G-network

In <a href="/facts/Queueing_theory/8NDl56EM">queueing theory</a>, a discipline within the mathematical <a href="/facts/Probability_theory/mFBn51rE">theory of probability</a>, a G-network (generalized queueing network, often called a Gelenbe network) is an open network of G-queues first introduced by <a href="/facts/Erol_Gelenbe/9w6XrywD">Erol Gelenbe</a> as a model for queueing systems with specific control functions, such as traffic re-routing or traffic destruction, as well as a model for <a href="/facts/Neural_networks/DDhJTfMc">neural networks</a>. A G-queue is a network of queues with several types of novel and useful customers:

<ul><li>positive customers, which arrive from other queues or arrive externally as Poisson arrivals, and obey standard service and routing disciplines as in conventional network models,</li>
<li>negative customers, which arrive from another queue, or which arrive externally as Poisson arrivals, and remove (or 'kill') customers in a non-empty queue, representing the need to remove traffic when the network is congested, including the removal of "batches" of customers</li>
<li>"triggers", which arrive from other queues or from outside the network, and which displace customers and move them to other queues</li></ul>
A <a href="/facts/Product-form_solution/NC3xSFck">product-form solution</a> superficially similar in form to <a href="/facts/Jackson%2527s_theorem_(queueing_theory)/voB5d1kI">Jackson's theorem</a>, 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. A powerful property of G-networks is that they are universal approximators for continuous and bounded functions, so that they can be used to approximate quite general input-output behaviours.

G-network open-in-new

G-network