Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Performance of discrete-time queueing systems
Computers and Operations Research
Mixed gated/exhaustive service in a polling model with priorities
Queueing Systems: Theory and Applications
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We consider a discrete-time gated vacation system. The available buffer space is divided into two subsequent queues separated by a gate and new customers arrive either before or after this gate. Whenever all customers after the gate are served, the server takes a vacation. After each vacation, the gate opens which causes all waiting customers to move to the buffer space after the gate. The model under investigation allows to capture performance of a.o. the exhaustive and the gated queueing systems with multiple or single vacations. Using a probability generating functions approach, we obtain expressions for performance measures such as moments of system contents at various epochs in equilibrium and of customer delay. We conclude with a numerical example.