The busy period in the fluid queue
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Joint Distributions for Interacting Fluid Queues
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
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Approximate analysis of a network of fluid queues
ACM SIGMETRICS Performance Evaluation Review
Continuous PEPA queues: individual behaviour in continuous queueing networks
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Fluid level in a reservoir with an on-off source
ACM SIGMETRICS Performance Evaluation Review
Response time distribution of flash memory accesses
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
A performance analysis of discrete-time tandem queues with Markovian sources
Performance Evaluation
Response time distribution of flash memory accesses
Performance Evaluation
A fluid analysis framework for a Markovian process algebra
Theoretical Computer Science
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Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional 'heavy traffic' approximations to the recent advances in bio-chemical system models. Here we present a simple approximate compositional method for analysing a network of fluid queues with Markov-modulated input processes at equilibrium. The idea is to approximate the on/off process at the output of a queue by an n-state Markov chain that modulates its rate. This chain is parameterised by matching the moments of the resulting process with those of the busy period distribution of the queue. This process is then used, in turn, as a separate Markov-modulated on/off process that feeds downstream queue(s). The moments of the busy period are derived from an exact analytical model. Approximation using two- and three-state intermediate Markov processes are validated with respect to an exact model of a tandem pair of fluid queues - a generalisation of the single queue model. The analytical models used are rather simpler and more accessible, albeit less general, than previously published models, and are also included. The approximation method is applied to various fluid queue networks and the results are validated with respect to simulation. The results show the three-state model to yield excellent approximations for mean fluid levels, even under high load.