WO2015055780A1

WO2015055780A1 - Traffic control

Info

Publication number: WO2015055780A1
Application number: PCT/EP2014/072256
Authority: WO
Inventors: Markus Forster; Raphael FRANK; Thomas Engel
Original assignee: Université Du Luxembourg
Priority date: 2013-10-16
Filing date: 2014-10-16
Publication date: 2015-04-23
Also published as: WO2015055780A4; LU92575B1

Abstract

Apparatus for, and method of, controlling a flow of traffic, the traffic comprising both participating and non-participating vehicles, comprising: determining at least one property of the participating vehicles; recommending a speed based on the determined properties of the participating vehicles, wherein recommended speed is based on a model of traffic flow, and wherein the model of traffic flow takes account of both participating vehicles and non-participating vehicles wherein a participating vehicle is a vehicle concerning which information to be used to recommend a speed is known.

Description

TRAFFIC CONTROL

TECHNICAL FIELD

This invention relates to apparatus for, and a method of, controlling vehicular traffic and, in particular, speed adjustment for a vehicle based on characteristics of neighbouring vehicles.

BACKGROUND

The occurrence of traffic jams for vehicular traffic are a well-known source of time and energy loss, as well as having negative environmental impacts. Traffic jams are usually a direct result of over-utilisation of the roads. However, the formation of such jams is not always straightforward.

It has been shown that reducing the speed limit on highways can increase the traffic flow.

Systems for controlling the speed of a vehicle are known. For example, cruise control is a well-known system for maintaining the speed of a vehicle constant without driver intervention. Furthermore, adaptive cruise control is able to maintain a constant speed as well as a minimum following distance ('headway') to the vehicle in front.

However, such systems suffer from the problem that they are only able to adapt the speed of the vehicle if the preceding vehicle is visible, and only based on the neighbouring preceding vehicle.

DE 10 2005 043 471 discloses a cruise control for a vehicle which obtains a speed difference of a neighbouring vehicle using radar, and a speed difference for a more remote vehicle using a wireless communication protocol. The gathered information is used to model two road sections corresponding to the neighbouring vehicle and the more remote vehicle, and vary the speed of the vehicle accordingly.

Furthermore, it is known to model traffic flow using equations previously applied to flow dynamics. One such model is the Lighthill-Whitham-Richard model and its application to describing traffic flow is discussed, for example, in Jian MA et al, "A study on multi-resolution scheme of macroscopic-microscopic traffic simulation model", Intelligent Transportation Systems (ITSC), 2011 14^th International IEEE Conference, ON IEEE, 5 October 2011 (2011-10-05), pages 1421-1426. A number of other traffic flow models are also described in this publication, but it was previously unknown to use these models to recommend speed.

It is therefore desirable to be able to reduce the instance of traffic congestion by taking into account the behaviour of vehicles other than the preceding neighbouring vehicle, and other vehicles for which information such as speed and position is known. Where the position of all vehicles relative to one another is known, and it is possible to communicate recommended speed alterations to all vehicles, it is relatively straightforward to control the traffic in an optimum manner. However, the drawback of such a system is that each vehicle must participate in the speed recommendation system at least insofar as each vehicle must report its position and speed (although the speed can be calculated from the position where the position information is detailed enough). Since the hardware required for such a system is unlikely to be fitted to all vehicles simultaneously, this is not a feasible approach.

It is an aim of invention to provide a device and a system for recommending speeds to a vehicle which is able to take account of both participating and non- participating vehicles. SUMMARY

According to a first aspect, the invention provides a method for controlling a flow of traffic, the flow of traffic comprising a plurality of vehicles, wherein one or more properties may be determined for certain of the vehicles of the flow of traffic, wherein a vehicle for which a property may be determined comprises a participating vehicle and wherein a vehicle for which a property cannot be determined comprises a non-participating vehicle, the method comprising:

determining at least one property of one or more participating vehicles; recommending a speed for a participating vehicle based on the determined property of the participating vehicles, wherein the recommended speed is determined with reference to a model of traffic flow, and wherein the model of traffic flow takes account of both participating vehicles and non- participating vehicles; and

communicating the recommended speed to a participating vehicle. The model of traffic flow may be the Lighthill-Whitham- Richard model. In an embodiment, the macroscopic model is as descripbed in M. Lighthill and G. Whitham, "On kinematic waves. II. A theory of traffic flow on long crowded roads," Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 229, no. 1178, pp. 317-345, 1955.

A density of participating and non-participating vehicles may be calculated based on information of two participating vehicles.

The properties used to recommend a speed may comprise positions of at least a first participating vehicle and a second participating vehicle. In a further embodiment, the properties used to recommend a speed may further comprise a speed of the first participating vehicle. In an embodiment, the speed recommendation is based on the speed of the first participating vehicle at a time when the positions are measured as well as at a preceding time.

The model of traffic flow may be used to determine a speed of a Shockwave for a first participating vehicle and the determined speed of the Shockwave may be used to recommend a speed for a second participating vehicle.

In certain embodiments of the invention, the term 'shockwave' indicates a moving disturbance in the flow of traffic and the shockwave may move in space or time, or both.

The first participating vehicle may precede the second participating vehicle in the traffic.

A further aspect of the invention extends to a traffic control device for controlling a flow of traffic, the traffic comprising both participating and non- participating vehicles, the device further comprising a sensor for determining at least one property of the participating vehicles, and a processing module, wherein the processing module recommends a speed based on the method as previously described.

The traffic control device may be adapted to be installed in a vehicle.

The traffic control device may further comprise a communications module, wherein the device is adapted to communicate with similar devices located in neighbouring vehicles by means of the communication module.

A further aspect of the invention relates to a traffic control system for controlling a flow of traffic, the flow of traffic comprising a plurality of vehicles, wherein one or more properties may be determined for certain of the vehicles of the flow of traffic, wherein a vehicle for which a property may be determined comprises a participating vehicle and wherein a vehicle for which a property cannot be determined comprises a non-participating vehicle, the system comprising a plurality of sensors, each sensor being associated with a corresponding vehicle, each sensor communicating with a processing module, wherein the processing module recommends a speed based on the method as previously described.

The sensor may determine a position of a corresponding vehicle.

The sensor may additionally determine a speed of the corresponding vehicle.

According to a further aspect, the invention provides for a computing device comprising a processor and memory, the memory comprising instructions which, when loaded by the processor cause the computing device to:

determine (110), for a flow of traffic, the flow of traffic comprising a plurality of vehicles, wherein one or more properties may be determined for certain of the vehicles of the flow of traffic, wherein a vehicle for which a property may be determined comprises a participating vehicle and wherein a vehicle for which a property cannot be determined comprises a non- participating vehicle, at least one property of one or more participating vehicles;

recommend (120) a speed based on the determined property of the participating vehicles, wherein the recommended speed is determined with reference to a model of traffic flow, and wherein the model of traffic flow takes account of both participating vehicles and non-participating vehicles; and

communicate the recommended speed to a participating vehicle.

DESCRIPTION OF ACCOMPANYING FIGURES

Embodiments of the invention are described with reference to the accompanying schematic diagrams where: Figure 1 is a schematic diagram of a device according to an embodiment of the invention;

Figure 2 is a schematic diagram of a system according to an embodiment of the invention;

Figure 3 is a flow diagram of a method of recommending a speed according to an embodiment of the invention;

Figure 4 illustrates the formation of a Shockwave;

Figure 5 illustrates two difference density charts; and

Figures 6 and 7 illustrate message forwarding in embodiments of the invention.

DESCRIPTION OF EMBODIMENTS

Embodiments of the invention are described hereafter with reference to the accompanying diagrams.

Figure 1 illustrates a traffic control device 10. The traffic control device 10 comprises a position and speed sensor 12 and a communications module 14. The position and speed sensor 12 and the communications module 14 are connected to a processor 16. The device 10 is located in a vehicle 18.

The device is used for controlling a flow of traffic in which the vehicle 18 is located. As illustrated in Figure 1, the traffic is composed of a plurality of vehicles 18, 28 and 32 travelling in the same direction in the same traffic lane. For the sake of simplicity, only three vehicles have been illustrated here. In practice, the traffic will be comprised of many more vehicles.

Vehicle 28 is equipped with a traffic control device 20 similar to the traffic control device 10. The device 20 comprises a position and speed sensor 22 and a communications module 24, both of which are connected to a processor 26. Since vehicles 18 and 28 are equipped with respective traffic control devices 10 and 20, which are able to determine properties such as speed and position of the respective vehicles, these vehicles are referred to as "participating vehicles". As used herein, "participating vehicles" are those vehicles which are part of the traffic flow concerning which information or properties to be used to recommend a speed is known. In the case of vehicles 18 and 28, the information known is the properties of the position and speed measurements delivered by respective position and speed sensors 12 and 22.

It is to be realised that embodiments of the invention operate where traffic includes two kinds of vehicles: vehicles for which properties can be determined and those for which such properties cannot be determined. In this context, the properties concerned are those which may influence the traffic flow. Such properties may be speed and position. In certain situations the vehicles may include sensors which are able to determine these properties for the vehicles in which the sensors are located, and communicate that information to another vehicle or to a central computer, which then uses that information to determine a recommended speed. In other instances the properties are determined by sensors located outside of those vehicles. In all these embodiments the term "participating vehicle" is used to refer to vehicles for which the properties may be determined and other vehicles are non-participating vehicles.

The communications module 16 of vehicle 18 communicates with the communications module 26 of vehicle 28 so that information may be passed from either vehicle to the other. The vehicle 32 lacks the means to determine its position and speed and communicate that to other vehicles. For this reason, vehicles of this type are referred to as "non-participating vehicles". The processors 16 and 26 devices 10 and 20 calculate a recommended speed for vehicle 18, based on information provided by the position and speed sensor 12 of vehicle 18, as well as information provided by position and speed sensor 22 of vehicle 20 and communicated via the communications module 26 of vehicle 28 to the communications module 14 of vehicle 18, as illustrated by communications signifier 30. The recommended speed is calculated according to the method described in greater detail below.

Figure 2 illustrates a traffic control system 40 comprising three traffic control devices 58, 88 and 98. In this embodiment the three traffic control devices 58, 88 and 98 are of the type illustrated in Figure 1. Therefore, device 58 comprises position and speed sensor 52, communicating module 54 and processor 56; device 88 comprises position and speed sensor 82, communicating module 84 and processor 86; and device 98 comprises position and speed sensor 92, communicating module 94 and processor 96.

The system 40 further comprises a central processor 100. The communications modules 54, 84 and 94 communicate data from the position and speed sensors 52, 82 and 92 with the central processor 100. The central processor 100 provides a position based routing table to distribute the messages to the vehicles that are in the reaction range. The processors 56, 86 and 96 calculate a recommended speed according to the method described and provide the necessary computations and architecture for the operation of the respective devices, in this embodiment.

As illustrated in Figure 2, the devices 58, 88 and 98 are installed in respective vehicles 50, 80 and 90 which are all part of the same traffic flow, together with vehicle 70. Vehicles 50, 80 and 90 are participating vehicles in the system 40 whereas vehicle 70 is a non-participating vehicle. The method for calculating a recommended speed is illustrated in Figure 3. In the initial step, step 110, the sensed data is collated. In this embodiment, the sensed data comprises the position and speed information for each participating vehicle. In further embodiments, the calculation may be based on position information only.

In the second step, step 112, it is assumed that the vehicle for which the speed recommendation is being calculated is vehicle i and that the closest adjacent downstream vehicle is vehicle j, and in this step, the relevant data for both vehicle i and vehicle j is collated.

It may be necessary in this step to reject information relating to vehicles where it is determined that the vehicle is not the closest downstream vehicle.

For the embodiment illustrated in Figure 2, the central processor 100 will collate the information for the vehicles i and j.

It is to be realised that, since embodiments of the invention are able to accommodate both participating and non-participating vehicles, account may also be taken of participating vehicles which are unable to communicate or for which only partial information exists. For the purposes of the embodiments of the invention described here, such vehicles will be considered non-participating vehicles.

It is to be realised that this is a particular advantage over many known systems which rely on all vehicles accounted for to be participating vehicles. A significant disadvantage to these known systems is that vehicles of different ages are found on the roads and that such systems are not able to operate if older cars, which have not been retrofitted to operate with those systems, are present.

In step 114, the traffic densities for the vehicles i and j is calculated based on their respective sensed data using a model of traffic flow which in this embodiment is the Lighthill-Whitham-Richard model. In the following step, step 116, the speed of the Shockwave triggered by vehicle j is calculated as described below.

On the basis of the calculated amounts, a safe speed for vehicle i is determined. This is the speed at which vehicle i is to travel to avoid a Shockwave forming and the traffic involving vehicle i and j becoming congested. Further details in this respect are provided below.

The main cause for the formation of shock waves is the combination of high traffic demand and unexpected driver actions. This means that, in dense traffic situations, even a minor flaw in driver behaviour or traffic even along the path can create a temporary overload that leads to the formation of a shock wave upward in the traffic stream.

Examples of physical perturbations are ramps, construction sites, a simple increase in traffic or reduction of lanes. Beyond that, small driving imperfections like the human tendency to delayed reaction can cause flow disruptions, leading to congestion.

Figure 4 demonstrates the formation of a shock wave in a simple one-lane road scenario. From left to right the graph depicts the same road segment at consecutive time steps. In the first time step, the leading vehicle slows down for some unknown reason, as depicted by arrow 130 against the driving direction. In the next time steps the vehicles that follow must adapt their speeds (arrows 132) in order not to crash into the lead vehicle. Hence, the new speed of the following vehicles must be decreased below that of the leading one. During the following time steps, this prescription to brake travels upstream forming a shock wave. Stop-and-Go traffic often seems to appear out of nowhere and the resulting congestions are often referred to as phantom jams. As one can see in Figure 4, vehicles are not able to react until the incident that triggered the wave is in line of sight. This means that hard braking manoeuvres are necessary to avoid a crash. Afterwards the motorists have to accelerate again when leaving the congested area. This implies a waste of energy and an increase in emissions.

Due to the fact that traffic density on a sufficiently long road segment is not uniformly distributed, clusters with high density and intermediate sections with lower densities occur.

The model of traffic flow is used in embodiments of the invention to estimate the traffic situation between two participating vehicles. The models used to describe the traffic flow may describe the observable traffic flow on a road segment by analogy with the physical equations for fluid dynamics. They give an overview of the general traffic situation without distinction between single vehicles. The observable values for this class of models are the vehicular density, p{x, t) the traffic flow Q (x, t) and the mean speed V(x, t) observed within a given road segment. The base equation for those models is the flow equation:

Q(x, t) = p(x, t)^■ V(x, t) (1) These parameters and other data used in embodiments of the invention can be measured with loop detectors, radar detectors or visual detectors. It is to be realised that embodiments of the invention are not limited to the manner in which the parameters are sensed. Obviously, it is easy to measure the flow as the number of vehicles N that pass the detector within a given time T. Additionally, most detectors are able to measure the speed of the passing vehicles, giving the mean speed by summing up single velocities v^. i E l, where I is an index set, and dividing the sum by the number of passing vehicles N. In mathematical notation this means: (2)

The sensed information used as a basis for the model of traffic flow may be position, speed and acceleration, but in embodiments of the invention, position and speed are sufficient.

It has been found useful to simulate embodiments of the invention to determine, as a first step, whether the use of a model of traffic flow can take account of vehicles for which no information is known. The Krauss car-following model has been used for microscopic traffic simulation of the vehicles on the observed road. As previously described, the Lighthill-Whitham-Richard (LWR) model is used to estimate of shock wave propagation upstream in the macroscopic traffic flow.

The Krauss car-following model is time-discrete and continuous in space, meaning that while the model states are evaluated for a distinct time step, the space is not divided into distinct cells. The Krauss car- following model is as described in S. Krauss, P. Wagner, and C. Gawron, "Metastable states in a microscopic model of traffic flow," Physical Review E, vol. 55, no. 304, pp. 55-97, 1997 and S. KrauB, "Microscopic modeling of traffic flow: Investigation of collision free vehicle dynamics," Hauptabteilung Mobilitat und Systemtechnik des DLR Koln, no. ISSN 1434-8454, 1998.

In further embodiments of the invention other vehicle simulation models may be used. For example, models such as the "Intelligent-Driver-Model" (IDM), "Optimal- Velocity-Model", "Full- Velocity-Difference-Model", "Newell-Model", etc. could also be used. In further embodiments, models known as the "Cellular- Automaton-Models" could alternatively be used (e.g. the "Nagel-Schreckenberg- Model"). Generally, there are also other models of traffic flow based on equations of fluid dynamics that may be used instead of the Lighthill-Whitham-Richard (LWR) model. However, the LWR model is advantageous in that the calculations for this model are simple and therefore quicker than they would be for other models.

The LWR model allows vehicles to be positioned at any location on the given road segment instead of in discrete cells.

The LWR model is based on the continuity equation:

The evolution of density over time is given by the spatial evolution of traffic flow. This holds true for homogeneous road segments where inputs and outputs are only possible at the borders of the observed segment. The model states that there exists a static relation between the traffic flow Q (x, t) and the vehicular density p(x, t) of the form:

Q(x, t) = Q(p(x, t)) (5) By substituting equation 5 into equation 4, we obtain the model equation of the LWR model, given as:

Since equation 6 is a Transport Equation, substituting the general wave ansatz p(x, t) = o ( — ct, t) into equation 6 we can rewrite it as:

v_t + C^■ v_x = 0 (V) and the solution for the LWR model giving the shock wave's propagation speed yields:

This means that the propagation speed of the shock wave is proportional to the gradient in the flow-density chart. Figure 5 illustrates the two important quantities, velocity and density relative to the actual density, where Figure 5 a is a speed density chart and Figure 5b is a flow density chart. For the triangular flow-density chart depicted in Figure 5b, one can read the propagation speed of a shock wave directly as the gradient of the flow-density chart if both points of interest are in the same traffic phase. For the free flow phase the shock wave travels downwards in the traffic flow with the maximum allowed speed v_max and therefore does not affect preceding vehicles. In contrast, in the congested phase the propagation speed becomes negative, hence the shock wave travels upstream in the traffic flow, interacting with the following vehicles with a speed c « —15 km/h, causing slow downs.

The network protocol used for communication in embodiments of this invention adhere to the IEEE 802. l ip standard for Wireless Access in Vehicular Environments. Message propagation can be realized by the use of the Cooperative Awareness Message.

Embodiments of the invention utilize a connectionless networking protocol based on beacons, meaning that vehicles broadcast their messages in a burst, only in case of a significant slowdown or if the speed falls below a given threshold. Each message has a certain Time To Live (TTL) to ensure that it reaches the neighbours that are within transmission range. The strategy is based on three distinct phases, namely the notification phase, the reception phase and the forwarding phase. The aim of the protocol is to redistribute the upstream vehicular density in a way that avoids the formation of a Shockwave in case of a temporary peak in traffic demand. The recommendation algorithm is lane-based, meaning that only vehicles in the same driving lane will get a speed recommendation from the system. This behaviour is motivated by the assumption that a slowdown recommendation for the left lane while having free-flowing traffic in the right lane will be disregarded by a human driver anyway.

An example of the multi-hop messaging behaviour is given in Figure 6. Due to a slowdown, the leading vehicle sends a beacon containing the needed information, depicted by the solid line. The second vehicle in the information chain receives this message, adapts its speed according to the described method, and sends a beacon containing its own slowdown information further upstream rebroadcasting the received message. This first forward is depicted by the dashed line. This chain of messages ends if the system decides that a vehicle should not recommend an action, or if there is no vehicle within transmission range to receive a message or if the maximum propagation radius is reached. In Figure 6 this situation occurs after the fifth hop.

During the notification phase a vehicle that has to slow down by more than a certain threshold Av_n or is moving with a speed lower than the minimum expected, v_min broadcasts a message

m_h = [id, x_s, y_s, x_o, y_o, t_o, v_o, v_0it^ (9) where h E H is a unique message identifier and id is a unique identification of the originating vehicle. x_s and y_s are the GPS-coordinates of the sending vehicle, whereas x₀ and y₀ are the GPS-coordinates of the originator. The remaining values are the timestamp of the originator at message creation (t₀)„ the actual speed of the originator at message creation O₀) and the speed of the originator one time step before message creation {v_0it__t) .. All values in the message except for id; t₀ and v_{o t}__t are functions of t. The indices have been omitted to improve readability. With reference to Figure 3, the notification phase covers step 110 where the sensed data is collated.

The distinction in the coordinates between sender and originator is required in the forward phase. An algorithm in pseudo code for the notification phase is:

Algorithm 1 Sender Algorithm

1 : procedure SENDCv^)

2: if my. v_t < my. v_t__t then

3 : m = [my. id, my. x, my. y, my. x, my. y, my. t, my. v_t, v^]

4: BROADCAST(m)

5: end if

6: end procedure

Every second, the protocol checks all received messages to select the most recent one. The speed of the messaging vehicle is then compared to the receiver's speed. If the sender's speed is lower than the receiver's, the protocol estimates the traffic situation between the source vehicle and the notified one. A speed recommendation is then given to the motorist to avoid the formation of traffic jams in the manner described below.

Vehicles receiving a message m_h have first to check if this message is relevant for them. This means that a vehicle i, receiving a set of messages M = {... , m_h m_k, rnj, ... } ; h, k, 1 £ H has first to find the message ni_j having the least distance to the originator.

Explicitly, this means

m_j = m _mh≡M{dist{i, m_h ) (10) where dist(a, b) ; a, b E A gives the distance between vehicles a and b on the road. The distance is computed with respect to spatial distance, being up-to-date, heading, driving lane and the relative speed compared to the maximum allowed one.

Hence, message m_y is considered the most recent information affecting vehicle i (the receiver) if the spatial distance between vehicle i and j is less than that between i and any other messaging vehicle, both vehicles are driving in the same direction, vehicle j is ahead of vehicle i and both vehicles are driving in the same lane. One constraint implemented here is that the speed for the messaging vehicle v_t is less than two third of the maximum allowed speed on the observed lane v_max. This corresponds to step 112 of the process of Figure 3.

As previously stated, only vehicles driving in the same lane are considered. A number of known ways in which to ignore vehicles in other lanes exist and may be used here. For example, visual means such as a camera may be used to recognise the lane, and this information may be passed between participating vehicles.

In the next step, step 114 of Figure 3, it is necessary to estimate the traffic situation between the receiving vehicle i and the sending vehicle j. To do this, the road segment between vehicle j and vehicle i must be considered as homogeneous; that is, equation 4 holds true. This means that it is possible to apply equation 6 and thus to estimate the density gradient in the interval [x xj ..

Embodiments of the invention use a Lighthill-Whitham-Richards model with a triangular fundamental diagram and the corresponding speed density chart, as depicted in Figure 5. This characteristic of the LWR model has some special properties. The model suggests that, in free flow, motorists will drive with the maximum possible or allowed speed v_max. The critical density, where the traffic turns from free flow to the congested phase, is given by: ^Pmax'

meaning that the optimal spacing between consecutive vehicles is given by the gap needed to drive with maximum speed v_max for the minimum time headway T plus the effective vehicle length ..

Pmax

For the LWR models with a triangular fundamental diagram, there are only three different propagation velocities for Shockwaves.

Free flow: the propagation speed of a Shockwave in free flow is equal to the maximum possible speed, meaning that the Shockwave propagates with exactly the same speed as the traffic flow, given by:

dQ \

(12)

^Cf^ree dp

P < Pk

Congested flow: on the right side of the fundamental diagram (Figure 5b), Shockwaves propagate with a constant speed upstream. This speed is given by the effective vehicle length and the minimum time headway as:

^Ccon3 dp (13)

p > p_k PmaxT

Free flow→ congested flow: the Shockwave propagation speed for transition from free flow to congested flow is given by the gradient between the corresponding points in the fundamental diagram for vehicle i and vehicle j. For [x,- > Xj] this means:

= c (14)

Pj-Pi

Cup can take any value between c_cong and v_max As one can easily see in Figure 5, equation 14 is the general solution for the Shockwave propagation speed, labelled by c.. This corresponds to step 116 of Figure 3. Knowing the velocities v; and v_y- of vehicles i and j, respectively, it is possible to estimate the densities p_t and p_j as:

Pa ⁼ _{v T i} ( ¹ ) · ^{' α e} ti'fi (^{1 5})

\Pmax'

Again, the idea behind this formula is that every motorist tries to travel with the maximum possible speed. In our case this means that only the traffic load ahead causes drivers to slow down.

The traffic flows Qj and Qj can be computed as:

Knowing the speed, density and flow for two communicating vehicles enables us to gather information about the traffic situation in the intervening space between them.

Our next step is to classify the situation according to the three Shockwave propagation possibilities. In case of free flow no action need be taken, because the traffic flow is propagating downstream with maximum possible speed. We do not have to take any action if the speed of the sender is greater than that of the receiver. In the other two cases, an action has to be performed to adapt the speed of vehicle i to the conditions given by vehicle j.

To do so, it is necessary to collect all the needed information. First, the distance between two communicating vehicles, being the range from the tail end of the leading vehicle to the front of the follower, is defined as:

d-i ^'· = Xj— Xt — l_eff (17) where ¾ and Xj are the positions of vehicles i and j respectively and l_eff is the

1

effective vehicle length. It holds true that =

Pmax

The time gap between the communicating vehicles is given by the formula: τ = (18) with Vi = v_t— Vj ; Vj ≤ v_t being the difference of the speeds of vehicle i and j, respectively, τ will be the duration of the speed recommendation.

By use of equation 14 we can compute the propagation speed of the Shockwave within the density gradient between the two vehicles. Knowing, that the Shockwave travels against traffic flow, the virtual distance between vehicle i and the tail end of the Shockwave, caused by vehicle j can be defined as:

Having all the relevant information as well as an estimate of the Shockwave propagation as given in equations 14 and 19 a safe speed v;_;safe for the following vehicle i can be computed as:

Hsafe = Vj + (20) where d j is the spatial distance between vehicle i and the tail end of the Shockwave caused by vehicle j, Vj the speed of vehicle j and τ the time in which vehicle i will reach vehicle j with the current velocities v, and v_y- as given by equation 18. This corresponds to step 118 of Figure 3.

In the final step, the anticipated speed i_;safe, given in equation 20, is recommended to the motorist for the duration τ, computed by equation 18 (step 120 of Figure 3).

For a better understanding of the computations, the functions used in the calculation are given as: Algorithm 2 Receiver Algorithm

l : k = (v_maxT + (1/Pmax))

2

3 function RECEIPT(seZ , M)

4 distance = 1£Ί0

5 nMSG = NULL

6 for message in M do

7 if DIST(self, message. ID) < distance then

nMSG = message

9 distance = DIST(self, message. ID)

10 end if

1 1 end for

12 return nMSG, distance

13 end function

14

15 function DRIVE(fj , ΐ^ , χ^ χ. )

16 if fj < Vj then

17 return v j

18 end if

19 Pi =MAX(GETDENSITYBYSPEEDO_i),p,_c)

20 Pj = MAX(GETDENSrTYBYSPEED(vy), p_k)

29 end function

30

31 function GETDENSITYBYSPEEDO)

32 return l/(vT + (l/p_max))

33 end function

Because the network is a multi-hop network with pure flooding, each receiver should relay each unique message exactly once during a forward phase (step 120 of Figure 3). Before forwarding, the values for x_s and y_s are changed to the relaying vehicles position. Also a new unique message identifier is created by concatenation of the old message identifier and the identifier of the relaying vehicle. An algorithm for the forward phase is as follows, where M_r is a list of already received messages to ensure the above mentioned behaviour of pure flooding. Algorithm 3 Forward Algorithm

1 : procedure FORWARD^)

2: if m not in M_r then

3: m = m d, m. xy, my. y, m. x, m. x, m. t, m. v_t, m. v_t_^

4: BROADCAST(m)

5: end if

6: end procedure

An alternative embodiment, illustrated in Figure 2, has a centralised processor. Such a centralized approach could easily be implemented on modern smartphones or as additional feature in state of the art navigation systems that already have mobile networking capabilities. An example of the message transmission with a client-server based approach is given in Figure 7. The network topology differs from the distributed approach in the way that each participating vehicle has a bidirectional communication link to a central server.

To ensure up to date routing tables, each vehicle, frequently transmits a unicast message m_p containing its current position and a timestamp to the central entity.

m_v = [id, x₀, y₀, t₀] (21) with id, being a unique identification of the originating vehicle, x₀ and y₀ are the GPS coordinates of the originating vehicle and t₀ is a timestamp of the originating vehicle. Those messages are depicted by the black, dotted lines in Figure 7. With the collected information the server always has a complete overview of the network topology. It is necessary to change the notification phase as follows.

If a vehicles that has to slow down by more than a certain value Av_n or is moving with a speed lower than the minimum expected mi_n, sends a message:

m_h = [id, x₀,y₀, t₀, v₀, v_{o t}_^ (22) to the central server. The values of this message are equal to the ones in equation 8 with the difference, that there is no necessity for a distinction between the coordinates of originator and sender because there will be no message forwarding. Based on the internal routing table, the server now delivers the message to all the participating vehicles.

An example of the notification procedure is given in Figure 7. The leading vehicle sends a notification message to the central server. This communication is displayed by the solid arrow from the leading vehicle to the server. After reception, the server relays this message to all vehicles that are within the predefined reaction range, given as dr. Those messages are depicted by the dotted lines. The last vehicle in the row will not receive a notification because it's not within the predefined reaction range, symbolized by the light-grey link between this vehicle and the server. The reception phase will be unchanged.

As already mentioned, there will be no forward phase because all vehicles within the reaction range will get the information at once by the server.

Claims

1. A method for controlling a flow of traffic, the flow of traffic comprising a plurality of vehicles, wherein one or more properties may be determined for certain of the vehicles of the flow of traffic, wherein a vehicle for which a property may be determined comprises a participating vehicle and wherein a vehicle for which a property cannot be determined comprises a non-participating vehicle, the method comprising:

determining (110) at least one property of one or more participating vehicles;

recommending (120) a speed for a participating vehicle based on the determined property of the participating vehicles, wherein the recommended speed is determined with reference to a model of traffic flow, and wherein the model of traffic flow takes account of both participating vehicles and non- participating vehicles; and

communicating the recommended speed to a participating vehicle.

2. The method according to claim 1 wherein the model of traffic flow is the Lighthill-Whitham-Richard model.

3. The method according to claim 1 or claim 2 wherein a density of participating and non-participating vehicles is calculated (114) based on the properties of two participating vehicles.

4. The method according to any preceding claim wherein the properties to be used to recommend a speed (120) comprise positions of at least a first participating vehicle and a second participating vehicle.

5. The method according to claim 4 wherein the properties further comprise a speed of the first participating vehicle.

6. The method according to any preceding claim wherein the model of traffic flow is used to determine (116) a speed of a Shockwave for a first participating vehicle and the determined speed of the Shockwave is used to recommend a speed for a second participating vehicle.

7. The method according to any preceding claim wherein the first participating vehicle precedes the second participating vehicle in the traffic.

8. A traffic control device (10, 20) for controlling a flow of traffic, the flow of traffic comprising a plurality of vehicles, wherein one or more properties may be determined for certain of the vehicles of the flow of traffic, wherein a vehicle for which a property may be determined comprises a participating vehicle and wherein a vehicle for which a property cannot be determined comprises a non-participating vehicle, the device further comprising a sensor (12, 22) for determining at least one property of the participating vehicles, and a processing module (16, 28), wherein the processing module recommends a speed based on the method of any of claims 1 to 7.

9. The traffic control device according to claim 8 adapted to be installed in a vehicle (18, 28, 50, 80, 90).

10. The traffic control device according to claim 8 or claim 9 further comprising a communications module (16, 26), wherein the device is adapted to communicate with similar devices located in neighbouring vehicles by means of the communication module.

11. A traffic control system for controlling a flow of traffic, the flow of traffic comprising a plurality of vehicles, wherein one or more properties may be determined for certain of the vehicles of the flow of traffic, wherein a vehicle for which a property may be determined comprises a participating vehicle and wherein a vehicle for which a property cannot be determined comprises a non-participating vehicle, the system comprising a plurality of sensors (52, 82, 92), each sensor being associated with a corresponding participating vehicle, each sensor communicating with a processing module (100) , wherein the processing module recommends a speed based on the method of any of claims 1 to 7.

12. The traffic control device according to any of claims 8 to 10 or the traffic control system according to claim 11 wherein the sensor determines a position of a corresponding vehicle.

13. The traffic control device according to claim 12 wherein the sensor additionally determines a speed of the corresponding vehicle.

14. A computing device comprising a processor and memory, the memory comprising instructions which, when loaded by the processor cause the computing device to:

communicate the recommended speed to a participating vehicle.