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A traditional wavelength-division multiplexed (WDM) backbone network with its rigid features is unsuitable for emerging diverse and high bitrate (400 Gb/s, 1 Tb/s) traffic needs. Flexible solutions employ new technologies such as bandwidth-variable optical cross connects (BV-OXC) with liquid crystal (LCoS) wavelength-selective switches (WSS), sliceable bandwidth-variable transponders (SBVT), etc. in a flex-grid network. Flex-grid network operates on variable spectral granularities (e.g., 12.5 GHz), and higher modulation formats (quadrature amplitude modulation). However, a greenfield deployment of flex-grid technologies may not be practical, due to cost of technology and usability. This leads to a brown-field network where both fixed-grid and flex-grid technologies co-exist with seamless interoperability. Thus traditional traffic routing and resource allocation techniques need to evolve in a mixed-grid infrastructure. Our study considers the dynamic routing and spectrum assignment (RSA) problem in a fixed/flex-grid co-existing optical network. It provisions routes for dynamic, heterogeneous traffic, ensuring maximum spectrum utilization and minimum blocking.