Abstract
We consider a network of queues with multiples classes of customers and restart signals. A restart signal makes a customer in the queue change its class and restart to the first step of service. The queues which receive signals can have an infinite server or a processor sharing discipline. The service time distributions are hyper-exponential, which can have high variance and are realistic for many real-world applications, such as transmission times over the internet. For distributions with large variability the restart mechanism can be useful. We prove that, under ergodicity condition, such a model has a product form steady-state distribution. This model contains two original features which were previously not allowed in a network of queues with negative customers: a part of the network is closed and some stations are Infinite Server queues.
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Fourneau, JM., Wolter, K. (2015). Mixed Networks with Multiple Classes of Customers and Restart. In: Gribaudo, M., Manini, D., Remke, A. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2015. Lecture Notes in Computer Science(), vol 9081. Springer, Cham. https://doi.org/10.1007/978-3-319-18579-8_6
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DOI: https://doi.org/10.1007/978-3-319-18579-8_6
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