Systems in stochastic equilibrium
Systems in stochastic equilibrium
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Product Form and Local Balance in Queueing Networks
Journal of the ACM (JACM)
Multiplicativity of Markov Chains with Multiaddress Routing
Problems of Information Transmission
State-dependent Coupling of Quasireversible Nodes
Queueing Systems: Theory and Applications
Traffic Flows and Product Form Solutions in Stochastic Transfer Networks
Queueing Systems: Theory and Applications
Insensitivity in processor-sharing networks
Performance Evaluation
ON THE STRUCTURE OF THE SPACE OF GEOMETRIC PRODUCT-FORM MODELS
Probability in the Engineering and Informational Sciences
Proceedings of the joint international conference on Measurement and modeling of computer 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
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This study concerns the equilibrium behavior of a general class of Markov network processes that includes a variety of queueing networks and networks with interacting components or populations. The focus is on determining when these processes have product form stationary distributions. The approach is to relate the marginal distributions of the process to the stationary distributions of “node transition functions” that represent the nodes in isolation operating under certain fictitious environments. The main result gives necessary and sufficient conditions on the node transition functions for the network process to have a product form stationary distribution. This result yields a procedure for checking for a product form distribution and obtaining such a distribution when it exits. An important subclass of networks are those in which the node transition rates have Poisson arrival components. In this setting, we show that the network process has a product form distribution and is “biased locally balanced” if and only if the network is “quasi-reversible” and certain traffic equations are satisfied. Another subclass of networks are those with reversible routing. We weaken the known sufficient condition for such networks to be product form. We also discuss modeling issues related to queueing networks including time reversals and reversals of the roles of arrivals and departures. The study ends by describing how the results extend to networks with multi-class transitions.