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On the busy-period distributions of M/G/1/K queues with state-dependent arrivals and FCFS/LCFS-P service disciplines. (English) Zbl 0576.60090
Summary: The busy-period distributions of M/G/1/K queues 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 ordinary M/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.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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