Introduction to queueing networks
Introduction to queueing networks
G-networks with multiple classes of negative and positive customers
Theoretical Computer Science
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Stochastic Automata Networks with Master/Slave Synchronization: Product Form and Tensor
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Complex synchronizations in Markovian models: a tensor-based proof of product form
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Networks of symmetric multi-class queues with signals changing classes
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
G-networks with synchronised arrivals
Performance Evaluation
An initiative for a classified bibliography on G-networks
Performance Evaluation
Markovian queueing network with complex synchronizations: Product form and tensor
Performance Evaluation
Bibliography on G-networks, negative customers and applications
Mathematical and Computer Modelling: An International Journal
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We continue the study of zero-automatic queues first introduced in Dao-Thi and Mairesse (Adv Appl Probab 39(2):429---461, 2007). These queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The simple M/M/1 queue and Gelenbe's G-queue with positive and negative customers are the two simplest 0-automatic queues. All stable 0-automatic queues have an explicit "multiplicative" stationary distribution and a Poisson departure process (Dao-Thi and Mairesse, Adv Appl Probab 39(2):429---461, 2007). In this paper, we introduce and study networks of 0-automatic queues. We consider two types of networks, with either a Jackson-like or a Kelly-like routing mechanism. In both cases, and under the stability condition, we prove that the stationary distribution of the buffer contents has a "product-form" and can be explicitly determined. Furthermore, the departure process out of the network is Poisson.