G-networks with multiple classes of negative and positive customers
Theoretical Computer Science
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Networks of queues with batch services, signals and product form solutions
Operations Research Letters
Multiclass G-Networks of Processor Sharing Queues with Resets
ASMTA '08 Proceedings of the 15th international conference on Analytical and Stochastic Modeling Techniques and Applications
Analytical Modeling for Operating System Schedulers on NUMA Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
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
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The purpose of this tutorial presentation is to introduce G-Networks, or Gelenbe Networks, which are product form queueing networks which include normal or positive customers, as well as negative customers which destroy other customers, and triggers which displace other customers from one queue to another. We derive the balance equations for these models in the context of multiple customer classes, show the product form results, and exhibit the traffic equations which - in this case, contrary to BCMP and Jackson networks - are non-linear. This leads to interesting issues of existence and uniqueness of the steady-state solution. Gelenbe Network can be used to model large scale computer systems and networks in which signaling functions represented by negative customers and triggers are used to achieve flow and congestion control.