This section comprises three parts: 1) the critical paths of closely spaced intersections, 2) the design of phase sequence for path-based progression, and 3) the improvement of full-actuated control by which prevents capacity loss.
Critical paths of closely spaced intersections
A critical path of closely spaced intersections is defined as a major demand path
of origin-destination flows. With the intersections being closely spaced, the origin-destination can be easily observed at the field side. Figure 3.13 gives an example of closely spaced intersections with four critical paths.
Stop line is essential in the computation of shockwaves. To evaluate the progression of a path, shockwaves of a path is introduced instead of shockwaves of an approach. Therefore, an important concept is introduced here, the stop line of a critical path. The stop line of a critical path is defined as the first stop line that one would encounter along with the critical path. In Figure 3.13, the stop line of each path is denoted as a thick black bar.
Phase sequences for critical paths
Most closely spaced intersections can benefit from signal progression, which avoids unnecessary stops and delays. The design of one- or two-way progression usually relays on a time-space diagram, which graphically illustrates how traffic propagates through intersections. The bandwidth of a time-space diagram is the portion of cycle which allows vehicle to go through all intersections in a group without stopping.
Figure 3.14(a) demonstrates a typical time-space diagram which contains a one-way bandwidth; the bandwidth allows vehicles to traverse through 3 intersections without stopping. However, designing phase sequences for closely spaced intersections may depend on path-based progression that cannot be analyzed easily by traditional time-space diagram.
From a signal timing perspective, phase sequence determines the quality of progression at signalized closely spaced intersections. Therefore, if one desires to conduct a multi-path progression, phase sequence must be designed carefully for
that use path-intersection diagram to design phase sequence. Figure 3.14(b) shows the designed phase sequences for each critical path corresponding to Figure 3.13. By the path-intersection diagram, one can easily arrange the phase sequences along each critical path.
Figure 3.13 Four critical paths in three closely spaced intersections
Path-based progressions are guaranteed by providing dedicate phases for each critical path. After designing phases for critical paths, phases on minor paths are arranged correspondingly in a manner that avoids conflict points on critical paths. The path-intersection diagram provides actuated control capabilities through their ability to respond to cycle-by-cycle variation in traffic demand while still being able to provide
progression for critical path movement.
Figure 3.14 (a)A one-way progression in time-space diagram. (b) A four-way progression in path-intersection diagram. The phase sequences are corresponding to Figure 3.13.
Enhanced actuated control
A full-actuated traffic control uses both detector information and a set of control parameters to operate the intersection in an efficient way. The full-actuated controller allocates green times for each approach corresponding to traffic demands. Little traffic demand on an approach would results a shorter green time which provides fast turnovers to serve other approaches.
As shown in Figure 3.15(a), the minimum green time is allocated to a phase once a detector associated with that phase is actuated by a vehicle. If vehicles continue to actuate the detector while the phase is green, an additional green time equal to the vehicle extension time is added to the phase. The green can be extended until it reaches the maximum green at which time the phase terminates in a condition called a “Max Out.” However, if no detector is actuated within a vehicle extension period (gap threshold), the phase is terminated in a condition called a “Gap Out.”
A defect of full-actuated control can be observed in Figure 3.15(b). If a vehicle stops on detection zone, the vehicle will continue to actuate the detector until “Max out”.
However, under stop-and-go condition, vehicles often stop on the detector until “Max out”. Although green time is allocated for the congested approach, no vehicles can be served. This prohibits the opportunity for traffics on different approaches to make use of the reserved capacity on intersection, and results a capacity loss.
(a) (b)
Figure 3.15 Full-actuated control with (a) gap out. (b)max out when a vehicle stops on detection zone.
To improve the defect, this research utilizes three new parameters to provide an enhanced actuated control operation (see Figure 3.16). The empty duration has a same physical meaning as gap duration, the axis “Gap duration” can be replaced by “Empty duration” in full-actuated control. A new parameter, Stopped duration, is introduced to overcome the problem of inefficient “Max out” problem. As a vehicle stops on the detection zone for an extensive time, a termination of current phase will be conducted as
“Stopped out.” This provides the opportunity for traffics on other approaches to be served. The concept of “Stopped out” is illustrated by new axis “Stopped duration” in Figure 3.16(b).
(a) (b) Figure 3.16 (a) Three traffic parameters: empty, moving and stopped durations. (b) Enhanced actuated control with a “stopped out” condition.
Dynamic green time model
With the above enhanced actuated control, we can construct the following model to optimize green times for closely spaced intersections. The key concepts include detecting the path shockwaves, dynamic green time formulation and optimize the path green time.
This subsection combines the vehicle stopped duration and shockwave theory to estimate the required green time of each critical path. The required green time will be dynamic adjusted according the critical path traffic demands. As shown in Figure 3.17, let point O be the origin of a Euclidean space, S be the duration that a vehicle stops on the detection zone, d be the distance from path stop line to detection zone and t1 be the begin time of a vehicle which stops on the detection zone. Using the "point-slope" form for straight-line equations, the line AC, line BC and point C can be calculated as
Similarly, if traffic follows the Greenshields model, the line CE, line OE and point E can be calculated as
Hence, the required green time g (line segment OE) is calculated as:
1
Figure 3.17 The relation between required green time and shockwaves.
Green time optimization model
With the above dynamic green time formulation, we can construct the following model to optimize green timings along all critical paths.
Under unstable condition, unbalanced green time may lead to a longer congestion
time than balanced green time. With different demand on paths, the overall congestion time can be minimal if the green time for each path is proportion to its corresponding traffic demand. If the green times of different paths were not proportion to its demand, some demands would have a longer congestion time compare to others. Therefore, the objective of green time optimization model becomes determine the optimal green time for each path. The optimal green time can be derived by balancing out the traffic demands on all paths. Balanced path green times also ensures less total delay time and short travel time [19]. The optimized green times are modeled as following equations.
Min g
where gi is the required green time for path i to discharge its traffic demand (which is calculated by Eq. 3.40); Gi is optimized green time for path i; G max and G min are the maximal and minimal value for the summation of optimized green times, respectively;
Gi,min and Gi,max are the lower and upper bound of green time for each critical path i, respectively. Eqs. (3.43)-(3.44) restrict the summation of optimized green time between maximal and minimal value. Eq. (3.45) requires that the green time for each path should satisfy its lower bound, but not exceed its upper bound.
Figure 3.18 Flowchart of actuated critical path control algorithm.
Control algorithm
The flowchart of the proposed algorithm is illustrated in Figure 3.18, there are six steps to form the critical path control method. The first 3 steps are focused on planning side; while the last 3 steps execute in the traffic signal controller. The first step finds the critical paths for closely spaced intersections. At the field side, one can collect traffic flow data to figure out the major origin-destination paths. The second step focused on designing phase sequences for multiple path-based progressions. The phase sequence is designed by the path-intersection diagram. Each path has a dedicated phase to progress the path movement. After phasing, the enhanced actuated control should be employed to prevent capacity loss. During the operation of actuated control, step four detects path shockwaves, including backward forming shockwave and backward recovery
shockwave. Step five predicts the required green time for each path by Eq. (3.40). The begin time and duration for a vehicle stopped on detection zone should be collected at this step. During the last step, required green times are optimized for all paths. The enhanced actuated control utilizes the optimized green time as the maximal green time for each critical path.
IV. Results and Discussion
In this chapter, the proposed models are tested with real networks to discuss their performance. These models include i) radar vehicle detection method in section 4.1 ii)three new traffic parameters in section 4.2 iii)shockwaves detection in section 4.3 iv)upstream flow and speed detection in section 4.4 and v) traffic signal control algorithm in section 4.5.
4.1 Radar vehicle detector
In this section, the radar system is first introduced and the requirements of radar sensor are also presented. The algorithm of vehicle classification and speed estimation will be shown in following subsections.
Table 4.1 The specifications of radar sensor.
Height 4 - 7 m
Central frequency 10.5 G Hz
Band width 50 M Hz
Pulse repeat frequency 1500 Hz
Down range resolution 3 m
Max Range 60 m
Max range shift frequency 30 K Hz Elevation angle/Azimuth angle 50 ° / 20 °
ADC 200 K Hz
FFT 128 points
Radar system
To support multi-lane capabilities, the FMCW radar detector is designed for roadside installation, as illustrated in Figure 4.1(a). The sensor is installed at a height of 5.2 meters above the ground and at a distance of 14 meters from the first lane. The maximal distance is 32 meters of the sensor from the most distant lane. The echo power of each lane is near-constant from the distance 14 to 32 meters. The dashed line is a curve that fits the echo power distribution of the vehicle on the road surface. The central frequency is 10.5 GHz. The vehicle width leads the radar with 50 M Hz band width and 3 meters down range resolution. The radar is designed to cover a maximum of eight lanes, and can be positioned a maximum of 60 meters from the roadside. The total frames per second, or the pulse repeat frequency, are 1500 Hz. Therefore, the max range shift frequency is 30 K Hz. The corresponding radar signal processing speed for ADC is 200 K Hz. Furthermore, the elevation and azimuth angles of the planar antenna are 50° and 20°. The specifications of the radar system are summarized in Table 4.1.
Figure 4.1 (a) Installation of radar sensor. There are four lanes. (b)The echo powers distribution for each lane of road.
Figure 4.2. Block diagram of the proposed X-band FMCW sensor system.
The building blocks of the X-Band FMCW of the radar are shown in Figure 4.2.
The sensor comprise two external antenna arrays, a single-chip CMOS transceiver (enclosed by the dashed line) and an external digital signal processing unit along with the necessary electronics. A power amplifier is added to increase output power level.
Dual planar antenna array are located at the transmitter output and the receiver input.
The planar antennas have an equivalent STC function. As shown inside the dashed lines, the radio frequency transceiver is a chip based on a standard 0.18 μm CMOS technology [45, 46]. The CMOS transceiver performs most of the required RF signal processing. A power amplifier is added to increase output power. Furthermore, a baseband digital signal processing unit is used for instantaneous and simultaneous assessment of range measurements. Figure 4.1(b) illustrates the beat frequency power distribution of the antenna corresponding to the installation in Figure 4.1(a). There are four echo power curves for four lanes. Generally, the echo power of most antennas decays at a rate 1 R4. For this specially designed planar antenna, the shorter range power decay can be cancelled by the near field interference. The dashed line, shown in
Figure 4.1(b), is the road surface curve. Restated, the echo power of the vehicle signal will stay on the four inter-points of the road surface curve. The empirical results, illustrated later in this section, show that complementing the magnitude of the vehicles with the second power of the frequency can obtain an accurate vehicle classification rate.
Vehicle classifier and speed estimation
Table 4.2 lists a data set to train two classifiers : SVM and LDA. The data had been collected on the Hsin-Lon road of the Chu-Pei city. Generally, users require installing the radar sensor as soon as possible. During the short setup time, the numbers of vehicle in four categories is skew. A good classifier requires an acceptable classification rate, after applying its learning algorithm to skew data constraints. The training data satisfies the short setup time and skew data constraints.
Table 4.2 Set of vehicles used to test the classifiers.
Motorcycle Small Medium Large
Total 30 145 12 4
After applying the K-means, LDA and SVM to the training data in Table 4.2, the classification rate is 42%, 93% and 94%, respectively. In Table 4.3, the rate results in K-means not being a good classifier in situations involving constraints. The LDA and SVM have a near identical leave-one-out recognition rate, and moreover this rate is acceptable. Both methods are good classifiers, and can resolve any associated environmental installation problems. The following paragraphs analyze and compares
Table 4.3 The classification rate of classifiers.
Table 4.4 Vehicles obtained from a field.
Category Motorcycle Small Medium Large
Type ID 1 2 3 4 5
Type motorcycle Car van Bus Truck
Subtotal 30 79 66 12 4
Total 191
Table 4.4 lists another testing data set that meets the short setup time and skew data constraints. The test data were obtained from a field site on a road in Chu-Pei city, Taiwan. The radar is installed as illustrated in Figure 3.1. The same traffic volume can be collected on a normal urban road within a 10-15 minutes period. The five vehicle types from the table can be classified into four categories. All vehicles from different lanes are merged into a single training data set. According to the radar equation, in Eq.
(4.1), the receiver power of the vehicle is decayed by 1/R4. As shown in Figure. 4.1(b), the planar antenna is specially designed to perform an SPC function which compensates for the decay in each lane. The receiver power of the road surface, indicated by the dashed line curve, resembles a curve with some power of the range. Therefore some software STC functions are tested, as shown in Eq. (3.3), to compensate for the decay of the road surface. Before extracting the features from the vehicle profile, amplitude of
K-means LDA SVM
42% 93% 94%
the profile is multiplied by some power of the frequency. Although the classifier is designed to classify vehicles into four categories, recognition rates remain an area of interest for numerous combinations of different vehicle types.
4
Table 4.5. Leave-one-out recognition rate for different classifiers and categories.
Category LDA( fm) SVM( fm) LDA( fm2) SVM(fm2) LDA( fm4) SVM( fm4)
1 vs. 2 vs. 3 vs. 4 vs. 5 73%(140/191) 76%(145/191) 76%(146/191) 82%(156/191) 78%(149/191) 71%(136/191) 1 vs. 2345 95%(182/191) 98%(187/191) 96%(183/191) 99%(189/191) 94%(180/191) 97%(186/191) 1 vs. 23 vs. 4 vs. 5 93%(177/191) 94%(180/191) 95%(181/191) 98%(186/191) 93%(178/191) 93%(177/191) 23 vs.45 96%(155/161) 97%(156/161) 97%(156/161) 99%(159/161) 96%(154/16) 96%(155/161) 23 vs. 4 vs. 5 96%(155/161) 96%(155/161) 98%(158/161) 98%(158/161) 96%(154/161) 95%(153/161) 2 vs. 3 vs. 4 vs. 5 72%(116/161) 75%(121/161) 75%(121/161) 80%(128/161) 76%(123/161) 71%(115/161) 2 vs. 3 76%(110/145) 75%(109/145) 77%(112/145) 79%(114/145) 78%(113/145) 74%(108/145) 4 vs. 5 88%(14/16) 94%(15/16) 88%(14/16) 94%(15/16) 94%(15/16) 100%(16/16)
Table 4.5 lists the test results for different powers of frequency for SVM and LDA.
The highlighted cells represent the highest leave-one-all recognition rates for different categories. SVM wins almost all scenarios in fm2cases. Table 4.6 lists the error matrix for a SVM( fm2
) case. Therefore, by compensating the received radar signal with power two of the frequency, SVM can obtain the best recognition rate. The first row ,” 1 vs. 2 vs. 3 vs. 4 vs. 5” , indicates a low recognition rate for each classifier. This low rate means that creating excessively narrow categories will result in a low recognition rate.
Comparing the third and fifth rows, “1 vs. 23 vs. 4 vs. 5” and “23 vs. 4 vs. 5”, reveals that the recognition rates are almost equal in the same classifier. Motorcycles can
generally be separated from other vehicle types. The second row, “1 vs. 2345”, confirms this. Examining the last two rows, “2 vs. 3” and “4 vs. 5”, reveals that car and van are difficult to separate, while bus and truck can generally be separated.
Table 4.6. Leave-one-out error matrix for SVM( fm2
) . Actual vehicle class
Detect vehicle class Motorcycle Small Medium Large
Motorcycle(1) 29 1 0 0
Small(2,3) 1 143 1 0
Medium(4) 0 1 11 1
Large(5) 0 0 0 3
Total 30 145 12 4
error (%) 3% 1% 8% 25
Recognition rate (%) 98% %
Table 4.7 shows the calibrated virtual loop length which is outputted from the video calibrating system. The far lane is slightly longer than the near lane. The planar antenna design is responsible for this effect. Figure 4.3 shows the vehicle length outputted by SVR. The estimated truck lengths are shorter than the visually measured lengths obtained from the video system, and the estimated motorcycle lengths are longer than the visually measured ones (see Figure 4.3 (b)). The reason is that total number of vans and cars is 75%. The training data is skew, leading SVR make length predictions for all vehicles that are close to those of cars. Figure 4.4 describes the vehicle speed. Since the estimates of motorcycle length are high, the motorcycle speed always exceeds that of visual measurements obtained using the video system (see Figure 4.4(b)). The situation for trucks is the reverse of the above, with estimates of length and speed being lower than the visual measurements.
Figure 4.3. Vehicle output lengths from SVR. The open triangles with dashed lines denote the lengths measured from the video calibrating system. Meanwhile, the rectangles with black lines represent the estimated lengths obtained using the proposed algorithm. (a) The vehicle lengths were outputted from SVR. (b) The motorcycle lengths outputted from SVR.
Figure 4.4. Estimated vehicle speeds. The open triangles with dashed line are the speeds measured from the video system. The rectangles with black line are the speeds estimated using the proposed algorithm. (a) Estimated speeds for all vehicle categories.
(b)Estimated speeds for motorcycles.
Table 4.7. Virtual loop length for each lane.
Lane1 Lane2 Lane3 Lane4
4.2 Three new traffic parameters
The test example in Table 4.8 involves two adjacent intersections with a 700 foot link at a fixed-timed traffic signal operating with 60-s cycle length and 23-s effective green interval. To determine the features of the three parameters and the effects of environmental change, eight scenarios were prepared and listed in Table 4.8: traffic flow changing from 48 vph to 2880 vph, different detector zone size (20, 50 feet), different vehicle detector distances to the stop bar (0, 30, 60,90,120,240 feet), and next intersection spill back. Figure 4.5 shows the results of one scenario involving changing flows and vehicle detector distances from the stop bar. Each point of each sub-graph is the average of 30 continued cycles which share the same traffic flow. Sub-graphs (a), (c) and (e) show the normal flow. Sub-graphs (b), (d) and (f) show the spill-back flow.
Notably, Moving time is directly proportional to traffic flow before the occurrence of traffic jams. Additionally, the Stopped time changes slowly when the vehicle detector is not far from the stop bar. Interestingly, the near vehicle detector has a smooth trend for each traffic parameter and the traffic parameters of the far vehicle always jump to some value. If the next intersection is spill-back, the Stopped time is greater than the red phase time and the Moving time is less than the green phase time. Table 4.8 lists the summarized relationships between three traffic parameters and the environment. The
Notably, Moving time is directly proportional to traffic flow before the occurrence of traffic jams. Additionally, the Stopped time changes slowly when the vehicle detector is not far from the stop bar. Interestingly, the near vehicle detector has a smooth trend for each traffic parameter and the traffic parameters of the far vehicle always jump to some value. If the next intersection is spill-back, the Stopped time is greater than the red phase time and the Moving time is less than the green phase time. Table 4.8 lists the summarized relationships between three traffic parameters and the environment. The