Australasian Transport Research Forum 2015 Proceedings
30 September - 2 October 2015, Sydney, Australia
Publication website: http://www.atrf.info/papers/index.aspx
A prospective way of ramp metering using vehicle
infrastructure integration system
Tuo Mao1, Vinayak Dixit2
1Department
of Civil and Environmental Engineering,
The University of New South Wales, Australia
Email: [email protected]
2Department
of Civil and Environmental Engineering,
The University of New South Wales, Australia
Email: [email protected]
Abstract
As Bluetooth and navigation devices are widely used on latest produced vehicles, vehicle
infrastructure integration (VII) system in Intelligent Transport System (ITS) has been given
flourishing expectation because of its detection accuracy and multiple-information collecting
capability. This paper suggests an ideal ITS environment where all vehicles are equipped with
certain VII device and all vehicles can be recognized by ITS which is capable of memorizing
all vehicles’ route choices. This paper proposed an innovative hypothetical theory and
algorithm of coordinated ramp metering which takes the advantage of VII system. This
algorithm integrates vehicle routing information with coordinated ramp metering by reading and
processing the vehicles’ average travel distance along the freeway. Comparison between new
coordinated ramp metering algorithm and traditional local ramp metering strategy has been
made and travel time saving is observed in new ramp metering algorithm.
1. Introduction
1.1 Vehicle infrastructure integration
Vehicle infrastructure integration is defined as the establishment of vehicle-to-vehicle and
vehicle-to-roadside communication capability by Paniati (2005). Potential addressed in
mobility, safety, and commercial benefits are clear.
From hardware aspect, the proof of concept (POC) test of vehicle infrastructure integration
was performed by the US department of transportation in the northwest suburbs of Detroit,
Michigan in Kandarpa et al. (2009)’s report. This report constructs a structure of vehicle onboard equipment (OBE) and roadside equipment (RSE). OBE consists a dedicated short-range
communications (DSRC) radio, a highly accurate on-board positioning system, an
appropriately configured on-board computer. RSE would be linked to the specialized VII
network. Communication between OBE and RSE, as well as between different OBEs, takes
the advantage of DSRC radio. 400 meters is the maximum communication range between
OBE and RSE is found in this test. Information passed by VII system referred to mobility, safety
and commercial applications. Mobility information contains position data and time label and
the accuracy of position data is 4.5 m at 95% circular error probable. It is also worth mentioning
that VII system has the capability of receive vehicles’ origin & destination (OD) and suggest
vehicle’s route information within the network enabler service. No traffic management and
transportation efficiency application and benefit analysis were performed during the POC test.
From the corresponding software aspect, effort has been made into traffic condition monitoring
(Ma et al., 2009, Li et al., 2008), collision avoidance (Wang et al., 2011, Chen and Cai, 2005),
and weather-related application (Petty and Mahoney III, 2007). Applications in traffic condition
monitoring and collision avoidance take advantage of real-time position data to better
understand traffic condition. In addition, weather-related application makes use of probe
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A prospective way of ramp metering using vehicle infrastructure integration system
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vehicle data to diagnose and predict road weather condition in order to reduce weather-related
accidents.
Few researches are referred to traffic management and control taking the advantage of VII.
Lee and Park (2008) Create a microscopic simulation test bed under the cooperative vehicleinfrastructure environment to evaluate route guidance application. The route guidance strategy
uses the average link travel times collected from probe vehicles through VII system. Later,
Park and Lee (2009) evaluate sustainability impact of route guidance system based on the
same test bed under cooperative vehicle-infrastructure environment.
Algorithm of variable speed limit (VSL) using the data provided by VII system is developed by
Sun et al. (2014). Information such as vehicle models, vehicles’ speed and position are
collected by VII system and utilized by VSL to keep the traffic flow at a high efficiency and
suppress propagation of shockwaves.
Above all, the VII system is mainly utilized for its real-time mobility data such as vehicle’s
velocity and position. No research has been made to research the other information such as
route information. The research gap exists in processing of the unused information and make
the most of VII system.
1.2 Ramp metering
A ramp meter, ramp signal or metering light is a device, usually a basic traffic light or a twosection signal (red and green only, no yellow) light together with a signal controller that
regulates the flow of traffic entering freeways according to current traffic conditions. It is the
use of traffic signals at freeway on-ramps to manage the rate of automobiles entering the
freeway. Ramp metering systems have proved to be successful in decreasing traffic
congestion and improving driving safety. Ramp meters are claimed to reduce congestion
(increase speed and volume) on freeways by reducing demand and by breaking up platoons
of cars. Two variations of demand reduction are commonly cited; one being access rate, the
other diversion (Piotrowicz and Robinson, 1995).
Ramp metering can be divided into local ramp metering and coordinated ramp metering.
ALINEA is a typical control strategy based on classical feedback theory which keeps the
mainline occupancy stay nearing a desired value by adjusting the corresponding ramp
metering ratio (Papageorgiou et al., 1991, Hou et al., 2011, Demiral and Celikoglu, 2011,
Abdel-Aty et al., 2007). FLOW, another local ramp metering algorithm, is an integrated, trafficresponsive metering algorithm which is determined by local conditions (Local Metering Rate
or LMR) or system capacity (Bottleneck Metering Rate or BMR) or on-ramp queue length
(Hasan et al., 2002).
HERO (heuristic ramp-metering coordination) can be classified into coordinated ramp metering
because it is extended from ALINEA by adding a heuristic coordination scheme which
overcomes the uncertainty of freeway capacity by identifying the critical downstream
occupancy for maximum throughput (Papamichail et al., 2010).
Kotsialos and Papageorgiou (2004) applied nonlinear discrete-time optimal control to ramp
metering by creating a macroscopic traffic flow model (METANET model) which divides a
motorway link into several sections with its on-ramps and off-ramps. By discretization of
freeway, dynamic real time simulation can be seen as a sum of several time intervals. During
each interval, each section of freeway contains its own time-dependent status vector and the
status vector is also determined by the control vector which represents ramp metering’s
influence. No-linear optimization was selected to solve the discrete-time model in the report.
The macroscopic traffic flow model connects coordinated signal control and the non-linear
optimal control which not only makes a system-wide optimization but also classifies a new
approach of ramp metering optimization (Hasan et al., 2002).
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1.3 Overview
All ramp metering methodologies take count in traditional loop detector data and none of them
uses data from VII system. No existing ramp metering algorithm has the capability of
understanding traffic demand, in other word, origin destination information have not been
utilized due to the lack of VII system broadcasting. However, VII system’s capability of
receiving routing requests and provide route guidance makes it possible for traffic engineer to
bypass traffic demand estimation and traffic assignment model and, instead, to read driver’s
origin-destination and route choice in real-time through VII system. For this point of view, this
paper describe an OD understanding ramp metering algorithm.
The rest of this paper is organized as follow.
2. Methodology
This section discusses VII system environment specification, the assumptions made, Route
information digitization, the theory development that guiding heuristic ramp metering strategy
and the innovative rules within ramp metering strategy.
2.1 VII system environment specification
To simplify the case, an ideal VII system environment is assumed. In this ideal environment,
all vehicles are equipped with standard on-board equipment and every entry ramp of the
research motorway are equipped with standard roadside equipment. The maximum reliable
communication distance between OBE and RSE is set to 400 meters. Communicative
information consists of vehicle position, time label, vehicle identification and vehicle speed.
2.2 Route information digitization
Since it is capable to track and read vehicle’s route information using VII system, the collected
data must be recorded and processed in a relatively easy way.
A solution come out of this paper is to transfer the origin-destination information into one
number, travel distance along the investigated motorway. The travel distance along the
motorway for vehicle #i is𝑙𝑖 .
The reasons using travel distance along the investigated motorway 𝑙𝑖 are (1) it turns a two-field
(origin and destination) format into one-field format; (2) it transfers the denotation of origin and
destination information into a quantified value for the ease of further decision making; and (3)
it is easy to process into a link-wide variable by taking average which will be discussed in the
following sections.
2.3 Existing ramp metering framework
The HERO algorithm built by Papamichail et al. (2010) can be divided into two level. The lower
level uses ALINEA (Papageorgiou et al., 1991), a local feedback ramp metering strategy. The
higher level applies a feed-forward disturbance compensation (FDC) strategy. FDC is a known
control theory methodology that enhances the robustness of a feedback controller such as the
ALINEA. The hybrid of two levels is a feedback feed-forward control scheme. The following
sections describe the local feedback ramp metering strategy and the FDC strategy
respectively.
2.3.1. ALINEA – local feedback ramp metering strategy
The local control unit in ALINEA comprises a single metered ramp that regulates the metering
rate r by adapting to traffic conditions monitored by one or several mainline detector stations.
The traffic conditions are namely the lane occupancy as measured by vehicle detectors.
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For each detector station on the mainline of the motorway, a critical occupancy denoted as
o crit is calibrated based on the flow-occupancy diagram showed in Figure 1.
Figure 1 Flow vs. occupancy diagram
At time-step k, for each detector j, the difference between measured occupancy from mainline
detector 𝑜𝑚𝑒𝑎𝑠,𝑗 (𝑘) and its critical occupancy 𝑜𝑐𝑟𝑖𝑡,𝑗 is denoted as 𝑑𝑗 (𝑘) which is shown in Eq.
⑴.
𝑑𝑗 (𝑘) = 𝑜𝑐𝑟𝑖𝑡,𝑗 − o𝑚𝑒𝑎𝑠,𝑗 (k)
⑴
An indicator 𝛼𝑗 (𝑘) is introduced to represent the inverse trend of on-ramp flow expectation from
lower level ramp metering in time step k. The difference 𝑑𝑗 (𝑘) is accumulated into indicator
𝛼𝑗 (𝑘) by the way shown in Eq.⑵.
𝛼𝑗 (𝑘) = 𝛼𝑗 (𝑘 − 1) + 𝑐(𝑑𝑗 (𝑘))
⑵
Where 𝑐(𝑑𝑗 (𝑘)) is an alpha-increment function which is shown in Figure 2.
Figure 2 Alpha increment function
The relationship between 𝛼𝑗 (𝑘) and according ramp metering ratio 𝑟𝑠 (𝑘) is shown in Eq.⑶.
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A prospective way of ramp metering using vehicle infrastructure integration system
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⑶
𝑟𝑠 (𝑘) = (1 − 𝛼𝑗 (𝑘)) × 𝑞𝑠 (k − 1)/𝑑𝑠 (𝑘)
where
𝑞𝑠 (k − 1) is the on-ramp flow in (k-1) time step.
𝑑𝑠 (𝑘) is the demand of the on-ramp at time step k, which is detected from upstream RSE or
loop detector station.
In time step k, the expected flow on ramp meter s is deducted by Eq. ⑷.
⑷
𝑞𝑠 (k) = (1 − 𝛼𝑗 (𝑘)) × 𝑑𝑠 (𝑘)
2.3.2. FDC strategy
The FDC is implemented by re-using a known ramp metering strategy called the DemandCapacity strategy. The FDC starts by estimating the motorway spare capacity N as a function
of the upstream arrivals A (the disturbance) and downstream nominal bottleneck capacity B.
N=B−A
⑸
To apply an effective disturbance compensation strategy, the locations of the capacity B and
the station measuring A must be configured by the user such that the distance between them
desirably does not exceed 2km with a maximum of 3km. In practice, between locations A and
B (the boundaries of the coordinated freeway section), see Figure 3 for an example, any of the
following could exist:
(1) Multiple metered ramps (𝑄1 , 𝑄2 , 𝑄3 )
(2) Unmetered on-ramps (U)
(3) Off-ramps (X).
Figure 3 Freeway coordinated section
For scenarios similar to Figure 3, Eq. ⑸ is generalised as
N = B−A−U+X
⑹
where U is the sum of the flows of all unmetered ramps (measured by detectors) in the section
and X is the sum of the flows of all off-ramps in the zone (measured by detectors).
Note that the section concept in the FDC strategy is not to be confused with the cluster of the
ALINEA strategy. The section is a local aggregation of ramps that can share the same
disturbance measurements. The dynamic cluster of the ALINEA is a wide-area coordination
strategy.
To apply FDC to the ALINEA strategy, a compensation parameter β is introduced to fit the
demand-capacity strategy, so Eq. ⑷ is modified to
𝑞𝑠 (k) = (1 − 𝛼𝑗 (𝑘)) (1 + 𝛽) × 𝑑𝑠 (𝑘)
⑺
where
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A prospective way of ramp metering using vehicle infrastructure integration system
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β=
N−∑𝑠∈𝑆 𝑑𝑠 (k)
∑𝑠∈𝑆 𝑑𝑠 (k)
⑻
and where ∑𝑠∈𝑆 𝑑𝑠 (k) is the sum of target flows of each metered ramps s in the section. These
flows are configured as estimates of the expected ramp demands.
As a result, flow N is shared between the metered ramps in proportion to their target flows
𝑑𝑠 (k) which are the expected unconstrained demands on each ramp.
Similarly to 𝛼𝑗 (𝑘) , the 𝛽 parameter gives an indication of the mainline spare (or lack of)
capacity.
If β > 0, it follows that N > ∑𝑠∈𝑆 𝑑𝑠 (k) indicates spare capacity is available or spare capacity is
on the rise.
If β < 0, it follows that N < ∑𝑠∈𝑆 𝑑𝑠 (k) indicates demand is larger than capacity or demand is
on the rise.
2.4 Extension
A hypothesis is suggested in this experiment that, for all on-ramps, the shorter average
distance vehicles travel along freeway the higher freeway output (off-ramp) flow, then more
drivers can be served in certain amount of time (especially rush hours). After this hypothesis,
heuristic rules that prefer drivers that travel a shorter distance along freeway is extended in the
HERO strategy.
2.4.1. Hypothesis
The hypothesis proposed is that, for all on-ramps, the shorter average distance vehicles travel
along the higher freeway output (off-ramp) flow, then more drivers can be served in certain
amount of time (especially rush hours). Ideally, shorter travel distance means getting off the
freeway sooner, and less downstream bottleneck experienced and caused, more vacancy for
the down-steam on-ramps, and in the end, more efficient the freeway services drivers.
2.4.2. Fitting in HERO strategy
In the hypothesis, preference for vehicles travel shorter distance along freeway is suggested.
Since for all on-ramps, a first-in-first-out (FIFO) rule must be obeyed, it is unrealistic to implicate
the preference for those preferred vehicles individually. Instead, a fuzzy way is proposed that
preference can be allocated onto each on-ramp by judging its average distance vehicles travel
along freeway. As the definition of average travel distance at on-ramp s on the freeway at time
step k, 𝐿̅𝑠 (𝑘) is defined as:
𝑁𝑘
∑
𝑙 (𝑘)
𝐿̅𝑠 (𝑘) = 𝑛=1𝑁 𝑛
⑼
𝑘
where
𝑙𝑛 (𝑘) is the travel distance of vehicle n,
And 𝑁𝑘 is number of vehicles awaiting at on-ramp s to merge into freeway.
An indicator 𝛾𝑠 represents the preference in average travel distance along freeway is
introduced at each on-ramp for higher-level FDC strategy. Eq. ⑺ and Eq. ⑻ can be transferred
into:
𝑞𝑠 (k) = (1 − 𝛼𝑗 (𝑘)) (1 + 𝛾𝑠 + 𝛽) × 𝑑𝑠 (𝑘)
⑽
where
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A prospective way of ramp metering using vehicle infrastructure integration system
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β=
N−∑𝑠∈𝑆(𝑑𝑠 (k)×(1+𝛾𝑠 ))
∑𝑠∈𝑆 𝑑𝑠 (k)
⑾
𝛾𝑠 is assumed to be no less than 0 and stands for the extent of preference at on-ramp s.
After applying indicator 𝛾𝑠 all on-ramps target flow is enlarged by adding a non-negative 𝛾𝑠 in
the multiplier bracket in Eq. ⑽ while the compensation parameter β is adjusted accordingly in
Eq. ⑾ to meet the demand-capacity conservation.
The key problem now becomes the determination of 𝛾𝑠 . The hypothesis above in 2.4.1 shows
that shorter average travel distance is preferred than longer one, so that 𝛿𝑖 is also leaning
towards to shorter average travel distance. The proposed way uses the inverse of average
travel distance as weight factor which is formed in Eq. ⑿.
𝛾𝑠 = 𝜇
1
̅̅̅̅
𝐿𝑠
⑿
1
𝐿𝑠
∑𝑠∈𝑆(̅̅̅̅)
where 𝜇 is a sensitivity valve that balance the lower level ALINEA strategy and higher level
HERO strategy. 𝜇 is 1 as default and need further calibration.
In this situation, 𝛾𝑠 will be positive and fit in the range of (0, 1).
3 Case study
3.1 Model description
A virtual network is used in this case study and the origin destination matrix is also artificial.
The model is built in PARAMICS. The researched segment is 4.6 km long and contains 2 onramps with ramp meters and 2 off-ramps. Mainstream of this section is two-lane and all ramps
are one-lane. The geometry brief diagram is shown in Figure 4.
Figure 4 Freeway geometry
There are three time periods in this simulation. The first period is a ten minute warm up period
which has a very low demands (approximately 0). The second period is 60 minute long and
the demand matrix for the second period is shown in Table 1. The third period is 50 minute
long and the demand is zero since it is a clearing period that allows all vehicles to arrive their
destination. In total, two hour is simulated in order to imitate peak hour traffic situation.
Table 1 Demand matrix
Origin\Destination
Demand (veh/hr)
A
𝑿𝟏
𝑿𝟐
B
349
170
3130
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A prospective way of ramp metering using vehicle infrastructure integration system
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𝑸𝟏
n/a
0
989
𝑸𝟐
n/a
n/a
793
As we can see, the mainstream has a relatively high traffic flow while certain vacancy can be
seen after off-ramps (𝑋1 and𝑋2 ). However the vacancy is not big enough to deal with the
demands of on-ramps (𝑄1 and𝑄2 ). So certain congestion should occur on this section and ramp
metering is applied to control on-ramps to avoid congestion. The HERO ramp metering
mentioned in the last chapter is translated into plug-in which is readable for PARAMICS.
The time step is set to 15 seconds, which means the traffic control centre collects data,
processes data and applies ramp metering strategy every 15 seconds. The coordination
distance in HERO is set to be 3 km.
3.2 Experiment design
The simulation contain several scenarios, including:



ALINEA only: ramp metering only depends on local detector stations (lower level only) ；
and only applies ALINEA strategy.
Average travel distance HERO: heuristic coordination strategy related to average travel
distance along freeway (higher level) is applied to overlap ALINEA (lower level).
No ramp metering: as a comparison, no ramp metering is performed in this case.
3.3 Results
The results are observed from the detector stations set on the mainstream every 500 meters
and the ramp metering log is generated by the plug-in when HERO makes decision.
A comparison of ramp metering rate before and after coordination is represented in a ramp
metering ratio log in Figure 5 and Figure 6.
Figure 5 Ramp metering ratio at ALINEA only scenario
ALINEA only scenario
node 132
node 44
ramp metering ratio
1.2
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
300
350
400
450
500
time step ID
In ALINEA only scenario, ramp metering ratio varies more rapidly and ramp metering ratio is
more sensitive to local detector station data. However in average travel distance HERO
scenario, ramp metering ratio is more smoothed due to the coordination operation between
node 132 and node 44. As shown in Figure 5 and Figure 6, an observable coordination starts
to kick in at about 150th time step (at 37.5 minute) and ends at about 300th time step (at 75
minute). Two phases can be observed, first phase when node 44 is preferred is from 150th time
step to 219th time step, and the second phase when node 132 is preferred is from 220th time
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step to 300th time step. Node 44 is preferred since its shorter travel distance in the first phase
while node 132 gets more preference in the second phase because of its large demand.
Figure 6 Ramp metering ratio at Average travel distance HERO scenario
Average travel distance HERO scenario
node 132
node 44
ramp metering ratio
1.2
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
300
350
400
450
500
time step ID
To further prove what ramp metering ratio represents, cumulative flow diagrams of node 132
and node 44 are shown in Figure 7 and
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A prospective way of ramp metering using vehicle infrastructure integration system
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Figure 8 respectively. Same flow pattern as the ramp metering ratio is shown.
Figure 7 Cumulative flow diagram of node 132
ramp node 132
1600
1400
1200
1000
800
600
400
200
0
hero
nothing
alinea
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A prospective way of ramp metering using vehicle infrastructure integration system
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Figure 8 Cumulative flow diagram of node 44
ramp node 44
1000
800
600
400
200
0
hero
nothing
alinea
As you can see, the ramp metering regulated traffic counts are less than the case without ramp
metering. This represents that ramp metering algorithms are functioning to prevent freeway to
be merged with too many vehicles and then prevent freeway from congestion.
To better understanding what are the two ramp metering algorithms, several loop detector data
have been derived from the experiments to demonstrate the functions of HERO and ALINIEA
comparing to the “no ramp metering” case.
Figure 9 Cumulative number of vehicles at mainstream before ramp node 132
mainstream before ramp 132
4000
3500
3000
2500
2000
1500
1000
500
0
hero
nothing
alinea
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Figure 10 Cumulative number of vehicles after ramp node 132
mainstream after ramp node 132
6000
5000
4000
3000
2000
1000
0
hero
nothing
alinea
Figure 11 Cumulative number of vehicles before ramp node 44
mainstream before ramp node 44
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
hero
nothing
alinea
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Figure 12 Cumulative number of vehicles after ramp node 44
mainstream after ramp node 44
6000
5000
4000
3000
2000
1000
0
hero
nothing
alinea
From Figure 7 to Figure 12, we can observe that the mainstream cumulative number of
vehicles are similar between the three experimental scenarios, which means the mainstream
have been fully occupied after the first onramp merging(Figure 10, Figure 11 and Figure 12).
The differences are the on-ramp merging number of vehicles and mainstream flowing vehicles.
In Figure 7 and Figure 8, no ramp metering (“nothing”) case merged more vehicles into the
freeway than ramp metering cases (“hero” and “alinea”) and in Figure 9, fewer mainstream
flow are allowed to enter this section of freeway. This means that more vehicles are congested
from the upstream.
In addition, total delays on freeway links are calculated in all scenarios respectively. The total
delay under no ramp metering scenario is 15622656.0 seconds. The total delay on freeway
links in ALINEA only scenario is 354205.1 seconds while the total delay on freeway links in
average travel distance HERO scenario is 223351.3 seconds. The delay results further prove
that ramp metering algorithms (both HERO and ALINEA) prevent freeway from congestions
and maintain freeway in an efficient condition during the peak hour. In the terms of performance,
the developed HERO algorithm provides more travel time saving than ALINEA while
maintaining freeway in similar uncongested traffic flow.
4 Conclusion
In this paper, a new coordinated ramp metering algorithm is developed which not only utilizes
latest VII system but also is capable of processing vehicle routes. A hypothesis is proposed
that vehicles that travel shorter distance along freeway are preferred. A hypothetical freeway
section model is built in PARAMICS to test the new algorithm. Results show that both HERO
and ALINEA strategy are effective in reduce mains stream congestion and provide travel time
savings than no ramp metering situation. In addition, the innovated coordinated ramp metering
strategy (average travel distance HERO) outputs more smoothed ramp metering ratio than
local ramp metering strategy (ALINEA). Benefit is gained in travel time saving in coordinated
ramp metering strategy (HERO) comparing to local ramp metering strategy (ALINEA).
5 Future works
A guess is that there is still room for new HERO strategy to gain more benefit by adjusting the
balance valve μ. By tuning μ, maybe new HERO strategy would pick up the ramp metering
ratio sensitivity in lower level ALINEA and the travel time saving in higher level HERO. So more
work certainly need to be done in the future.
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A prospective way of ramp metering using vehicle infrastructure integration system
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More methodology needs to be worked out to process vehicle routes information to make better
understanding of traffic demands. Not only heuristic ways but also traffic dynamic models need
to be researched.
More case studies need to be done when there is a more complicated 3 or more on-ramps
coordination.
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