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

当我们设计队列大小、链路带宽和其他网络参数时，我们假设连续的数据包在统计上是独立的。我们做出这个假设是因为(1)我们没有一个很好的方法来指定这种依赖关系，(2)我们有用的底层数学工具就是基于这个假设的，(3)它给了我们很好的结果。然而，在宽带和/或广域网络中，我们不再清楚我们是否取得了令人满意的结果。在这个研究项目中，概率上下文无关文法理论被提出作为一种工具来描述网络中连续分组之间的统计相关性。我们将尝试扩展基础数学，即N-Type分支过程，以便它可以指定队列大小、链路带宽和其他网络参数。最后，我们将比较来自经典设计和从这个新设计到实际测量的规格。对于这个项目的SGER部分，我们将开发一个令人信服的例子。这个例子将展示如何使用概率上下文无关文法来指定网络中连续分组之间的统计相关性。它将说明如何使用基础数学的当前状态(N-Type分支过程)来指定网络参数(数据包队列、链路带宽等)。比经典的设计技术(假定数据包独立)更现实。这个说明性的例子将用于一个扩展研究项目的后续提案。

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.