A computer-implemented method for using multi-dimensional geometry in simulations of packet flows through network devices, is provided. The computer-implemented method includes receiving an input object for traffic simulation of network devices, comprising a source and destination host ranges and source and destination port ranges, and protocol, application and vulnerability ranges, targeted for the destination host ranges. The computer-implemented method further includes representing blocked traffic of the simulated traffic by an intersection of at least two n-dimensional cuboids in n-dimensional space. The computer-implemented method further includes subtracting an access control list shape from an input shape to obtain a concave form representing permitted host, port, protocol, application, and vulnerability combinations of ranges. The computer-implemented method further includes decomposing the obtained concave shape into multiple convex shapes that satisfy a set of predetermined input conditions.