Vacations in GIX/MY/1 systems and Riemann boundary value problems

Vacations in GIX/MY/1 systems and Riemann boundary value problems

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Article ID: iaor20002523
Country: United States
Volume: 27
Issue: 3/4
Start Page Number: 351
End Page Number: 366
Publication Date: Apr 1997
Journal: Queueing Systems
Authors:
Keywords: GI/M/1 queues, vacation models, bulk queues
Abstract:

We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities of the embedded Markov chain are found in terms of Riemann boundary value problems, and a necessary and sufficient condition of ergodicity is proved. Explicit formulas are obtained for the case where the generating function of the arrival group size is rational. Resonance between the vacation rate and the system is studied. Complete formulas are given for the cases of single and geometric arrivals.

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