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The incompressible temporally developing turbulent boundary layer (TBL) and spatially developing turbulent boundary layer (SBL) with and without blowing is analyzed using the map-based stochastic one-dimensional turbulence (ODT) model. An understanding of these idealized flows is of fundamental relevance for boundary layer-type problems, which are frequently encountered in several applications, from atmospheric sciences to engineering. In the ODT model, the flow variables are resolved on all scales along a wall-normal, 1-D domain. These variables are evolved by a deterministic process representing molecular diffusion and by a stochastic process modeling the effect of turbulent advection and pressure fluctuations. Due to the reduction in dimensionality, the model is particularly appropriate for high Reynolds number flow. It is shown that the ODT model is able to capture salient features of the turbulent boundary layer-type flows by comparing the results with various available reference direct numerical simulation (DNS), large eddy simulation (LES) and experimental results. The comparison is presented for the mean velocity profiles, turbulent velocity fluctuation profiles (up to fourth order), the skin friction coefficient and shape factor for different bulk (Reb) and momentum Reynolds numbers (Reθ) using fixed model parameters. The influence of the model parameters is also discussed for various momentum Reynolds numbers for each investigated flow configuration. The results discussed in this thesis suggest that the ODT model is an economical and reasonably accurate approach for the simulation of turbulent boundary layer flows.