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The influence of dependence on data network models

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

Bernardo D'Auria  and
Sidney I. Resnick
Bernardo D'Auria*
Affiliation:
EURANDOM
Sidney I. Resnick*
Affiliation:
Cornell University
*
∗ Current address: Departamento Estadística, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911 Leganés, Madrid, Spain.
∗∗ Postal address: School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: [email protected]
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Abstract

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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 long-range 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.

Keywords

Bursty trafficM/G/∞ input modelinfinite-source Poisson modelnetwork modelinglimit distributionLévy processGaussian limit

MSC classification

Primary: 90B15: Network models, stochastic 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 90B22: Queues and service 90B18: Communication networks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 1 , March 2008 , pp. 60 - 94
Copyright
Copyright © Applied Probability Trust 2008 

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