The normal practice in modelling of Controlled Radical Polymerization (CRP) is to apply Monte Carlo based stochastic simulation algorithms assuming the processes to be Markovian. We argue that such an approach overlooks the delayed nature of some processes involved in CRP and do suggest the methodology that overcomes this deficit. The proposed methodology offers the analytical representations for the probability density functions corresponding to the delayed processes as in the cases when the amount of delay is known exactly as it is unknown. Moreover, to improve the accuracy and efficiency of our modelling approach for computation of branching fraction in CRP, we replace the random walk Monte Carlo with the analytical solution. The comparison of the novel methodology with the traditional simulation methods and the experimental data is provided.