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

  • Laszlo LakatosEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 678)


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.


Queue length Discrete cyclic-waiting system Geo/G/1 


  1. 1.
    Koba, E.V.: On a GI/G/1 queueing system with repetition of requests for service and FCFS service discipline. Dopovidi NAN Ukrainy 6, 101–103 (2000). (in Russian)zbMATHGoogle Scholar
  2. 2.
    Koba, E.V., Pustova, S.V.: Lakatos queuing systems, their generalization and application. Cybern. Syst. Anal. 48, 387–396 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lakatos, L., Szeidl, L., Telek, M.: Introduction to Queueing Systems with Telecommunication Applications. Springer, Berlin (2013)CrossRefzbMATHGoogle Scholar
  4. 4.
    Lakatos, L., Efroshinin, D.: Some aspects of waiting time in cyclic-waiting systems. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 115–121. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-35980-4_13 CrossRefGoogle Scholar
  5. 5.
    Lakatos, L., Efrosinin, D.: A discrete time probability model for the waiting time of optical signals. Commun. Comput. Inf. Sci. 279, 114–123 (2014)zbMATHGoogle Scholar
  6. 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 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Eotvos Lorand UniversityBudapestHungary

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