Research on Intersection Signal Switching Model under Emergency Situation

Abstract

The frequent occurrence of the city emergency leads to rapid development of emergency traffic management which is an important part in the Emergency Rescue System. In the intersection with heavy traffic, the emergency rescue vehicles often with increased delay, reduced safety, and sometimes even with a collision, which restrict the efficiency of the rescue. This paper established the intersection signal control optimization model based on detail analysis of emergency rescue vehicles traffic characteristics and traffic signal control. The models, on one hand, were able to guarantee the emergency vehicles through the intersection quickly and without delay; on the other hand, could ensure the minimum impact to other vehicles in the process of the emergency vehicles through the intersection. Finally, the model’s practicality was verified by real cases.

1. Introduction

In modern life, the emergency events, natural disasters, and the non resistance events happen frequently. Moreover, these events are unpredictable and bring to several damages. Statistics show that every year our country has big loss because of the disasters (such as the natural disasters, accidents, the social and public events), and the loss caused by rescue that does not come in time increased year by year [1]. Therefore, the accurate and reliable traffic control measures are an effective way to reduce the response time of the emergency vehicle, improve the efficiency of the emergency rescue, and reduce the loss of lives and property. But in the process of the emergency response, the emergency vehicle often with increased delay, reduced safety, and even with a collision in intersections. According to the results of the emergency vehicle accident investigation in Virginia, about 31% accidents of the emergency vehicles' happened in the intersection. Moreover, the consequences are even more serious than happened in other places [2]. Therefore, the study on signal optimization control under emergency situations has an important significance in emergency rescue, traffic safety, and traffic management.

For the research on the right-of-way of the emergency vehicle, the scholars in transportation area in different countries focused on different aspects. Bachelder and Foster proposed the emergency vehicles preferred system based on the induction coils [3]. Mussa and Selekwa raised one conversion process of the traffic signal timing based on quadratic optimization method [4]. Nelson and Bullock pointed out that the signal control should back to normal operation rapid and safely after the emergency vehicles through the intersection [5], but the conversion mode of the signal control they proposed back to normal often used the ways of smooth, add only, or dwell, all of which are set according to the experience and are hard to adapt to the change of complex traffic condition.

In recent years, as the development of intelligent agent technology, many domestic scholars put forward the methods to solve the traffic problem based on this innovative, real-time and intelligent technology. Cao fulu (Chang^’an University) proposed a kind of urban traffic signal optimization control system for the optimization of signal control through the coordination of the intelligence agents between adjacent intersections. Cheng Xiangjun (Beijing Jiaotong University) presented one distributed traffic signal coordination control method based on the multiagent technology, this method makes the vehicles through the intersection without delay under the higher utilization of the each phase in crossing traffic time.

We can conclude from the above analysis that the current study is mainly concentrated in the hardware and system design of the signal priority. The purpose of emergency signal optimization control can be expressed as one objective function, and this function subjects to some restrictions. We are able to obtain the optimal control strategy by the mathematical programming model and various kinds of optimization methods.

2. Signal Conversion Control

2.1. Control Process

This paper chooses the four phase signals cross-intersection as the research object. The signal optimization control measures under emergency situations are built according to the traffic conditions when the emergency vehicle’s detector detects the request vehicles. The control process as in Figure 1.

Figure 1 

Intersection signal conversion control process under emergency conditions.

2.2. Vehicle Detector Position Setting

2.2.1. General Vehicle Detector Position Setting

As shown in Figure 2, the position of the general vehicle detector can be expressed as 𝐿_VD=𝐿_QD+𝐿_DD, (2.1) where, 𝐿_VD is the setting distance of other vehicle's detector; 𝐿_QD is the length of the other queuing vehicles under peak traffic condition; 𝐿_DD is the length of the slowly moving vehicles under the peak traffic condition.

Figure 2 

Classification of the traffic vehicle.

To ensure the emergency vehicle could pass through the intersection safely and without delay, we must make sure the other vehicles in front of the emergency vehicle dissipated in time. 𝐿_QD can be determined by the average value of multiple times measurements. 𝐿_DD is difficult to detect, it can be replaced by the sum of the mean value and two times standard deviation of 𝐿_QD [6], as follows: 𝐿_QD=1𝑋=𝑛^𝑛_𝑖=1𝑥_𝑖𝐿,𝑖=1,2,3,…𝑛,_DD=𝐿_QD+2𝜎=𝑋+21𝑛^𝑛_𝑖=1𝑥_𝑖−𝑋. (2.2) Then, 𝑥_𝑖 is the detected length of the other queuing vehicles under peak traffic condition; 𝑋 is the average queue length of the other vehicles; 𝜎 is the standard deviation of the other vehicle queue length.

2.2.2. Emergency Vehicle Detector Position Setting

The setting distance of the emergency vehicle detector should be able to guarantee that it has enough time to dissipate the vehicles before the emergency vehicle arrived at the intersection. So, there exists 𝑡_ED=𝐿𝑣_ED, (2.3) where 𝑡_ED is the ideal travel time of emergency vehicle from the detected position to the intersection parking line; 𝐿 is the distance between the emergency vehicle detector and intersection; 𝑣_ED is the ideal average speed of the emergency vehicle.

In actual situation, the emergency vehicle could reach the intersection in any time. Assume the driving direction is already known, according to the different signal phase condition when the signal control machine receives the detected information from the emergency vehicle, the location of the emergency vehicle's detector can be set as follows.

(1) The signal phase of the emergency vehicle's driving direction is green:

Then, the disappearing time of the other vehicles is: 𝑡_CL=𝐿_QD+𝐿_DD𝑣_QD, (2.4) where 𝑡_CL is the disappearing time of the other vehicles before the emergency vehicle appears; 𝑣_QD is the dissipation speed of the other vehicle’s queue in front of the emergency vehicle.

There should be a certain safety time interval between the last dissipated vehicle and the emergency vehicle. The formula is as follows: 𝑡_ED−𝑡_CL≥𝑡_SI, (2.5) where 𝑡_SI is the time interval between the last dissipated vehicle and the emergency vehicle.

So the minimum distance of the emergency vehicle's detector in this condition is 𝐿₁≥𝑡_SI+𝐿_QD+𝐿_DD𝑣_QD×𝑣_ED. (2.6)

(2) The signal phase of the emergency vehicle's driving direction is yellow.

According to the conduct process we proposed above, the minimum distance of the emergency vehicle's detector in this condition is 𝐿₂≥𝑡_SI+𝑡_SL+𝐿_QD+𝐿_DD𝑣_QD×𝑣_ED, (2.7) where 𝑡_SL is the loss of the start time (see Figure 4).

(3) The signal phase of the emergency vehicle’s driving direction is red.

The minimum distance of the emergency vehicle’s detector in this condition is in Figure 3𝐿^′₃≥𝑡_SI+𝑡_SL+𝐿_QD+𝐿_DD𝑣_QD+𝑡_AR−𝑡^′_AR×𝑣_ED, (2.8) where 𝑡_AR is the all red light duration of this phase; 𝑡^′_AR is the faded signal time of this red phase.

Figure 3 

The location of emergency vehicle detector (green).

Figure 4 

The location of emergency vehicle detector (yellow).

In practical situations, it is not easy to ensure 𝑡^′_AR, which could be resolved by use the “real position” and the “virtual position”. The “real position” is the actual position of the emergency vehicle detector. The formula is as follows: 𝐿₃≥𝑡_SI+𝑡_SL+𝐿_QD+𝐿_DD𝑣_QD+𝑡_AR×𝑣_ED. (2.9)

The “virtual position” is the position set by 𝐿^′₃. In this condition, we should deduct the setting position of emergency rescue vehicle’s detector during the red signal phase. So there exists: 𝐿₃≥𝐿^′₃ (see Figure 5).

Figure 5 

The location of emergency vehicle detector (red).

Therefore, the minimum distance of the emergency vehicle detector is: 𝐿=max𝐿₁,𝐿₂,𝐿₃=𝐿₃. (2.10)

2.3. Optimal Control

At first, divide the entire process into three periods: detection period, before, and after the intersection period.

2.3.1. Detection Period

After the distance of the emergency vehicle detector is determined, the information about emergency vehicle, such as the location, speed, and the direction can be determined. The formula as follows [7–9]: 𝑡_HG=𝑡^′_ED−𝑡_SW+𝑡^′_CL+𝑡_SI,𝑡^′_ED=𝐿𝑣^′_ED,𝑡^′_CL=𝑡_SL+𝐿^′_QD+𝐿^′_DD𝑣_QD,𝑡^′_ED>𝑡^′_CL, (2.11) where 𝑡_HG is the green time that other phases obtained; 𝑡_SW is the loss time of conversion; 𝑡^′_CL is the detected time of the dissipated vehicles in front of the emergency vehicle; 𝑡^′_ED is the time from the position that emergency vehicle is detected to the stop line; 𝑣^′_ED is the detected travel speed of the emergency vehicle; 𝐿^′_QD is the actual queue length of other vehicles in emergency vehicle driving direction; 𝐿^′_DD is the detected length of the slowly moving vehicles in emergency vehicle driving direction.

Once the control machine request received the request of the emergency vehicle, we could decide whether to carry out the signal priority control by the formulas we proposed above according to the signal phase and fixed signal timing cycle.

2.3.2. The Optimization before the Vehicles through the Intersection

The optimization purpose of this period is(1)to guarantee the emergency vehicle safety and without delay;(2)to minimize the influence to other vehicles.

According to the actual situation and with above optimization goals, we could implement optimization methods by different control measures, which can be specified as [10–13]

(1) The signal phase in emergency vehicle's driving direction is green when the detector detected emergency vehicle to ensure the safety when the emergency vehicles passes through the intersection. We do not consider the emergency vehicles through the intersection in the yellow signal phase.

(i) Assume 𝑡_GR>𝑡^′_ED>𝑡^′_CL.

The signal control plan is still running as normal. 𝑡_GR is the remaining signal time of this green phase in emergency vehicle's driving direction when the detector detected emergency vehicle; 𝑡_AG is the full signal time of this green phase in emergency vehicle's driving direction.

(ii) Assume 𝑡^′_ED≥𝑡_GR>𝑡^′_CL.

The signal control plan is changed according to the difference between the surplus green time of this phase and the required time for emergency vehicles arrived.

(a) If 𝑡^′_ED−𝑡_GR−𝑡_SW−𝑡_SI≥𝑇, the signal control will be switched to normal, and the next phase can get the time for green is 𝑡_HG=𝑡^′_ED−𝑡_GR−𝑡_SW−𝑡_SI. After 𝑡_HG, convert the green signal phase to the emergency vehicle's driving direction.

(b) If 𝑡^′_ED−𝑡_GR−𝑡_SW−𝑡_SI<𝑇, extend the show time of the green light phase, there exist 𝑡_DG=𝑡^′_ED−𝑡_GR+𝑇_EI. Where, 𝑇 is the time of the static car needed to through the intersection as usual. 𝑡_DG is the extended time of the green signal phase in the emergency vehicle's driving direction. 𝑇_EI is the time of the emergency vehicle needed to through the intersection.

(iii) If 𝑡^′_ED>𝑡^′_CL>𝑡_GR, the signal control plan is changed according to the difference between the surplus green time of this phase and the required time for emergency vehicles arrived also.

(a) If 𝑡^′_ED−𝑡^′_CL−𝑡_SW−𝑡_SI≥𝑇, the signal control will be switched as normal, and the next phase can get the time for green is 𝑡_HG=𝑡^′_ED−𝑡^′_CL−𝑡_SW−𝑡_SI. After 𝑡_HG, convert the green signal phase to the emergency vehicle's driving direction.

(b) If 𝑡^′_ED−𝑡^′_CL−𝑡_SW−𝑡_SI<𝑇, extend the time of the green signal phase and the extended time is 𝑡_DG=𝑡^′_ED−𝑡_GR+𝑇_EI.

(2) The signal phase in emergency vehicle’s driving direction is yellow when the detector detected emergency vehicle.

(i) Assume 𝑡^′_ED−𝑡^′_CL−𝑡_SW−𝑡_SI+𝑡_YR≥𝑇.

The signal control machine will be switched as normal, and the next phase can get the time for green is 𝑡_HG=𝑡^′_ED−𝑡^′_CL−𝑡_SW−𝑡_SI−𝑡_YR. Where, 𝑡_YR is the remaining signal time of this yellow phase in emergency vehicle's driving direction when the detector detected emergency vehicle; 𝑡_AY is the full signal time of this yellow phase in emergency vehicle's driving direction, there exists 0≤𝑡_YR≤𝑡_AY. After 𝑡_HG, convert the green signal phase to the emergency vehicle's driving direction until the emergency vehicle passed the intersection.

(ii) Assume 𝑡^′_ED−𝑡^′_CL−𝑡_SW−𝑡_SI+𝑡_YR<𝑇.

In this case, convert the green signal phase to the emergency vehicle's driving direction until the emergency vehicle passed the intersection.

(3) The signal phase in emergency vehicle's driving direction is red when the detector detected emergency vehicle.

(i) Assume 𝑡^′_CL<𝑡^′_ED<𝑡_RR.

The other phases can get the time for green is 𝑡_HG=𝑡^′_ED−𝑡^′_CL−𝑡_SI. After that, convert the green signal phase to the emergency vehicle's driving direction and the break time of the red light in the emergency vehicle's driving direction is 𝑡_DT=𝑡_RR−(𝑡^′_ED−𝑡^′_CL−𝑡_SI)+𝑡_SW. Where, 𝑡_RR is the remaining signal time of this red phase in emergency vehicle's driving direction when the detector detected emergency vehicle; 𝑡_AR is the full signal time of this red phase in emergency vehicle's driving direction.

(ii) Assume 𝑡^′_ED≥𝑡_RR.

(a) If 𝑡_RR≤𝑡^′_ED−𝑡^′_CL−𝑡^′_CL≤𝑡_RR+𝑡_AG, the signal control machine will be switched as normal.

(b) If 𝑡_RR+𝑡_AG<𝑡^′_ED−𝑡^′_CL−𝑡^′_CL, extend the time of the green signal phase and the extended time is 𝑡_DG=𝑡^′_ED−𝑡_RR−𝑡_AG+𝑇_EI.

(c) If 𝑡^′_ED−𝑡^′_CL−𝑡_SI<𝑡_RR, convert the green signal phase to the emergency vehicle's driving direction and the break time of the red light in the emergency vehicle's driving direction is 𝑡_DT=𝑡_RR−(𝑡^′_ED−𝑡^′_CL−𝑡_SI)+𝑡_SW.

(4) Pedestrians scheme under the emergency situation.

Convert the pedestrian traffic light in emergency vehicle's driving direction to red until the emergency vehicle passed the intersection and make speakers or tips to notice to the crowd in the meantime.

2.3.3. The Optimization after the Vehicles Passes through the Intersection

The control process of the emergency vehicle under the emergency situation can be described in Figure 6.

Figure 6 

The priority control process of the emergency vehicle.

According to the Figure 6, the following relationships can be calculated: 𝑡_𝑁𝑡=𝐶−^D+𝑡_ED𝐶,𝑡_RE=𝑡_𝑁+𝑛𝐶−𝑡_SI, (2.12) where 𝑡_𝑃 is the time interval between the moment of the emergency vehicle detected and the beginning of next signal cycle; 𝑡_D is the time interval between the beginning of the signal cycle and the moment of the emergency vehicle detected; 𝑡_RE is the time length of the intersection signal optimization control after the emergency vehicles through the intersection; 𝑚,𝑛 is the signal cycle number.

In this period, establish the optimal model with the minimum delay of other vehicles' as the optimization target. Such that [14–18] min𝑍=min²⁴_𝑙=1^𝐾_𝑗=1𝑘=1max0,𝑄^𝑖_𝑗𝑙(𝑘−1)+⁴_𝑖=1𝑞^𝑖_𝑗𝑙(𝑘)−𝜇^𝑖_𝑗𝑙⋅𝜆_𝑗𝑙×𝑔^𝑖(𝑘,(𝑘)=)s.t.:𝐶⁴_𝑖=1𝑔^𝑖(𝑘),𝑔^𝑖_min≤𝑔^𝑖(𝑘)≤𝑔^𝑖_max,_𝐾𝑘=1𝐶(𝑘)=𝑡_RE=𝑡_𝑁+𝑛⋅𝐶−𝑡_SI,𝑄(𝑘)=²⁴_𝑙=1𝑗=1𝑄^𝑖_𝑗𝑙(𝑘)≤𝑄_𝑣,𝑄^𝑖_𝑗𝑙(𝑘)=max0,𝑄^𝑖−1_𝑗𝑙+𝑉𝐴^𝑖_𝑗𝑙(𝑘)−𝑉𝐷^𝑖_𝑗𝑙(𝑘),𝑉𝐴^𝑖_𝑗𝑙(𝑘)=𝑞^𝑖_𝑗𝑙(𝑘)⋅𝑔^𝑖(𝑘),𝑉𝐷^𝑖_𝑗𝑙=𝜇^𝑖_𝑗𝑙⋅𝜆_𝑗𝑙⋅𝑔^𝑖(𝑘),𝑄⁰_𝑗𝑙(𝑘)=𝑄⁴_𝑗𝑙(𝑘−1), (2.13) where 𝑖 is the number of the traffic signal phases, the maximum is 4; 𝑗 is the driving direction of the intersection, 1, 2, 3, and 4 represent East, South, West and North; 𝑙 is the direction of the lane, 1, 2 represent the direction of left and straight; 𝑘 is the signal control cycle and 𝐾 is the maximum number of it; 𝑉𝐴^𝑖_𝑗𝑙(𝑘) is the actual number of the reached vehicles in the 𝑖 signal phase of 𝑘 signal cycle and 𝑙 lane of the 𝑗 direction; 𝑉𝐷^𝑖_𝑗𝑙(𝑘) is the actual number of the past vehicles in the 𝑖 signal phase of 𝑘 signal cycle and 𝑙 lane of the 𝑗 direction; 𝑄^𝑖_𝑗𝑙(𝑘) is the number of queuing vehicles in the 𝑖 signal phase of 𝑘 signal cycle and 𝑙 lane of the 𝑗 direction; 𝑞^𝑖_𝑗𝑙(𝑘) is the average arrival rate of the vehicles in the 𝑖 signal phase of 𝑘 signal cycle and 𝑙 lane of the 𝑗 direction; 𝑔^𝑖(𝑘) is the duration of the effective green signal phase-in the 𝑖 signal phase of 𝑘 signal cycle; 𝜆_𝑗𝑙 is the saturated flow rate in the 𝑙 lane of the 𝑗 direction; 𝑇_LS is the loss time of each signal cycle; 𝑄_𝑣 is the average queue length of each signal cycle under normal conditions; 𝜇^𝑖_𝑗𝑙 is the traffic state of the 𝑙 lane of the 𝑗 direction in the 𝑖 signal phase, if the car can move, 𝜇^𝑖_𝑗𝑙=1, else 𝜇^𝑖_𝑗𝑙=0.

The proposed optimization models could be solved with the genetic algorithm and the simulated annealing algorithm by applying the MATLAB tool.

2.3.4. The Control Strategy When through the Continuous Intersections

Take different control measures according to the traffic volume and the distance between the adjacent intersections.

If 𝐿_𝑁≥𝐿, take the priority control independently for each intersection by the above method. Otherwise, take the joint priority control for the adjacent intersections. Where, 𝐿_𝑁 is the distance between the adjacent intersections. The process of the joint priority control is shown in Figure 7.

Figure 7 

The process of the joint priority control.

Set the controller of the largest vehicles' intersection as the main controller. The process of detection period and the optimization of the period before passed intersection are the same as analyzed in Section 2.3.2. After the emergency vehicle passed the intersections, take the optimization measures according to the sum of the vehicles in different directions in the adjacent intersections. Then, assign appropriate green signal time to the different directions of the adjacent intersections.

3. Experimental Analysis

3.1. First Period

The selected experimental data and the average length of the vehicles' queue are shown in Tables 1 and 2.

Table 1 

Basic data of the experimental analysis.

Table 2 

The average length of the vehicles' queue.

The average speed of the dissipating vehicles is 3.3 m/s and the setting position of the detector are shown in Table 3.

Table 3 

The setting distance of the detectors.

3.2. Second Period

Select eight groups of data to simulate, as in Tables 4 and 5.

Table 4 

The second simulation of the optimization control (low traffic).

Table 5 

The second simulation of the optimization control (high traffic).

It is clearly shown in Tables 4 and 5 that all the emergency vehicles can pass through the intersection without delay and just cause little influence to other vehicles in most cases.

3.3. Third Period

Apply the first group data in Table 5 to calculate in MATLAB program, the results are shown in Table 6.

Table 6 

The optimization of the green light duration.

Apply the data in Table 6 to the simulation environment, the length of the other vehicles’ queue are shown in Table 7.

Table 7 

The length of the other vehicles' queue.

Calculate the eight groups data, the average delay of emergency vehicle and other vehicles' are shown in Table 8.

Table 8 

The average delay of the other vehicles.

4. Conclusion

This paper aims to establish the optimization model of the signal switching under emergency situations. On one hand, the models could guarantee the emergency vehicles are able to through the intersection safe and without delay; on the other hand, pass could ensure the minimum impact to other vehicles in the intersection during the processing of emergency vehicles pass through. Finally, real cases are employed to verify the practicality of the models. The models and algorithms can be also provided to some relevant management departments as the decision-making reference.