Jam density and stopbar location estimation with trajectory data at signalized intersections

Jam density, or its reciprocal jam spacing, is a parameter difficult to estimate. In fact, most traffic signal control and traffic state estimation studies published until date generally assume a given value, with no estimation from data whatsoever. Nevertheless, estimating jam density is crucial, since any deviation from its true value will propagate to queue lengths and volume estimates. In the possession of only trajectory data, its estimation is even harder since not all vehicles are observed. In this paper, we first define the data generating process of the jam spacing parameter using sparse trajectory data. Then, we propose several estimators to estimate jam spacing and its variance. We use as measurements the distances between successive vehicle stops. The first estimator is a Maximum-Likelihood estimator (MLE) of a Geometrically Skewed Normal (GSN) distribution, to be used whenever there is lane information. The second estimator is a MLE of a shifted GSN with Normal Stopbar (SGSN-NSB) to be used when observed distances are measured from the stopbar estimate. In addition, we propose two least-squares counterparts, LSE and LSE-SB, based on least absolute remainders. Finally, we assess and compare the bias and efficiency of the estimators in both synthetic and real-world data, obtaining satisfactory results. MLE estimators are shown to outperform their LSE counterparts in both situations.