Analysis of a Queueing Model with Flexible Priority, Batch Arrival, and Impatient Customers

In this study, we consider a multi-server priority queueing model with batch arrivals of two types of customers, a finite buffer, and two input finite buffers for storing customers that cannot be admitted for service immediately upon arrival. The transition of a customer from an input buffer to the main buffer can occur after an exponentially distributed time. Customers residing in the input and main buffers are impatient. The four-dimensional Markov chain is used to describe the dynamics of the system under consideration. It is analyzed via the derivation of its generator and providing an effective algorithm for computing its steady-state probabilities. Formulas for calculating the system's major performance metrics are established. Numerical results demonstrating the suggested methods' viability and the effect of variation of transition rates of customers from the input buffers are presented.