The general goal of traffic modeling is to predict the size of traffic flows in individual roads of the modeled road network. A commonly employed technique is the user-equilibrium (UE) traffic assignment (TA). There are multiple algorithms for solving TA with different convergence speeds. One of the fastest algorithms is the Improved Traffic Assignment by Paired Alternative Segments (iTAPAS) algorithm. In this paper, an optimized implementation of the iTAP AS algorithm is described and compared to its original implementation and to the sequential and parallel versions of the B algorithm, which we implemented during our previous research. An important part of the paper is the discussion of the parallelization of the iTAP AS algorithm, which is our ultimate goal.