The BCD queue and its ramifications

We introduce a process similar to the birth-death process and use it as a starting point for defining queueing models much in the same way as the birth-death process can be used for this purpose. Steady-state distributions for this process and the corresponding queues are derived. Generalizations allowing nonexponential service times are also studied.     

State-dependent Coupling of Quasireversible Nodes

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.     

Poisson flows in single class open networks of quasireversible queues

This paper analyzes open networks of quasireversible nodes with a single class of customers and in equilibrium. A simple argument shows, under a stability conditions, that a flow on a link of such a network is Poisson if and only if the link is not part of a loop. This loop criterion is shown to apply to the usual quasireversible networks with bounded service rates.