In this paper, we present a quality-of-transmission (QoT) aware dynamic routing, modulation level, and spectrum assignment scheme referred to as QoT-aware RSA. The proposed QoT-aware RSA has three stages: path computation with QoT-aware modulation level assignment, path selection, and spectrum assignment. Two schemes are presented in the path computation stage namely, modified Dijkstra and K-shortest-path algorithms. A closed-form expression is derived to model the fiber nonlinearity effects and the impairments of intermediate routers. This expression is utilized to estimate the network dependent QoT and the transmission reach of the modulation levels. We propose to select the best path in terms of optical signal-to-noise ratio (OSNR) metric. Furthermore, the traffic-balancing spectrum assignment method is utilized to serve the incoming request. The proposed scheme is evaluated using extensive numerical simulations based on both random and deterministic traffic models. The results of simulation reveal that the path selection and spectrum assignment methods can affect the average OSNR performance. Furthermore, the results show that the proposed path selection and spectrum assignment schemes outperform other existing alternatives in the literature.