Weather-Tuned Network Perimeter Control

A Network Fundamental Diagram Feedback Controller Approach

Maha Elouni and Hesham Rakha

Center for Sustainable Mobility, Virginia Tech Transportation Institute,

3500 Transportation Research Plaza, Blacksburg, VA 24061, U.S.A.

Keywords: NFD, PI Controller, Gating, Inclement Weather.

Abstract: Inclement weather has been shown to increase congestion, justifying the need for weather-responsive traffic

control. From one side, all existing weather-responsive controllers currently operate on freeways or limited

road segments. From the other side, existing controllers operating on networks do not take into

consideration the weather effect on the network fundamental diagram (NFD). This paper describes the

development of a macroscopic weather-tuned perimeter controller. First, an NFD-based proportional-

integral perimeter controller (PC) is implemented in INTEGRATION, tuned using clear weather data and

then tested for clear and inclement weather conditions. In order to respond to weather changes, new sets of

control parameters were tuned for each weather and given to the controller. This weather-tuned perimeter

controller (WTPC) is compared to the regular PC. Simulation results show that the WTPC reduces

congestion inside the protected sub-network better than PC. Also, it improves the performance of the full

network (inside and outside the protected sub-network) in terms of average speed and total delay. Compared

to the non-perimeter control case, WTPC increases the average speed of the entire network by 28.61% for

rain and 42.64% for snow conditions. Total delay is decreased by 33.26% and 42.02% for rain and snow,

respectively.

1 INTRODUCTION

Traffic managers employ various management

strategies to maintain safety and improve roadway

mobility. This task becomes more challenging with

adverse weather, as weather events may increase

both crash rates and congestion. According to the

Federal Highway Administration (FHWA, 2017),

22% of vehicle crashes are weather-related crashes.

Of these, 46% occurred in rainy conditions and 13%

in snowy or sleety conditions. Average speed, traffic

volumes, saturation flow rates, free-flow speed, and

travel time delays are also negatively affected by

inclement weather on arterials and freeways.

(Romain et al.) found that there is an average

decrease of 15.5% in capacity and 9% in free-flow

speed and (Agarwal et al., 2005, Maze et al., 2006)

reported capacity reductions of 4–30% and speed

reduction rates of 3–15% during rainy conditions.

(Xu et al., 2013), studied the impact of rain in a

network finding that heavy rain and rainstorms

reduced the network critical accumulation and

maximum production by 10.5%, 16.7% and 21%,

18.7% respectively. (Tsapakis et al., 2013),

considered different intensities of rain, snow, and

temperature levels to study the effect of weather on

travel times in an urban network, finding that total

travel time increases due to light, moderate, and

heavy rain by 0.1–2.1%, 1.5–3.8% and 4.0–6.0%,

respectively. They found light snow increases travel

time by 5.5–7.6% and heavy snow increases delays

by 7.4 to 11.4%. (Rakha et al., 2008) demonstrated

that traffic stream jam density is not affected by

weather conditions, and that reductions in free-flow

speed and speed-at-capacity increase as the rain and

snow intensities increase. Precipitation intensity

affects the roadway capacity only during snow. The

authors developed weather adjustment factors to

calculate the free-flow speed, speed-at-capacity, and

capacity as a function of precipitation type, intensity

and visibility level.

(Pisano and Goodwin, 2004) introduced the idea

of weather responsive traffic management, analyzing

the impacts of adverse weather on traffic flow and

presenting three categories of operational strategies

that may improve safety, mobility and productivity.

Elouni, M. and Rakha, H.

Weather-Tuned Network Perimeter Control.

DOI: 10.5220/0006679900820090

In Proceedings of the 4th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2018), pages 82-90

ISBN: 978-989-758-293-6

The operational strategies are classified into three

categories: 1) treatment strategies like coordination

with maintenance managers for snow or ice control;

2) control strategies such as signal timing, ramp

metering, and variable speed limits; 3) advisory

strategies like public notification of road closure and

warning systems (Systematics, 2003).

Concerning control strategies, (Goodwin and

Pisano, 2004) introduced some successful methods

to change signal timings in response to weather. The

authors identified the parameters that need to be

modified to simulate weather impacts on arterial

traffic flow using CORSIM. Their studies revealed

that weather-responsive signal timing could improve

mobility by increasing average speed and reducing

delays. (Papageorgiou et al., 2008) found that

variable speed limits decrease the slope of the flow

occupancy diagram at under-critical conditions,

increase the critical occupancy, and enable higher

flows at the same occupancy values in overcritical

conditions. These strategies mitigate localized

weather impacts on relatively short road segments

(Pisano and Goodwin, 2004).

This paper describes the implementation of a

weather-tuned control strategy on a macroscopic

level. The control strategy is based on the

macroscopic fundamental diagram (MFD) also

known at the Network Fundamental Diagram

(NFD), which gives an aggregated view of the

network characteristics: density, flow, and space

mean speed. NFD’s physical model was initially

proposed by (Godfrey, 1900). It was observed with

dynamic features in a congested urban network in

Yokohama by (Geroliminis and Daganzo, 2008).

Their analyses and simulations have shown that

NFDs are curves that can be reproduced under

homogeneous conditions in urban networks. They

have also shown that NFDs are a property of

infrastructure and not of demand, which means that

the average flow in a network is at maximum for the

same density value, regardless of the time-varying

origin-destination (O-D) tables.

Further research has been conducted for the

investigation of NFDs using empirical and simulated

data. (Buisson and Ladier, 2009) were the first to

test how the NFD changes if the congestion is not

homogeneous within the network. (Ji et al., 2010)

recreated inhomogeneous conditions in an urban

freeway traffic simulation with several on-ramps,

finding that inhomogeneous congestion leads to a

reduction in flow. They presented control strategies

to be followed using ramp metering to create

homogeneous traffic states. (Mazloumian et al.,

2010) and (Geroliminis and Sun, 2011) found that

the spatial variability of vehicle flow density affects

the shape, the scatter, and the existence of an NFD.

In fact, heterogeneous networks might not have a

well-defined NFD, especially in the decreasing part

of the NFD, as scatter becomes higher when

accumulation increases, leading to the appearance of

a hysteresis loop. In order to address this issue, (Ji

and Geroliminis, 2012) created clustering algorithms

to create homogeneous sub-networks to obtain small

variance of link densities within a cluster. This

approach is useful for large congested networks with

strong heterogeneity. NFD-based traffic flow might

then be used in single-region cities (Daganzo, 2007)

(Haddad and Shraiber, 2014) or in multi-region

cities, each having a well-defined NFD (Aboudolas

and Geroliminis, 2013, Haddad and Geroliminis,

2012).

The idea of perimeter control (or gating) based

on the NFD consists of attempting to maintain the

accumulation around a set point (which corresponds

to the maximum throughput) in order to avoid the

oversaturation or congestion regime (Figure 1).

Figure 1: NFD of a network.

(Li et al., 2012) investigated a perimeter control

strategy of an oversaturated network using the NFD

concept. The optimization goal was to maximize

capacity utilization of the network and prevent

queue spillback. The phase sequence and offset were

optimized by a Genetic Algorithm (GA) to minimize

the network delay. They have implemented the

signal timing outputs in TRANSYT-7F and showed

that their proposed model performs better than

TRANSYT-7F in congested networks. However, the

approach proposed a fixed signal timing method

which is not adapted to the real-time traffic

conditions. There are many works in the literature

that overcome that issue and operate real time

perimeter control. They use different techniques like

the standard proportional integral (PI) controller

(Keyvan-Ekbatani et al., 2012), Robust PI controller

(Haddad and Shraiber, 2014) and Model Predictive

Weather-Tuned Network Perimeter Control

controller (Sirmatel and Geroliminis, 2016).

However our focus will be in standard proportional

integral Controller because it is simple and

computationally cheap.

(Keyvan-Ekbatani et al., 2012) described a

simple real-time feedback-based gating concept,

which exploits the urban NFD for smooth and

efficient traffic control operations. They used a

standard proportional-integral (PI) feedback

controller, and applied the method to a network in

Chania, Greece and tested it using the microscopic

traffic simulator AIMSUN. Although simple, the

method has been proven to be very efficient.

Compared to the non-control case, the average

vehicle delay per km was reduced by 35%, the mean

speed increased by 39.2% and the total number of

vehicles that exit the overall network increased.

The method assumed that the real-time

measurements of all links within the protected

network are fed to the regulator which is not

convenient in terms of implementation cost for a

real-time system. (Keyvan-Ekbatani et al., 2013),

demonstrated that feedback-based perimeter control

is possible with much less real-time measurements

than in their previous work.

The aforementioned strategies assume that the

gating is applied directly at the border of the

protected network. However, in reality, this could

not always be satisfied due to some restrictions such

as unavailability of proper links to store the gated

vehicles. For that reason, (Keyvan-Ekbatani et al.,

2015) included a time delay in the feedback-

perimeter control strategy so that it handles the

metering at some junctions further upstream from

the protected network.

All these works assume that the links on which

the perimeter control is applied are long enough to

handle the queues of the gated vehicles. In order to

overcome that limitation and also to obtain a more

homogeneous density distribution in PN, (Keyvan

Ekbatani et al., 2016) combined the feedback

perimeter control strategy with the adaptive traffic

signals control. They applied the gating at the

borders of the PN and traffic-responsive adaptive

signal control strategy inside the PN. The

combination of these two strategies led to higher

overall vehicle throughputs and hence shorter

queues at the boundary of the PN, higher speeds and

lower network delays.

(Keyvan-Ekbatani et al., 2017) proposed

strategies for queue and delay balancing at the gated

links under perimeter control. Their approaches

could be used for flow distribution among the gated

links, especially in multi-region perimeter control as

they reduce the impact of queuing on NFDs of the

regions.

All of the mentioned works are very interesting

and effective. However, they do not consider the

effect of weather on the NFD. Also, they did not test

the efficiency of the control method for different

weather conditions which are the objectives of this

paper. Consequently, the objectives and the

contributions of this work are as follows: (1)

Implement a feedback-based standard proportional

integral perimeter control (PC) strategy in the

INTEGRATION micro-simulator. (2) Study its

impacts on the protected network’s (PN’s) NFD and

on the full network (FN) for different weather

conditions. The full network is the zone inside and

outside the protected network. (3) Develop a

weather-tuned perimeter control (WTPC) strategy

and evaluate its impact on the NFD of the PN and on

the performance of the FN. (4) Compare the WTPC

with the PC and the non-control (NPC) cases. (5)

Validate the obtained results of the WTRC by

testing it for different rain and snow intensities.

2 NETWORK DESCRIPTION

AND MACROSCOPIC

FUNDAMENTAL DIAGRAM

2.1 Network Setup

The modelled network was used for studying the

impact of the implemented PC strategy on the NFD.

For that reason, a PN was identified; this is the sub-

network that needs to be protected from congestion.

The PN corresponds to the zone surrounded by the

green rectangle in the middle of the network in

Figure 2.

Figure 2: Grid network modelled in INTEGRATION.

VEHITS 2018 - 4th International Conference on Vehicle Technology and Intelligent Transport Systems

The PN contained 91 links, as shown in Figure 2.

The yellow chevrons represent the four links where

gating was applied. The gated links were long

enough such that they were able to accommodate the

queues caused by gating without spilling back onto

other links. Future work will integrate queue spill

back prevention strategies. All links were one way

and each link had only one lane.

The full network (FN) comprised 36 signalized

intersections running on a fixed-time plan. The

origins and destinations are represented by blue

circles (Figure 2). Loop detectors were placed on

each link in the network to collect the needed

measurements, and those measurements were

collected every cycle (60 s in this study). The traffic

demand was loaded for 75 minutes, with demand

increasing during the first 37.5 minutes, and

decreasing during the second 37.5 minutes,

representing realistic demand behaviour. In order to

ensure that the network was empty at the end of the

simulation, the total simulation time was set to be

176 minutes (approximately 3 hours). A feedback

dynamic traffic assignment was activated to reflect

realistic driver behaviour during congested

conditions.

2.2 NFD Equations Derivation

In this work, the NFD is presented based on the total

time spent (TTS) and the total travelled distance

(TTD), which are calculated from the loop detectors

measurements. The TTS (in veh.h/h) corresponds to

the number of vehicles in all the network links and is

calculated using Equation (1).



(



)

=

.





()



∈

=





(



)

∈

(1)

where z is the link; Z is the set of measurements

links , k = 0, 1, 2, … is an index reflecting the cycle

number; T is the duration of the cycle; 





(



)

is the

measured number of vehicles on link z during cycle

k. It is calculated by Equation (2).







(



)

=



.



.







( −1)

100

(2)

where 



is the length of link z; 



is the number

of lanes on link z; 



is the jam density; 



is the

measured time-occupancy (in %) on link z during

cycle k.

The TTD (in veh.km/h) corresponds to the length

weighted sum of the corresponding network link

flows. It is calculated using Equation (3).



(



)

=



(



)

.



∈

(3)

where 



(



)

is the measured flow on link z

during cycle k.

Figure 3: NFD of the protected network (PN).

Running a simulation in INTEGRATION, we

obtain the NFD presented in Figure 3. The

maximum throughput occurs in a TTS range of

[1800, 3000]. Note that the NFD has a decreasing

area corresponding to the congestion regime,

indicating the need for a control strategy to mitigate

congestion in the PN.

3 IMPLEMENTATION OF THE

PERIMETER CONTROLLER

(PC)

3.1 Mathematical Modelling

In order to avoid congestion inside the PN, a PI PC

is applied based on the NFD. The idea of the PC is

to maintain the TTS around a set value 



, which

corresponds to the maximum TTD. In our case,





= 2000ℎ.ℎ/ℎ, which is within the range of

the TTS values corresponding to the maximum TTD

[1800, 3000].

Figure 4: System and feedback controller structure.

The system and feedback controller structure is

represented in Figure 4. The process, shown in

Equation (4), is what happens in the PN—its input is





, which corresponds to the PN’s entering flow,

Weather-Tuned Network Perimeter Control

and its output is

TTS. Further details about the

derivation of the process of Equation (4) can be found in

(Keyvan-Ekbatani et al., 2015, Keyvan-Ekbatani et al.,

2012).

∆

(

+1

)

= ∆

(



)

+.Δ



()

(4)

where Δ =  −̅ and ̅ corresponds to the

steady state variable used in the model linearization.

The desired steady state is common in control

engineering, and in this case, it corresponds to the

region where the TTD is maximal. Note that 







.  and  are two model parameters that can be

found using a least squares approximation of the

simulated data (



, TTS) around the maximum TTS

range.

The controller’s inputs are TTS and 



, and its

output is the ordered flow that should enter the PN.

Equation (5) corresponds to the proportional-integral

feedback regulator equation.





(



)

=



(

−1

)

−





(



)

−

(

−1

)



+



(



−

(



)

(5)

where 



and 



are the proportional and integral

gains, respectively. These can be found by manual

fine-tuning or using control engineering methods.

More details about finding these gains can be found

in (Keyvan-Ekbatani et al., 2012, Keyvan-Ekbatani

et al., 2015).

The controller ordered flow 



is distributed

among the gated links. The flow entering the PN

from each gated link has to be between two bounds:





and 



. These bounds can be calculated

based on the minimum and maximum green times,

respectively.

The controller always works in the background

and the fixed signal timings are set for all signals.

Once the TTS is close to (i.e., 85% of) the set value





, the controller is activated and the signal

timings are calculated based on the controller

ordered flow 



. When the TTS decreases, to less

than 85% of 



, the controller is deactivated and

the signals display the fixed timings again.

3.2 Use of the Perimeter Control (PC)

for Clear Weather Conditions

Since INTEGRATION is a stochastic micro-

simulator, simulations were run for the PC case and

the NPC case using five different random seeds. The

parameters used in these simulations are as follows:

 = 0.678,  = 0.0973, 



=6.96, 



=3.31,







= 1826.66ℎ/ℎ, and 



= 2000ℎ.ℎ/ℎ.

Table 1: Performance metrics of the PC for the FN using

five different seeds.

Average Max Min

NPC: Speed (km/h) 16.00 16.97 14.182

PC: Speed (km/h) 18.89 19.33 18.23

Difference (%) 18.75 35.34 7.75

NPC: Delay (s) 261.31 340.95 220.65

PC: Delay (s) 187.34 194.45 183.25

Difference (%) -26.25 -12.59 -46.12

Completed trips 9068 9079 9053

Table 1 shows that the PC improved the

performance of the full network FN. On average, it

increased the average speed by 18.75% and

decreased the total delay by 26.25% compared to the

NPC case.

For the performance inside the PN, Figure 5

clearly shows that the control algorithm decreased

the congestion. Note that the decreasing NFD area in

Figure 5(a) no longer exists in Figure 5 (b).

(a)

(b)

Figure 5: (a) NFD using 5 different seeds for NPC; (b)

NFD using 5 different seeds for the PC.

VEHITS 2018 - 4th International Conference on Vehicle Technology and Intelligent Transport Systems

4 PC AND WTPC FOR

INCLEMENT WEATHER

4.1 Weather Modelling in

INTEGRATION

Rakha et al. studied the impact of weather on free

flow speed, speed at capacity and capacity. They

developed weather adjustment factors (in Equation

(6)) to compute these three traffic stream parameters

based on precipitation intensity  (cm/h) and

visibility level  (km) for each of the rain and snow

cases (Rakha et al., 2008, Rakha et al., 2012).

 = 



+



+







+



+







+





(6)

In this work, the calibrated model parameters 



through 



are chosen to be the Twin Cities

parameters because it has the highest WAF (Table 1

in (Rakha et al., 2012)). These WAF are multiplied

by the clear conditions speeds and capacity.

The authors also modelled vehicle deceleration

and acceleration behaviour for inclement weather.

They provided rolling and friction coefficients for

different roadway surface conditions (including wet

and snowy surfaces).

In order to model different weather conditions in

INTEGRATION, the set of inputs containing the

free flow speed, speed at capacity, capacity, rolling

coefficient and coefficient of friction are calculated

and given to the software.

The PC uses for inclement weather the same set

of parameters used for clear weather conditions

which is the following:  = 0.678,  = 0.0973,





=6.96, 



=3.31, 





= 1826.66ℎ/ℎ, and





= 2000ℎ.ℎ/ℎ.

However, the WTPC uses a specific set of

parameters for each weather condition. For clear

weather, it uses the parameters defined above: =

0.678,  = 0.0973, 



=6.96, 



=3.31, 





1826.66ℎ/ℎ, and 



= 2000ℎ.ℎ/ℎ. The

obtained re-tuned parameters are  = 0.755, =

0.214, 



=3.17, 



=2, 





= 1600ℎ/ℎ,





= 2000ℎ.ℎ/ℎ for the rain conditions and

 = 0.0864,  = 0.758, 



= 0.114, 



=1.2,







= 1613ℎ/ℎ, 



= 2000ℎ.ℎ/ℎ for the

snow conditions.

The NFD plots of the PN for both rain and snow

conditions are presented in Figure 6(a) and (b). The

blue curves correspond to the NFDs for the NPC, the

red to the NFDs for the PC, and the green curves to

the NFDs for the WTPC. As the curves show, the

values of TTS for the WTPC case were lower than

those for the PC and NPC cases, indicating that the

WTPC performed better than the PC in decreasing

congestion inside the PN.

The results of Table 2 show that the WTPC

algorithm outperformed the PC algorithm for both

the rain and snow cases in terms of increasing the

average speed and decreasing the total delay of the

FN (not only PN). Compared to the NPC case, the

WTPC increased the speed by 28.61% and the total

delay by 33.26% for the rain conditions. For the

snow conditions, an improvement in the range of

42% is shown for both the average speed and total

delay.

(a)

(b)

Figure 6: (a) NFD for rain; (b) NFD for snow.

In order to further test the efficiency of the

WTPC, simulations for different rain and snow

intensities were performed for the NPC, PC, and

WTPC cases.

Weather-Tuned Network Perimeter Control

Table 2: Performance Metrics on the FN for the NPC, PC and WTPC Cases.

Performance

metrics

Strategy

Rain Snow

Value

% Difference w.r.t

NPC

Value

% Difference w.r.t

NPC

Avg. Speed

NPC 11.23 - 6.52 -

PC 13.75 22.43 8.85 35.73

WTPC 14.44 28.61 9.30 42.64

Avg. Total

Delay

NPC 402.52 - 803.42 -

PC 283.73 -29.51 478.27 - 40.47

WTPC 268.65 -33.26 465.77 - 42.02

Table 3: Performance metrics of the FN with respect to (w.r.t) NPC for the PC and WTPC cases for different rain and snow

intensities.

Performance Metrics Strategy Moderate Rain High Rain Moderate Snow High Snow

% Difference in Avg.

Speed

PC 21.14 17.95 49.82 48.25

WTPC 30.50 24.68 59.62 53.24

% Difference in Avg.

Delay

PC -33.97 -23.62 -50.3 -46.74

WTPC -39.97 -31.57 -54.87 -49.06

(a) (c)

(b) (d)

Figure 7: (a) moderate rain, (b) high rain, (c) moderate snow, (d) high snow.

5 VALIDATION FOR

DIFFERENT RAIN AND SNOW

INTENSITIES

Two different precipitation intensities were chosen

for each weather conditions. Each weather condition

was run with its corresponding set of parameters as

described above. No further parameter tuning is

done. Depending of the weather (clear, rain or

snow), the corresponding set of control parameters is

loaded to INTEGRATION for the WTPC. For the

PC, the same set of parameters tuned originally for

clear weather conditions is loaded to

INTEGRATION whatever the weather is.

VEHITS 2018 - 4th International Conference on Vehicle Technology and Intelligent Transport Systems

Table 3 shows the relative difference of each

performance metric for the PC and WTPC with

respect to NPC for different rain and snow

intensities. All the results show that the WTPC

outperformed the PC in improving the mobility of

the entire transportation system.

The PN NFD plots of each scenario are presented

in Figure 7. In all the plots, the green curves

corresponding to the WTPC have the lowest TTS

values, which means that they were the most

effective in reducing the congestion inside the PN.

6 CONCLUSIONS

A Perimeter Control (PC) strategy based on the NFD

was implemented in the INTEGRATION micro-

simulator. It was tested for different weather

conditions and was proven to be efficient. Because

the method was proven to be efficient, and due to the

need for a macroscopic weather responsive traffic

management strategy, a weather-tuned perimeter

control (WTPC) model was developed and tested for

different precipitation types (rain and snow) and

intensities. The WTPC was shown to outperform

the regular PC in decreasing congestion inside the

protected network (PN), in increasing the average

speed and in decreasing the total delay of the full

network (FN).

An application of this work in a real network will

be a future objective. Another future objective will

be combining this control strategy with a routing

strategy to manage the queues on the gated links. A

generalization of this work will be done so that it

could be applied to any network.

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