Abstract
The packet delay variation, commonly called delay jitter, is an important quality of service parameter in IP networks especially for real-time applications. In this paper, we propose the exact and approximate models to compute the jitter for some non-Poisson FCFS queues with a single flow that are important for recent IP network. We show that the approximate models are sufficiently accurate for design purposes. We also show that these models can be computed sufficiently fast to be usable within some iterative procedure, e.g., for dimensioning a playback buffer or for flow assignment in a network.
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This work was supported by Grant No. 121949-2012 from the Natural Sciences and Engineering Research Council of Canada.
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Appendix: A Notation
Appendix: A Notation
For the sake of completeness, we recall the definitions of the distributions used in the paper.
1.1 A.1 Gamma
The cdf is the regularized gamma function
The parameters are related to the mean m and variance v = s 2 of the distribution by
which we can solve to get
1.2 A.2 Pareto
The Pareto Type I P(x; x m , α) with scale x m and shape α has a density function given by
The Pareto parameters α and x m are related to the mean m and variance v = s 2 by
For α > 2, we can solve (74–75) to get
1.3 A.3 Normal
We denote the pdf of the standard normal distribution
and the corresponding cdf
The error function is given by
and we have the relation
The pdf of a normally distributed random variables X with location μ and scale σ is given by
and the corresponding cdf by
1.4 A.4 Truncated Normal
The pdf of the truncated normal is that of a normal random variable X with location and scale parameters μ and σ and truncated to the interval [0, ∞], is given by
which is simply a gaussian distribution with support [0, ∞] with the appropriate normalization. The mean m and variance v = s 2 are given by
where we have defined
Note that the parameters μ and σ need not exist for an arbitrary choice of m and s.
1.5 A.5 Log-Normal
This is the distribution of a random variable X such that logX is normally distributed. The pdf for location μ and scale σ is given by
The mean m and variance v = s 2 are given by
which can be inverted to give
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Dbira, H., Girard, A. & Sansò, B. Calculation of packet jitter for non-poisson traffic. Ann. Telecommun. 71, 223–237 (2016). https://doi.org/10.1007/s12243-016-0492-0
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DOI: https://doi.org/10.1007/s12243-016-0492-0