Dynamic Modeling Of Lane Distribution Impact In Complex Freeways
Traffic dynamics have been the focal point of research aiming to provide a better understanding of traffic phenomena and to be integrated in traffic management for recurrent congestion. The aim of the study is to ameliorate complex highway and/or freeway networks performance by forecasting traffic regimes based on lane vehicle allocation, traffic characteristics and their synergies on impending traffic conditions for control and modeling purposes. In order to define the prevailing traffic regimes, model-based Bayesian clustering was employed on flow-density relationships for exploratory data mining. In addition, the stochastic cluster analysis was invoked to uncover the time span of morning and evening peak hours, refining and reducing the input data space and enhancing noise reduction. On the contrary to distance-based clustering, in a preliminary phase, two explicit homogeneous groups (congested/not congested regimes for morning and evening peak hours) were probabilistically determined via the Bayesian propositional logic, regarding the number of existing regimes as well as the peak hours period. With this approach, a metric cluster definition was avoided, as two hypotheses were formed, represented by two models. The null hypothesis H_0:κ=1, with κ the true unknown number of clusters, is examined versus the hypothesis H_1: κ=k, with k a pre-specified number of clusters. Assuming that each model is equally likely to be expressed, the posterior probability of null hypothesis was estimated, thus the Bayesian factor (BF) included, with small values signalizing evidence against H_0. To approximate the BF, Markov chain Monte Carlo (MCMC) techniques were evoked. Partitioned sampling from the mixture distribution of traffic flow and density was obtained through the Metropolis-Hastings algorithm, so as to constraint the draws to high probability areas. Based on the optimised reduced data space of the respective regimes, piecewise/segmented modeling was introduced to address the parameterization of network dynamics. Piecewise models were studied to delineate stream patterns, as they are additive models that inherit linear models properties, enhancing thus description’s flexibility. Lane vehicle allocation and spatiotemporal variables were provided as representative parameters of driver’s behaviour (Table 1), where lddrR is the lane density distribution ratio of the right lane, lddrL the lane density distribution ratio of the left lane, ΔVMR-ML the speed difference between median right and median left lane, ΔVMR-R the speed difference between median right and right lane, ΔVML-L the speed difference between median left and left lane, and kR, kL, kMR, kML the density of the right, left, median right and median left lanes respectively. Initially, static models were developed, for both peak and off peak hours, with the lane density distribution ratio (LDDR) as response variable, as well as the differences of speed per adjacent and non-adjacent lanes and lane density. The proposed models indicated strong precision, particularly for off-peak hours. However, potentially, the fluctuating behaviour within traffic states transitions during peak hours, led to a dynamic modeling approach with time-related parameters. The persistence on lane scale yielded significant improvement on accuracy, confirming the aforementioned presumption. The models’ assessment was conducted with empirical data from a complex freeway network, with successive on and off ramps and four to six lanes per direction in the mainline (Fig. 1), that features pronounced congested condition during peak hours. The study site is located in district 11 of San Diego County, U.S. (I5-N and I5-S). The traffic dataset was consisted of aggregated measurements (intervals of Δt=5 min), of flow, speed and occupancy per lane, and it is part of the Caltrans Performance Measurement System (PeMS). Further on this on-going study, several types of networks will be evaluated either with ITS control policies or deprived, aiming to assess the stationarity of the static and dynamic models.