Perspectives of Internet based Road Network Trafﬁc

Flow Modelling and Control

Apostolos Kotsialos

School of Engineering and Computing Sciences, Durham University

South Road, Durham, DH1 3LE, U.K.

Abstract. This paper is concerned with possible future internet applications

within the framework of trafﬁc ﬂow modelling and control. Two modelling re-

lated uses are described based on the assumption that vehicles in the near future

will be equipped with smart on-board devices that can communicate with each

other through reliable ad-hoc wireless networks. This capability opens new ways

of thinking about trafﬁc ﬂow and requires the explicit consideration of the drivers’

behaviour when more information is available to them pertaining to downstream

trafﬁc conditions. Finally, a web-based application for supporting ramp metering

is discussed as well.

1 Introduction

The ubiquitous trafﬁc light is probably the most important device related to road trafﬁc

control. It was introduced at the beginning of the 20th century for improving the safety

of road junctions, by giving right of way to passing vehicles. A century later and with

the advent of transport telematics, the trafﬁc light and its operation is still a hot topic

of research. The scope of course is much wider now, but the simple fact remains that

a device introduced a hundred years ago is still the effector of our most sophisticated

trafﬁc control strategies. Why has this simple device endured a century of use? The

reason is that it is a simple and effective means of communication, highly tuned to

human cognition norms.

The advent of the internet and wireless communication networks has brought for-

ward a new communications medium which interfaces both with transport units/infra-

structure and drivers. Personalised devices are increasingly becoming connected and in-

teractive getting access in diverse databases and having signiﬁcant computation power

for data processing and decision making support. This personalised device, in the form

of GPS, smartphones, tablets etc, can now become the new trafﬁc control sensor and

effector. This technology has the potential to become the new “trafﬁc light” and in that

sense the new Variable Speed Limit (VSL) sign and Variable Message Sign (VMS) as

well. The added feature is the personalised information and the custom demand for traf-

ﬁc control decisions on the vehicle level. With the exception of special types of vehicles

(ambulances, buses etc) it is difﬁcult for the trafﬁc light at a junction to be aware of each

of the queued vehicles needs, as at most there can be some OD information estimate

available. Personalised devices can communicate this information effectively pre-trip

Kotsialos A. (2011).

Perspectives of Internet based Road Network Trafﬁc Flow Modelling and Control.

In Proceedings of the 1st International Workshop on Future Internet Applications for Trafﬁc Surveillance and Management, pages 55-66

DOI: 10.5220/0004473100550066

 SciTePress

and en-route. This gives rise to a whole new range of trafﬁc control strategies which go

beyond the minimisation of an aggregate control objective, and go to the custom made

individual and collective trafﬁc management decisions. Important questions regarding

the level of aggregation and emergent trafﬁc ﬂow behaviour need to be posed and an-

swered. Hence, for trafﬁc control purposes, the internet can be viewed as an additional

extra system layer added to the classical Infrastructure-Vehicle-Driver (IVD) transport

system. The internet and wireless communication technologies facilitate the addition of

Information in that triplet, i.e. the IVD-Information (IVDI) transport system.

This calls for a revision of trafﬁc ﬂow models both at the micro and the macro

(hence also at the meso) level and that should be fed to trafﬁc surveillance and control

applications. Trafﬁc ﬂow models should include information in a more fundamental and

structured way as one of the constituent elements of trafﬁc. Especially Model Predictive

Control (MPC) for integrated control measures in mixed corridors, has to gain a lot in

terms of efﬁciency from this revision. Thus, the internet calls for a new generation of

trafﬁc controllers over wide mixed corridors where information is a system component,

rather than an external input.

As connectivity becomes an essential and widely adopted feature of our societies,

similar to water and electricity network access, internet access for drivers, vehicles and

on-board devices will become the norm. We can envisage a distributed virtual traf-

ﬁc control centre spread over wide geographic areas using robust, highly reliable and

redundant communications networks, and mobile computing power to support trafﬁc

management in terms of surveillance and control. This can be achieved by adopting

hierarchical, decentralised and peer-to-peer architectures using networks of sensors and

also notions of networked control over limited bandwidth communication channels.

Hopefully, this effort will result to the introduction of new notions, ideas, concepts and

technologies that will last for the good part of this century.

This paper is structured as follows. Section 2 provides a brief overview of some

ideas about ways of using the internet for trafﬁc modelling and control purposes. Sec-

tion 3 describes a possible application affecting microscopic car following dynamics;

macroscopic modelling is discussed in section 4. Section 5 discusses the use of web-

based applications affecting driver departure in support of ramp metering operations.

Section 6 concludes this paper.

2 Internet based Applications for Trafﬁc Management

The internet is a diverse network of clients and servers communicating using different

protocols. Its most important feature is the networked structure supporting its robust-

ness. Within the framework of trafﬁc management systems, the most obvious use of

internet for surveillance and control purposes is exploitation of the information dissem-

ination potential of cyber space. In this case, the general model is that of a driver receiv-

ing information and responding to it. The informed drivers make their choices based on

this, something which may be viewed as a limiting factor to the application of control

measures. Indeed, the prevailing paradigm with respect to trafﬁc control applications is

that of a TCC being responsible for the operation of compulsory control measures in an

effort to regulate some crucial trafﬁc variable(s). Responsibility and liability for these

operations are placed on the trafﬁc authority. Drivers are required to comply with the

control measures’ operational decisions, e.g. in case of ramp metering they have to wait

at the on-ramp until they get a green light to enter into the mainstream; in case of com-

pulsory variable speed limits, they must observe the speed limit communicated to them.

The scope of internet based applications in this framework is limited as it is deﬁned by

the needs of the information/communication infrastructure and software development.

However, there are other possibilities worth exploring by changing the way trafﬁc

control measures operate. High connectivity and real-time information may be used for

designing the trafﬁc control operations. This can be done by means of timely delivery

of information allowing or motivating drivers to behave in such ways as to optimise the

trafﬁc ﬂow process. This requires accepting the fact that drivers are intelligent agents

able to operate efﬁciently in changing environmental conditions. Hence, a new type

of control approach can be envisaged, that assigns more emphasis on driver behaviour

rather than just TCC issued compulsory suggestions or actions. Thus, information as

disseminated by internet based applications can be considered as a structural element

of modelling and control design of road network trafﬁc.

The key feature in this approach is the support of emergence, i.e. the process by

which a desired global road network-wide macro-state emerges from the application

of local interactions in the micro-state. This is a potential of information intensive ap-

plications that needs to be tapped. By informing drivers with the appropriate pieces of

information individual decision making and driver behaviour can be steered towards es-

tablishing a desired global state. This scenario supports the “informed drivers” who are

responsible for their own decision; the trafﬁc authority is responsible for facilitating the

efﬁcient and reliable collection and dissemination of information, and the maintenance

of this infrastructure, rather than the control measures’ decision making.

Different applications can be envisaged based on this approach. Three such scenar-

ios are discussed here. The ﬁrst one is based on classical microscopic car-following

dynamics. The second, is a comment on the analysis of macroscopic dynamics based

on non-local information. Finally, a third one is concerned with the possibility of using

the internet for managing the demand in conjunction with ramp metering.

3 Changing the Car-following Dynamics

In this section a possible application of ad-hoc wireless networks [1] is considered

for changing the behaviour of a trafﬁc stream towards more efﬁcient use of the road

capacity.

Let us consider a homogeneous trafﬁc stream moving along a single-lane motorway

as shown in Figure 1, [2], [3], [4]. Modelling of this stream on the microscopic level

is usually done by considering the car-following dynamics theory developed in the 50s

and 60s. One of the most common general family of model are those developed by Gen-

eral Motors (GM) researchers and are based on the stimuli-response driver behaviour

description. In these models, drivers respond to external stimuli and the response is a

function of the drivers’ sensitivity and the stimuli’s strength, i.e.

response = f (driver sensitivity, stimulus strength) . (1)

Fig. 1. Car-following with interactions on consecutive vehicles.

In the GM models, the response is always expressed as the vehicle’s acceleration

or deceleration. The general car-following model set can be viewed in Figure 2. The

leading vehicle has index n and the follower n +1. Vehicle n + 1 responds, i.e. changes

its acceleration proﬁle, to changes in the state of the leader n. L

is the vehicles n’s

length and x

(t) is its position at time t. The gap between the follower and the leader is

n+1

and their distance at time t is considered to be x

(t) − x

n+1

(t). Then, the general

(`, m) car-following model reads

¨x

n+1

(t + ∆t) =

α ˙x

n+1

(t + ∆t)

(t) − x

n+1

(t)]

[ ˙x

(t) − ˙x

n+1

(t)] (2)

where α is the driver n + 1 sensitivity to changes in the relative speed between vehicles

n and n + 1, ˙x

(t) − ˙x

n+1

(t) at time t and their distance. Driver n + 1 reacts with a

delay ∆t and this is inﬂuenced by the speed at the time of reaction t + ∆t. The pair

(`, m) are parameters that allow consideration of a whole family of models, but for our

purposes here the (` = 1, m = 0), i.e.

¨x

n+1

(t + ∆t) =

α [ ˙x

(t) − ˙x

n+1

(t)]

(t) − x

n+1

(t)]

(3)

Fig. 2. Car-following model setup.

These car-following models have proved very useful and they are in constant im-

provement since they are at the core of most microscopic simulators. The pattern of

eqn. (1) is preserved, and essentially it models the interaction between two consecutive

vehicles in a trafﬁc stream, Figure 1. The drivers’ visual sensor and perception of speed

allows them to react to the next downstream vehicle motion. Now, let us assume that

the same kind of information is given to the follower, through an on-board device, re-

garding the vehicle with minimum speed within range R from vehicle n + 1. Hence, it

is assumed that each vehicle in the trafﬁc stream has an on-board device with a range R

that discerns the vehicle f at detectable distance x

(t) − x

n+1

(t) further downstream

and has the smallest speed of all vehicles downstream n + 1 within distance R. Hence,

driver n + 1 receives two stimuli of the same nature, but from different sources:

– a stimulus from the vehicle n immediately downstream through visual perception

and

– a stimulus from the on-board device for the downstream vehicle f with the mini-

mum speed within distance R.

Obviously, the design of such an on-board device is not a trivial task and requires the

study of drivers’ behavioral and cognitive features, but this is not within the scope of

this discussion. It is sufﬁcient to assume that this information is transmitted via a robust

communication network in the form shown in Figure 3, where each vehicle sends its

location and speed to those preceding it. Furthermore, let us assume that the drivers’

reaction to both stimuli above follows the same model of eqn. (1). Then the acceleration

(drivers’ response) is given by

¨x

n+1

(t + ∆t) = min



α [ ˙x

(t) − ˙x

n+1

(t)]

(t) − x

n+1

(t)]

[ ˙x

(t) − ˙x

n+1

(t)]

(t) − x

n+1

(t)]



(4)

where a

the drivers’ sensitivity to the stimulus coming from the on-board device.

Fig. 3. Car-following with vehicle interactions with on-board devices.

Again, eqn. (4) models an idealised situation, since the trafﬁc ﬂow process is much

more complex. However, it does provide an initial insight into how to use information

for improving the use of road capacity without the direct implementation of a trafﬁc

control measure.

In order to see that, let us conduct a simulation experiment using models (3) and (4)

for a 10 km road stretch with vehicles with the following parameters:

– vehicle maximum speed possible v

max

= 120 km/h;

– vehicle maximum acceleration γ

max

= 12, 960.0 km/h

;

– vehicle maximum deceleration γ

min

= 19, 440.0 km/h

;

– stimulus sensitivities α = α

= 29.412 km/h.

Now, assume that the lead vehicle of the trafﬁc stream, i.e. the ﬁrst vehicle that en-

ters the road, moves at maximum up to a point where it decelarates (with maximum

constant deceleration) for some reason over a period of time. After that, it moves with

constant speed for a time period after which, it begins to accelerate (with maximum

constant acceleration) until it reaches its maximum speed. Afterwards it moves with

constant maximum speed, having the road empty in front of it. The result of this pat-

tern of motion of the stream lead vehicle for a length of 10 km can be seen in the

time-distance diagram in Figure 4. A number of shockwaves are created and high den-

sity areas can be discerned. This is a typical pattern formed predicted by car-following

theory.

Fig. 4. Time-distance diagram for normal car-following.

Let us assume now the scenario of Figure 3 and the application of eqn. (4) for a

range R = 16 meters. The results are shown in the time-distance diagram of Figure

5. The earlier warning produced by the on-board devices results to better utilisation

of the road facility, since more vehicles are served per unit of time, where service in

this framework is the arrival of a vehicle at point 10 km downstream the road. Figure

6 depicts the time-space diagram of model (4) when the range is set to 100 meters. In

this case, the efﬁciency of the resulting trafﬁc stream is reduced, but the high concen-

tration areas, observed in Figures 4 and 5, are dispersed, which means an improvement

to safety. Figure 7 depicts the exponentially smoothed outﬂows at the end of the road.

It can be shown that for any trafﬁc system, the minimisation of the total time spent by

vehicles in it, travelling and queueing, is equivalent to the maximisation of the time

weighted system outﬂows, [5]. Hence, the trafﬁc stream’s efﬁciency of the three dif-

ferent scenarios is shown in Figure 7. The most efﬁcient is the one where the peak in

outﬂows happens earlier, which clearly is the scenario with anticipation R = 16 me-

ters. The most inefﬁcient is the scenario with R = 100 meters, but as mentioned it is

the safest.

Fig. 5. Time-distance diagram for on-board based car-following with R = 16 m.

Fig. 6. Time-distance diagram for on-board based car-following with R = 100 m.

The main issue to be noted here is the capability provided by the on-board devices

for achieving a desirable trafﬁc state, in terms of efﬁciency or safety, without the direct

mediation of the TCC, e.g. by providing compulsory speed advice to drivers. It is the

drivers themselves that do the decision making and based on that process the desired

trafﬁc state emerges. The trafﬁc authority need only provide the networking support

applications that will allow the setup of a robust, reliable and fast communication net-

work.

This kind of analysis has been based here on a lot of idealised assumptions, but

this line of reasoning can be extended to more realistic situations, where a lot of the

parameters characterising the system are stochastic variables rather than deterministic.

More detailed results will be reported elsewhere.

Fig. 7. Smoothed system outﬂows for the three scenarios.

4 The Impact of On-board Devices on Macroscopic Models

Macroscopic trafﬁc ﬂow models describe trafﬁc in terms of vehicular density, average

speed and volume (ﬂow). The vehicle conservation equation that lies in the core of

every macroscopic model reads [6], [7]

∂ρ(x, t)

∂t

∂

∂x

[ρ(x, t)v(x, t)] = 0. (5)

where ρ(x, t) and v(x, t) are the vehicular density and average speed at point x at time t,

respectively. When the trafﬁc ﬂow is in equilibrium at point x at time t, the relationship

between speed and ﬂow is given by the fundamental diagram V [ρ(x, t)]. Second order

models use an empirical speed equation in conjunction with the conservation equation

(5). One of the possible forms of this equation reads [8], [9]

v(x, t + τ ) = V [ρ(x + ∆x, t)] (6)

Equation (6) states that the average driver will need some time τ to react to the stimulus

provided by trafﬁc density downstream at distance ∆x. A similar assumption was made

for the microscopic models, but here the behaviour is averaged. A Taylor expansion

argument on both sides of (6) yields the following dynamic speed equation [9]

v(x, t) + τ

∂v(x, t)

∂t

+ τv

∂v(x, t)

∂x

V [ρ(x, t)] −

ρ(x, t)

∂ρ(x, t)

∂x

⇒

∂v(x, t)

∂t

= −

∂v(x, t)

∂x

[V [ρ(x, t)] − v(x, t)]

−

ρ(x, t)

∂ρ(x, t)

∂x

(7)

where due to microscopic considerations

∆x =

0.5

(8)

has been used and ν is a model parameter given by

ν = −0.5

∂V

∂ρ

> 0 (9)

which is constant when a linear fundamental diagram is assumed.

The key parameter that is of interest here is the determination of ∆x. In the original

approach, eqn. (8) gives sufﬁcient small values to ∆x for the Taylor expansion theorem

to be valid. However, with the use of on-board devices in a scenario as that shown in

Figure 3, the distance ∆x in eqn. (6) can take much larger values. Hence, the Taylor

expansion argument is not straightforward anymore. New or revised models need to be

developed that will consider the impact of information from on-board devices to the

macroscopic description of trafﬁc.

5 Using the Internet for Improving Ramp Metering Control

Ramp metering is one of the most effective control measures applied in motorway net-

works. Figure 8 depicts its basic principle of operation. An on-ramp o is used by demand

originating from the residential areas adjacent to the motorway d

(k) (veh/h) during pe-

riod k. Vehicles are queued into the on-ramp forming a queue of length w

(k) (number

of vehicles). A trafﬁc light installed at entrance of the on-ramp to the motorway main-

stream regulates the inﬂow q

(k) (veh/hour) from the queue into the trafﬁc stream of

the ﬁrst segment of link µ.

Fig. 8. Ramp metering control measure setup.

One of the most efﬁcient approaches to coordinated ramp metering is based on

discrete-time nonlinear optimal control. The general discrete time nonlinear optimal

control problem reads [10]

Minimise

J = ϑ [K] +

K−1

k=0

ϕ [x(k), u(k), d(k)] (10)

subject to

x(k + 1) = f [x(k), u(k), d(k)] , x(0) = x

(11)

i,min

≤ u

(k) ≤ u

i,max

∀i = 1, . . . , m (12)

where K is the time horizon, k the discrete time index, x the system’s state vector, u

the bounded control vector and d the disturbance vector, i.e. the uncontrolled inputs to

the process. ϑ and ϕ are smooth cost functionals. f is the controlled process’s model.

In the case of ramp metering of a motorway network, a discrete time nonlinear

macroscopic model of the whole network is developed based on a discretisation scheme

of the macroscopic equations, e.g. eqns. (5) and (7). The objective function selected

represents an appropriate cost criterion; the most commonly used is the TTS, which can

easily be expressed in terms of the model’s macroscopic variables [10]. The state vector

consists of the density and average speed of the segments into which the motorway

has been divided into and the queue lengths at the origins (on-ramps and motorway

entrances). The control vector consists of the ramp metering inﬂow rates allowed and

regulated by the trafﬁc light at every on-ramp. Finally, the disturbance vector consists

of the demand originating from the adjacent residential area and the outﬂows of the

vehicles to their destination off-ramps.

This approach to ramp metering strategy design has been shown to be very effective

and tends to exploit the capacity of the on-ramps in an optimal way. Detailed investi-

gations have revealed that one of the most important parameters for the efﬁcient use

of ramp metering is the storage capacity of the on-ramps, i.e. the maximum number of

vehicles that can be stored into the on-ramps at any given point in time [10]. This is

a crucial parameter for the surrounding surface road network as well, since small on-

ramps tend to spill vehicles into residential areas and therefore degrade environmental

conditions in sensitive areas. Hence, high demands d will result to higher queues. But if

a maximum queue constraint is imposed on the ramp metering strategy, then efﬁciency

will have to be sacriﬁced to the beneﬁt of reduced interference of motorway with urban

street trafﬁc (for reasons of equity as well).

The ramp metering strategy itself cannot do anything to change this condition, since

d is a disturbace, i.e. an uncontrolled input to the trafﬁc ﬂow process. It is exactly here

that internet applications can be used to support the operation of coordinated ramp

metering. It is relatively straightforward for a trafﬁc authority to set up a web-based

service informing in real time drivers who want to use the motorway network and access

it via a speciﬁc on-ramp (or a set of possible on-ramps) about the travel conditions and

expected travel time as they are waiting home to depart. This information can be highly

customised to the individual needs. Such a service would result to drivers changing their

departure time from their homes, e.g. to the morning commute.

In terms of ramp metering control, a service like this exploits the storage capacity of

the residential areas. Instead of storing vehicles just in the limited space of the on-ramps,

an on-line application providing a motive to drivers to wait and depart later, stores

the demand further upstream the on-ramps without degrading environmental conditions

in residential areas. That increase in storage capacity will increase the efﬁciency of

ramp metering strategies. Furthermore, real time demand distribution could take place

by providing advice regarding which on-ramp should be used for the trip. Obviously,

this requires a highly reliable service and real-time information given to users and the

development of the appropriate interfaces, but this is something feasible with existing

technology without major problems.

6 Conclusions

In this paper a few ideas have been put forward regarding the future use of internet

for trafﬁc ﬂow modelling and control. Two modelling related uses have been described

based on the assumption that vehicles in the near future will be equipped with smart on-

board devices that can communicate with each other through reliable networks setting

up their own internet. This capability opens new ways of thinking about trafﬁc ﬂow and

requires the explicit consideration of the drivers’ behaviour when more information is

available to them pertaining to downstream trafﬁc conditions.

A discussion was provided under idealised assumptions regarding the microscopic

dynamics of a trafﬁc stream and how the information provided by such on-board de-

vices can be used to achieve the same effect as if there was a trafﬁc control strategy

explicitly used. The second example was concerned with possible changes or revi-

sions in the macroscopic modelling of trafﬁc, were again the impact of information

on driver behaviour needs to be considered, as it becomes an important feature. Finally,

the use of a classical web-based application has been described, that can work in con-

junction with and in support of ramp metering operations. By providing information

about travel times and trafﬁc conditions and even suggestions, the time of departure can

be inﬂuenced so that in effect the residential areas are used as storage areas for vehicles,

similarly to the use of the on-ramp storage capacity from ramp metering strategies.

These ideas, brieﬂy described here, can be further elaborated as they offer some

good research directions to be followed and pose signiﬁcant challenges.

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