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 the transient regime, as well as the one under the stationary regime. We investigate the 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 under the transient regime, we prove that it is only an increasing function of $k$.