Article ID: | iaor20102717 |
Volume: | 64 |
Issue: | 4 |
Start Page Number: | 359 |
End Page Number: | 382 |
Publication Date: | Apr 2010 |
Journal: | Queueing Systems |
Authors: | Kella Offer, Mandjes Michel, Boxma Onno |
Keywords: | vacation models |
This paper considers queues with server vacations, but departs from the traditional setting in two ways: (i) the queueing model is driven by Lévy processes rather than just compound Poisson processes; (ii) the vacation lengths depend on the length of the server's preceding busy period. Regarding the former point: the Lévy process active during the busy period is assumed to have no negative jumps, whereas the Lévy process active during the vacation is a subordinator. Regarding the latter point: where in a previous study (Boxma et al. in Probab. Eng. Inf. Sci. 22:537–555, 2008) the durations of the vacations were positively correlated with the length of the preceding busy period, we now introduce a dependence structure that may give rise to both positive