Research Article
Network of Queues with Inert Customers and Signals
@INPROCEEDINGS{10.4108/icst.valuetools.2013.254369, author={Jean Michel Fourneau and Thu Ha Dao Thi and Minh Anh Tran}, title={Network of Queues with Inert Customers and Signals}, proceedings={7th International Conference on Performance Evaluation Methodologies and Tools}, publisher={ICST}, proceedings_a={VALUETOOLS}, year={2014}, month={1}, keywords={queuing networks signals product-form}, doi={10.4108/icst.valuetools.2013.254369} }- Jean Michel Fourneau
Thu Ha Dao Thi
Minh Anh Tran
Year: 2014
Network of Queues with Inert Customers and Signals
VALUETOOLS
ACM
DOI: 10.4108/icst.valuetools.2013.254369
Abstract
We introduce the concept of inert customers in a generalized queue with signals. A signal interacts with the customers when it arrives in a non empty queue. Then, it disappears instantaneously. Ordinary customers wait for service and eventually receive service if they do not interact with a signal heforehand. An inert customer does not receive service. It stays in the queue until an interaction with a signal makes it disappear. As it is present in the queue, it has an effect on the service capacity. We consider multiple classes of ordinary customers and a symmetric queueing discipline for ordinary and inert customers. In this paper we consider two types of interaction between signals and inert customers: the deletion of one inert customer and the deletion of a group of inert customers. Despite this deep modification of the model, the queue is still quasi-reversible. Therefore we prove that such a network of queues have a steady-state product form solution.
We illustrate this approach with various examples consisting in PS and LIFO queues.