分组交换与信息传输的数学相似性
The Mathematical Parallels Between Packet Switching and Information Transmission
摘要：
所有的通信网络都由传输系统和交换系统组成，尽管它们通常被视为两个独立的问题。通信信道通常受到来自各种源的噪声的干扰。在电路交换网络中，可靠的通信需要在噪声信道上进行比特的容错传输。然而，在分组交换网络中，不仅比特会被噪声破坏，而且沿着连接路径的资源也会受到竞争。因此，服务质量（QoS）由缓冲器延迟和分组丢失确定。本文的主题是表明，传输噪声和数据包竞争实际上有类似的特点，可以驯服可比的手段，以实现可靠的通信，并确定了一些交换和传输之间的类比。带限信号的采样定理是数字通信和信号处理的基础。近年来，流量矩阵的Birkhoff-von Neumann分解在分组交换中得到了广泛的应用。相对于降低分组交换的复杂性，我们表明，双随机流量矩阵的分解起着类似的作用，在数字传输中的采样定理。我们的结论是，分组交换系统是由数学定律，是类似于香农在他的开创性的1948年的论文，通信的数学理论所设想的数字传输系统。
英文摘要：
All communication networks comprise of transmission systems and switching systems, even though they are usually treated as two separate issues. Communication channels are generally disturbed by noise from various sources. In circuit switched networks, reliable communication requires the error-tolerant transmission of bits over noisy channels. In packet switched networks, however, not only can bits be corrupted with noise, but resources along connection paths are also subject to contention. Thus, quality of service (QoS) is determined by buffer delays and packet losses. The theme of this paper is to show that transmission noise and packet contention actually have similar characteristics and can be tamed by comparable means to achieve reliable communication, and a number of analogies between switching and transmission are identified. The sampling theorem of bandlimited signals provides the cornerstone of digital communication and signal processing. Recently, the Birkhoff-von Neumann decomposition of traffic matrices has been widely applied to packet switches. With respect to the complexity reduction of packet switching, we show that the decomposition of a doubly stochastic traffic matrix plays a similar role to that of the sampling theorem in digital transmission. We conclude that packet switching systems are governed by mathematical laws that are similar to those of digital transmission systems as envisioned by Shannon in his seminal 1948 paper, A Mathematical Theory of Communication.
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