Busy-period and blocking behavior of finite queues with state-dependent Markov renewal arrivals

The busy-period length distributions and blocking probabilities are considered for finiteG/G/1/K queues with state-dependent Markov renewal arrivals. The Laplace-Stieltjes transforms of the distributions and blocking probabilities are given for the non-preemptive and last-come-first-served preemptive resume (or repeat) service disciplines. For Erlangian (or deterministic) service times in particular, it is proved that the busy-period length (the number of blocked customers) for the non-preemptive discipline is smaller (larger) than for the preemptive resume discipline.