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 threaten the economic prosperity and quality of life in many societies. According to a report by 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 imposes huge impact on traffic emissions because it interrupts traffic flow (for good reasons) and creates additional deceleration, idle and acceleration driving modes to the otherwise cruise driving mode. Traffic emissions are very sensitive to the driving modes, thus reducing idleness at intersections likely leads to significantly reduced traffic emissions. While recent research has primarily focused on developing real-time adaptive signal control systems, implementation of such systems on a large scale may be many years away, due to the associated high implementation and maintenance costs. Because a large number of signal control systems in use today are still pre-timed, further improvements in their efficiency can yield significant improvements in the management of traffic flows, and mitigation of congestion and emissions.

Many of state-of-the-practice pre-timed systems are operated 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 time 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 for the condition of this particular time of day. The timing plan is often obtained by using optimization tools such as TRANSYT-7F, with the inputs of design flows, the mean values of traffic flows, for the time-of-day intervals. However, real-world travel demands are intrinsically fluctuating, and traffic flows at intersections may vary significantly even for the same time of day and day of week. As an example, Figure 1 displays hourly arrivals at two crossing streets, 34th Street and University Avenue, in Gainesville, Florida, during 9 a.m. to 11 a.m. on weekdays over a period of four months. The flows present significant day-to-day variations. Consequently, an issue that traffic engineers may be confronted with is to determine the flows to use to optimize signal timings. This issue was hardly a concern in old days because the data collection used to be resource demanding, and traffic data were only collected for a couple of days. As the advancement of portable-sensor and telecommunications technologies make high-resolution traffic data more readily available, chances for traffic engineers to raise such a question become more prevalent. This is particularly true in re-timing efforts for those closed-loop control systems with fiber optic connections.

Use of the average flows may not be a sensible choice. Previous studies have pointed out that if the degree of variability of traffic flows is significant, optimizing signal timing with respect to the average flows may incur considerable additional delay, compared with the timing obtained by taking this variability into account. If the degree of variability is small, use of the average flows in conventional timing methods will only lead to small losses in average performance (efficiency). However, it may still cause considerable losses in the performance against the worst-case scenarios or the stability of performance (robustness), thereby causing motorists’ travel times to be 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 answer the question of what flows to use for signal optimization. More rigorously, our research was to investigate a methodology of signal timing optimization for pre-timed control under demand fluctuations. The proposed methodology proactively considers demand uncertainty in 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 the average performance across all possible demand scenarios. Robust timing plans also allow slower deterioration of performance. It is noted that the signal timing process is normally time-consuming. Thus it is rarely repeated unless changes in traffic conditions are so significant that the system begins performing poorly. It has been estimated that traffic experiences an additional 3 percent to 5 percent delay per year as a consequence of not retiming signals as conditions evolve over time. Therefore, it is desirable to have timing plans that accommodate or tolerate these changes in traffic to a greater extent.

Practically, motorists and traffic engineers may be more concerned with worst-case scenarios where substantial delay may occur. To address such a risk-averse attitude on one hand and avoid being too conservative on the other hand, 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 a large number of binary variables. Existing algorithms, such as branch and bound, are not able to solve it efficiently, 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 that the robust plans perform much better against high-consequence scenarios. As a side effect, the average performance is also improved.