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Processor sharing G-queues with inert customers and catastrophes: a model for server aging and rejuvenation. (English) Zbl 1443.68035

Summary: We consider open networks of queues with processor-sharing discipline and signals. The signals deletes all the customers present in the queues and vanish instantaneously. The customers may be usual customers or inert customers. Inert customers do not receive service but the servers still try to share the service capacity between all customers (inert or usual). Thus a part of the service capacity is wasted. We prove that such a model has a product-form steady-state distribution when the signal arrival rates are positive.

MSC:

68M20 Performance evaluation, queueing, and scheduling in the context of computer systems

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