilities of system size are derived explicitly by using iterative method. Some useful measures of effectiveness are also derived and discussed. Finally, some important queueing models are derived as the special cases of this model.