Waiting time analysis of multi-class queues with impatient customers (Q2844474)

The authors first analyze the two-class non-preemptive priority \(\mathrm{M}/\mathrm{GI}/1+\mathrm{M}\) queue in Section 2 (the last symbol \(\mathrm{M}\) indicates that customers have exponential reneging times). They allow general and different service times distributions for each class as well as different reneging rates. In Section 3, they extend the problem to two-class multi-server queues. They assume identical exponential service time distributions for both classes yet retain different reneging rates in Section 3.1 and different deterministic patience limits in Section 3.2. In Section 4, they consider the FCFS policy when serving \(k\) classes of customers. In all models, the paper obtains the Laplace transform of the virtual waiting time by employing the level-crossing technique. Eventually, it gives the steady-state system performance measures.