Monotonicity Properties for Multiserver Queues with Reneging and Finite Waiting Lines

We consider a markovian multiserver queue with a finite waiting line in which a customer may decide to leave and give up service if its waiting time in queue exceeds its random deadline. We focus on the performance measure in terms of the probability of being served under both transient and stationary regimes. We investigate monotonicity properties of first and second order of this performance with respect to the buffer size, say k. Under the stationary regime, we prove that our service level is strictly increasing and concave in k, whereas we prove under the transient regime that it is only increasing in k.