In this paper, we deal with an $D/GI/1$ vacation system with impatient customers. We give a sufficient condition for the existence of a limit distribution of the waiting time and integral equations are derived in both reneging and balking scenarios. Explicit solutions are given when vacation times are exponentially distributed and service times are either exponentially distributed or deterministic.
On First Come, First Served Queues with Two Classes of Impatient Customers
Remaining loads in a PH/M/c queue with impatient customers
Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
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