On the busy-period distributions ofM/G/1/Kqueues by state-dependent arrivals and FCFS/LCFS-P service disciplines

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The busy-period distributions ofM/G/1/Kqueues with state-dependent arrival rates are considered. Two recursion formulas for the Laplace–Stieltjes transforms of the busy periods under the FCFS and preempt resume LCFS service disciplines are obtained. It is shown that the busy-period distributions for the two service disciplines are, in general, different, in contrast to the fact that they coincide for ordinaryM/G/1 queues. For deterministic service times and arrival rates non-increasing in the number of customers in the system, stochastic ordering between these two busy periods is also established.