State-Dependent M/G/1 Queue with Multiple Vacations

Gi-Ren Liu

Department of Mathematics

National Cheng Kung University

girenliu@mail.ncku.edu.tw

    In this talk, we consider an M/G/1 queue, whose state depends on the workload. When the workload is equal to zero, the state will switch to the sleep state from the awake state. In order to avoid the ping-pong effect, the duration of the sleep state is determined by a sleep timer and the accumulated workload during the sleeping period. Hence, the waiting time for each service request depends on the system state. The random Sleep-Awake schedule has been used extensively in the design of modern communication systems for reducing the energy cost. For example, during the power saving mode, the message delivery will be delayed at some level. In view of that there exists a trade-off between the energy saving ratio and the service-communication delay, the waiting time analysis can provide a guideline for the operators to set up the length of sleep time for the Sleep-Awake scheme to maintain reasonable service delay and reduce the impact of buffer overflow. A recent work on the waiting time analysis for a restricted-length M/G/1 queue with multiple vacations will be presented in this talk. The details of its application on the design of green routers can be referred to [1] and [2].

Keyword: Waiting Time Analysis, Sleep-Awake scheme, M/G/1 queue, multiple vacations.