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The influence of dependence on data network models. (English) Zbl 1157.90349
Summary: 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 of the authors [Adv. Appl. Probab. 38, No. 2, 373–404 (2006; Zbl 1103.90029)] 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.

##### MSC:
 90B15 Stochastic network models in operations research 60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.) 90B22 Queues and service in operations research 90B18 Communication networks in operations research
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