Mathematical Problems in Engineering

Volume 2015, Article ID 954295, 9 pages

http://dx.doi.org/10.1155/2015/954295

## Development of an Optimization Traffic Signal Cycle Length Model for Signalized Intersections in China

^{1}Jiangsu Key Laboratory of Urban ITS, Jiangsu Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Si Pai Lou No. 2, Nanjing 210096, China^{2}School of Highway, Chang’an University, Middle of Nanerhuan Road, Xi’an 710064, China

Received 15 December 2014; Revised 4 March 2015; Accepted 13 March 2015

Academic Editor: Rafael Toledo-Moreo

Copyright © 2015 Yao Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The primary objective of this study is to develop an optimization traffic signal cycle length model for signalized intersections. Traffic data were collected from 50 signalized intersections in Xi’an city. Using comprehensive delay data, the optimization cycle length model is re-recalibrated to the Chinese traffic conditions based on the Webster delay model. The result showed that the optimization cycle length model takes vehicle delay time, pedestrian crossing time, and drivers’ anxiety into consideration. To evaluate the effects of the optimization cycle length model, three intersections were selected for a simulation. The delay time and queue length based on the optimization cycle length model and the TRRL model were compared. It was found that the delay times and queue lengths with the optimization cycle length model were significantly smaller than those with the TRRL model. The results suggested that the optimization traffic signal cycle length model was more optimal than the TRRL model.

#### 1. Background

The intersection is an important part of urban road networks, the smooth flow of which plays a key role in the vehicle speed and operating efficiency of the entire road network. However, during the past two decades, with motorization rapidly increasing, more and more bottleneck effects have been exposed at intersections in urban areas. In recent years, transportation professionals in China have developed signalized intersections. There are lots of benefits for developing the signalized intersections. On the one hand, the control afforded by the traffic lights separates the conflicting traffic flows in time and improves vehicle safety and operation efficiency; on the other hand, the vehicles on the approach are suspended periodically, causing delays. Therefore, the traffic signal cycle plays a key role in intersection traffic control. A reasonable cycle length can effectively alleviate or prevent traffic congestion and reduce emissions, noise pollution, energy consumption, and travel delay time.

Probabilistic cycle length calculation was first taught at the Yale School of Highway Traffic in the 1950s and earlier, which used the Poisson tables to determine a cycle that would serve some percentage (based on probabilities) of waiting queues for successive cycles [1]. This is linked to the objective of reducing cycle failures as the authors indicate. However, it has also been recommended that the method is useful only in light traffic conditions.

During the past decades, several studies have been conducted that address traffic signal cycle length. One class of methods seeks to minimize the delay time of vehicles at intersections [2–8]. The most well-known and typical traffic signal cycle length models are the TRRL model and the ARRB model.

The TRRL model [3] has been widely used. In developing the TRRL model for the optimal minimum delay cycle length, it was assumed that the effective green times of the phases were in the range of their respective flow ratio values. The TRRL model is given aswhere represents the optimal cycle length (sec); represents the total lost time (sec); and represents the sum of the critical flow ratio of all phases.

The ARRB model [4] introduced the “parking compensation coefficient” to the TRRL model and it was combined with the vehicle delay time to evaluate the degree of optimization of the signal timing program. The ARRB model is given aswhere represents the optimal cycle length (sec); represents the parking compensation coefficient; and represents sum of the critical flow ratio of all phases.

Although the above models are widely used, they have some limitations: (1) under near-saturated or saturated conditions, the optimal cycle length formulation proposed by Webster becomes infeasible because it generates an unreasonably large cycle length as the intersection critical flow ratio approaches one; (2) it becomes inapplicable if the intersection critical flow ratio is equal to or greater than one.

The* Highway Capacity Manual* [9] also proposed the cycle length model and the delay time model of signalized intersections. The delay time model, which can be applied to variety of saturation states, has been widely used. The cycle length model is based on the expected saturation; therefore, it does not guarantee that the cycle length would produce the minimum delay at an intersection. It is given aswhere represents the cycle length (sec); represents the total lost time (sec/cycle); represents the sum of the critical phase traffic volumes (veh/h); represents the reference sum flow rate (1710PHFfa), (veh/h); PHF represents the peak-hour factor; and represents the area type adjustment factor [0.9 if central business district and 1.0 otherwise].

Day et al. [8] evaluated the effectiveness and efficiency of Webster’s cycle length and the HCM intersection saturation metric. The authors showed that calculations from Webster’s model and the HCM provided a framework for identifying periods of time when the cycle length could be substantially shortened, periods of the day when an increase in the cycle length would provide some modest improvements, and periods of the day when the cycle length was adequate and capacity problems could be addressed by adjusting the splits. A similar study conducted by Cheng et al. [7] compared Webster’s minimum delay cycle length model and the HCM 2000 optimal cycle model and recommended an exponential-type cycle length model.

Based on the idea of minimizing the delay time, many optimization cycle length models were developed using linear or nonlinear regression methods and probabilistic approaches among others [10–12]. Lan [10] proposed a nonlinear optimal cycle length. Using the optimal timing variables obtained based on the delay minimization criterion, the functional relationship between the optimal cycle lengths and the traffic flow parameters, including the intersection critical flow ratio, the total lost time, and the duration of the analysis period, was established through a nonlinear regression analysis. The formulation was found to generate fairly accurate estimates of optimal cycle length with a 5.7% average deviation from the analytical solutions. Han and Li [11] studied a probabilistic approach to cycle length optimization. Based on the idea of selecting a cycle length that is small enough to ensure low delay while providing adequate capacity to handle most of the fluctuating demand conditions, a five-step framework was proposed for carrying out the analyses. Subsequent sensitivity analyses, level-of-service assessments, and cycle failure rate estimations were conducted on the basis of random demand. It was found that longer cycle lengths did not yield the optimal delay results and, with extremely short cycle lengths, the delay was usually high because of a lack of capacity and hence frequent cycle failures were guaranteed.

A second class of methods is based on studies aimed at optimizing the cycle length for a saturated or oversaturated intersection [13–15]. Chang and Lin [13] studied the optimal signal timing for an oversaturated intersection. The authors presented a timing decision methodology which considers the whole oversaturation period and discrete dynamic optimization models were developed. The optimal cycle length and the optimal assigned green time for each approach were determined for the case of two-phase control. It was found that the proposed discrete type performance index model is a more appropriate design for congested traffic signal timing control.

A third class of methods is based on taking the factor of emissions, fuel, and other environmental factors into consideration when developing the cycle length model [5, 6, 16]. Li et al. [5, 6] established a signal timing model which optimizes signal cycle length and green time by using integrated optimization of the traffic quality, fuel consumption, and emission pollution. It was found that when the signal cycle length increased from 20 to 200 s, there was an optimal value corresponding to the performance index function. When the traffic flow rate was larger, the optimal signal cycle length corresponding to the performance index function increased. However, the parameters of the model are complicated and difficult to obtain and is therefore useful for the purpose of study only and is not practical in engineering practice.

The fourth class of methods is based on simulation and an intelligent algorithm to optimize the cycle length or to develop an optimization cycle length model [17–19]. Using the theory analysis and computer simulation test, Yang et al. [19] established a delaying calculation model of through running and left-turning vehicles on a roundabout. Based on the model, an optimal cycle length calculation method targeting minimum delay was derived, which was suitable for the multiapproach going in coordination with roundabout controls. Park et al. [17] evaluated a stochastic signal optimization method based on a genetic algorithm using the microscopic simulation program CORSIM. According to the method, the cycle length, the green ratio, and the phase difference were optimized at the same time. Kim et al. [18] compared the performance between an artificial neural network (ANN) and analytical models for real-time cycle length design. It was found that the ANN model provides optimal cycle lengths stably adjusted by the minimum value, the maximum value, and the cycle increment, while the analytical model promotes congestion under certain operational conditions.

As can be seen by the brief general discussion above, most of the previous studies focused on the optimal cycle length. A variety of methods and models were put forward either based on the minimum delay time or minimum emission or considering the oversaturation consideration of an intersection. Even though previous studies have, to some extent, improved the traffic signal cycle, they suffer from several limitations. The literature review indicated that the following issues have not been addressed in previous studies: (1) most of the previous cycle length models only aimed at one target (minimum delay time or minimum emission) or only applied to the saturation status; however, a cycle length model of a different status was not considered and (2) most of the cycle length models did not consider the factor of pedestrian crossing and that a long cycle length would cause driver anxiety, which could reduce the traffic safety of the intersection.

The primary objective of this study was to develop and evaluate a new optimization traffic signal cycle length for signalized intersections in China. More specifically, the study presented in this paper focused on the following two tasks: (1) to develop an optimization traffic cycle length model for signalized intersections and (2) to evaluate the effects of the optimization cycle length model.

#### 2. Data Collection

Field data collection was conducted at 50 signalized intersections in Xi’an which is one of the typical biggest cities in China. The sites were carefully selected such that their geometric design and traffic control feathers represent the most common situations in major cities in China. To achieve the research objective, the following criteria were applied in the site selection process.(1)The selected intersection should be a typical signalized intersection (i.e., four-leg intersection or T-leg intersection). Roundabouts and other deformity intersections must not be included.(2)The selected signalized intersections should include different types (i.e., where different grade roads intersect), for example, the intersection of a main road and a minor arterial road and the intersection of a main road and branch road.(3)Two hours of traffic data of each selected sites should be recorded in peak period.

The traffic data of the selected signalized intersection, including the traffic volume, delay time, cycle length, green split, and saturation, were investigated, among which the direct traffic data were traffic volume and cycle length and the indirect traffic data were delay time, green split, and saturation. The calculation methods of the indirect traffic data were shown as follows.

*Delay Time*. The individual sample survey method was used to determine the delay time, which is given aswhere represents the total delay time and represents the total number of suspended vehicles; represents the interval time; the average delay time of each vehicle at the approach; and represents the total volume at the approach.

*Green Split*. The green split is given aswhere represents the green split; represents the effective green time; and represents the cycle length.

*Saturation*. The saturation is given aswhere represents the saturation for phase ; represents the traffic volume; represents the green split; represents the saturation traffic volume; and represents the saturation degree of the intersection.

In order to collect all the traffic data mentioned above, the following detailed information were collected during the investigation: (1) the exact time at which each phase began and ended, as well as the cycle time; (2) the number of vehicles at every approach of each intersection at 15-minute intervals; and (3) the number of delayed vehicles at every approach at 15-second intervals as well as the number of queued vehicles and nonqueued vehicles. The data collection results are shown in Table 1.