In this thesis, we first study delay systems with different classes of impatient customers. We analyze the M/GI/1+M queue serving two priority classes under the static non-preemptive priority discipline. We also study the multi-server priority queue considering two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to obtain the steady-state system performance measures. In the second part, we consider the steady-state waiting time distributions of a two class M/GI/1 queue operating under a dynamic priority discipline. We find an accurate approximation for the steady-state waiting time distribution of the low-priority customers which allows us to study how they are penalized as the priority parameter increases. We also obtain bounds for the variance of the waiting time of high-priority customers.MAS
