Traffic congestion is already one of the greatest issues in many cities [1
] of China, where it is no longer feasible to continue to increase capacity in the form of new roads or lanes to accommodate the ever-rising travel demand due to the limited land resources. With a higher capacity for moving people than private cars, public transit vehicles have been widely recognized as a more efficient way for trips in megalopolis. However, the uncertainty of the travel time of buses that may be caused by the uncertainty of dwell time for passenger loading and unloading, the delay of traffic signal control at an intersection, and the delay of traffic congestion along the bus routes will affect the service level of public transit systems [3
]. Hence, implementing the strategy of “bus priority” would be an effective solution to relieve traffic congestion and improve mobility, in which reducing the bus delay at intersection is a very important factor.
In some traditional signal timing methods, the length of the cycle is determined to minimize the total delay of vehicles, and the green split is decided according to the ratio of traffic volumes in different phases, during which buses and private vehicles are regarded as the same. However, considering the capacity of bus is much larger than that of private vehicle, the traditional method is rather unfair for the phase that contains more bus traffic and cannot reflect a people-oriented traffic management philosophy [4
]. Moreover, it cannot reduce the delay of public transport vehicles at intersections and ensure the implementation of a “bus priority” strategy by using these traditional timing schemes. Therefore, the signal timing design problem based on bus priority has become a research hotspot in the field of urban traffic management.
In order to ensure bus priority, a bus lane is usually set on the approaches of intersections to make sure that the running of buses is not affected by private vehicles. Due to the difference of the operation characteristics between public transport vehicles and private vehicles, the saturation of bus lanes and common lanes will be different, which may lead to an unequal saturation of each phase at the intersection. Thus, the signal timing of such intersections is different from that of ordinary intersections, in which the running characteristics of traffic flows in two types of lanes should be considered at the same time. Therefore, the purpose of this paper is to present a new mathematical framework for the signal timing optimization model of intersections equipped with bus lanes in terms of bus priority.
2. Literature Review
Many studies have been conducted on the signal control optimization of single intersections. Since delay of vehicles is a comprehensive indicator that involves many factors, many studies are based on it. Furth et al. [7
] divided intersection delay into three scenarios, such as no priority, absolute priority, and conditional priority situations. The result showed that absolute priority increased delays significantly compared with no priority. Zhang et al. [5
] established a signal planning model with average people delay as the target, and green time was decided by the passenger quantity and the saturation of phases. Richardson [8
] used perceived, budgeted delay to evaluate the justification of bus priority signal intersections. By analyzing the evaluation index of the bus priority scheme at an intersection, Zheng [9
] proposed matter element analysis to select the bus priority schemes which contribute to selecting and evaluating the bus priority signal scheme. In addition, many researchers have developed new procedures to study delay at independent intersections. Wu [10
] researched the implementation of bus priority signals and proposed two pre-signal bus priority ways without detectors: only social vehicles were controlled by pre-signals, while buses had priority; both social vehicles and buses were controlled by pre-signals. They also gave the signal timing and compared the delay for the two schemes.
As the direct beneficiary of a bus priority strategy, the status of the bus traffic can directly reflect the effectiveness of the signal control method. In many previous studies, therefore, the bus traffic-related parameters are given more consideration when modelling the signal control problem. Mirchandani et al. [11
] analyzed the schedule status of buses, the passenger counts in buses, and real-time optimization of the phasing that considers all the vehicles in the network. Based on these parameters, they proposed a bus priority model and changed signals to integrate traffic signal control and bus priority. Jacobson et al. [12
] put forward a model of delays at signalized intersections under a bus preemption scheme. Experiments have shown that proper signal cycle and bus operation speed benefit bus preemption. Dion [13
] developed an optimization algorithm that minimizes the number of parking times and the distribution of delays, considering the impacts of transit vehicles.
In addition to adjusting the departure time and frequency of buses, the influence of the bus priority strategy on other participants in the traffic system may also determine the application results. Sun et al. [14
] presented a bus priority signal control algorithm based on frequency and demand intensity, considering the impact of bus priority on social vehicles. Based on transit priority control theory, Yang et al. [15
] developed methods for transit priority signals at signalized intersections and proposed the optimal system. The linear programming model and examples were used to demonstrate the way to design transit priority signals in a fixed cycle. Zhou and Gan [16
] proposed a queue jumper lane at intersections to increase transit bus priority. It is worth mentioning that this study used the VISSIM microscopic model to simulate and evaluate effects such as bus delay and general vehicle operations. These studies promote the implementation of a bus priority strategy and improve the traffic efficiency of single point signalized intersections.
As urban infrastructure construction progresses, the distances between intersections become shorter and shorter. Signal control optimization of a single intersection cannot satisfy the demand of urban traffic management. The signal control of different intersections should be considered in a more comprehensive way, and hence, the coordinated signal control is developed. Liu [17
] proposed a two-layer bus priority control model under a coordination in which the upper layer was the overall coordinated control and the lower layer was the intersection control. Aiming at the comprehensive benefits of social traffic and buses, Wang [18
] established a two-layer optimization model, in which the upper layer was progression control and the lower layer was bus priority control. The model was applied to evaluate the effect of arterial signal progression and bus delay. Liu et al. [6
] analyzed vehicle queuing at intersections, signal timing, and bus operation conditions to build a hardware system and specific methods to the transit signal priority. Guan et al. [19
] explored bus priority within a traffic signal control strategy and developed the control strategy of bus departure intervals and traffic flow on the road which was set as a bus detector. The optimal strategy was to minimize the total delay time of the passengers.
In view of the effectiveness of coordinated signal control, the network-based signal control is also proposed. However, since too many factors are involved in the area of signal control, most related studies are limited to theoretical analysis, with few practical applications conducted. Zhang et al. [20
] suggested the whole traffic system to evaluate the implementation effect of the bus priority measure. The evaluation index covered the four aspects of social economy, traffic function, environmental influence, and resource utilization, and these four aspects are given through calculation. Salter et al. [21
] put forward a computer simulation model to calculate the average delay, queue lengths, passenger delay, and bus travel time to evaluate the effects of bus-priority schemes. Chang et al. [22
] applied the INTEGRATION simulation package to the Columbia Pike Corridor in Arlington, Virginia, and evaluated the influence of bus signal priority strategy on bus service reliability. Khasnabis et al. [23
] presented the NETSIM simulation model to evaluate the bus priority strategies in intersections.
However, most of these studies focused on the benefits of vehicles, meaning that the traditional way of optimizing signal timing is to take the maximum benefits of all vehicles, including buses and private vehicles, as the optimization goal. That would be rather unreasonable since the capacity of a bus is typically 15 to 20 times the capacity of a private vehicle and the delay of buses would have a much higher effect than the delay of private cars. In these studies, the concept of a people-oriented priority strategy was not fully considered in the signal timing process.
Based on that, this paper attempts to propose a bi-level optimization model, in which passenger delay is explicitly considered in the process of signal timing optimization, aiming to improve the priority capacity of the buses at the intersection and reduce the loss of other private vehicle traffic benefits caused by the bus priority measures. Then the numerical calculation and simulation based on a real case are conducted to demonstrate the performance and applicability of the proposed model.
The signal timing optimization method needs to be implemented through a signal control systems. Many signal control systems have been developed to cover different application scenarios. Such systems can be classified into three main types, signal control, coordination control, and area control system, according to the object of application. The control mechanism of such systems also varies, including fixed-time control, actuated control, and adaptive control [24
]. The microprocessor optimized vehicle actuation (MOVA) system is an advanced vehicle actuated controller, which is suitable for optimizing single signalized junctions at the microscale. A coordinated signal control system commonly includes the split cycle offset optimization technique (SCOOT), which is a vehicle actuated systems for optimizing multiple linked signalized junctions at the city scale or within certain zones of a city, and the Sydney coordinated adaptive traffic system (SCATS), which works on a combination of coordinated vehicle actuation and fixed time plans [25
]. In area signal control systems, the traffic network study tool (TRANSYT) and the signal optimization program (SIGOP) are two common fixed time control design systems, which calculate the timings offline using historical, measured traffic data. The signal timing optimization method proposed in this paper, which can optimize the signal time cycle based on vehicle flow approaching a single junction, works significantly better for high traffic flow and is focused on increasing junction capacity. Therefore, the optimization process and characteristic of the proposed method similar to MOVA systems and can be utilized in isolated junctions or independently in several junctions in a city.
The remainder of this paper is organized as follows: Section 3
presents the basic framework of this specific signal timing design problem by giving the representation of the objective functions, in which the related parameters and constraints are elaborated. The bi-level optimization model of signal timing is proposed in Section 4
. In Section 5
, a solution framework based on the differential evolution (DE) algorithm is proposed. A case study based on a real-world intersection of Beijing is carried out in Section 6
to demonstrate the performance and applicability of the proposed model, in in which the results of two signal timing plans are compared by using the VISSIM simulation. Finally, in Section 7
, a summary concludes this paper.
This paper combined the concept of bus priority with the traditional way of a signal timing optimization problem. To solve this problem, a new methodology was proposed in which the passenger delay was explicitly considered in the process of signal timing optimization. The optimization problem modeled in the form of a bi-level optimization program aimed to minimize the average passenger delay at intersection and vehicle delay in lane simultaneously. Then the model was solved with the DE algorithm and applied to a real case of Beijing city. The application results showed that the optimization model can not only improve the priority capacity of the buses at the intersection but also reduce the loss of other private vehicle traffic benefits caused by the bus priority measures, which reflect the people-oriented priority strategy in the optimization process. By using the optimization model, the signal timing scheme can be adjusted in real time simply according to the change of traffic flow on bus lanes and ordinary lanes. Hence, the approach presented is a practical, effective, and feasible way to alleviate the traffic congestion, which can be used as a tool to help transport managers make bus priority policies while considering a network perspective.
However, caution should be taken while directly referring to this conclusion. First of all, the optimization model, which considered the intersection as an isolated entity, may not work well for connected signal system where several consecutive signals are connected. Secondly, the optimization model only considers updating signal timing scheme based on the traffic data collected in a fixed period of time, such as peak time, which may not be deployable for the near-real-time traffic data. Finally, in order to improve the quality and efficiency of the proposed solution algorithm, the sensitivity analysis was conducted to set the values of control parameters inherent in this algorithm. However, the robustness analysis of this solution algorithm is not considered in this study. For future studies, the robustness analysis of the DE-based solution algorithm can be conducted by comparing with some other optimization algorithms such as a genetic algorithm or ANN-based optimization. Several extensions may be considered. From modeling viewpoint, one may consider incorporating more traffic participants, such as micro-bus, taxi, into overall vehicular volumes in the modeling process to better optimize signal timing in dimensions. Another research area is that given the low cost and effectiveness of the signal timing optimization model utilized in the present study and the rapid spread of data networks, a systematic signal timing methodology integrating all signalized intersections may be developed in further research. These are the focus of our ongoing research.