Cell migration is based on an actin treadmill, which in turn depends on recycling of G-actin across the cell, from the rear where F-actin disassembles, to the front, where F-actin polymerizes. To analyze the rates of the actin transport, we used the Virtual Cell software to solve the diffusion-drift-reaction equations for the G-actin concentration in a realistic three-dimensional geometry of the motile cell. Numerical solutions demonstrate that F-actin disassembly at the cell rear and assembly at the front, along with diffusion, establish a G-actin gradient that transports G-actin forward "globally" across the lamellipod. Alternatively, if the F-actin assembly and disassembly are distributed throughout the lamellipod, F-/G-actin turnover is local, and diffusion plays little role. Chemical reactions and/or convective flow of cytoplasm of plausible magnitude affect the transport very little. Spatial distribution of G-actin is smooth and not sensitive to F-actin density fluctuations. Finally, we conclude that the cell body volume slows characteristic diffusion-related relaxation time in motile cell from approximately 10 to approximately 100 s. We discuss biological implications of the local and global regimes of the G-actin transport.