Some universal limits for nonhomogeneous birth and death processes

Authors:
A. Zeifman;S. Leorato;E. Orsingher;Ya. Satin;G. Shilova
Affiliations:
Aff1 Aff2;University of Rome `La Sapienza', Rome, Italy;University of Rome `La Sapienza', Rome, Italy;Vologda State Pedagogical University, Vologda, Russia;Vologda State Pedagogical University, Vologda, Russia
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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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驴 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.