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Since light-paths are the basic connections in wavelength routed networks, their effective establishment is very important. Routing and Wavelength Assignment (RWA) techniques can be divided into two categories. The first category (pure RWA) concentrates on setting up light-paths under the assumption of an ideal physical layer. However, this assumption could be suitable for opaque networks, where a signal is regenerated at each optical switch along its path. On the other hand, as an optical signal propagates along a light-path to its destination in a transparent (all-optical) network, the signal's quality degrades because there is no signal regeneration, thus increasing Bit-Error-Rate (BER) of the signal. However, users would not accept a light-path with a high BER. Even it is not acceptable if the establishment of a light-path causes the BER of other existing light-paths to become unacceptably high. Therefore, considering physical layer impairments, the quality of a light-path must be checked during the light-path setup in the second category. In this article, the operations of dynamic RWA techniques proposed in transparent networks for the second category are reviewed in detail. These techniques are called Quality of Transmission Aware (QoT-aware) RWA and are grouped in two groups: integrated QoT and RWA, and QoT after Pure RWA. Each group can be further divided into direct modelling and indirect modelling sub-groups. A comprehensive discussion is also provided to compare dynamic QoT-aware RWA techniques based on different network and physical layer parameters.