Matrix analytic method and working vacation queues - a survey.

*(English)*Zbl 1183.90128Summary: As a generalization of classic queueing models with vacations, the working vacation queues were introduced in 2002, where the server serves customers at a lower rate rather than completely stopping service during the vacation period. This type of vacation models can be applied in performance evaluation of optical communication networks, production and service systems, and other fields. In recent years, the research on working vacation queues has considerable developments. This paper is intended to provide a survey of the research in this area. Furthermore, it demonstrates that the matrix analytic approach developed by Neuts et al. is a powerful tool in analyzing the working vacation queues. Using this method, the stationary distributions and stochastic decomposition structures of the major performance measures can be derived. Based on these results, a theoretical framework for analyzing working vacation queues is established.

##### MSC:

90B22 | Queues and service in operations research |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |