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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In Vehicular Networks, communication success usually depends on the density of vehicles, since a higher density allows having shorter and more reliable wireless links. Thus, knowing the density of vehicles in a vehicular communications environment is important, as better opportunities for wireless communication can show up. However, vehicle density is highly variable in time and space. This paper deals with the importance of predicting the density of vehicles in vehicular environments to take decisions for enhancing the dissemination of warning messages between vehicles. We propose a novel mechanism to estimate the vehicular density in urban environments. Our mechanism uses as input parameters the number of beacons received per vehicle, and the topological characteristics of the environment where the vehicles are located. Simulation results indicate that, unlike previous proposals solely based on the number of beacons received, our approach is able to accurately estimate the vehicular density, and therefore it could support more efficient dissemination protocols for vehicular environments, as well as improve previously proposed schemes.

The convergence of wireless telecommunication, computing, and transportation technologies facilitates that our roads and highways can be both our transportation and communication platforms. These changes will completely revolutionize when and how we access services, communicate, commute, entertain, and navigate, in the coming future. Vehicular Networks (VNs) are wireless communication networks that support cooperative driving among communicating vehicles on the road. Vehicles act as communication nodes and relays, forming dynamic vehicular networks together with other nearby vehicles. VNs involve vehicle-to-vehicle (V2V) [

The specific characteristics of vehicular networks favor the development of attractive and challenging services and applications. Though traffic safety has been the primary motive for the development of these networks [

One issue to keep in mind when making any proposal related to vehicular networks is to study in detail how it behaves when modifying all the possible factors [

Traditionally, in Transportation Systems, vehicle density has been one of the main metrics used for assessing the road traffic conditions. A high vehicle density usually indicates that the traffic is congested. Currently, most of the vehicle density estimation techniques are designed for using infrastructure-based traffic information systems. Hence, these approaches require the deployment of vehicle detecting devices such as inductive loop detectors, or traffic surveillance cameras [

In this paper we focus on the vehicle density awareness in urban environments, and we present a solution to estimate the density of vehicles based on the number of beacons received per vehicle, and the roadmap topology. We consider that vehicles, able to precisely estimate the vehicular density in their neighborhood, can adjust their diffusion scheme according to this density. When using our density estimation proposal, an adaptive system could increase successful communication probability in sparse networks by increasing its data dissemination rate, or reduce the channel contention in high density scenarios by reducing the number of broadcast messages.

The paper is organized as follows: in Section 2 we review previous works closely related to our proposal, highlighting the similarities and differences. In Section 3 we present in detail our proposal for real-time estimation of vehicular density. In Section 4 we measure the estimated error to assess the goodness of our proposal. In Section 5 we compare our proposal with a density estimation method that only relies on the information provided by the beacons received. Finally, in Section 6 we present the main conclusions of this work.

Despite the importance of determining the vehicular density to improve the support for vehicular network applications, so far there have not been enough studies that explored the density estimation in order to improve wireless communications in vehicular environments. Next, we will discuss the most relevant works in this field. Tyagi

Tan and Chen [

Shirani

Artimy [

Stanica

Other authors use the Kalman filtering technique for the estimation of traffic density. For example, Balcilar and Sonmez [

All of these works established the importance of vehicular density awareness for neighboring areas, but none has deepened in the analysis of the accuracy of the method used to estimate this density, the best time period to gather the required data, or the effect of the topology in the results obtained. In most cases, this estimation does not take place in real time or requires infrastructure deployment. Moreover, most of the works regarding the use of Vehicular Networks only use the number of beacons to estimate the vehicular density. In this paper, we demonstrate how existing approaches can be highly inaccurate, since the characteristics of the simulated roadmap can significantly affect the obtained results, making the estimation erroneous.

The main objective of this paper is to propose a mechanism that allows estimating the density of vehicles in a specific area by using Vehicular Networks. In particular, we intend to estimate the vehicular density taking into account the number of beacons received and the topological features of the selected area (which can be obtained from the in-vehicle GPS unit).

Our method consists of three phases. In the first phase, we first analyze the features of different cities (see Section 3.1). During the second phase, the vehicles obtain the number of beacons received (see Section 3.2). Finally, in the third phase, each vehicle can estimate the vehicular density in its neighborhood by applying an equation that requires as input parameters the values, in terms of roadmap complexity and beacons received, obtained in the previous phases. Next subsections present the different phases of our mechanism.

An important issue to our vehicular density estimation approach is to obtain the different features of each roadmap (e.g., the number of streets, the number of junctions, the average distance of segments, and the number of lanes per street).

The roadmaps used to achieve the density estimation were selected in order to have different profile scenarios (

We consider that the parameters that better correlate with the complexity of the roadmap are the number of streets and the number of junctions. Hence, we also added a column labeled as

After performing the topological analysis of the studied maps, we need to obtain the number of beacons received by each vehicle during a certain period of time. This period is very important, since it will affect the number of beacons received, and the accuracy of the vehicular density estimation.

According to the results obtained in Section 3.3.1. in our scheme, we obtain the number of beacons received during 30 seconds. We consider that each vehicle sends one beacon per second, and that these messages, unlike warning messages, are not disseminated by the rest of the vehicles. These considerations can be found in many previous Vehicular Network studies, so they could be considered quite realistic.

The simulation results shown in this article have been obtained using the ns-2 simulator [^{−1}, as this is the maximum rate for broadcasting in 802.11p. The MAC layer was also extended to include four different priorities for channel access. Therefore, application messages are categorized into four different Access Categories (ACs), where AC0 has the lowest and AC3 the highest priority.

The purpose of the 802.11p standard is to provide the minimum set of specifications required to ensure interoperability between wireless devices when attempting to communicate in potentially fast-changing communication environments. For our simulations, we chose the IEEE 802.11p because it is expected to be widely adopted by the industry.

We tested our model by evaluating the performance of a Warning Message Dissemination mechanism, where each vehicle periodically broadcasts information about itself, or about an abnormal situation (icy roads, traffic jam,

As for vehicular mobility, it has been obtained with CityMob for Roadmaps (C4R) [

As expected, complex roadmaps present a number of beacons received lower than simple roadmaps for a similar vehicular density. In addition, we found that the simpler cities present a high similitude in terms of results, being more difficult to estimate the vehicular density in complex cities compared with simple cities.

After observing the direct relationship between the topology of the maps, the number of beacons received, and the density of vehicles, we proceed to obtain a function to estimate, with the minimum possible error, each of the curves shown in

To propose a method able to accurately estimate the density of vehicles, based on the number of beacons received and the roadmap topology, we made a total of 4,000 experiments. These experiments involved the simulation of controlled scenarios (

In order to obtain the best approach, we have tested some different functions (exponential, logarithmic, ^{2} in urban scenarios, according to the number of beacons received, and the SJ ratio (

In this equation,

As mentioned before, our proposal is based on two key factors: (i) the roadmap topology, which is provided by the in-vehicle GPS systems, and (ii) the number of beacons received at a given period of time. Hence, in a vehicular density estimation system, it is very important to decide how much time is dedicated to gather important and necessary data in order to better estimate the density of vehicles at any given time.

In order to determine the optimal period of time that should be considered to estimate the density in vehicular environments, thereby enhancing the performance of the density estimation process, we made a total of 600 experiments including six different time periods (

^{−2}, respectively. As shown, complex maps are more affected by vehicular density variations, since messages encounter more difficulties to be propagated in these kinds of maps, especially in lower density scenarios. Regarding the optimal time period, since results are quite linear, a larger time period seems to be the best option; notice that this solution requires fewer calculations, thereby reducing the overhead. However, a more thorough analysis should be made to determine the optimal time period required to gather the number of beacons received.

To find the best period, we also analyzed the error committed when using different time periods. Specifically, we fitted the function coefficients to each period, and then calculated the absolute error committed.

Our vehicular density estimation approach uses three different parameters: (i) the number of beacons received, (ii) the number of junctions, and (iii) the number of streets. As for the number of junctions, it is only necessary to count the junctions between different street segments. However, regarding the number of streets, we realized that different alternatives could be selected to obtain the number of streets in a given roadmap.

Basically, the different alternatives are: (i) the number of streets obtained in SUMO [

To determine the accuracy of our proposal, we proceed to measure the estimated error.

Finally,

As previously mentioned, other vehicular density estimation proposals rely on the use of infrastructure elements to estimate the vehicle density (e.g., [

In order to assess the importance of the topology, we compared our proposal with a beacon-based approach, where the vehicular density is estimated by only using the number of beacons received. To make a fair comparison, we followed the same methodology in both approaches.

We tested four different density estimation functions that are only based on the number of beacons received, trying to obtain the lowest sum for the squared absolute error. Specifically, we have tested three different polynomial functions (

^{−2}). However, they underestimate the number of vehicles in high density environments, and, most importantly, they overestimate the density of vehicles in Simple maps.

Therefore, the advantages of using our vehicular density estimation proposal are clear in terms of accuracy. Our approach requires using GPS and digital maps, but these requirements are currently fulfilled by most of the vehicles in many countries.

This paper proposes a method that allows vehicles to estimate the vehicular density in their neighborhood at any given time by using Vehicular Networks. Our proposal allows scientists to improve their proposals, or propose new solutions, based on our findings.

Unlike existing proposals, our vehicular density estimation mechanism accounts not only for the number of beacons received per vehicle, but also for the map topology in the region where the vehicles are located. Our method consists of three phases: (i) we first analyze the features of different cities, (ii) the vehicles obtain the number of beacons received, and (iii) each vehicle estimates the vehicular density in its neighborhood by applying an equation that requires as input parameters the values in terms of roadmap complexity and beacons received.

Results show that our proposal allows estimating the vehicular density for any given city with a high accuracy. We also demonstrated that the characteristics of the roadmap are very useful in order to accurately estimate the vehicular density in a given scenario.

In the future, we plan to apply our proposed vehicular density estimation approach to implement more efficient and adaptive information dissemination schemes, specially designed for urban environments. We consider that, by using our density estimation proposal, an adaptive system could increase the probability of successful communication in sparse networks by increasing its data dissemination rate, or reduce the channel contention in high density scenarios by reducing the number of broadcast messages. Therefore, we plan to apply our proposal to the Profile-driven Adaptive Warning Dissemination Scheme (PAWDS) [

This work was partially supported by the

Scenarios used in our simulations. Fragments of the cities of: (

Number of beacons received when varying the vehicular density.

3D representation of our density estimation function.

Number of beacons received per vehicle when varying the time period and the city roadmap when simulating: (^{−2}, and (^{−2}.

Different criteria when counting the number of streets.

Comparison between simulated and estimated average results.

Absolute error histogram.

Graphical comparison between simulated and estimated results for each function.

Map features.

Rome | 1655 | 1193 | 77.0296 | 1.0590 | 1.3873 |

Rio de Janeiro | 542 | 401 | 167.9126 | 1.1135 | 1.3516 |

Valencia | 2829 | 2233 | 60.7434 | 1.0854 | 1.2669 |

Sydney | 872 | 814 | 138.0716 | 1.2014 | 1.0713 |

Amsterdam | 1494 | 1449 | 90,8164 | 1.1145 | 1.0311 |

Madrid | 628 | 715 | 183.4947 | 1.2696 | 0.8783 |

San Francisco | 725 | 818 | 171.4871 | 1.1749 | 0.8863 |

Los Angeles | 287 | 306 | 408.2493 | 1.1448 | 0.9379 |

Parameters used for the simulations.

| |
---|---|

roadmaps | Rome, Rio de Janeiro, Valencia, Sydney, Amsterdam, Madrid, San Francisco, and Los Angeles |

number of vehicles | [100, 200, 300…1000] |

number of collided vehicles | 3 |

roadmap size | 2000 |

warning message size | 256 |

beacon message size | 512 |

warning messages priority | |

beacon priority | |

interval between messages | 1 second |

MAC/PHY | 802.11p |

radio propagation model | |

mobility model | |

channel bandwidth | 6 |

max. transmission range | 400 |

Average percentage difference with respect to the mean value.

Rome | 29.49% |

Rio De Janeiro | 5.85% |

Sydney | 15.82% |

Amsterdam | 14.96% |

Madrid | 6.44% |

Los Angeles | 4.70% |

Proposed equation coefficients.

a | -1.1138191190298828E+03 |

b | -1.0800433554686800E+01 |

c | 3.1832185406821718E+03 |

d | -4.0336415134812398E-01 |

f | -3.0203454502011946E+03 |

g | 2.8542014049626700E-03 |

h | 9.5199929660347175E+02 |

i | 3.5319225007012626E+01 |

j | 1.6230525995036607E-01 |

k | -1.6615888771467137E+01 |

Absolute error when varying the time period.

10 | -5.073593E-03 | 1.483517E-03 |

20 | -1.515514E-03 | 1.048494E-03 |

60 | 2.377369E-01 | 1.241401E+03 |

120 | 7.621857E+00 | 1.548736E+03 |

180 | 5.128145E+00 | 1.492756E+03 |

Number of streets obtained depending on the criterion used.

Rome | 2780 | 1484 | 1655 |

Rio de Janeiro | 758 | 377 | 542 |

Amsterdam | 3022 | 796 | 1494 |

Madrid | 1387 | 1029 | 628 |

Density estimation error.

Minimum | -2.612027E+01 | -2.284800E-01 |

Maximum | 2.169529E+01 | 5.713108E-01 |

Mean | -3.176197E-10 | 1.023340E-02 |

Std. Error of Mean | 1.360303E+00 | 1.714082E-02 |

Median | 1.698901E-01 | -1.359121E-03 |

Beacons-only functions' coefficients.

a | 1.8294269144848133E+01 | 2.2768425534110406E+01 | 3.9047236513533704E+01 | 1.9087154795377430E+02 |

b | 4.1367349228558270E+00 | 3.2941345206538704E+00 | -1.3847115600040454E+00 | 1.6327793099067961E+02 |

c | -2.1509124292378768E-02 | 7.0289357151021746E-03 | 2.9758692872675790E-01 | 2.5673041989256740E-02 |

d | - | -2.5558429762904153E-04 | -6.4713013709561500E-03 | 4.4055843266582620E+01 |

f | - | - | 4.2741298952571685E-05 | 6.8666406701129157E-01 |

Comparison between our SJ Ratio and the Beacon-based density estimation approaches.

Beacons-only Quadratic | 1.3823448453520384E+05 | 41.5684 |

Beacons-only Cubic | 1.3799411801756185E+05 | 41.5322 |

Beacons-only Quartic | 1.3609380737712432E+05 | 41.2453 |

Beacons-only Preece-Baines Growth | 1.3123134971478261E+05 | 40.5017 |