Some universal limits for nonhomogeneous birth and death processes |
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| Authors: | A Zeifman S Leorato E Orsingher Ya Satin G Shilova |
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| Institution: | (1) Vologda State Pedagogical University, S. Orlova, 6, Vologda, Russia;(2) Vologda Science Coordination Centre CEMI RAS., Vologda, Russia;(3) University of Rome ‘La Sapienza’, P.le A. Moro, 5, Rome, Italy |
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| Abstract: | In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are
studied, which are helpful to describe a nonhomogeneous BDP X = X(t), t≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration of the BDP). We find conditions of existence of the means and determine
bounds for their values, involving also the truncated BDP XN. Finally we present some examples where these bounds are used in order to approximate the double mean.
AMS Subject Classification: Primary: 60J27 Secondary: 60K25 34A30 |
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| Keywords: | Birth and death rates Kolmogorov differential equations Logarithmic norm Exponential stability |
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