Ramp metering is an effective measure to alleviate freeway congestion. Traditional methods were mostly based on fixedsensor data, by which origindestination (OD) patterns cannot be directly collected. Nowadays, trajectory data are available to track vehicle movements. OD patterns can be estimated with weaker assumptions and hence closer to reality. Ramp metering can be improved with this advantage. This paper extracts OD patterns with historical trajectory data. A validation test is proposed to guarantee the sample representativeness of vehicle trajectories and then implement coordinated ramp metering based on the contribution of onramp traffic to downstream bottleneck sections. The contribution is determined by the OD patterns. Simulation experiments are conducted under reallife scenarios. Results show that ramp metering with trajectory data increases the throughput by another 4% compared with traditional fixedsensor data. The advantage is more significant under heavier traffic demand, where traditional control can hardly relieve the situation; in contrast, our control manages to make congestion dissipate earlier and even prevent its forming in some sections. Penetration of trajectory data influences control effects. The minimum required penetration of 4.0% is determined by a ttest and the Pearson correlation coefficient. When penetration is less than the minimum, the correlation between the estimation and the truth significantly drops, OD estimation tends to be unreliable, and control performance becomes more sensitive. The proposed approach is effective in recurrent freeway congestion with steady OD patterns. It is ready for practice and the analysis supports the realworld application.
National Natural Science Foundation of China61773293Shanghai Sailing Program19YF1435100Joint Laboratory for Future Transport and Urban Computing of AutoNaviShanghai Transportation Information Center1. Introduction
Ramp metering has been proved to be an effective measure to relieve freeways congestion. It regulates the traffic volume at entry ramps with traffic signals, to keep the mainline traffic operating at the desired level and avoid capacity drop [1]. Proper entry control reduces the probability of breakdowns on the mainline while also considering the throughput of other traffic [2].
Researches on ramp metering can be dated back to 1965 when Wattleworth first proposed a linear programming model to generate a fixedtime control scheme to alleviate peakhour freeway congestion with static origindestination (OD) information [3]. With realtime measurement available, reactive ramp metering strategies have been proposed. The bestknown strategies are the demandcapacity (DC) strategy, the occupancy (OCC) strategy, and the ALINEA. DC strategy allowed ramp volume to make up the difference between the estimated capacity of mainline and measured upstream volume. OCC strategy calculated the metering rate by comparing the measured occupancy and the target value [4]. ALINEA was a feedback regulator, aiming to maintain capacity flow downstream of the merge area [5]. All these three strategies are local ramp metering based on simple logic. Field results showed their effectiveness [6]. Some extension versions were also proposed such as PIALINEA [7] and ITCALINEA [8]. They belong to local ramp metering strategies.
Coordinated ramp metering considers coordination among ramps. Cooperative algorithms, such as HELPER [9] and HERO [10], determined critical ramps whose downstream mainline sections are in most serious congestion and then force its upstream onramps to reduce metering rates accordingly. Bottleneck algorithms, such as FLOW [11], ZONE [12], and SWARM [13], calculated metering rates based on volume reduction in the mainline bottleneck. The above two kinds of algorithms are rulebased ones. The logic is like “IF traffic condition, THEN control scheme”, which is easy to implement.
Another kind of coordinated ramp metering control is optimal control. Started in the 1960s, the optimizing models inputted historical data and outputted static or timeofday control schemes [14]. In the 1990s, realtime measurements were considered. The approach used a rolling horizon to get a dynamic optimal control scheme [15]. Optimal control can generate the best solution in spite of complex modeling and computing. Among them, linear programming was relatively easy to solve, so it had been first developed and implemented [16]. Nonlinear relationships of traffic systems had also been discussed and applied to ramp metering [17].
A majority of these researches were based on macroscopic traffic models, including Cell Transmission Model [18], Payne–Whitham model [19], and METANET [20]. They adopted models to describe the relationships among variables and simulate the evolution of freeway systems. Artificial intelligence was also employed to ramp metering. These techniques included fuzzy logic [21], neural networks [22], iterative learning [8], and other heuristic methods [23].
For most coordinated ramp metering, origindestination (OD) demand is a vital input. Traditionally, OD matrices were derived from surveys, which were timeconsuming and usually not precise enough due to subjective response and small sample size. With the development of traffic detection technology, many methods were proposed to estimate OD with different data sources. Generally, they can be divided into two categories—the fixedsensorbased methods and the trajectorybased ones.
Fixed sensors include loop detectors, radar detectors, and video sensors. They collect traffic information like volume, occupancy, and speed at certain locations. A lot of researches were conducted to estimate OD with fixedsensor data. One of the most primitive approaches is proportional distribution method [24]. It regarded that the OD volume on freeways is in proportion to the volume at entrance ramps. Obviously, this assumption was too strong. A gravitybased model was then proposed [25]. It assumed that the trip distances meet Gamma distribution, which implied that too long or too short trips are of little possibility. Also, estimated travel time distributions were applied to OD matrix estimation [26]. Besides, commonly used models include generalized least square model [27], the maximum entropy model [28], and Bayesian theory [29]. Since fixed sensors cannot capture traffic’s origin and destination, these methods had to introduce assumptions to estimate OD.
Trajectory data record the movement of individual vehicles and thus provide a more reliable data source for OD estimation. The first kind of data is returned by detectors on vehicles, such as floating car data collected by GPS equipment [30] and vehicle trajectory data returned by mobile navigation applications [31]. Since not all vehicles are equipped with GPS devices or not all travelers use navigation apps, this kind of data is sample data. Penetration rate influences estimation accuracy [32]. The second kind of data is collected by widely distributed fixed sensors, like automatic license plate recognition data [33] and Bluetooth and WiFi data [34]. Different from traditional fixed sensors, they identify each vehicle or traveler via an identification (ID), which makes trajectory reconstruction possible.
Nowadays highquality trajectory data have become available. Previous researches have utilized trajectory data to estimate traffic state parameters such as OD flows [31], queue length [35], delay [36], and travel time [37]. Results showed that estimation accuracy was improved with trajectory data. If traffic parameters estimated by trajectory data could be applied to ramp metering, the control performance is supposed to be improved. However, limited research or practice has implemented it since highquality trajectory data were not available. Low frequency (e.g., > 30 seconds of record interval) and low penetration (e.g., <10%) are usual situations. Thus, most existing ramp metering controls were still based on fixedsensor data—typically loop detector data. The OD table was estimated by link counts [19]. Instead of estimating OD tables, some researches introduced offramp exit percentages to predict freeway flows [38]. Vehicles from different origins have the same probability to leave the mainline when they come to an offramp [39]. This assumption is not necessarily true. Others assumed that the OD flows were perfectly known and the studies were conducted under ideal scenarios [18]. However, these researches have a long distance from practice.
The contribution of this paper includes (1) proposing and implementing coordinated ramp metering with real trajectory data; (2) comparing the control performance of the proposed approach and the traditional method under different traffic demand intensity; (3) analyzing the influence of penetration rate on control performance and determining a minimum value. The remaining part of this paper is organized as follows: Section 2 introduces the bottleneck algorithm implemented in this research. Section 3 explains the process of weights calibration with trajectory data. Section 4 presents simulation experiments settings. Section 5 compares the experiment results. Section 6 analyzes the sensitivity on penetration rate. Section 7 concludes this paper.
2. Bottleneck Algorithm
The bottleneck algorithm is essentially a rulebased algorithm for coordinated ramp metering control. Ramp metering rates are calculated, respectively, on the basis of system capacity constraints and local conditions. The more restrictive metering rate is selected and finally adjusted to constraints including maximum queue length and minimum metering rate.
Figure 1 shows relevant variables of bottleneck sections and onramps. i is mainline section index, j is onramp index, and k is the time step. A mainline section i is defined as a bottleneck if its average occupancy oi is over the threshold oithres (see (1)); at the same time the total entering flow (including inbound flow qiin and onramp flow qion) is more than the total exiting flow (including outbound flow qiout and offramp flow qioff) (see (2)).(1)oik>oithres(2)qiink+qionk>qioutk+qioffk
Ramp metering variables of bottleneck section i and onramp j.
A bottleneck metering rate rjB is calculated if there exists a bottleneck on the freeway. On the basis of the metering rate rj in the last time step, entering traffic is reduced to alleviate congestion in bottleneck sections. The volume reduction is determined according to the law of traffic volume conservation. For bottleneck section i, its volume reduction qireduce is the difference between the total entering flow and the total exiting flow (see (3)). Then the reduction is distributed to its area of influence, i.e., its upstream onramps according to weights Wj,i (see (4)). The weights calculation is discussed in Section 3.4 in detail. When there are more than one bottlenecks, their areas of influence overlap. Onramp volume reduction qj,ireduce can be calculated from each bottleneck. The maximum volume reduction is used to calculate the bottleneck metering rate (see (5)).(3)qireducek+1=qiink+qionkqioutk+qioffk(4)qj,ireducek+1=qireducek+1·Wj,i(5)rjBk+1=rjkmaxiqj,ireducek+1
Then, a local metering rate rjL is calculated on the basis of the local condition of onramp j using demandcapacity strategy. To be specific, if the mainline occupancy downstream of the onramp oj does not reach the threshold ojthres, the metering rate is the difference between capacity qjcap and mainline traffic flow upstream of the onramp qjin; otherwise, it equals the preset minimum value rjmin (see (6)). The occupancy threshold ojthres is corresponding to the state when the mainline reaches capacity flow.(6)rjLk+1=qjcapqjink,ojk≤ojthresrjmin,ojk>ojthres
If onramp j is the nearest onramp upstream of bottleneck section i, then the inbound flow upstream of the bottleneck section i equals mainline traffic flow upstream of the onramp j (see (7)). Also, the onramp flow of the bottleneck section i is the minimum of the flow corresponding to the metering rate and the flow corresponding to the vehicles waiting in the onramp j plus the arriving vehicles (see (8)).(7)qiink=qjink(8)qionk=minrjk,djk+njkTwhere rj is the executed metering rate, dj is the vehicle arriving rate, nj is the initial vehicle number on the ramp, and T is the duration of one time step.
The system metering rate rj′ adopts the more restrictive of the bottleneck metering rate rjB and the local metering rate rjL.(9)rj′k+1=minrjLk+1,rjBk+1Then, the metering rate is adjusted to prevent the vehicle queue of each onramp exceeding the storage capacity Nj. The vehicle queue in the next time step is the initial vehicles on the ramp plus arriving vehicles and then minus released vehicles (see (10)). Thus deduce the minimum metering rate to satisfy the queue limits rjqueue (see (11)).(10)njk+djk+1rjk+1T≤Nj(11)rjqueuek+1=djk+1+njkNjTBesides, the metering rate should be no less than the preset minimum value rjmin. Thus, the final metering rate is the maximum of rj′, rjqueue and rjmin.(12)rjk+1=maxrj′k+1,rjqueuek+1,rjminFinally, the metering rate is converted to green time gj.(13)gjk+1=rjk+1rjsat×Cjwhere rjsat is the saturation flow (usually 1800 pcu/h) and Cj is the signal cycle. Figure 2 presents the flow chart of the bottleneck algorithm described above.
The flow chart of the bottleneck algorithm.
3. Weights Calibration3.1. Data Description
Data used in this research include trajectory data, loop detector data, and a corresponding road network map. Trajectory data is collected from a typical week, from 23 October 2017 to 29 October 2017, including about 13 million records. The indicators include a timestamp, vehicle ID, speed, location in terms of longitude, latitude, and road ID matched to the road network map. Vehicle trajectory data are collected by mobile navigation applications. They are a kind of crowdsourced data. With the development of mobile Internet technology, a great number of drivers use mobile navigation applications such as Google Map and Amap during their trips. To provide realtime navigation service, these mobile applications frequently collect and update vehicle location and movement, as shown in Figure 3. Each vehicle is assigned an ID, with which its trajectory can be accurately reproduced. Mobile phones with these navigation applications are essentially mobile sensors. The vehicle trajectory data can be regarded as an improved version of floating car data with higher collection frequency and higher penetration.
An example of vehicle trajectory data.
Loop detector data cover the mainline and ramps of NorthSouth Elevated Road in Shanghai, China. The duration is from 1 October 2017 to 31 October 2017. There are about 0.9 million records of traffic statistics in 5 minutes, including volume, occupancy, and speed. Detectors can be located to map via loop ID. Besides, the map contains information about the road network, such as road name, length, width, and number of lanes of the link.
3.2. OriginDestination Extraction
Origins and destinations of trips can be extracted from vehicle trajectory data. Generally, trips are distinguished by different purposes. Vehicle trajectory is divided into multiple trips based on dwell time and dwell location [33]. In this research, the problem is discussed in freeway networks where vehicles normally keep moving. Also, trajectory is collected every 5 seconds on average, forming a chain of continuous records as shown in Figure 3. These advantages simplify the process of OD extraction. When a vehicle first appears in the freeway network, the corresponding record is regarded as the origin of a trip. The following records all belong to this trip until one record appears at a nonadjacent road or the time gap between this record and the previous sequence is large enough. Then this record signifies a new trip. Since normally there does not exist trip purposes on the freeway, the OD extraction algorithm only needs to examine temporal and spatial continuity for trajectory records in the same trip.
Figure 4 presents a flow chart to extract OD pairs from trajectory data. First, all trajectory data are ordered by vehicle ID and timestamp. The algorithm compares two contiguous records. If they have the same vehicle ID, their time gap is less than a threshold (e.g., 10 minutes), and the path is continuous, then these two records belong to the same trip and the temporary destination is updated to the latter record; otherwise, the former record is the destination of this trip and the latter record is the origin of a new trip. Figure 5 shows an example of ordered trajectory data. They are divided into several trips through Figure 4. In this way, the origin and the destination of each trip and their corresponding location and time are extracted.
The flow chart of the algorithm to extract origindestination from trajectory data.
An example of origins and destinations of trips extracted from vehicle trajectory data.
3.3. Validation Test
In order to verify that the OD pairs extracted from trajectory data are representative samples, we count the number of vehicles passing through a link within a given time interval from trajectory data and count the flow volume of the same link within the same time interval from loop detector data. The former is sample since not all vehicles return trajectory data. Pearson correlation coefficient ρ is utilized to evaluate the linear correlation between the link counts extracted from trajectory data X={x1,…,xn} and the link counts collected by loop detectors Y={y1,…,yn}, where n is the size of the statistics, which equals the link number times the interval number.(14)ρ=∑i=1nxixyiy∑i=1nxix2∑i=1nyiy2
ρ ranges from 1 to +1, where ρ>0 is a positive correlation, ρ<0 is a negative correlation, and 0 is no linear correlation. The larger ρ indicates a stronger correlation. In general, ρ≥0.7 means a strong linear correlation. Trajectory data are regarded as representative samples if they pass this validation test.
3.4. Weights Calculation
Proper selection of weights is important to the control effect. If the volume reduction of a bottleneck is distributed too much to an onramp where vehicles do not destine for the bottleneck, then the metering rate is too restrictive. On the contrary, if too many vehicles are allowed into the freeway but they do not get off the freeway before the bottleneck; the metering rate is too loose. Accurate OD estimation provides valuable information for weights calculation [11]. In this research, the weights calculation is based on the OD patterns extracted from trajectory data. The traffic demand from one onramp to different destinations is the onramp demand times its destination choices proportion. Trajectory data provide representative samples of OD pairs to calculate this proportion. Let dj,l be the traffic demand from onramp j to destination l, xj,l be the corresponding number of trips extracted from trajectory data, and v be the number of destinations. Then,(15)dj,l=dj·xj,l∑l=1,…,vxj,lThe traffic demand from onramp j to bottleneck i is calculated by the sum of dj,l where destination l locates downstream of bottleneck i.(16)dj,i=∑ldj,lWeights Wj,i are the weights of onramp j to the bottleneck i, proportional to traffic demand dj,i.(17)Wj,i=dj,i∑jdj,iThere exists ∑jWj,i=1 for each bottleneck section. Weights matrix is as (18). u and m are, respectively, the number of onramps and bottlenecks.(18)Wu×m=W1,1⋯W1,m0⋱⋯⋱⋮Wj,i⋮0⋯⋱⋮00Wu,m
4. Simulation Experiments4.1. Network Description
A real urban freeway in Shanghai is simulated using the microscopic simulation software PTV VISSIM. The freeway is of 7.5 km in length, with 4 onramps, 3 offramps, and freewaytofreeway ramps. The north end locates at a suburban area and the south end is in downtown. Figure 6 annotates the length of mainline sections and onramps. The first and second row of the pictures shown in Figure 6, respectively, show onramps in the real world and in the simulation.
Test site with multiple ramps of NorthSouth Elevated Road (southbound) in Shanghai, China.
4.2. Simulation Settings
Experiments simulate freeway operation on weekdays’ morning peak (7:00 – 10:00), a typical recurrent congestion scenario. Data of 24 October 2017 (Tuesday) are utilized to get simulation inputs of traffic demand patterns, as shown in Figure 7. Vehicle Inputs are derived from loop counts. Vehicle routes and their relative flows are set according to the OD patterns extracted from trajectory data. Besides, speed limits on mainlines and on ramps are respectively 80 km/h and 40 km/h, as in the real world.
Traffic demand patterns of the test site.
4.3. Control Parameters Settings
Bottlenecks usually exist at merging areas downstream of onramps, weaving areas upstream of offramps and lanedrop areas. There are four bottlenecks in this freeway network. Figure 8 shows the relationship between occupancy o and flow q for each bottleneck. A sigmoidal function fits best [40].(19)qo=a·c·o·111+ebc·owhere a,b,c are all regression parameters. The occupancy threshold othres is set corresponding to the capacity flow. When othres=[0.28,0.27,0.25,0.22], the flow of the bottleneck section reaches the maximum of the fitted curve. In this freeway network, occupancy downstream of the onramp and occupancy of the bottleneck section are measured by the same loop detector. Thus, they have the same thresholds. In addition, for all controlled onramps, signal cycles C are 60s, saturation flow rsat is 1800 pcu/h· lane, and minimum metering rate rmin is 60 pcu/h· lane.
The relationship between occupancy and flow volume at four bottleneck sections.
Bottleneck 1
Bottleneck 2
Bottleneck 3
Bottleneck 4
4.4. Scenarios and Cases
The simulation experiments on three cases: (1) no control realworld case; (2) control with loop data—adopting a classic method “gravity model” to estimate OD with loop counts [25]; (3) control with trajectory data—implementing the proposed approach. Control schemes are conducted under three scenarios: (1) realworld traffic demand; (2) 20% less traffic demand for the mainline and all onramps; (3) 20% more traffic demand for the mainline and all onramps. Besides, to prepare simulation environments, there is no control for the first 15 minutes in all experiments. For each scenario and each case, we run 20 experiments with different random seeds and then take averages.
5. Results and Analysis5.1. Linear Correlation
There exists a strong linear correlation between link counts from trajectory data (X) and those from loop data (Y), as shown in Figure 9. Their relation can be fitted as X=0.1347Y+5.815. This means the penetration of the trajectory data reaches 13.5%, much higher than traditional floating car data. Also, the Pearson correlation coefficient ρ is 0.8775. Thus, the trajectory data pass the validation test and can be used to calculate weights matrix.
The linear relationship between link counts from trajectory data and those from loop data.
5.2. Weights Matrix
There are 4 onramps and 4 bottleneck sections, so the weights matrix is in the size of 4×4. Table 1 compares the results of the weights matrix generated from different data sources. Results show that the estimation with only loop data is more easily affected by ramp volumes. Taking the traffic contribution of bottleneck 2 for instance, the result attaches more importance to onramp 1 as it has much more volume than onramp 2. However, vehicle trajectories reveal that traffic entering from onramp 1 massively exits at the immediate downstream offramp (offramp 1) and does not reach bottleneck 2, because offramp 1 connects to another freeway. Similar results can be found in other bottleneck sections. With only fixedlocation measurements, the OD estimation deviates more from the reality.
Weights matrix calculated with loop data and trajectory data.
Loop data
Bottleneck 1
Bottleneck 2
Bottleneck 3
Bottleneck 4
Onramp 1
1.00
0.87
0.38
0.16
Onramp 2
0.00
0.13
0.06
0.02
Onramp 3
0.00
0.00
0.56
0.24
Onramp 4
0.00
0.00
0.00
0.58
Trajectory data
Bottleneck 1
Bottleneck 2
Bottleneck 3
Bottleneck 4
Onramp 1
1.00
0.78
0.18
0.08
Onramp 2
0.00
0.22
0.05
0.02
Onramp 3
0.00
0.00
0.76
0.20
Onramp 4
0.00
0.00
0.00
0.70
5.3. Mainline Performance
Experiments are performed under three scenarios and three cases. To evaluate the performance, 25 loop detectors are evenly placed on the mainline. The mainline is divided into 25 sections of 300 meters in length on average. Four onramps are, respectively, near section 3, 7, 15 and 24. Figure 10 presents mainline occupancies profiles of each experiment, and Table 2 lists performance indicators of average occupancy, average vehicle flow, and mean speed.
Mainline performance indicators.
Demand level
Cases
Occupancy
Vehicle flow
Speed
%
% change
veh/h
% change
km/h
% change
80%
No control
21.99

2466

68.64

Control with loop data
18.76
15%
2271
8%
71.94
5%
Control with trajectory data
18.06
18%
2278
8%
71.88
5%
100%
No control
35.74

2817

57.24

Control with loop data
29.18
18%
2883
2%
63.22
10%
Control with trajectory data
27.90
22%
2974
6%
65.48
14%
120%
No control
44.02

2616

50.01

Control with loop data
42.55
3%
2646
1%
50.97
2%
Control with trajectory data
39.74
10%
2743
5%
54.02
8%
Mainline occupancies profiles.
Realworld simulation is as in Figure 10(d); the most serious congestion appears in the bottleneck around onramp 4. The congestion spreads to upstream mainline over time. Congestion also forms in the rest three bottlenecks sometimes. The ramp metering control with loop data or trajectory data brings significant improvement, as shown in Figures 10(e) and 10(f). Their average occupancies are, respectively, reduced by 18% and 22%. Vehicle flows are increased by 2% and 6%. The congestion is reduced around the fourth bottleneck. It forms later and disappears earlier. Traffic condition is also improved in the rest mainline sections. Congestion is slightly reduced at the beginning and almost eliminated after 75 minutes.
When traffic demand reduces by 20%, traffic congestion only occurs at the fourth bottleneck. To eliminate the congestion, entering traffic is controlled at upstream onramps even if there is no congestion around these ramps. Mean speed increases by 5% but vehicle flow decreases by 8%. The control effect with loop data and with trajectory data is of little difference.
When traffic demand increases by 20%, traffic conditions become significantly worse in the first two bottleneck sections. The ramp control with loop data hardly improves the situation. In contrast, the control with trajectory data shows better performance, because the control parameters of weights are selected more properly. The control effect is remarkable especially between section 10 and section 25, as more upstream entering traffic can be controlled by ramp metering. It even prevents bottleneck activation around onramp 3. Occupancy is reduced by 10% under the control with trajectory data, compared to a 3% reduction under the control with loop data. Vehicle flow and speed are both raised more with trajectory data.
5.4. Overall Travel Time
To reveal whether time saved on the mainline exceeds onramp delay caused by ramp metering, the simulation measures travel time of vehicles from different origins, i.e., the upstream mainline and four onramps, as shown in Figure 11. For demand level of 100%, the average travel time weighted by flow volume reduces by 19%. The travel time of upstream traffic is reduced by 29%, which means more than 4 minutes are saved for each trip. The travel time of vehicles entering from 4 onramps is reduced by 7%, 28%, 23%, and 16%, respectively.
The travel time of vehicles from different origins.
Demand level of 80%
Demand level of 100%
Demand level of 120%
For demand level of 80%, the travel time of traffic from onramp 1 and onramp 3 is increased by about 75%, which means ramp metering does not bring benefits for these vehicles. However, other traffic’s travel time is saved a little. On average, travel time is increased by 33%. Controls with different data have little difference under these two scenarios.
For demand level of 120%, the average travel time is increased by 6% with loop data and reduced by 11% with trajectory data. This result manifests significant advantage of ramp metering with trajectory data. It improves the mainline traffic operation, without the sacrifice of traffic from onramps.
6. Sensitivity Analysis
The penetration of trajectory data is supposed to influence the control effect. It is necessary to study its sensitivity on penetration rate and the minimum required value. A simple random sampling is used to lower the penetration rate. In order to reduce random noise, the sampling is done 50 times for each penetration rate and we take averages.
Figure 12(a) depicts the relationship between Pearson correlation coefficient ρ and the penetration rate p. With p decreasing, ρ reduces increasingly faster. We need to determine the critical penetration pc, below which ρ drops significantly faster. The secondorder difference ∆2ρ is used to evaluate the changing speed of the descending slope. ∆2ρ where p≤pc should be significantly larger than ∆2ρ where p>pc. A ttest is applied to determine whether two groups of ∆2ρ divided by pc are significantly different from each other. When the penetration rate reduces to 4.0%, the ttest rejects the null hypothesis at the default 5% significance level; see Figure 12(b). The penetration of 4.0% is regarded as the minimum value, above which samples of vehicle trajectories are able to represent the characteristics of all vehicles and below which the reliability is not guaranteed.
The relationship between the Pearson correlation coefficient and the penetration rate.
The profile of ρ and p
The profile of ∆2ρ and p
Simulation experiments are performed under different penetration rates. Figure 13 compares indicators of occupancy, vehicle flow, and speed relative to the scenario of no control. Control effects get worse when penetration reduces. When the penetration rate is less than the minimum required value of 4.0%, the performance becomes more sensitive. The reason is that less penetration leads to less reliable results. When trajectory data volume is not sufficient, weight calibration tends to be improper and ramp metering becomes less effective in that way.
Mainline performance indicators under different penetrations.
7. Conclusion
This paper extracts OD patterns from trajectory data, validates the representativeness of the sample vehicle trajectories, and applies the historical OD patterns to coordinated ramp metering. To verify its advantage, the bottleneck algorithm is implemented with different data sources—loop data (traditional control) and trajectory data (our approach). A real urban freeway is simulated to test control effects.
Simulation experiments show that ramp metering with trajectory data increases another 4% throughput compared to traditional control under current traffic demand. The advantage is more significant under heavier demand. When traditional control can hardly relieve the congestion and even increase average travel time by 6%, our approach increases throughput by 5% and reduces travel time by 11%. However, their control performance shows little difference under low demand. The reason is that trajectory data can help accurate estimation of traffic contribution for bottleneck sections. This information is more important to effective control when traffic condition is oversaturated. Also, the control performance is affected by the penetration of trajectory data. The minimum required penetration is 4.0%, below which the OD estimation tends to become unreliable, and correspondingly the control has no advantage over the traditional one.
The approach proposed in the paper is free of strong assumption and complex computing; hence it is ready for practice. Experiments simulate real road networks and traffic demand patterns. The experiments are more persuasive than those under virtual scenarios. However, there are some limitations of the proposed approach. The bottleneck metering rate is calculated only when bottlenecks have been detected. Also, there exists a time lag between control actions being taken and having effects to the bottlenecks. Thus, it is only suitable to alleviate recurrent freeway congestion with steady OD patterns.
Future researches plan to improve models by further utilizing information recorded by vehicle trajectories. Prediction can be included to activate control before congestion forming. Feedback modules can also be added to increase robustness.
Data Availability
The data used to support the findings of this study have not been made available due to data security.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This research was supported by National Natural Science Foundation of China (Grant no. 61773293), Shanghai Sailing Program (Grant no. 19YF1435100), Joint Laboratory for Future Transport and Urban Computing of AutoNavi, and Shanghai Transportation Information Center.
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