Product form in networks of queues with batch arrivals and batch services
Queueing Systems: Theory and Applications
Markovian network processes: congestion-dependent routing and processing
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
State-dependent Coupling of Quasireversible Nodes
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Markov network processes with product form stationary distributions
Queueing Systems: Theory and Applications
State-Dependent Coupling in General Networks
Queueing Systems: Theory and Applications
Insensitivity in processor-sharing networks
Performance Evaluation
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 paper focuses on product form and related tractable stationary distributions in a general class of stochastic networks with finite numbers of nodes such that their network states are changed through signal transfers as well as internal transitions. Signals may be customers in traditional queueing applications, but we do not make any restriction on their effects at departing as well as arriving nodes. They may also instantaneously move around among different nodes. Furthermore, signal routing may depend on the whole network state. For analytical simplicity, we assume that the state space is countable. For such a network, we propose an abstract model, called a stochastic transfer network, and consider the stationary distribution of the network state. We introduce conditional traffic rates for arrivals and departures. Using them, we consider when the network has product form or some other tractable stationary distributions.