This paper attempts to quantify the impact of traffic incidents on travel time reliability using a newly proposed multi-state travel time reliability model. Given that the multi-state travel time reliability model provides significantly better fits when compared to using a single-mode density function, it is possible to quantify the incident impacts more accurately. In order to obtain travel times, the study simulates weekday traffic on a section of I-66 over 17 days, once with incidents and once without them, using the INTEGRATION microscopic traffic simulation software. The simulated travel time data sets are then used to fit a three-state travel time reliability model (three normal distributions) to calibrate the parameters of the density function using the Expectation Maximization (EM) algorithm. The study demonstrates that incidents do not introduce an additional component distribution when congestion has already onset; instead they increase the mean travel time and variability in travel times for the congested conditions. For instance, the 90th percentile travel time of the second component distribution increases by up to 93 percent. Additionally, the study addresses technical issues related to the calibration and interpretation of the model from a practical standpoint.