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On the Queue Length in the Discrete Cyclic-Waiting System of Geo/G/1 Type

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Distributed Computer and Communication Networks (DCCN 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 678))

Abstract

We consider a discrete time queueing system with geometrically distributed interarrival and general service times, with FCFS service discipline. The service of a customer is started at the moment of arrival (in case of free system) or at moments differing from it by the multiples of a given cycle time T (in case of occupied server or waiting queue). Earlier we investigated such system from the viewpoint of waiting time, actually we deal with the number of present customers. The functioning is described by means of an embedded Markov chain considering the system at moments just before starting the services of customers. We find the transition probabilities, the generating function of ergodic distribution and the stability condition. The model may be used to describe the transmission of optical signals.

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References

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  6. Lakatos, L.: On the waiting time in the discrete cyclic–waiting system of Geo/G/1 type. In: Vishnevsky, V., Kozyrev, D. (eds.) DCCN 2015. CCIS, vol. 601, pp. 86–93. Springer, Heidelberg (2016). doi:10.1007/978-3-319-30843-2_9

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Authors and Affiliations

  1. Eotvos Lorand University, Budapest, Hungary

    Laszlo Lakatos

Authors
  1. Laszlo Lakatos
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Correspondence to Laszlo Lakatos .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University , Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Lakatos, L. (2016). On the Queue Length in the Discrete Cyclic-Waiting System of Geo/G/1 Type. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-51917-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51916-6

  • Online ISBN: 978-3-319-51917-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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