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- W2107260166 abstract "We study the functionals of a Poisson marked process<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Pi$><mml:mi>Π</mml:mi></mml:math>observed by a renewal process. A sequence of observations continues until<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Pi$><mml:mi>Π</mml:mi></mml:math>crosses some fixed level at one of the observation epochs (the first passage time). In various stochastic models applications (such as queueing with<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$N$><mml:mi>N</mml:mi></mml:math>-policy combined with multiple vacations), it is necessary to operate with the value of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Pi$><mml:mi>Π</mml:mi></mml:math>prior to the first passage time, or prior to the first passage time plus some random time. We obtain a time-dependent solution to this problem in a closed form, in terms of its Laplace transform. Many results are directly applicable to the time-dependent analysis of queues and other stochastic models via semi-regenerative techniques." @default.
- W2107260166 created "2016-06-24" @default.
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- W2107260166 date "2001-01-01" @default.
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- W2107260166 title "On functionals of a marked Poisson process observed by a renewal process" @default.
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- W2107260166 doi "https://doi.org/10.1155/s0161171201005221" @default.
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