This paper presents a study of the repair process performed in five Colombian power distribution systems using queuing theory concepts. It represents the input and service processes of the queuing system by means of stochastic point process models and assesses the repair process performance indexes applying a procedure of sequential Monte Carlo simulation. Results shows: i. The power law stochastic point process model is recommended as the first choice for representing the input and service processes because it fits even in those cases of samples with low tendency for which the fit to renewal process models failed. ii. Although the traffic intensity parameter gives at a glance the tendency of the repair process performance, to know when an index is higher o lower than a given value, it is necessary to apply the assessment procedure.