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The Total Overflow during a Busy Cycle in a Markov-Additive Finite Buffer System

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Book cover Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance (MMB&DFT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5987))

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Abstract

We consider a finite buffer system where the buffer content moves in a Markov-additive way while it is strictly between the buffer boundaries. Upon reaching the upper boundary of the buffer the content is not allowed to go higher and for every additional input into the system a penalty must be paid (to negotiate buffer overflow). At the lower boundary (empty buffer) the process terminates. For this system we determine the joint distribution of the total overflow and the last time of being at the upper boundary. The analysis is performed using excursion theory for Markov-additive processes.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, UK

    Lothar Breuer

Authors
  1. Lothar Breuer
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Editor information

Editors and Affiliations

  1. Institute for Computer Science and Business Information Systems, University of Duisburg-Essen, Schützenbahn 70, 45127, Essen, Germany

    Bruno Müller-Clostermann  & Klaus Echtle  & 

  2. Institute for Experimental Mathematics, Computer Networking Technology Group, University of Duisburg-Essen, Ellernstr. 29, D-45326, Essen, Germany

    Erwin P. Rathgeb

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© 2010 Springer-Verlag Berlin Heidelberg

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Breuer, L. (2010). The Total Overflow during a Busy Cycle in a Markov-Additive Finite Buffer System. In: Müller-Clostermann, B., Echtle, K., Rathgeb, E.P. (eds) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance. MMB&DFT 2010. Lecture Notes in Computer Science, vol 5987. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12104-3_16

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  • DOI: https://doi.org/10.1007/978-3-642-12104-3_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12103-6

  • Online ISBN: 978-3-642-12104-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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