Lihui Zhang, Yafeng Yin and Scott Washburn
Department of Civil and Coastal Engineering
University of Florida
Traffic congestion is one of the most severe problems that threatens the economic prosperity and quality of life in many societies. According to a report by the Federal Highway Administration, traffic congestion in the U.S. costs approximately $200 billion a year in wasted gas and time, and poor signal timing is responsible for 5 percent of that cost. Additionally, signal timing has a significant impact on traffic emissions because it interrupts traffic flow (for good reasons) and creates additional deceleration, idle, and acceleration driving modes in addition to the otherwise cruise driving mode. Traffic emissions are highly sensitive to driving modes; thus, reducing idleness at intersections likely leads to significantly lower emissions. While recent research has primarily focused on developing real-time adaptive signal control systems, implementation at a large scale may be many years away due to the associated high implementation and maintenance costs. Because many signal control systems in use today are still pre-timed, further improvements in their efficiency can significantly enhance traffic flow management and mitigate congestion and emissions.
Many state-of-the-practice pre-timed systems operate in a time-of-day mode, in which a day is segmented into a number of time intervals, and a signal timing plan is predetermined for each interval. Typically, three to five plans are run in a given day. The basic premise is that the traffic pattern within each interval is relatively consistent, and the predetermined timing plan is best suited to the conditions at this time of day. The timing plan is often obtained using optimization tools such as TRANSYT-7F, with inputs of design flows and mean traffic flows for the time-of-day intervals. However, real-world travel demands are inherently variable, and traffic flows at intersections may vary significantly even at the same time of day and day of the week. As an example, Figure 1 shows hourly arrivals at two crossing streets, 34th Street and University Avenue, in Gainesville, Florida, from 9 a.m. to 11 a.m. on weekdays over a four-month period. The flows present significant day-to-day variations. Consequently, traffic engineers may be confronted with the issue of determining the flows to use to optimize signal timings. This issue was hardly a concern in the old days because data collection was resource-intensive, and traffic data were collected for only a couple of days. As advances in portable-sensor and telecommunications technologies make high-resolution traffic data more readily available, the chances for traffic engineers to raise such a question become more prevalent. This is particularly true for re-timing efforts in closed-loop control systems with fiber-optic connections.
Using average flows may not be a sensible choice. Previous studies have shown that if the variability in traffic flows is significant, optimizing signal timing with respect to average flows can incur considerable additional delay compared with the timing obtained by accounting for this variability. If the degree of variability is small, using average flows in conventional timing methods will only lead to small losses in average performance (efficiency). However, it may still cause considerable performance losses against worst-case scenarios or degrade performance stability (robustness), thereby making motorists’ travel times highly variable. On the other hand, if the highest observed flows are used instead, the resulting timing plans may be over-protective and unjustifiably conservative. The average performance is very likely to be inferior.
Our goal in this research was to determine which flows to use for signal optimization. More rigorously, our research investigated a methodology for signal timing optimization in pre-timed control under demand fluctuations. The proposed methodology proactively accounts for demand uncertainty when developing robust signal timings. Compared with those from conventional timing approaches, robust timing plans are expected to perform better under high-demand scenarios without compromising average performance across all demand levels. Robust timing plans also allow for slower performance deterioration. It is noted that the signal timing process is normally time-consuming. Thus, it is rarely repeated unless traffic conditions change significantly enough that the system begins to perform poorly. It has been estimated that traffic experiences an additional 3 percent to 5 percent delay per year due to not retiming signals as conditions evolve over time. Therefore, it is desirable to have timing plans that accommodate or tolerate these traffic changes to a greater extent.
In practice, motorists and traffic engineers may be more concerned with worst-case scenarios in which substantial delays may occur. To address such a risk-averse attitude on the one hand and avoid being too conservative on the other, we optimized signal timings against a set of worst-case or high-consequence scenarios. More specifically, given a set of demand scenarios and their corresponding probability of occurrence, and based on a cell-transmission representation of traffic dynamics, we formulated a stochastic programming model to simultaneously determine cycle length, green splits, phase sequences and offsets to minimize the mean of the delays exceeding the -percentile (e.g., 90th percentile) of the entire delay distribution, i.e., mean excess delay. The stochastic programming model is simple in structure but contains many binary variables. Existing algorithms, such as branch-and-bound, are not efficient for this problem, particularly when the optimization horizon is long and the network size is large. We developed a simulation-based genetic algorithm to solve the model. The model and algorithm were tested on two networks (see Figure 2 for one testing network) and the resulting robust timings were compared with traditional timing plans via a CORSIM simulation study. The results show that the robust timing plans outperform the traditional plans, with the mean delay reduced by approximately 20 percent and the mean excess delay reduced by 18 percent. It demonstrates that the robust timing plans perform much better in high-consequence scenarios. As a side effect, the average performance is also improved.