Real-time vehicular queue length is an important parameter describing the temporal and spatial state of a traffic stream. A queue is the direct outcome of bottlenecks or roadway congestion, which causes longer travel times and delays and adversely impacts roadway performance. Therefore, in this thesis, two congestion scenarios, namely two roadway bottleneck cases (bottleneck over a roadway lane due to a merging lane/ramp and bottleneck due to a lane closure induced by an incident) and two signalized intersection cases (undersaturated and oversaturated) have been investigated to estimate the back of queue. The proposed methodology for real-time queue estimation is based on a GPS-based probe-vehicle trajectory data analysis obtained from a Paramics simulation environment applied in combination with an input-output technique. An extension of the queue estimation method of Lawson, Lovell and Daganzo (1996), based on a more realistic fundamental diagram of traffic flow, has also been proposed for bottleneck situations. Although the proposed methodologies maintain some strict assumptions, it has been found that the probe-based proposed methodology with a probe market share of around 30 percent is enough to outperform the theoretical Lawson et al. queue estimation model for all the case studies. Last, but not the least, this thesis should be considered as the first known contribution that focuses on the input-output technique and probe-vehicle information in the estimation of a real-time vehicular queue.