Systems in stochastic equilibrium
Systems in stochastic equilibrium
Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Closed queueing networks with batch services
Queueing Systems: Theory and Applications
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
Markov network processes with product form stationary distributions
Queueing Systems: Theory and Applications
Traffic Flows and Product Form Solutions in Stochastic Transfer Networks
Queueing Systems: Theory and Applications
State-Dependent Coupling in General Networks
Queueing Systems: Theory and Applications
ON TRUNCATION PROPERTIES OF FINITE-BUFFER QUEUES AND QUEUEING NETWORKS
Probability in the Engineering and Informational Sciences
State-dependent rates and semi-product-form via the reversed process
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
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 seminal paper of Jackson began a chain of research on queueing networks with product-form stationary distributions which continues strongly to this day. Hard on the heels of the early results on queueing networks followed a series of papers which discussed the relationship between product-form stationary distributions and the quasireversibility of network nodes. More recently, the definition of quasireversibility and the coupling mechanism between nodes have been extended so that they apply to some of the later product-form queueing networks incorporating negative customers, signals, and batch movements.In parallel with this research, it has been shown that some special queueing networks can have arrival and service parameters which depend upon the network state, rather than just the node state, and still retain a generalised product-form stationary distribution.In this paper we begin by offering an alternative proof of a product-form result of Chao and Miyazawa and then build on this proof by postulating a state-dependent coupling mechanism for a quasireversible network. Our main theorem is that the resultant network has a generalised product form stationary distribution. We conclude the paper with some examples.