Modeling traffic flow on oversaturated arterials

Traffic congestion is a national issue in the United States and has gotten worse in regions of all sizes. Now, more and more intersections are operated in oversaturated situations where the traffic demand exceeds the capacity of the system. Although a significant amount of literature has been devoted to how to manage oversaturated traffic signal systems, our understanding of the characteristics of oversaturation remains limited, particularly with regard to identification of oversaturation and the transition process from under-saturated condition to oversaturation. It has become increasingly obvious that successful traffic management requires efficient methods to identify and model oversaturated conditions.;This research moves towards a better understanding of oversaturation, by (1) providing coherent methodologies to quantify oversaturation and (2) developing a simplified model to describe oversaturation at signalized intersections based on high-resolution traffic signal data collected by the SMART-SIGNAL (Systematic Monitoring of Arterial Road Traffic Signals) system. In particular, the research focuses on the following four areas: (1) Quantification of oversaturation: Traditional definitions of oversaturation are not applicable for existing detection systems. This research circumvents this issue by quantifying the detrimental effects of oversaturation on signal operations, both temporally and spatially. In the temporal dimension, the detrimental effect is characterized by a residual queue at the end of a cycle, which occupies a portion of green time in the next cycle. In the spatial dimension, the detrimental effect is characterized by a downstream spillover, which blocks the traffic and reduces usable green time. From these observations, we derive two types of an oversaturation severity index (OSI): one temporally-based (T-OSI) and one spatially-based (S-OSI). Both T-OSI and S-OSI are designed to yield a ratio between the unusable green time due to detrimental effects and the total available green time in a cycle, using high resolution traffic signal data. T-OSI is quantified by estimating the residual queue length; and S-OSI is quantified by measuring the time period of spillover. Since different types of OSI (T-OSI or S-OSI) point to different underlying causes of oversaturation, this research has the potential to provide guidance for the mitigation strategies of signal oversaturation. (2) Real-time queue length estimation for congested intersections: To quantify T-OSI, this research proposes a novel shockwave-based algorithm to estimate time-dependent queue length even when the signal links are congested with long queues, a situation that the traditional input-output approach for queue length estimation cannot handle. Using high-resolution "event-based" traffic signal data, the new algorithm first identifies traffic state changes; and then applies Lighthill-Whitham-Richards (LWR) shockwave theory to estimate maximum and minimum (i.e. residual) queue length. This algorithm is also applicable for other aspects of arterial performance such as travel time, delay, and level of service. (3) Queue-Over-Detector (QOD): To quantify S-OSI, we study a phenomenon we call Queue-Over-Detector (QOD). QOD occurs when a vehicle stops and rests on a detector for a period of time creating a large occupancy value. This research demonstrates that a main cause of QOD is spillover from downstream intersections. Thus QOD identification can be used to quantify oversaturation in the spatial dimension, i.e. S-OSI. This research also briefly studies the relationship between QOD and the cycle-based arterial fundamental diagram (AFD) by microscopically investigating individual vehicle trajectories derived from event-based data. Results show that proper treatment of QOD results in a stable form of the AFD which clearly identifies three different regimes, under-saturation, saturation, and over-saturation with queue spillovers. Achieving a stable form of the AFD is of great importance for traffic signal control because of its ability to identify traffic states on a signal link. (4). Traffic flow modeling for oversaturated arterials: The culmination of this research project is a simplified traffic flow model for congested arterial networks, which we call the shockwave profile model (SPM). Unlike conventional macroscopic models, in which space is often discretized into small cells for numerical solution, SPM treats each homogeneous road segment with constant capacity as a section; then categorizes the traffic within each section simply as free-flow, saturated, or jammed. Traffic dynamics are analytically described by tracing the shockwave fronts which explicitly separate these three traffic states. SPM is particularly suitable for simulating traffic flow on congested signalized arterials, especially with queue spillover problems. In SPM, queue spillover can be treated as either extending a red light or creating new smaller cycles. Since only the essential features of arterial traffic flow, i.e., queue build-up and dissipation, are considered, SPM significantly simplifies arterial network design and improves numerical efficiency. For these reasons, we fully expect this model to be adopted in real-time applications such as arterial performance prediction and signal optimization.