A storage process by semi-Markov input
Keyword(s):
A sequence of random variables η 0, η 1, …, ηn , … is defined by the recurrence formula ηn = max (η n–1 + ξn , 0) where η 0 is a discrete random variable taking on non-negative integers only and ξ 1, ξ 2, … ξn , … is a semi-Markov sequence of discrete random variables taking on integers only. Define Δ as the smallest n = 1, 2, … for which ηn = 0. The random variable ηn can be interpreted as the content of a dam at time t = n(n = 0, 1, 2, …) and Δ as the time of first emptiness. This paper deals with the determination of the distributions of ηn and Δ by using the method of matrix factorisation.
Keyword(s):
2006 ◽
Vol 13
(01)
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pp. 25-35
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2019 ◽
Vol 33
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pp. 7809-7815
1980 ◽
Vol 9
(1)
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pp. 1-18
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