A fluid model for systems with random disruptions
Operations Research - Supplement to Operations Research: stochastic processes
A storage model with a two-state random environment
Operations Research - Supplement to Operations Research: stochastic processes
Analysis of a single-server queue interacting with a fluid reservoir
Queueing Systems: Theory and Applications
Markov-modulated Feedforward Fluid Networks
Queueing Systems: Theory and Applications
A TANDEM FLUID QUEUE WITH GRADUAL INPUT
Probability in the Engineering and Informational Sciences
An approximate compositional approach to the analysis of fluid queue networks
Performance Evaluation
Approximate analysis of a network of fluid queues
ACM SIGMETRICS Performance Evaluation Review
Stationary analysis of fluid level dependent bounded fluid models
Performance Evaluation
On a generic class of two-node queueing systems
Queueing Systems: Theory and Applications
Queueing analysis of a butterfly network for comparing network coding to classical routing
IEEE Transactions on Information Theory
Tandem fluid queues fed by homogeneous on-off sources
Operations Research Letters
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Motivated by recent traffic control models in ATM systems, we analyse three closely related systems of fluid queues, each consisting of two consecutive reservoirs, in which the first reservoir is fed by a two-state (on and off) Markov source. The first system is an ordinary two-node fluid tandem queue. Hence the output of the first reservoir forms the input to the second one. The second system is dual to the first one, in the sense that the second reservoir accumulates fluid when the first reservoir is empty, and releases fluid otherwise. In these models both reservoirs have infinite capacities. The third model is similar to the second one, however the second reservoir is now finite. Furthermore, a feedback mechanism is active, such that the rates at which the first reservoir fills or depletes depend on the state (empty or nonempty) of the second reservoir.The models are analysed by means of Markov processes and regenerative processes in combination with truncation, level crossing and other techniques. The extensive calculations were facilitated by the use of computer algebra. This approach leads to closed-form solutions to the steady-state joint distribution of the content of the two reservoirs in each of the models.