Constructions of Linear Compressors, Nonovertaking Delay Lines, and Flexible Delay Lines for Optical Packet Switching

Queueing theory is generally known as the study of the performance of queues. In this paper, we are interested in another aspect of queueing theory, the constructions of queues via switched delay lines (SDLs). We consider three types of discrete-time queues: linear compressors, nonovertaking delay lines, and flexible delay lines. These three types of queues correspond to certain conditional nonblocking switches and (in a strict sense) nonblocking switches in switching theory. Analogous to their counterparts in switching theory, there exist multistage constructions for these three types of queues. Specifically, we develop a two-stage construction of a linear compressor. For nonovertaking delay lines and flexible delay lines, however, we develop a three-stage construction. Moreover, a flexible delay line can also be constructed by a layered Cantor network. As applications of these constructions, we show two optical switch architectures that achieve exact emulation of output-buffered switches.