Reducing Congestion in Obstructed Highways with Traffic Data Dissemination Using Ad hoc Vehicular Networks

3.1. Vehicular Modelling

To accurately simulate vehicular behaviour, there are several key components: a driver model to develop how real people will drive under certain circumstances, a lane-changing model to make realistic decisions on when it would be advantageous to change lane and a roadway with rules (e.g., drive on the left in the UK).

A car following algorithm will contain at least a desired velocity, a safe time separation when following other vehicles and acceleration and braking criteria [9]. At each simulation time step the acceleration is calculated for each vehicle. The parameters of these models can be changed to emulate more aggressive and more considerate drivers, as required.

When modelling vehicular networks over large areas (such as metropolitan areas) the flow of vehicles on a single road behaves as an incompressible fluid according to , where is the average density of vehicles (cars/km) and is the average velocity on the road (km/h) [11]. At microscopic levels of simulation (across any field size) each vehicle is treated as an individual entity, which greatly increases the computational requirements of the system but provides a more realistic and component-based approach to modelling.

The Intelligent Driver Model (IDM) in the simulator follows the MOBIL model [10] developed by Treiber. MOBIL operates as a car-following model such that the acceleration and braking are defined by the distance from the car in front. The function of such an acceleration is shown in

(1)

where

(2)

for acceleration on an open road , velocity , desired velocity , distance to front vehicle, desired dynamic distance to front vehicle , velocity difference , a safe time delay between vehicles , a comfortable braking value , a minimum distance between vehicles and finally an exponent which is adjusted in order to mimic real vehicular flow patterns.

Lane changing algorithms add a necessary level of complexity to the IDM. In order to decide whether to change lane or not, the current acceleration must be calculated for the current lane and the acceleration in the new lane (with regard to the car behind and in front in the original lane). If the acceleration in the new lane is greater than that in the current lane, there is an advantage to be gained by changing lane. Many models, including those in the original simulator, include a bias in the model for particular lanes, which simulates the real scenario of slow lanes and fast lanes.

3.2. MAC Layer Protocol

In simulating wireless fidelity networks, the majority of simulations use the IEEE 802.11 protocols [12], as these offer the best simulation of the MAC layer functionality. The IEEE 802.11 MAC layer uses a distributed coordination function (DCF), which has been simulated in [13], to ensure efficient communication on the medium, and implements controls to reduce collisions. More recently the IEEE 802.11p standard has been tested in [2] specifically for intervehicular communications. This allows the foundation of underlying strengths in the 802.11 suite to be enhanced for vehicular networks.

The MAC layer in the simulator operates using an adapted version of IEEE 802.11 which removes the interframe spacing (IFS) model, enabling equal priority for all network traffic. Due to implementation, and the need for simplicity in the model, our implementation of 802.11 does not suspend the backoff timer when the medium is busy during that frame, as 802.11 does.

The network backoff when the medium is busy operates as shown in [11]

(3)

where is the number of times it has previously had to back off in succession. and are the minimum and maximum possible back off time, respectively. is often set at 0. The medium is defined as busy if any car within the transmitters interference range, , is currently broadcasting.

Every car within the transmission range, represented by , (which is usually twice as small as the interference range) will receive the message with probability .

3.3. Radiowave Propagation

In the modified simulator the reception of messages is performed by a basic algorithm controlled by the simulation engine. In advanced network simulators the realistic reception of messages depends on the signal strength at the receiver. The basic propagation model is the Friis free-space calculation, which extends the ideal free-space propagation formula ( ) [14] where is received power and is the distance from transmitter) to incorporate the antenna gain(both transmit and receive). The Friis model, however, will only hold true with a clear line-of-sight (LOS) between transmitter and receiver, and assumes no level of multipath or shadowing of the radiowave (which becomes very apparent in urban and highway scenarios [15]). Friis operates as shown in

(4)

where is the received power at distance with respect to the antenna gain and height and the system loss .

One method of altering the propagation of messages through the simulated network, is to change the transmitted power and therefore the transmission range. By transmitting information further the message has a greater probability of retransmission in sparse networks and also a faster dissemination through the system [16]. The main disadvantage of having a large transmission range is that information propagates further, eventually reaching a point where the information usefulness is low, and so takes up bandwidth and time for almost redundant data. In a system with limited time and bandwidth this can cause localised problems, where more pertinent (i.e., geographically closer) information is lost to redundant data.

4.1. Epidemic Message Passing Algorithm

The propagation of messages through a system requires an efficient delivery algorithm. In our simulation we use a probabilistic information dissemination protocol, which is fully defined in Nekovee and Bogason's work [11]. We assume that all vehicles know their location (via GPS technology) and that each message contains information about location and time of creation. To ensure that propagation does not extend to unnecessary distances from the source each message has a Time-To-Live (TTL) setting.

The algorithm allows for a reasonable amount of retransmission and dissemination through the network and balances the relevance of the information with the distance from the source. To this end, information can disseminate quickly and efficiently and also reduce information spreading to vehicles which do not require the information (as discussed previously, this can cause more pertinent information to be lost).

The probability for rebroadcasting, , as described by Nekovee [17] is obtained from

(5)

where and are the number of times the car has received that particular message from front and back, respectively, and is a protocol parameter which controls redundant transmissions. In the case of directional message propagation, (5) is modified such that if a message is propagating in either direction it is only kept alive by nodes near the head or tail of the group. In this case the rebroadcasting probability, , is computed from

(6)

where is the count of messages received from the direction of message propagation (e.g., if is forward, is the count of messages received from vehicles in front), and is the count of messages received from the opposite direction.

4.2. Variable Speed Limit

The initial algorithm we introduce reduces the value of the desired velocity ( in (5)) by a fixed amount when the vehicle has received the warning message. This achieves an overall slowdown in the network which can reduce the time delay between free-flow and gridlock (where ) at the obstacle. This particular algorithm change has a transient effect on the network, such that the system will still become congested over time. The idea for this came from the London Orbital (M25) variable speed limit which operates on parts of the motorway.

The value we reduce by is of great importance. Initial tests showed that reducing the desired velocity too much (i.e., a reduction of over 10 m/s) when infected, the effect on the network was to cause congestion further back in the system, such that gridlock (i.e., all vehicles in the field of simulation are static) occurs much sooner. By reducing the value of by 2.7 m/s the network slowed well, and the time delay between free-flow and gridlock was increased without causing congestion further back in the network.

An important algorithmic change is the return to the normal value of once the obstacle has been passed geographically, otherwise the recovery from the obstacle will take a greater amount of time. We did test a proportional change in the desired velocity as the obstacle was approached, but this provided little observable effect at great distances and a highly-negative effect closer to the obstacle, as cars were congesting more smoothly but to a greater extent.

The results of this algorithm change were both transient and often detrimental to the overall velocity of vehicles in the system, so the change was dropped from the final algorithm described in Section 4.3. The reason for this negative effect is thought to be related to the size of field we are simulating. In future simulations we will explore a much larger field, where we expect the effect of the algorithm to become more pronounced as the distance from the obstacle increases.

4.3. Lane Changing Algorithm

The original lane change model, shown in (7), operates by determining an acceleration advantage (toward a goal velocity) to be gained by changing lane and then testing if a gain threshold is reached by the advantage. Early incarnations of our changes to the algorithm worked to forcibly increase the advantage if a message had been received and the vehicle was in the lane with the obstacle. This has some positive effects, but can cause problems when the message propagates a large distance back through the system. In the case of the message propagating beyond the reasonable extent of the need to change lane, this approach causes unnecessary congestion in the adjacent lane to the obstacle resulting in total congestion in a short time.

At the start of the simulation several static variables are applied to the model. A changing threshold is applied that indicates the increased acceleration the lane change will yield; this is set by default at 0.3 ms for cars in the field. The other value is the `politeness factor' which reduces the overall calculated advantage and which simulates the care drivers take when changing lane (i.e., the model may say it is advantageous to change lane, but the driver may be too polite or hesitant to do so).

The basic algorithm operates by calculating a value of advantage ( ), the disadvantage this causes to other ( ) and then calculates whether a function of these values reaches a changing threshold. If the threshold is reached the vehicle changes lane:

(7)

where is the acceleration in the new lane and is the acceleration in the old lane. refers to a weighting to keep the vehicle in the slow lane, as operates in reality:

(8)

where is the acceleration of the car behind in the old lane if the vehicles changes lane and is the acceleration of the car behind in the new lane if change lane. These values are then entered into the following equation to return true or false to changing lane:

(9)

where is the politeness factor and is the changing threshold. The form of (9) is multiplicative so the values of and have a significant impact on each other. In the following equations, these values are only calculated if the vehicle has been infected with a message. If a vehicle is ignorant, it will continue to use the algorithm in (9). The initial change we made was to add a value to in (10) as such

(10)

This is very much a brute force approach and as such does not truly represent real driving in a highway, where the value of would increase as the vehicle approaches the obstacle and drop to zero after the obstacle has been passed. This proportional addition to is shown in

(11)

In this adaption of the original algorithm, the value is calculated as a function of the location of the obstacle and the vehicle's distance to it. This value is capped at a maximum (currently 20) to prevent unrealistic behaviour (i.e., cutting in with zero safety headway), which means the effect is noticeable but quite subtle, when compared to the brute force method in (10). This means that as the vehicle approaches the obstacle the incentive to change lane becomes greater, reducing the appearance of congestion at the obstacle in the same lane.

6.1. Velocity Experiments

These experiments test the effectiveness of the algorithm as vehicle velocity changes, to see if the algorithms are suited to an urban (slow) or highway (fast) environment. When ignorant (no messages have been received), the cars will still attempt to change lane to avoid the obstacle, but only as part of the original lane-changing algorithm, and so congestion builds up in a short amount of time, for most simulations. Below a certain network load the road will never become congested, so the vehicular load of the experiment was varied for each experiment. The vehicular load on the road was also set low enough so that the algorithm could affect the flow of cars as, at high loads, this would not be possible. To this end there is, in any system, a critical value of vehicular load after which no action can prevent or reduce congestion.

Some early simulations with low vehicular loads showed that it is sometimes more efficient to be ignorant of the obstacle, and this must be taken into account, as in this case the best course of action is to drive normally, using the normal algorithm.

Figures 2 and 3 show results from a sample of the experiments we ran to test this theory. By varying all the parameters available we found that certain velocities, transmission ranges, and vehicular load had different levels of effectiveness to the overall congestion in the system. In the main the results showed that our algorithm always produced a positive effect. In order to produce valid data we ran several simulations with the same parameters and then averaged this data, to show results for a typical case.

Figures 2 and 3 show the number of cars exiting the field in a simulation run as an aggregate over time. Both show an advantage for infected cars using the advanced lane-changing algorithm, but the advantage is greater at higher velocities, where the vehicles have more distance between them for the same vehicular load, meaning they can more easily change lane.

We found, and Figures 2 and 3 corroborate this, that the advanced algorithm increased the time before congestion began to build up and then once congested, the infected cars still moved through the system more efficiently. By running the simulation for 15 minutes we can monitor the development of congestion in the system and how the flow is affected by the changed algorithm.

The results show interesting behaviour, beyond the reduction of congestion in the system. By analysing the first 5–7 minutes of simulation time, we can see that the development of congestion is also slower once vehicles do start to slow down. This is because of the algorithm moving vehicles into the opposite lane to the obstacle, reducing the load on the lane with the obstacle and therefore reducing the number of stopped vehicles behind the obstacle which, when changing lane, cause a dramatic slowdown in the new lane. This reduction in stop-and-go vehicular formation is also seen elsewhere in the field when the cars are infected with the warning message and switch to our adapted algorithm.

6.2. Position of Lane Change

A factor that affects the build-up of congestion in the system is related to the location of the lane change. The following results show where the lane change occurs with no communication and then using our enhanced lane change algorithm with communication active. The simulation settings were set at 2200 cars/hour load, speed limit of 120 km/h and a transmission range of 100 m.

During the simulation the message propagates backwards towards position 0 and, with the advanced algorithm, the location of the lane-change also reduces. When the system starts to slow and vehicular density increases, the lane-change moves right back, causing a slower build-up of congestion and a greater amount of free vehicular flow, as shown by Figure 4. This does place greater load on the opposite lane to the obstacle, but the reduction of stop-and-go behaviour negates this. In Figure 4 the rapid reduction in position of most lane changes between 395–405 seconds and again at 475–500 seconds represents a period when the propagation of the message is continuous, and the periods of little change (of lane change position) are due to reduced propagation of the warning message. The initial peak of lane change position between 0 and 35 seconds represents the initialisation of the system, that cars can change lane very close to the obstacle due to the road being less loaded. The data to produce this result came from a single typical simulation, with parameters set as per the previous paragraph.

6.3. Transmission Method Experiments

In this experiment the available transmission methods are tested with the new algorithm, to see how they affect the overall congestion in the system. Figure 5 shows a simulation run until congestion is present at the origin of the field (i.e., position = 0). The simulation is stopped when the congestion reaches the origin as after this point the algorithm is not affecting the vehicular flow. The values represent the proportion of cars leaving the field in relation to the cars entering . This indicates how vehicles are flowing through the system, where an increase of the gradient represents free flow and a decrease represents congestion.

The models shown in Figure 5 are simple flooding, where the message is rebroadcast just once, edge detection which is explained in Section 3.1, and distance detection, which is a different probabilistic method and a mixture of edge and distance detection. These models are all running in the simulation, but the mixed (edge detection and distance detection) offers the best simulation of a real epidemic protocol.

As can be seen in Figure 5 the edge detection method alone offers little improvement over no propagation, and the simple flooding and distance detection methods offer a good initial advantage (0–200 seconds) but then suffer very fast congestion build-up. The mixture of edge and distance detection algorithm, with our changes to the lane change model offers excellent results keeping near free flow until ca. 420 seconds, when the network then slows and starts to congest, but this takes longer (ca. 250 seconds from the first slowdown) than the other algorithms.

The addition of this propagation method and the changed algorithm prevent several congestion-causing situations to occur. The main situation avoided is when vehicles are unable to change lane to avoid the obstacle and begin to slow down, but then do change lane causing the cars behind to slow. This cause has been seen to initiate the build-up of congestion by earlier warning of the obstacle so that the cars can change lane at a high velocity. Another behaviour of the system is that when the congestion is initiated, the cars will fill up behind the obstacle, unable to change lane. With the adapted algorithm the extra incentive to change lane means that the opposite lane fills first and so vehicles can still move, increasing the time before the whole system becomes congested.

6.4. System Velocity

The average velocity through a system is of great importance. If a higher average velocity can be achieved the number of vehicles passing through the area of congestion will be higher than if there is much slowing of vehicles. Figures 6 and 7 show the average velocity calculated for intervals of 10 metres on the axis and an interval of 30 seconds across the axis. Each point represents the average velocity at that time/position interval. In both figures there is a noticeable slowdown as the vehicles pass the obstacle. This can be accounted for by the IDM attempting to retain a minimum safe distance between vehicles.

Figure 6 shows that after an initial even velocity through the field, congestion begins to build up at the position of the obstacle between 100 and 200 seconds, which causes a slowdown further back to position 0. By time of 330 seconds the congestion has reached position 0, and the average velocity falls from 20–25 ms to 0–5 ms .

As can be seen in Figure 7, there is a uniform average velocity before and after the obstacle during the whole period of the simulation (10 minutes). This reinforces the results from the other simulations and proves that there is a better flow of vehicles through the network, as well as a reduction in the build-up of congestion, when effective transmission of the road condition occurs.

We note that for both figures there is a spike in velocities (between time 0–10 and position 1200–1400). This is the period when the first cars are leaving the field. As they have no cars in front they can accelerate up to the full speed limit unhindered. To remove this artefact future simulations will have a "warm-up" period, with low vehicular load, that initialises the field.

6.5. Varying Penetration Rate of Radio-Equipped Vehicles

In all of the simulation studies and results presented in Section 5, we have assumed that 100% of the vehicles in the simulated field are radio equipped and therefore able to receive and retransmit (where necessary) the data about the upcoming incident or congestion. This is a somewhat idealised view of how deep uptake of radio-equipped vehicles will be. More likely, as vehicle manufacturers and radio equipment providers begin releasing the products to operate and support a VANET, the ratio of equipped vehicles will increase. Due to the critical safety-of-life applications of VANET, it is important to study the efficiency and resilience of simulated applications, to study the point at which they become usable and reliable. This simulation study involved the same system as in previous experiments, but here the proportion of equipped vehicles is increased from 10% to 90%. The plots in Figure 8 show the flow trajectories of vehicles in the system.

We ran each simulation several times, to ensure no artifactual or erroneous data was included in our results, but the results shown here represent only one simulation. As can be seen at low penetration rates (10%–40%) the vehicles reach the obstruction and begin to congest, but between 60% and 70% there is a noticeable improvement, or smoothing, of the vehicles velocity through the field of study. The figures show that above 70%, where there is still some congestion build-up around the obstruction, the propagation of information to vehicles further away, and the change to the lane-changing algorithm this triggers, allows for more steady driving through the field of study, and less congestion.