Mixed Networks with Multiple Classes of Customers and Restart

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.