Some universal limits for nonhomogeneous birth and death processes

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 (...

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Bibliographic Details
Published inQueueing systems Vol. 52; no. 2; pp. 139 - 151
Main Authors Zeifman, A., Leorato, S., Orsingher, E., Satin, Ya, Shilova, G.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.02.2006
Subjects
Approximation
Cauchy problems
Childbirth & labor
Estimating techniques
Mathematical functions
Mortality
Pedagogy
Studies
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-006-4353-9