Queueing Systems

, Volume 52, Issue 1, pp 105–118 | Cite as

Sample path large deviations for a family of long-range dependent traffic and associated queue length processes

  • Kurt Majewski


We consider the long-range dependent cumulative traffic generated by the superposition of constant rate fluid sources having exponentially distributed inter start times and Pareto distributed durations with finite mean and infinite variance. We prove a sample path large deviation principle when the session start time intensity is increased and the processes are centered and scaled appropriately. Properties of the rate function are investigated. We derive a sample path large deviation principle for a related family of stationary queue length processes. The large deviation approximation of the steady-state queue length distribution is compared with the corresponding empirical distribution obtained by a computer simulation.


Pareto distribution Fluid source Rate function 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Siemens AGMünchenUSA

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