Trip travel time reliability is an important measure of transportation system performance and a key factor affecting travelers’ choices. This paper explores a method for estimating travel time distributions for corridors that contain multiple bottlenecks. A set of analytical equations are used to calculate the number of queued vehicles ahead of a probe vehicle and further capture many important factors affecting travel times: the prevailing congestion level, queue discharge rates at the bottlenecks, and flow rates associated with merges and diverges. Based on multiple random scenarios and a vector of arrival times, the lane-by-lane delay at each bottleneck along the corridor is recursively estimated to produce a route-level travel time distribution. The model incorporates stochastic variations of bottleneck capacity and demand and explains the travel time correlations between sequential links. Its data needs are the entering and exiting flow rates and a sense of the lane-by-lane distribution of traffic at each bottleneck. A detailed vehicle trajectory data-set from the Next Generation SIMulation (NGSIM) project has been used to verify that the estimated distributions are valid, and the sources of estimation error are examined.