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Some universal limits for nonhomogeneous birth and death processes

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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 X N . Finally we present some examples where these bounds are used in order to approximate the double mean.

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Authors and Affiliations

  1. Vologda State Pedagogical University, S. Orlova, 6, Vologda, Russia

    A. Zeifman, Ya. Satin & G. Shilova

  2. Vologda Science Coordination Centre CEMI RAS., Vologda, Russia

    A. Zeifman

  3. University of Rome ‘La Sapienza’, P.le A. Moro, 5, Rome, Italy

    S. Leorato & E. Orsingher

Authors
  1. A. Zeifman
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  2. S. Leorato
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  3. E. Orsingher
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  4. Ya. Satin
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  5. G. Shilova
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Correspondence to A. Zeifman.

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AMS Subject Classification: Primary: 60J27 Secondary: 60K25 34A30

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Zeifman, A., Leorato, S., Orsingher, E. et al. Some universal limits for nonhomogeneous birth and death processes. Queueing Syst 52, 139–151 (2006). https://doi.org/10.1007/s11134-006-4353-9

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  • DOI: https://doi.org/10.1007/s11134-006-4353-9

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