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In this paper, we explore new optical time-division multiplexing (OTDM) ring architectures. The objective of our study is to achieve high space-reuse efficiency of each time slot without using time-slot interchanges, which are expensive and difficult to implement in the optical domain. Although a TDM slot is often compared to a wavelength channel in a wavelength-division multiplexing (WDM) network, we show that the intrinsic propagation delay in an OTDM network will lead to a phenomenon, called a slot cycle in the paper, that has no counterpart in WDM networks. By exploring the concept and the algebraic relationship between the frame size and the total propagation delay of the ring, we discover a novel OTDM ring architecture that achieves a high space-reuse efficiency without using time-slot interchanges. The equivalent of this architecture in the WDM domain can only be achieved with the use of many wavelength converters. We also study the efficiency of the architecture based on different types of traffic demand models in the network.