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BUSY PERIODS IN FLUID QUEUES WITH MULTIPLE EMPTYING INPUT STATES

<05>The paper’s main result overcomes a major limitation in previous models of fluid queues that has prevented their use in many important application domains. The result, which allows arbitrary fluid arrival rates at the inputs to a queue, has formed the basis of several subsequent performance modelling studies involving both continuous and discrete processes, for example battery power management (http://doi.ieeecomputersociety.org/10.1109/MASCOTS.2011.61), renewable energy systems (http://pubs.doc.ic.ac.uk/energy-networks-valuetools/energy-networks-valuetools.pdf) and flash memory (http://arxiv.org/pdf/1209.3315v1.pdf). It also has applications in the approximate analysis of fluid queue networks where the ‘on’ periods of a queue are determined by the busy periods (with arbitrary fluid rates) of upstream queues.