M/M/1 queues with working vacations (M/M/1/WV)

The classical single server vacation model is generalized to consider a server which works at a different rate rather than completely stops during the vacation period. Simple explicit formulae for the mean, variance, and distribution of the number and time in the system are presented. The distributional results generalize the classical vacation decomposition with no service during a vacation. This model approximates a multi-queue system whose service rate is one of the two speeds for which the fast speed mode cyclically moves from queue to queue with an exhaustive schedule. This work is motivated and illustrated by the analysis of a WDM optical access network using multiple wavelengths which can be reconfigured.