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Tandem Retrial Queueing System with Correlated Arrival Flow and Operation of the Second Station Described by a Markov Chain

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Computer Networks (CN 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 291))

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Abstract

Tandem queues are good mathematical models for description of information transmission in various communication systems and networks. These queues play also an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, their investigation is interesting for theory and applications. In this paper, we consider tandem queue suitable for modeling the systems and networks where information flows are correlated and bursty what is typical for many modern telecommunication networks. Possible correlation of customers inter-arrival times and batch arrivals are taken into account via of consideration of the Batch Markovian Arrival Process (BMAP) as input stream to the system. The system consists of two stations. The service time at the station 1 is assumed to be generally distributed. There is no buffer at this station, and customers who meet the busy server repeat attempts to enter the system in random time intervals. The service process at the station 2 is assumed to be described by the continuous time Markov chain with a finite state space. This assumption holds good, e.g., if the station 2 has a finite buffer, consists of a finite number of identical or heterogeneous servers where the service time distribution is assumed to be of PH (PHase) type. Markov chain embedded at service completion epochs at the station 1 and the process of system states at arbitrary time are under study. Ergodicity condition and algorithms for computing the steady state probabilities are presented.

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Author information

Authors and Affiliations

  1. Sangji University, Wonju, Kangwon, 220-702, Korea

    Chesoong Kim

  2. Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

    Alexander Dudin & Valentina Klimenok

Authors
  1. Chesoong Kim
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  2. Alexander Dudin
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  3. Valentina Klimenok
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    Andrzej Kwiecień

  2. Institute of Informatics, Silesian University of Technology, ul. Akademicka 16, 44-100, Gliwice, Poland

    Piotr Gaj

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Piotr Stera

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© 2012 Springer-Verlag Berlin Heidelberg

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Kim, C., Dudin, A., Klimenok, V. (2012). Tandem Retrial Queueing System with Correlated Arrival Flow and Operation of the Second Station Described by a Markov Chain. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2012. Communications in Computer and Information Science, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31217-5_39

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  • DOI: https://doi.org/10.1007/978-3-642-31217-5_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31216-8

  • Online ISBN: 978-3-642-31217-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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