Abstract
Single-server queues in which the server takes vacations arise naturally as models for a wide range of computer, communication, and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload, and queue length processes. In the present study, we allow the length of a vacation to depend on the length of the previous active period (viz. the period since the previous vacation). Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution, both for single and multiple vacations. We conclude by discussing several special cases, including polling models, and relate our findings to results obtained earlier.
| Original language | English |
|---|---|
| Pages (from-to) | 537-555 |
| Number of pages | 19 |
| Journal | Probability in the Engineering and Informational Sciences |
| Volume | 22 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 2008 |
Bibliographical note
Funding Information:The authors are grateful to the referee for several interesting questions and useful suggestions. Part of this work was done while the third author visited EURANDOM and CWI as a Stieltjes visiting professor. The third author is also supported by grant 964/06 from the Israel Science Foundation and the Vigevani Chair in Statistics. The research of the first and second author was done within the framework of the BRICKS project and the European Network of Excellence Euro-NGI.