Introduction to queueing networks
Introduction to queueing networks
G-networks with multiple classes of negative and positive customers
Theoretical Computer Science
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
Discrete Event Dynamic Systems
An initiative for a classified bibliography on G-networks
Performance Evaluation
Bibliography on G-networks, negative customers and applications
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.00 |
We continue the study of zero-automatic queues first introduced in [3]. 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 0-automatic queues are quasi-reversible [3]. 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 content has a "product-form" and can be explicitly determined.