Controlling Packet Loss of Bursty and Correlated Traffics in a Variant of Multiple Vacation Policy

  • Abhijit Datta Banik
  • Sujit K. Samanta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7753)


This paper presents a finite-buffer single server queue where packets arrive according to a batch Markovian arrival process (BMAP). Partial batch acceptance strategy has been analyzed in which the incoming packets of a batch are allowed to enter the buffer as long as there is space. When the buffer is full, remaining packets of a batch are discarded. The server serves till system is emptied and after that it takes a maximum H number of vacations until it either finds at least one packet in the queue or the server has exhaustively taken all the vacations. We obtain some important performance measures such as probability of blocking for the first-, an arbitrary- and the last-packet of a batch, mean queue lengths and mean waiting time of packet. The burstiness of the correlated traffic influences the probability of packet loss which makes buffer management to satisfy the Quality of Service (QoS) requirements.


Buffer management correlated arrivals variant of multiple vacation policy packet loss probability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Azad, A.P.: Analysis and Optimization of Sleeping Mode in WiMAX via Stochastic Decomposition Techniques. IEEE Journal on Selected Areas in Communications 29, 1630–1640 (2011)CrossRefGoogle Scholar
  2. 2.
    Banik, A.D.: The infinite-buffer single server queue with a variant of multiple vacation policy and batch Markovian arrival process. Applied Mathematical Modelling 33, 3025–3039 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Çinlar, E.: Introduction to stochastic process. Printice Hall, N.J. (1975)Google Scholar
  4. 4.
    Dudin, A.N., Shaban, A.A., Klimenok, V.I.: Analysis of a queue in the BMAP/G/1/N system. International Journal of Simulation 6, 13–23 (2005)Google Scholar
  5. 5.
    Grassmann, W.K., Taksar, M.I., Heyman, D.P.: Regenerative analysis and steady state distributions for Markov chains. Operations Research 33, 1107–1116 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Ke, J.C.: Operating Characteristic analysis on the M [X]/G/1 system with a variant vacation policy and balking. Applied Mathematical Modelling 31, 1321–1337 (2007)zbMATHCrossRefGoogle Scholar
  7. 7.
    Lucantoni, D.M.: New results on the single server queue with a batch Markovian arrival process. Stochactic Models 7, 1–46 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Lee, H.S., Srinivasan, M.M.: Control policies for the M X/G/1 queueing system. Management Science 35, 708–721 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Lucantoni, D.M., Meier-Hellstern, K.S., Neuts, M.F.: A single-server queue with server vacations and a class of non-renewal arrival process. Advances in Applied Probability 22, 676–705 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Miao, G., Himayat, N., Li, Y., Swami, A.: Cross-layer optimization for energy-efficient wireless communications: a survey. Wireless Communications Mobile Computing 9, 529–542 (2009)CrossRefGoogle Scholar
  11. 11.
    Neuts, M.F.: A versatile Markovian point process. Journal of Applied Probability 16, 764–779 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins Univ. Press, Baltimore (1981)zbMATHGoogle Scholar
  13. 13.
    Niu, Z., Shu, T., Takahashi, Y.: A vacation queue with set up and close-down times and batch Markovian arrival processes. Performance Evaluation 54, 225–248 (2003)CrossRefGoogle Scholar
  14. 14.
    Samanta, S.K., Gupta, U.C., Sharma, R.K.: Analyzing discrete-time D-BMAP/G/1/N queue with single and multiple vacations. European Journal of Operational Research 182(1), 321–339 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Tian, N., Zhang, Z.G.: Vacation queueing models: Theory and applications. International Series in Operations Research and Management Science. Springer, New York (2006)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Abhijit Datta Banik
    • 1
  • Sujit K. Samanta
    • 2
  1. 1.School of Basic SciencesIndian Institute of Technology SamantapuriBhubaneswarIndia
  2. 2.Department of MathematicsNational Institute of Science and TechnologyBerhampurIndia

Personalised recommendations