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This paper studies the connection-assignment problem for a time-division-multiplexed (TDM) wavelength-routed (WR) optical wavelength-division-multiplexing (WDM) network. In a conventional WR network, an entire wavelength is assigned to a given connection (or session). This can lead to lower channel utilization when individual sessions do not need the entire channel bandwidth. This paper considers a TDM-based approach to reduce this inefficiency, where multiple connections are multiplexed onto each wavelength channel. The resultant network is a TDM-based WR network (TWRN), where the wavelength bandwidth is partitioned into fixed-length time slots organized as a fixed-length frame. Provisioning a connection in such a network involves determining a time-slot assignment, in addition to the route and wavelength. This problem is defined as the routing, wavelength, and time-slot-assignment (RWTA) problem. In this paper, we present a family of RWTA algorithms and study the resulting blocking performance. For routing, we use the existing shortest path routing algorithm with a new link cost function called least resistance weight (LRW) function, which incorporates wavelength-utilization information. For wavelength assignment, we employ the existing least loaded (LL) wavelength selection; and for time-slot allocation, we present the LL time-slot (LLT) algorithm with different variations. Simulation-based analyses are used to compare the proposed TDM architecture to traditional WR networks, both with and without wavelength conversion. The objective is to compare the benefits of TDM and wavelength conversion, relative to WR networks, towards improving performance. The results show that the use of TDM provides substantial gains, especially for multifiber networks.