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

Shanthikumar, J. George; Sumita, Ushio

J. Appl. Probab. 22, 912-919 (1985).

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

Keywords:

stochastic ordering; busy-period distributions; queues with state- dependent arrival rates; recursion formulas