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SUMMARY:Busy Periods in Fluid Queues with Multiple Emptying Input States -
  Prof. Peter Harrison\, Imperial College London.
DTSTART:20091012T133000Z
DTEND:20091012T143000Z
UID:TALK20766@talks.cam.ac.uk
CONTACT:Neil Walton
DESCRIPTION:A semi-numerical method is derived to compute the Laplace tran
 sform of the equilibrium busy period probability density function  in a fl
 uid queue with constant output rate when the buffer is non-empty.  The inp
 ut process is controlled by a continuous time semi-Markov chain (CTSMC) wi
 th $n$ states such that  in each state the input rate is constant.  The ho
 lding time in states with net positive output rate -- so called {\\em empt
 ying states} -- is assumed to be an exponentially distributed random varia
 ble\, whereas in states with net positive input rate -- {\\em filling stat
 es} -- it may have an arbitrary probability distribution.  The result is d
 emonstrated by applying it to various systems\, including fluid queues wit
 h two on-off input sources. The latter exercise in part shows consistency 
 with prior results but also solves the problem in the case where there are
  two emptying states.  Numerical results are presented for selected exampl
 es which expose discontinuities in the busy period distribution when the n
 umber of emptying states changes\, e.g. as a result of increasing the flui
 d arrival rate in one or more states of the controlling CTSMC. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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