Empirical Testing Of The Infinite Source Poisson Data Traffic Model

Guérin, Charles-Antoine; Nyberg, Henrik; Perrin, Olivier; Resnick, Sidney I.; Rootzén, Holger; Stărică, Cătălin

doi:10.1081/stm-120020386

Cited by 37 publications

(37 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This model has attracted a lot of attention under the name of infinite-source Poisson model in the literature on teletraffic; see Konstantopoulos and Lin [23], Mikosch et al [28], Guerin et al [13], Maulik et al [27], and Maulik and Resnick [26].…”

Section: Proposition 21 the Variance Of The Input A T Is Given Bymentioning

confidence: 99%

Scaling Limits for Cumulative Input Processes

Mikosch

Samorodnitsky

2007

Mathematics of OR

View full text Add to dashboard Cite

We study different scaling behavior of very general telecommunications cumulative input processes. The activities of a telecommunication system are described by a marked-point process T n Z n n∈ , where T n is the arrival time of a packet brought to the system or the starting time of the activity of an individual source, and the mark Z n is the amount of work brought to the system at time T n . This model includes the popular ON/OFF process and the infinite-source Poisson model. In addition to the latter models, one can flexibly model dependence of the interarrival times T n − T n−1 , clustering behavior due to the arrival of an impulse generating a flow of activities, but also dependence between the arrival process T n and the marks Z n . Similarly to the ON/OFF and infinite-source Poisson model, we can derive a multitude of scaling limits for the input process of one source or for the superposition of an increasing number of such sources. The memory in the input process depends on a variety of factors, such as the tails of the interarrival times or the tails of the distribution of activities initiated at an arrival T n , or the number of activities starting at T n . It turns out that, as in standard results on the scaling behavior of cumulative input processes in telecommunications, fractional Brownian motion or infinite-variance Lévy stable motion can occur in the scaling limit. However, the fractional Brownian motion is a much more robust limit than the stable motion, and many other limits may occur as well.

show abstract

Section: Proposition 21 the Variance Of The Input A T Is Given Bymentioning

confidence: 99%

Scaling Limits for Cumulative Input Processes

Mikosch

Samorodnitsky

2007

Mathematics of OR

View full text Add to dashboard Cite

show abstract

“…However, traffic measurements in some cases [23], [24] do not show an agreement with the Gaussian marginal distribution. It is pointed out in [23] that if the statistical multiplexing of a large number of sources cannot smooth out the overall traffic when some of the individual sources are busty, the generalized central limit theorem [25] should be applied, resulting in an α-stable marginal distribution that models well both the burstiness and self-similarity.…”

Section: Related Workmentioning

confidence: 91%

Calculation of Loss Probability in a Finite Size Partitioned Buffer for Quantitative Assured Service

Cheng¹,

Zhuang²,

Wang³

2007

IEEE Trans. Commun.

View full text Add to dashboard Cite

Abstract-This paper proposes an approximate yet accurate approach to calculate the loss probabilities in a finite size partitioned buffer system for the achievement of a quantitative assured service in differentiated services networks. The input is modeled as a fractional Brownian motion (FBM) process including J classes of traffic with different packet loss requirements. A first-in firstout buffer partitioned with J −1 thresholds is used to provide J loss priorities. Heuristic expressions of the loss probabilities for all the J classes are derived, and validated by computer simulations. The proposed loss calculation technique is then extended to a general input process by using the recently proposed traffic substitution technique, where both long-range dependent and short-range dependent input sources are equivalent to a properly parameterized FBM. We also apply the loss calculation to admission control, where the partition thresholds are optimally configured for quality of service guarantee and maximal resource utilization. Computer simulation results demonstrate that resource allocation based on the accurate finite buffer loss analysis results in much more efficient resource utilization than that based on the classic large-buffer overflow approximation.Index Terms-Fractional Brownian motion (FBM), long-range dependence (LRD), loss probability, quantitative assured service, traffic substitution.

show abstract

“…Some of the models assumed constant rate user inputs. For these large time scale cumulative input models, it is difficult to find agreement with existing data sets (Guerin et al (2003)). …”

Section: Introductionmentioning

confidence: 99%

“…Dependence and network models 63 Guerin et al (2003); Heffernan and Resnick (2005);Hernández-Campos et al (2005); Leland et al (1994); Maulik et al (2002); Park and Willinger (2000); Resnick (2003Resnick ( ), (2004aReidi and Willinger (2000); Sarvotham et al (2005);and Willinger et al (1995). With these assumptions, the counting function of the points…”

Section: Model Descriptionmentioning

confidence: 99%

The influence of dependence on data network models

D’Auria¹,

Resnick

2008

Adv. Appl. Probab.

View full text Add to dashboard Cite

Consider an infinite-source marked Poisson process to model end user inputs to a data network. At Poisson times, connections are initated. The connection is characterized by a triple (F, L, R) denoting the total quantity of transmitted data in a connection, the length or duration of the connection, and the transmission rate; the three quantities are related by F = LR. How critical is the dependence structure of the mark for network characteristics such as burstiness, distribution tails of cumulative input, and longrange dependence properties of traffic measured in consecutive time slots? In a previous publication (D'Auria and Resnick (2006)) we assumed that F and R were independent. Here we assume that L and R are independent. The change in dependence assumptions means that the model properties change dramatically: tails of cumulative input per time slot are dramatically heavier, traffic cannot be approximated by a Gaussian distribution, and the decay of dependence cannot be measured in the traditional way using correlation functions. Different network applications are likely to have different mark dependence structure. We argue that the present independence assumption on L and R is likely to be appropriate for network applications such as streaming media or peer-to-peer networks. Our conclusion is that it is desirable to separate network traffic by application and to model each application with its own appropriate dependence structure.

show abstract

Empirical Testing Of The Infinite Source Poisson Data Traffic Model

Cited by 37 publications

References 46 publications

Scaling Limits for Cumulative Input Processes

Scaling Limits for Cumulative Input Processes

Calculation of Loss Probability in a Finite Size Partitioned Buffer for Quantitative Assured Service

The influence of dependence on data network models

Contact Info

Product

Resources

About