In queueing theory, a discipline within the mathematical theory of probability, a G-network (generalized queueing network,[1][2] often called a Gelenbe network[3]) is an open network of G-queues first introduced by Erol Gelenbe as a model for queueing systems with specific control functions, such as traffic re-routing or traffic destruction, as well as a model for neural networks.
[4][5] A G-queue is a network of queues with several types of novel and useful customers: A product-form solution superficially similar in form to Jackson's theorem, but which requires the solution of a system of non-linear equations for the traffic flows, exists for the stationary distribution of G-networks while the traffic equations of a G-network are in fact surprisingly non-linear, and the model does not obey partial balance.
This broke previous assumptions that partial balance was a necessary condition for a product-form solution.
satisfy Then writing (n1, ... ,nm) for the state of the network (with queue length ni at node i), if a unique non-negative solution
satisfies the global balance equations which, quite differently from Jackson networks are non-linear.
G-networks have been used in a wide range of applications, including to represent Gene Regulatory Networks, the mix of control and payload in packet networks, neural networks, and the representation of colour images and medical images such as Magnetic Resonance Images.
The response time for a tandem pair of G-queues (where customers who finish service at the first node immediately move to the second, then leave the network) is also known, and it is thought extensions to larger networks will be intractable.