  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.
