Using Probabilistic Context-Free Languages and the BranchingProcess to Model Packet Dependence in Telecommunications Traffic Simulations and Calculations

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When we design queue sizes, link bandwidths, and other network parameters, we assume that successive packets are statistically independent. We make this assumption because (1) we don't have a good way to specify such dependencies, (2) our useful underlying mathematical tools are based on this assumption, and (3) it has given us decent results. However, in broadband and/or wide-area networks, it's no longer clear we're getting decent results. In this research project, the theory of Probabilistic Context-Free Grammars is proposed as a tool for specifying statistical dependence among successive packets in a network. We will try to extend the underlying mathematics, the N-Type Branching Process, so it can specify the queue sizes, link bandwidths, and other network parameters. Eventually, we will compare the specifications from the classical design and from this new design to real measurements. For the SGER component of this project, we will develop a convincing example. This example will show how a Probabilistic Context-Free Grammar can be used to specify statistical dependence among successive packets in a network. It will illustrate how the current state of the underlying mathematics (the N-Type Branching Process) can be used to specify network parameters (packet queues, link bandwidths, etc.) more realistically than does the classical design technique (that assumes packet independence). This illustrative example will be used in a follow-up proposal for an extended research project.