A Model of a Packet Aggregation System

  • Jung Ha Hong
  • Oleg Gusak
  • Neal Oliver
  • Khosrow Sohraby
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4263)


The decision and ability to aggregate packets can have significant impact on the performance of a communication system. The impact can be even more substantial when the system operates under a heavy load. In this paper, we present a queuing model which describes a packet encapsulation and aggregation process. Using this model, we provide analysis of the end-to-end delay of a packet transmitted by the system. The analytical model is verified by a simulation model of the system. We calculate the maximum number of packets in a single frame for which packet aggregation minimizes the average total delay of a packet. It is numerically shown that when the load is high, the higher the variability of the packet service time, the higher the maximum allowed number of packets in the frame should be to achieve the minimum average total packet delay. However, the impact of the variability of the packet service time is insignificant when the system load is moderate or low.


Service Time Markov Chain Model Probability Generate Function Laplace Stieltjes Transform Markov Modulate Poisson Process 
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  1. 1.
    Akar, N., Oguz, N.C., Sohraby, K.: A Novel Computational Method for Solving Finite QBD Processes. Communications in Statistics, Stochastic Models 16.2 (2000)Google Scholar
  2. 2.
    Akar, N., Oguz, N.C., Sohraby, K.: Matrix-Geometric Solution in Finite and Infinite M/G/1 Type Markov Chains: A Unifying Generalized State-Space Approach. IEEE J. on Selected Areas in Communications 16(5) (1998)Google Scholar
  3. 3.
    Akar, N., Sohraby, K.: An Invariant Subspace Approach in M/G/1 and G/M/1 Type Markov Chains. Communications in Statistics, Stochastic Models 13(3) (1997)Google Scholar
  4. 4.
    Bailey, N.T.J.: On queuing process with bulk service. J. of Royal Statistical Association 16 Series B, 80–87 (1954)Google Scholar
  5. 5.
    Chaudhry, M.L., Templeton, J.G.C.: A First Course in Bulk Queues. Wiley, New York (1983)MATHGoogle Scholar
  6. 6.
    Chaudhry, M.L., Medhi, J., Sim, S.H., Templeton, J.G.C.: On a two hetrogeneous-server Markovian queue with general bulk service rule. Sankhyā 49 Series B, pp. 35–50 (1987)Google Scholar
  7. 7.
    Flanagan, W.A.: Voice over Frame Relay. Telecom Books, New York (1997)Google Scholar
  8. 8.
    Medhi, J.: Waiting time distribution in a Poisson queue with general bulk service rule. Management Sci. 21, 777–782 (1975)MATHCrossRefGoogle Scholar
  9. 9.
    Medhi, J.: Recent Developments in Bulk Queueing Models. Wiley Eastern, New Delhi (1984)Google Scholar
  10. 10.
    Medhi, J.: Stochastic Models in Queueuing Theory, 2nd edn. Academic Press, London (2003)Google Scholar
  11. 11.
    Neuts, M.F.: A general class of bulk queues with Poisson input. Ann. Math. Stat. 38, 759–770 (1967)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Neuts, M.F.: Matrix-Geometric Solutions to Stochastic Models-An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1981)Google Scholar
  13. 13.
    Sim, S.H., Templeton, J.G.C.: Steady state results for the M/M(a,b)/c batch service system. Euro. J. Operations Research 21, 260–267 (1985)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jung Ha Hong
    • 1
  • Oleg Gusak
    • 1
  • Neal Oliver
    • 2
  • Khosrow Sohraby
    • 1
  1. 1.Dept. of Computer Science and Electrical EngineeringUniversity of Missouri – Kansas CityKansas CityUSA
  2. 2.Intel EuropeParsippanyUSA

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