Socio-behavioral Scheduling of Time-Frequency Resources for Modern Mobile Operators

  • Alexander Dudin
  • Evgeny Osipov
  • Sergey Dudin
  • Olov Schelén
Part of the Communications in Computer and Information Science book series (CCIS, volume 356)


This article presents a mathematical foundation for scheduling of batch data produced by mobile end users over the time-frequency resources provided by modern mobile operators. We model the mobile user behavior by Batch Markovian Arrival Process, where a state corresponds to a specific user data activity (i.e. sending a photo, writing a blog message, answering an e-mail etc). The state transition is marked by issuing a batch of data of the size typical to the activity. To model the changes of user behavior caused by the environment, we introduce a random environment which affects the intensities of transitions between states (i.e., the probabilities of the user data activities). The model can be used for calculating probability of packet loss and probability of exceeding the arbitrarily fixed value by the sojourn time of a packet in the system conditional that the packet arrives to the system at moments when the random environment has a given state. This allows to compute the realistic values of these probabilities and can help to properly fix their values that can be guaranteed, depending on the state of the random environment, by a service provider.


batch Markovian arrival process random environment phase type service time distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kim, C., Dudin, A., Klimenok, V., Khramova, V.: Performance analysis of multi-server queueing system operation under control of a random environment. Trends in Telecommunications Technologies, 315–344 (2010)Google Scholar
  2. 2.
    Dahlman, E., Parkvall, S., Sköld, J.: 4G: LTE/LTE-Advanced for Mobile Broadband. Elsevier (2011) ISBN: 978-0-12-385489-6,Google Scholar
  3. 3.
    Lucantoni, D.M.: New results on the single server queue with a batch Markovian arrival process. Comm. Statist.-Stochastic Models 7, 1–46 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Neuts, M.F.: Matrix-geometric solutions in stochastic models. The Johns Hopkins University Press (1981)Google Scholar
  5. 5.
    Ramaswami, V.: Independent Markov processes in parallel. Comm. Statist.-Stochastic Models 1, 419–432 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Ramaswami, V., Lucantoni, D.: Algorithms for the multi-server queue with phase-type service. Comm. Statist.-Stochastic Models 1, 393–417 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Kim, Ch., Dudin, S., Taramin, O., Baek, J.: Queueing system MAP/PH/N/N + R with impatient heterogeneous customers as a model of call center. Applied Mathematical Modelling (2012) Scholar
  8. 8.
    Kim, C., Klimenok, V., Orlovsky, D., Dudin, A.: Lack of invariant property of the Erlang loss model in case of MAP input. Queueing Systems 49, 187–213 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Kim, C., Klimenok, V., Mushko, V., Dudin, A.: The BMAP/PH/N retrial queueing system operating in Markovian random environment. Computers and Operations Research 37, 1228–1237 (2010)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alexander Dudin
    • 1
  • Evgeny Osipov
    • 2
  • Sergey Dudin
    • 1
  • Olov Schelén
    • 2
  1. 1.Belarusian State UniversityMinskBelarus
  2. 2.Lulea University of TechnologyLuleaSweden

Personalised recommendations