POSACC: Position-Accuracy Based Adaptive Beaconing Algorithm for Cooperative Vehicular Safety Systems

Cooperative vehicular safety systems are expected to revolutionize the driving experience by providing road safety applications based on incident detection. Two vital quality parameters for cooperative safety applications are the position accuracy and communication reliability of the status information. The receiver may take erroneous decisions if the received data does not correspond to the latest situation of the transmitter (e.g., position, velocity, and trajectory of the target vehicle). In this paper, we propose and evaluate a POSition-ACCuracy (POSACC) based adaptive beaconing algorithm for cooperative vehicular safety systems. POSACC integrates three different control mechanisms to guarantee specific performance metrics. It adopts the position accuracy and communication reliability as the highest priority metrics, due to their direct impact on the vehicle’s systems capability to avoid potential traffic accidents in real-time. In addition, it guarantees the priority metrics, maintaining the vehicle’s warning distance, channel load, and end-to-end latency into the operative range of cooperative safety applications. POSACC is compared with three different state-of-the-art adaptive beaconing algorithms; ETSI DMG, LIMERIC, and DC-BTR&P. Extensive evaluation results show that POSACC successfully controls the beacon rate, transmission power, and the size of the minimum contention window. Simulation results also demonstrate that POSACC is more effective than the benchmark algorithms by guaranteeing the operational requirements of cooperative safety applications in a wider range of traffic situations.


I. INTRODUCTION
Cooperative vehicular safety systems are being designed to provide accident-free and efficient road systems [1].The new paradigm relies on equipping the vehicle with wireless communication devices to increase its perception about the The associate editor coordinating the review of this manuscript and approving it for publication was Muhammad Naeem .surrounding environment.Cooperative safety applications aim to detect potential crashes on the road and to notify vehicles in advance.The communication on these systems relies on the IEEE 802.11p [2] radio access technology in the 5.9 GHz frequency band, which specifies the mediumaccess-control (MAC) and physical (PHY) layers of Wireless Access in Vehicular Environments (WAVE) [3].The IEEE 802.11pMAC layer is based on the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol and includes the Outside of the Context of a Basic Service Set (OCB) operation mode recently defined in [4].The IEEE 802.11pPHY layer is based on the IEEE 802.11a standard, but it uses channels of 10 MHz to reduce the negative impact of multipath delay spread and Doppler effect [5].
Cooperative vehicular safety systems rely on the continuous exchange of status information between neighboring vehicles on a common control channel (CCH).To make neighbors aware of its presence, each vehicle regularly transmits one-hop broadcast messages, called beacons.The beacons are formally known as Basic Safety Messages (BSM) [6] in the US or Cooperative Awareness Messages (CAM) [7] in Europe.These messages include information about the status of the transmitting vehicle; such as its position, speed, acceleration, and heading.The beaconing process allows the receiving vehicle to create a Local Dynamic Map (LDM) based on the status information of its neighborhood [7].The status information is used by cooperative safety applications to detect and mitigate potential crashes in real-time (e.g., the crash risk can be estimated by analyzing the movement status of vehicles) [7].
Finding the appropriate beacon transmission rate for each vehicular scenario is essential for the proper performance of cooperative safety applications.The beacon transmission rate is directly related to the position accuracy perceived by neighboring vehicles [8].In realistic scenarios, some vehicles could have high dynamics (high speed and acceleration), whereas other vehicles could have low dynamics (low speed and acceleration).This may lead to differences in position accuracy since position error depends on beacon rate and vehicle dynamics.In traffic jams, a beacon transmission rate of 1 beacon/s could be enough to provide the position accuracy needed for most safety-related applications.However, this beacon rate is not enough to achieve the required level of position accuracy on a multi-lane high-speed highway with frequent lane changes.The technical report of the Vehicle Safety Communications Consortium (VSCC) [9] specifies that 10 beacon/s is the minimum beacon rate required to meet the position accuracy of several safety-related applications, while some safety-critical applications can demand a beacon rate up to 50 beacon/s.
The operational requirements of cooperative safety applications can be defined mainly in terms of position accuracy, communication reliability, and end-to-end latency [10], [11].The European Telecommunication Standards Institute (ETSI) has specified in the technical specification ETSI TS 101 539-3 [10] that cooperative safety-critical applications, such as Longitudinal Collision Risk Warning (LCRW) (e.g., safety-relevant lane change and safety-relevant vehicle overtaking), demand a position accuracy equal or less than 1 m with a confidence level of 95 %, a communication range of 300 m in a line of sight situation and when the channel load is at a relaxed state, and an end-to-end latency equal or less than 300 ms.Similarly, cooperative safety-critical applications, such as Intersection Collision Risk Warning (ICRW) (e.g., turning collision risk warning and merging collision risk warning) defined by ETSI in ETSI TS 101 539-2 [11], require a position accuracy equal or better than 2 m with a confidence level of 95 %, a communication range of 300 m in a line of sight situation and when the channel load is at a relaxed state, and an end-to-end latency equal or less than 300 ms.ETSI also specifies in [10], [11] that the required communication range may be reduced in certain situations (e.g., in congested channel situations).
Congestion and awareness control approaches have been proposed in the literature [12], [13] to provide reliable and efficient vehicular communications.However, both approaches have drawbacks in terms of road safety.Congestion control approaches [14]- [17] aim at keeping the channel load below a certain target threshold and to achieve local/global fairness.However, these approaches usually do not consider the operational requirements of safetyrelated applications or vehicle dynamics.In contrast, awareness control approaches [7], [18]- [21] can consider road safety or vehicle dynamics, but they usually are not designed to simultaneously satisfy the operational requirements of cooperative safety applications.Furthermore, channel busy ratio (CBR) is generally used as a priority metric; however other critical metrics directly related to road safety, such as position error, packet collision rate, packet delivery ratio (PDR), and end-to-end latency are not considered.

A. CHALLENGES OF BEACONING APPROACHES
A high beacon rate is desirable from the viewpoint of providing fresh information and ensuring that vehicles have high levels of awareness [20].However, a high beacon rate also could lead to a congested channel, especially, in scenarios with a high vehicular density.Channel congestion leads to a degradation of communication reliability caused by packet collisions [22].Even if the channel is not congested, a high beacon transmission rate can still cause severe interference due to the hidden terminal problem and the CSMA/CA Distributed Coordination Function (DCF) procedure of IEEE 802.11p [23].Simultaneously, packet collisions have a negative impact on position accuracy.This underlying trade-off also applies to the beacon transmission power [24].A high beacon transmission power increases the probability of successful reception of a single transmission, but at the same time increases the probability of packet collisions for all transmissions.
A contradictory behavior is also observed regarding the size of the minimum contention window used by the backoff algorithm in IEEE 802.11p.Beacons are usually transmitted with the highest priority access category [13].Due to the short temporal validity of beacons, the size of the minimum contention window used by the backoff algorithm in IEEE 802.11p is often kept small.However, reducing the size of the minimum contention window increases the probability of packet collisions in broadcast communications where no exponential backoff is considered [25].The probability of packet collisions can be reduced by increasing the size of the minimum contention window; but, it has a negative effect on end-to-end latency.
Meeting the operational requirements of cooperative safety applications is a very challenging task.The responsibility for meeting the requirements of a specific performance metric in the worst-case scenario (more demanding applications) can lead to not meeting the requirements of these and other applications in other metrics.In this context, we propose a novel POSition-ACCuracy (POSACC) based adaptive beaconing algorithm for cooperative vehicular safety systems.It aims to satisfy the operational requirements of cooperative safety applications.POSACC is compared with relevant state-ofthe-art beaconing algorithms via a realistic simulation framework and considering performance metrics directly related to road safety.
The contribution of this paper is threefold: 1) We adopt the position accuracy and communication reliability as the highest priority metrics due to their direct impact on the decision-making process, in realtime, of cooperative safety applications.We establish a design strategy that reduces the conflict between the required goals.The strategy focuses on providing the position accuracy and communication reliability required by cooperative safety applications, maintaining the vehicle's warning distance, channel load, and end-to-end latency into the operative range of the cooperative safety applications.2) We design three different control mechanisms to guarantee specific performance metrics.We design a beacon rate control mechanism that adapts the beacon rate depending on vehicle movement status to achieve the desired position accuracy.In addition, we design a transmission power control mechanism that computes the vehicle's transmission power depending on its movement status to maximize the probability of successful reception of beacon messages at the target warning distance.Finally, we design a control mechanism that computes the size of the minimum contention window depending on the maximum reported size of the LDM database in order to minimize the probability of packet collisions.3) We propose an adaptive beaconing algorithm, called POSACC, to simultaneously guarantee the operational requirements of cooperative safety applications.Extensive evaluation results show that POSACC successfully controls the beacon rate, transmission power, and the size of the minimum contention window.Simulation results also demonstrate that POSACC is more effective than three state-of-the art algorithms: ETSI DMG [7], LIMERIC [15], and DC-BTR&P [26], by adapting to the vehicle dynamics as well as guaranteeing the operational requirements of cooperative safety applications in a wider range of traffic situations.
The remainder of this paper is organized as follows.Section II reviews related work.Section III introduces the control mechanisms and POSACC algorithm.Section IV describes the simulation setup.Section V evaluates the performance of the proposed algorithm, whereas Section VI presents conclusions and future works.

II. RELATED WORK
In the ETSI EN 302 663 standard [27], ETSI has defined a 10 MHz common control channel for vehicular communications at 5.9 GHz, known as the ITS-G5 radio channel.To enable cooperative awareness within ITS-G5, ETSI also has delivered the standard ETSI EN 302 637-2 [7] specifying the rules for the exchange of CAMs.The cooperative awareness basic service is mandatory for all nodes operating in ITS-G5.In this service, vehicles regularly broadcast their status data by using the CSMA/CA protocol with no acknowledgments or retransmissions.One key problem of the beaconing activity is the channel congestion that can arise due to the aggregated load.In this context, ETSI has defined the Cross-Layer Decentralized Congestion Control (DCC) Management Entity to avoid overloading the ITS-G5 radio channel [28].Channel congestion can limit the transmission of event-driven messages, such as the Decentralized Environmental Notification Messages (DENMs) defined by ETSI in ETSI EN 302 637-3 [29].Channel congestion can also negatively affect the proper performance of cooperative safety applications.In the following, we overview some congestion and awareness control approaches.Some examples of congestion control approaches available in the literature are PULSAR [14], LIMERIC [15], FABRIC [16], and DCC [17].Two of the most important current congestion control approaches are PULSAR [14] and LIMERIC [15].Both approaches adapt the beacon rate based on the channel load and set the transmission power to a fixed value.PULSAR relies on a binary rate control using the Additive Increase Multiplicative Decrease (AIMD) technique.To fulfill the global fairness design principle, vehicles share two-hop CBR information.In LIMERIC, the underlying function linearly controls the beacon rate of each vehicle according to local CBR measurements.LIMERIC converges to a fair and efficient channel utilization in deterministic environments.To ensure the convergence in very dense scenarios, it uses an effective gain saturation technique.PULSAR and LIMERIC are able to maintain the channel load below a certain target threshold independently of the vehicular traffic density.In LIMERIC, noisy CBR measurements produce unfairness in rate allocations [30].
FABRIC [16] is based on a network utility maximization problem.In FABRIC, the beacon rate of each vehicle in the one-hop neighborhood is recursively optimized.To enable this, it is proposed that all vehicles share their beacon rates.The main drawback of FABRIC is controlling the speed of convergence in practical scenarios [20].ETSI has also specified a set of DCC mechanisms [17] that adapt the beacon transmission parameters to keep the channel load below a target threshold.All the mechanisms rely on a state machine that distinguishes three states: relaxed, active, and restrictive, in increasing order of channel congestion.State transitions are driven by the channel load conditions locally measured by each node during a sampling interval.DCC is naturally oscillatory, which implies unstable state transitions [31].
Several awareness control approaches exist in the literature.For example, the awareness control approach proposed by ETSI is the dynamic message generation mechanism [7], which we call here ETSI DMG.It adapts the beacon rate depending on the changes in position, velocity, and heading of the transmitting vehicle.This approach aims to limit the position error perceived by neighboring vehicles while implicitly controls the channel load.ETSI DMG has a synchronization problem for cooperative maneuvers that degrades its performance [32].It also suffers from a divergence effect that leads to oscillations in the beacon rate [33].IVTRC [18] is an awareness control approach that also considers the position accuracy as a design goal.It controls the beacon rate depending on differences from position predictions.However, beaconing based on position prediction has serious drawbacks for road safety, as specified in [34].Further, in situations where the channel load increases, IVTRC reduces the beacon transmission rate of vehicles at the cost of decreasing the position accuracy.
Other awareness control approaches available in the literature are INTERN [19], NORAC [20], TTCC [21], and DC-BTR&P [26].INTERN [19] assigns the beacon transmission rates required by the applications, and then equitably shares the excess capacity.It also controls the transmission power to generate certain level of awareness.NORAC [20] is a rate and awareness distributed control approach based on non-cooperative game theory.The underlying congestion control mechanism limits the bandwidth usage of each vehicle and reduces the beaconing rate in congested situations.NORAC assigns a beacon transmission rate to each vehicle proportional to its requirements while ensuring fairness between vehicles with the same requirement.Similarly, TTCC [21] aims to satisfy the constraints on channel availability, whereas the safety of the surrounding traffic situation is captured with a time-tocollision metric.TTCC increases the beacon transmission rate of the vehicles involved in more dangerous situations, so it yields higher rates and better usage of channel capacity.
DC-BTR&P [26] is an awareness control approach designed to satisfy the position accuracy requirements of cooperative safety applications.This approach is based on the dynamic control of the beacon rate and transmission power.The underlying control mechanisms limit the position error perceived by neighboring vehicles and reduce packet collisions.However, such benefits are achieved at the cost of decreasing the communication range of vehicles with higher dynamics.This issue is critical for road safety because drivers need to be notified at a sufficient distance from the expected impact to initiate a maneuver, as defined by ETSI technical specifications [10], [11].

A. LIMITATIONS RELATED TO ROAD SAFETY
The primary motive for using vehicular communications is to improve road safety.Therefore, congestion and awareness control approaches not only should prevent channel congestion or improve cooperative awareness, but also ensure the quality of service required for the proper performance of cooperative safety applications.ETSI specifies that safety applications such as LCRW [10] and ICRW [11] have strict operational requirements in terms of position accuracy, communication reliability, and end-to-end latency, as shown in Table 1.However, most of the current congestion and awareness control approaches have not been designed to satisfy the requirements simultaneously.
The main drawback of congestion control approaches such as PULSAR [14], LIMERIC [15], FABRIC [16], and DCC [17] is that they do not explicitly consider the operational requirements of cooperative safety applications or vehicle dynamics.Congestion control approaches generally adapt beacon rate based only on the channel load, without considering the traffic situation of neighboring vehicles.This could be critical for road safety in vehicular scenarios such as a highway with a traffic jam in one direction, resulting in a congested channel, and a free-flow condition in the opposite direction with high-speed vehicles.The vehicles in free-flow are forced to reduce their beacon rates due to channel congestion even if they require a high beacon rate to maintain a certain level of position accuracy.In addition, the interference generated by the vehicles in the traffic jam can significantly affect the communication reliability of vehicles in free-flow, reducing the effectiveness of cooperative safety applications.
Regarding current awareness control approaches, most of them have not been designed to simultaneously satisfy the operational requirements of cooperative safety applications.Some awareness control approaches aim to maintain a certain level of position accuracy.For instance, ETSI DMG [7] and IVTRC [18] adapt the beacon transmission rate according to the vehicle dynamics to limit the position error perceived by neighboring vehicles.ETSI DMG does not consider an additional control mechanism to guarantee communication reliability in dense traffic situations.IVTRC mitigates packet collisions, but at the cost of reducing the beacon rate, which directly affects the position accuracy.In contrast, INTERN [19] does not consider the position accuracy or vehicle dynamics.Furthermore, it also has difficulties to guarantee the beacon rates and warning distances required by the safety applications.This issue is represented by feasible regions [19] where the requirements of all vehicles could be satisfied without overloading the channel.Another drawback is that the feasible regions change with the vehicular density, so it is a challenge to avoid the regions where the requirements are not satisfied.
NORAC [20] and TTCC [21] aim to improve cooperative awareness by increasing the beacon rate of certain vehicles.However, these approaches have not been designed to satisfy a pre-defined position accuracy, nor do they have a mechanism to mitigate packet collisions.Improving cooperative awareness is not sufficient to guarantee the quality of service required by safety-critical applications.The main reason is that increasing the beacon rate also leads to more packet collisions, especially for high vehicular densities and low minimum contention windows [25], [35].Further, CBR is generally used as a priority metric, and other critical performance metrics directly related to road safety, such as position error, packet collision rate, PDR, and end-to-end latency are not considered.
Finally, DC-BTR&P [26] defines a minimum fixed transmission power independently of the vehicle dynamics.Further, it reduces packet collisions by decreasing the communication range of vehicles with higher dynamics.This issue is critical for road safety because vehicles with high speed should use a higher transmission power in order to increase their notification capacity.Another limitation is that vehicles adapt the beacon transmission parameters based on their own dynamics, without considering information from the surrounding environment.Therefore, in this paper, we design the POSACC approach to overcome these issues and guarantee the operational requirements of cooperative safety applications.

B. APPROACHES USED AS BENCHMARK
As a benchmark for comparison, we utilize three different beaconing approaches; ETSI DMG [7], LIMERIC [15], and DC-BTR&P [26].ETSI DMG is the awareness control approach specified by European standards, whereas LIMERIC is one of the most important congestion control approaches available in the literature.ETSI DMG adapts the beacon rate depending on vehicle dynamics to provide a target position accuracy.In contrast, LIMERIC adapts the beacon rate based on the locally measured CBR to maintain the channel load below a certain target threshold and to achieve fairness.We also include our previous approach DC-BTR&P, which is an awareness control algorithm that adapts the beacon rate and transmission power to provide a target position accuracy and reduce interference.The evaluation of these beaconing approaches will help understand their benefits and limitations when referring to road safety.

III. PROPOSED ALGORITHM
This section presents the design of the POSition-ACCuracy (POSACC) based adaptive beaconing algorithm for cooperative vehicular safety systems.POSACC aims to satisfy the operational requirements of cooperative safety applications.The POSACC system architecture is illustrated in Fig. 1.We assume that each vehicle obtains its own location from the Global Positioning System (GPS) device, as well as its own movement parameters (e.g., velocity, acceleration, and heading) from on-board sensors.Each vehicle also has an LDM database, where the beaconing information from its neighbors is stored.One entry is created for each neighboring vehicle.The LDM database provides information from the surrounding traffic situation (e.g., the number of neighboring vehicles as well as their movement parameters).Entries are updated at beacon receptions.If a neighbor does not announce its presence once the entry expiration time has been reached, the entry is erased from the LDM database.Cooperative safety applications require fresh status information to successfully detect possible threats.If a hazardous situation is detected, the safety-critical application provides warnings to the driver or it may trigger collision avoidance actions (e.g., in autonomous driving).
To fulfill the design goals, POSACC utilizes three different control mechanisms: • Beacon rate control: it adapts the beacon rate depending on vehicle dynamics to provide the required position accuracy.
• Transmission power control: it adapts the transmission power depending on vehicle dynamics to guarantee the required warning distance.
• Contention window control: it takes advantage of the LDM database information to adapt the size of the minimum contention window by minimizing the probability of packet collisions.In the following subsections, the control mechanisms and POSACC algorithm are presented in detail.

A. BEACON RATE CONTROL MECHANISM
The beacon rate control mechanism adapts the beacon rate in real-time to limit the position error perceived by neighboring vehicles.In this mechanism, the beacon rate is controlled according to the transmitter vehicle dynamics.Therefore, the beacon rate is reduced when the vehicle has low dynamics, alleviating the channel load and decreasing the interference on its neighbors.Furthermore, the resulting beaconing load is implicitly controlled by the relationship between average velocity and traffic density [34].As a consequence, the channel load remains stable when more vehicles drive at lower velocities.
Fig. 2 illustrates relevant time parameters that influence position accuracy.If the event of looking up the vehicle's position in the LDM database is uniformly distributed between the minimum and maximum time difference of the beacon transmission event, the average position error (E) perceived by neighboring vehicles is [34], where E min is the minimum error resulting from the transmission delay (t D ), and E max is the maximum error resulting from the beacon interval and transmission delay.We assume constant acceleration during the beacon interval.So, from kinematic equations, E is expressed as a function of velocity (v i ) and acceleration (a i ) of the transmitting vehicle (n i ), where I b i is the beacon interval of n i (equal to the inverse of beacon transmission rate, R b i ).We assume beacon messages of the same size (b z ) and equal data-rate (R D ), so t D is the same for all vehicles, In the general case of a i = 0, the discriminant (D) and solutions (I b i{1,2} ) of the quadratic function are computed as follows, Otherwise, if a i = 0, the solution (I b i ) is computed using the linear equation, Fig. 3 shows the numerical solutions of the beacon interval by using (3) for different setups: acceleration (deceleration),  velocity, and average position error.To better relate the analysis with real traffic scenarios, velocity is shown in kilometers per hour.In the analysis only positive solutions (0 < I b i ) are considered.A real root in the interval (0, 1] exists in most traffic situations.However, the root may be outside the range (0, 1] in acceleration (see Fig. 3a, v i = 30 km/h and E i = 5 m), or even the root may not exist in deceleration (see Fig. 3b, v i = 30 km/h and E i = 5 m).Fig. 4 shows the beacon interval computed by using ( 5) and ( 6) in the accelerated and uniform movement for different average position errors.As expected, an increase in velocity demands a shorter beacon interval to guarantee the desired position accuracy.The beacon interval not only responds to changes in velocity, but also to variations of acceleration.Note that the impact of acceleration is especially significant at low velocities since for a short beacon interval the velocity variation is low.
Algorithm 1 shows the steps followed by the beacon rate control mechanism to compute the beacon transmission rate in real-time depending on the vehicle movement status.On each beacon transmission, the vehicle n i gets its velocity

Algorithm 1 Beacon Rate Control Mechanism
Compute I b i{1,2} using (5); Compute I b i{1,2} using (5); v i and acceleration a i , and sets the desired position accuracy E i .Lines 1-20 involve the decisions associated depending on the movement status of n i : repose (Line 1-2), the beacon transmission rate is set to 1 beacon/s equivalent to the minimum value required for the proper performance of the less demanding vehicular applications [7]; accelerated movement (Line 3-7), the beacon transmission rate is computed using (5); uniform movement (Line 8-11), the beacon transmission rate is computed according to (6); deceleration (Line 12-20), in order to notify with immediacy to surrounding vehicles a possible braking [34], it is set a critical beacon interval (I b c ).We demonstrate the applicability of the beacon rate control mechanism in [26].

B. TRANSMISSION POWER CONTROL MECHANISM
We design the transmission power control mechanism based on the "Dynamic Safety Shield" concept presented by ETSI in [10], [11].The dynamic safety shield is a virtual dynamic area surrounding the transmitting vehicle, as shown in Fig. 5.The size of the safety area is estimated by the transmitting vehicle in real-time.In order to react to a potential crash, a driver needs to be informed at a sufficient distance from the expected impact to initiate a maneuver [10], [11].From the transmitting vehicle's point of view, this means that it has to guarantee that its beacon messages are received within a certain distance, which we denote as target warning distance.The target warning distance (d w i ) depends on the velocity v i of the transmitting vehicle n i , and the required safety time (t s ).Acceleration (deceleration) is not taken into account to avoid undesired oscillations on the warning distance.The safety time must consider the maximum latency time (e.g., 300 ms [10], [11]), the average driver's reaction time (e.g., 1.5 s [36]), the required action time (e.g., 0.75 s [37]), and a certain time margin.
We adopt the model based on Nakagami-m proposed by Killat et al. in [38] and used in [23], [26], [39] to compute the probability of successful reception of beacon messages in the presence of a single transmitter-receiver pair.This analytical model has been validated based on extensive evaluations via a discrete-event network simulator, achieving a perfect match [38].The model combines the Nakagami-m distribution fast fading model and the Friis/Two-Ray-Ground path loss model.The probability of successful reception (P SR ) is computed depending on the distance (d) between the transmitter and receiver as follows [38], where the crossover distance, d c o = 4π h t h r λ , depends on the wavelength of the signal (λ) and the height of the antennas (h t ), (h r ), and The Friis path loss model is considered for distances equal to or less than d c o .The Two-Ray-Ground path loss model is used for distances greater than d c o .The intended communication range (CR) depends on the configured transmission power.CR is the maximum achievable communication distance when only assuming path loss according to Friis/Two-Ray-Ground and neglecting fast fading effects.Fig. 6 shows P SR for different intended communication ranges and distances between the transmitter and receiver over a crossover distance of 556 m, equivalent to a carrier frequency of 5.89 GHz and antenna heights of 1.5 m.
The transmission power control mechanism computes the optimal vehicle's transmission power (P T i ) to maximize the probability of successful reception P SR at the target warning distance.This control mechanism aims to ensure that the beacons are received at the target warning distance with certain reliability (r t ).If the values of the intended communication range CR that satisfy the condition P SR ≥ r t are grouped into a discrete set S = {CR 1 , CR 2 , ..., CR s }, the valid value of CR in (7) or ( 8) that maximizes P SR at the target warning distance can be computed by solving the following optimization problem, Algorithm 2 describes the steps followed by the transmission power control mechanism to compute the optimal beacon transmission power in real-time depending on the vehicle movement status and the desired safety time.On each beacon transmission, the vehicle n i gets its velocity v i and sets the desired safety time t s .The target warning distance d w i is computed according to basic kinematic equations (see Line 1).A minimum warning distance (d w o ) is guaranteed in Lines 2-3.This is especially useful in low dynamic situations.The P SR optimization function and the propagation model (used to compute the transmission power) are defined in Lines 4-9.We use the Newton-Raphson method to compute the intended communication range CR that maximizes P SR at the target warning distance under the restriction P SR ≥ r t (see .Note that the first value of CR that satisfies the restriction is selected.Finally, the transmission power P T i is computed by evaluating the valid value CR 1 in the chosen model (see Line 15).window to ensure a high probability of medium access.The initial contention window size is limited by the minimum contention window.For broadcast communication, there is no error-handling (e.g., no acknowledgments) and hence no exponential backoff growth [25].As the contention window size is not increased, the size of the minimum contention window always defines the upper limit for the backoff counter.This limits the prioritization and increases the probability of packet collisions.
To compute the probability of packet collisions, we utilize the analytical model proposed by Bianchi in [40].Bianchi's work is regarded as a standard in this research field.His model allows analyzing the performance of broadcast communications in vehicular networks based on IEEE 802.11p [25], [41], [42].Applying Bianchi's model to vehicular communications where no exponential backoff is considered, the probability of packet collisions (p) can be computed as follows, where N is the number of contending vehicles, and τ is the probability of a vehicle transmitting in a randomly chosen slot within the contention window size (CW ) with no exponential backoff, Fig. 7 shows the probability of packet collisions for integer values 1 of CW in the range from 3 to 1023 [4].Note that the probability of packet collisions p is significantly high for small values of minimum contention windows, even if there is a low number of contending vehicles.Since interference cannot be completely eliminated in the IEEE 802.11pDCF procedure, the proposed control mechanism focuses on achieving the lowest possible value of the probability of packet collisions.
We design the contention window control mechanism to perform a linear distribution of the size of CW according to N .Let CW max be the maximum value of CW and N max be the maximum value of N .We denote as p * the probability of packet collisions resulting from the evaluation of N max and CW max in (10) and (11), respectively.We utilize the linear function of the probability of packet collisions p = mCW that satisfies the condition p(CW max ) = p * , so the slope is m = p * CW max .The solution CW > 0 for each N > 1 that satisfies the condition p(CW , N ) = p(CW ) (intersection point) can be computed by finding the zero of the following function, The value of CW that minimizes P can be computed by solving the optimization problem, min We design the control mechanism to provide the lowest value of p by using Bianchi's model when CW = CW max and N = N max .For example, if CW max = 1023 and N max = 500, the lowest value of p according to Bianchi's model is p(1023, 500) = p * = 0.62 (see Fig. 7).However, p(1023) = p * = 0.62 is the maximum value of probability of packet collisions according to p.As we are interested in the intersection point between both functions, the optimal FIGURE 8. Numerical solutions of the minimum contention window computed by using (12) for CW max = 1023 and N max = 500.
value of the minimum contention window CW provides the lower probability of packet collisions in the interval (0, p * ], for each N in the interval 1 < N ≤ N max following a linear distribution.Fig. 8 shows the numerical solutions of CW computed by using (12) for different numbers of contending vehicles.
The proposed mechanism focuses on the collision domain of the transmitting vehicle in saturation condition, as specified by Bianchi's model assumptions [40].The saturation condition assumption means that the control mechanism is able to operate in the worst-case scenario.This is a key design assumption since communication reliability is critical in safety communications.We reduce the number of contending vehicles N to the number of neighbors of the transmitting vehicle.This is a valid assumption since Bianchi's model [40] only focuses on the collision domain of the transmitter, neglecting the impact of the hidden terminals.Further, computing the number of contending vehicles in ad-hoc scenarios is a challenge because it involves the vehicles within the carrier-sensing-range.
To fulfill the steady-state principle of Bianchi's model [40], vehicles compute the optimal size of CW based on the maximum LDM database size ( N ) reported on their neighborhood.Vehicles attach to the beacon the maximum value between its LDM database size and the maximum size announced by their neighbors, as shown in Fig. 9. Initially, vehicles n 1 and n 2 announce that their LDM databases are empty.At step 3, the vehicle n 3 announces a maximum LDM database size equal to 2. At step 5, the maximum size reported by the vehicles converges to the same value.The dissemination process allows vehicles to see the system in a steady-state.
Algorithm 3 describes the steps followed by the contention window control mechanism to compute the optimal size of the minimum contention window in real-time.On each beacon transmission, the vehicle n i gets the maximum LDM database size Ni reported on its neighborhood.Lines 1-13 involve the decisions associated with the calculation of CW i depending on Ni .The smallest size of the minimum contention window CW min is set in Lines 1-2.The Newton-Raphson method is

Algorithm 3 Contention Window Control Mechanism
5 Compute p * using ( 10) and ( 11 used to compute the optimal size of the minimum contention window when 1 < Ni ≤ N max (see .Note that the optimal size of CW i is computed with an accuracy (σ ) of one slot (see Lines 7 and 9).Finally, the largest value of the minimum contention window CW max is set in Lines 12-13.

D. POSACC ALGORITHM
POSACC controls the beacon transmission parameters based on the vehicle dynamics and surrounding situation.POSACC integrates the control mechanisms described above to provide the position accuracy and communication reliability required by cooperative safety applications.It also focuses on maintaining the vehicle's warning distance, channel load, and endto-end latency into the operative range of cooperative safety applications.
POSACC takes advantage from the relationship between average velocity and traffic density [34] to reduce the conflict between the design goals.The interference is decreased  without affecting the position accuracy and warning distance.In addition, a balance between the end-to-end latency and beacon interval is maintained in order to avoid packet losses due to expiration time reached.
Algorithm 4 describes the steps followed by POSACC on each beacon transmission.First, the beacon rate is computed depending on vehicle movement status to guarantee the desired position accuracy (see Line 1).Then, the optimal vehicle's transmission power is computed to maximize the probability of successful reception at the target warning distance (see Line 2).Finally, the optimal size of the minimum contention window is computed depending on the maximum LDM database size reported in the neighborhood of the transmitting vehicle to minimize the probability of packet collisions (see Line 3).

IV. SIMULATION SETUP
This section presents the simulation setup in detail.The basic settings of the evaluation scenario, as well as communication parameters, are introduced in Section IV-A.The configurations of ETSI DMG, LIMERIC, DC-BTR&P and POSACC are given in Section IV-B.

A. SCENARIOS AND BASIC CONFIGURATION
We conduct our simulations using the Veins framework [43] with the IEEE 802.11pMAC/PHY model introduced by Eckhoff and Sommer in [44].We assume a dedicated CCH that is solely used by safety applications.Consequently, the beaconing process occurs on the CCH without considering multi-channel operation.The evaluation scenario is a oneway two-lane highway with a total length of 3 km.Vehicles are randomly located on the first kilometer of the highway.To address a wide range of vehicular situations (e.g., from low vehicular density -high average speed to high vehicular density -low average speed), we define eight different traffic setups, as shown in Table 2.
The transmission power is set to 20 dBm [2].We utilize the Two-Ray Interference model [45] with a dielectric constant r = 1.02 to simulate the radio signal propagation.This model has been validated based on an extensive set of road measurements, capturing complex signal effects, especially at short and medium distances [45].The beacons have 378 bytes [15] and are transmitted with a priority corresponding to the voice access category (AC_VO) [4], [13].Each vehicle is 5 m long, 2 m wide, with a maximum acceleration of 2.5 m/s 2 , and deceleration up to 4.5 m/s 2 .We utilize omnidirectional antennas with a height of 1.5 m [38] and a data-rate equal to 6 Mbps [4].In order to validate statistically the results, we conducted a total of 800 simulations with random seeds: 8 traffic setups, 5 beaconing algorithms configurations, and 20 repetitions.The most important simulation parameters are given in Table 3.

B. CONFIGURATION OF THE ALGORITHMS
POSACC is compared with two relevant state-of-the-art beaconing algorithms, such as ETSI DMG [7] and LIMERIC [15].POSACC is also compared with our previous adaptive beaconing algorithm, DC-BTR&P [26].We developed a new simulation model using the Veins framework, which captures the full operation mode of the four adaptive beaconing algorithms.
As specified in [7], ETSI DMG transmits a new CAM if one of the following conditions has been detected: • The difference between current and previous position exceeds 4 m (e.g., pos ≥ 4 m); • The difference between current and previous velocity exceeds 0.5 m/s (e.g., vel ≥ 0.5 m/s); • The difference between current and previous heading exceeds 4 • (e.g., head ≥ 4 • ); CAM trigger rules are checked at a time interval denoted as Status Monitoring and Decision Interval (SMDI).
In LIMERIC [15], each vehicle adapts its beacon transmission rate such that the channel load converges to a specified threshold.The beacon rate of vehicle j at time instant t is computed according to, where rC is the aggregate rate of all vehicles participating in congestion control, rg is the goal for the total rate, and α and β are adaptation parameters that control stability, fairness, and steady-state convergence.
To ensure convergence in very dense scenarios, LIMERIC introduces a novel gain saturation approach.The modified linear rate-control equation based on ( 14) with gain saturation is, where X is a threshold that limits the update offset.We utilize LIMERIC with the gain saturation approach [15] for comparison purposes.The CBR is measured at a fixed time interval of 200 ms, as specified in [14].This time interval is denoted as Channel Monitoring and Decision Interval (CMDI).DC-BTR&P [26] adapts the beacon rate and transmission power of the vehicle j to provide the desired position accuracy.The beacon rate is adjusted according to the beacon rate control mechanism presented in Section III-A.The transmission power is computed as [26], where Pt min is a minimum fixed transmission power, Pt max is the maximum allowed transmission power, L o is the channel load threshold, φ is a weight factor which controls the impact of the beacon rate Rb j on the transmission power, and L j is the channel load on j.
In POSACC, we specify an average position error of 1 m according to cooperative safety-critical applications, such as LCRW [10] and ICRW [11].The critical beacon interval is set to 0.2 s [34], achieving a good trade-off between position tracking and the generated interference.We set a minimum warning distance of 50 m, which is within the minimum safety range used in [19].We define a safety time of 5 s, that is long enough to include a maximum latency of 300 ms [10], [11], an average driver's reaction time of 1.5 s [36], a required action time of 0.75 s [37], and a margin of 2.45 s.To achieve a high probability of successful reception of beacon messages, the target reliability is set to 0.99.According to [4], an interval from 3 to 1023 is used for the contention window.As specified in [46], an optimal contention window must keep a balance between the expired beacons and the collided ones.Since the trade-off between communication reliability and end-to-end latency depends on N max , two different setups are investigated.We set the maximum value of N to 200 and 500 vehicles, which are values into the range of the vehicular density studied in [15].The algorithms settings are shown in Table 4.

V. EVALUATION
POSACC relies on the adaptation of beacon rate, transmission power, and the size of the minimum contention window.Therefore, we first verify the aforementioned three points in Section V-A.Then, we present the performance of POSACC and compare it with ETSI DMG, LIMERIC, and DC-BTR&P in Section V-B.

A. PERFORMANCE OF THE CONTROL MECHANISMS
POSACC controls in real-time the beacon rate, transmission power, and the size of the minimum contention.Therefore, the first step is to evaluate the performance of the iteration processes.We use small scale Matlab simulations based on data-sets to evaluate the complexity of the iteration processes.Fig. 10 shows that the Newton-Raphson based control mechanisms solve the optimization problems with a really low number of iterations.
To better understand how POSACC reacts to vehicular traffic dynamics, we illustrate in Fig. 11 the acceleration and velocity of a generic vehicle in the scenario during 100 s of the simulation time.Since the impact of the acceleration on the beacon interval computed by the beacon rate control mechanism is more significant at lower velocities, we show the mobility pattern of the vehicle in the traffic scenario of 70 veh/km/lane (40 km/h).
Fig. 12a illustrates the adjustment that POSACC imposes in real-time on the beacon interval to achieve an average position error of 1 m.The beacon rate corresponding to the beacon interval required by POSACC is shown in Fig. 12b.In accelerated movement, an increase in velocity demands an increase in the beacon rate computed by POSACC, ensuring that for high-velocity situations the beacon interval is shortened to guarantee the target position accuracy, as shown in the interval from 10 s to 30 s. POSACC not only responds to variations in speed but also to changes of acceleration, as shown in the interval from 3 s to 10 s.In this time interval, the vehicle moves with a velocity of 6.2 m/s (22 km/h) and the beacon interval (beacon rate) oscillates between 0.32 s  (4 beacon/s) and 0.2 s (5 beacon/s).Positive or zero acceleration leads to a beacon interval close to 0.32 s, as predicted by ( 5) and (6) (see Fig. 4).Nevertheless, when the vehicle slows down, POSACC sets a critical beacon interval equal to 0.2 s.Consequently, surrounding vehicles are more likely to detect sudden braking.
For comparison purposes, we also include in Fig. 12 the beacon interval (beacon rate) computed by ETSI DMG and LIMERIC in the same traffic scenario.Note that POSACC and DC-BTR&P utilize the same beacon rate control mechanism.The vehicle dynamics is also taking into account by ETSI DMG.However, the asynchrony between the CAM trigger limit and the SMDI leads to oscillations in the beacon rate.For instance, if the vehicle has a constant speed of 12 m/s going straight ahead, it is expected that ETSI DMG generates exactly 3 beacon/s considering pos ≥ 4 m (see [7]).Accordingly, the requirements of the vehicle dynamics are not fully fulfilled implying a potential risk for road safety.This divergence effect has been reported in [33].On the contrary, POSACC achieves a stable beacon transmission rate once the velocity has increased and the impact of the acceleration is negligible, as shown in the interval from 30 s to 100 s.LIMERIC adjusts the beacon transmission rate based on the measured CBR without taking into account the specific vehicle dynamics.As specified in [30], noisy CBR measurements produce unfairness in rate allocation even with gain saturation.
Both POSACC and DC-BTR&P adapt the communication range and transmission power in real-time depending on vehicle dynamics, as shown in Fig. 13.Initially, the vehicle moves with low dynamics, so POSACC computes an intended communication range of 140 m to guarantee the default minimum warning distance of 50 m with reliability equal to 0.99.As velocity increases, POSACC increases the size of the safety shield by adjusting the warning distance to ensure a safety time of 5 s.For instance, in the traffic scenario of 30 veh/km/lane, the vehicle moves with a maximum velocity of 22.2 m/s (80 km/h) in the interval from  13 s to 70 s, resulting in a warning distance and intended communication range of 111 m and 310 m, respectively.Accordingly, POSACC increases the transmission power up to 15.7 dBm to maximize the probability of successful reception of beacon messages at the computed warning distance.In contrast, DC-BTR&P reduces the communication range and transmission power as the vehicle's velocity increases, as shown in Fig. 13.DC-BTR&P aims to mitigate packet collisions at the cost of decreasing the vehicle's warning distance.This strategy is suitable for urban environments where the vehicles' mobility pattern usually shows a continuous change between acceleration, deceleration, and repose (see [26]).However, on a highway, this issue is critical for road safety because drivers need to be notified at a sufficient distance from the expected impact, as specified in [10], [11].Note that even in the traffic setup of the lowest velocity (80 veh/km/lane), the design of DC-BTR&P leads to a stable transmission power less than 9 dBm.Fig. 14 demonstrates de effectiveness of POSACC to control the size of the minimum contention window in realtime on different traffic situations.Note that the dissemination of the maximum LDM database size ensures global fairness in the calculation of the optimal size of the mini- mum contention window, as well as the steady-state principle (see [40]).In POSACC, the size of the minimum contention window increases as more vehicles are registered in the LDM database, as defined by (12).Vehicles converge to the same optimal size of the minimum contention window.This not only minimizes the probability of packet collisions in the neighborhood of the transmitting vehicle but also decreases the negative impact of the hidden terminals.Fig. 15 shows the average transmission parameters computed by the beaconing algorithms on each traffic scenario.POSACC adapts to vehicular traffic dynamics by using the proposed control mechanisms.Note that the design strategy reduces the conflict between the required goals.The beacon rate and transmission power decrease for higher traffic densities, since the velocity of the vehicles is reduced and more vehicles are involved in interferences.Further, the size of the minimum contention window decreases as the beacon rate increases because the traffic density is reduced and the end-to-end latency becomes more critical.For instance, in the traffic scenario of 10 veh/km/lane (100 km/h), POSACC increases the transmission rate up to 14 beacon/s to limit the average position error to 1 m, but at the same time, it sets the smallest size of the minimum contention window (e.g., 200 and 300) to reduce the latency and minimize the probability of packet collisions.

B. PERFORMANCE OF THE POSACC ALGORITHM
This subsection presents the evaluation results of POSACC compared with ETSI DMG, LIMERIC, and DC-BTR&P in terms of position accuracy, communication reliability, channel load, and end-to-end latency.
Fig. 16 shows the histograms with the relative probability of the average and maximum position error achieved by the beaconing algorithms in the traffic setups of 50 veh/km/lane (60 km/h) and 10 veh/km/lane (100 km/h).As defined by (1), the maximum position error is twice the average position error.We can observe the effectiveness of POSACC to achieve an average position error of 1 m.However, ETSI DMG only achieves half of the position accuracy provided by POSACC.Unlike ETSI DMG and POSACC, LIMERIC cannot guarantee a pre-defined position error.Note that the position error increases as the velocity of the vehicle increases.The reason is that LIMERIC controls the beacon transmission rate according to the channel load, without taking into account the vehicular traffic dynamics.The gain saturation technique limits the transmission rate to 10 beacon/s in low density -high speed scenarios (see Fig. 15).Despite that a beacon rate of 10 beacon/s provides a good position accuracy on a wide range of traffic conditions, this transmission rate is not enough to achieve an average position error of 1 m in vehicular scenarios where the velocity exceeds 80 km/h, as shown in Fig. 16b.Fig. 17a illustrates that the position accuracy achieved by POSACC is better than the ETSI DMG and LIMERIC in each traffic setup.Note that 95 % of the maximum position error population falls below 2 m, which means that most of the vehicles compute an average position error of 1 m.Further, POSACC also achieves lower peaks of the maximum position error on all conditions, as shown in Fig. 17b.Both algorithms ETSI DMG and LIMERIC have limitations when applied to cooperative safety-critical applications.Trigger conditions in ETSI DMG lead to low beacon rates in order to alleviate the channel load and maintain a certain level of awareness.However, packet losses have more impact on position error at lower beacon rates.This means that for each beacon lost in ETSI DMG, the position error increases by 4 m.Accordingly, the peak values of the maximum position error in ETSI DMG increase up to 24 m, as shown in Fig. 17b.In addition, ETSI DMG has the worst performance in the traffic setup of 60 veh/km/lane, achieving a 95 % cut-off error higher than 6 m.This analysis is supported by the packet delivery ratio (PDR) shown in Fig. 18.The vertical lines in Fig. 18 represent the 25th and 75th percentiles.We can observe that the mean PDR achieved by ETSI DMG in the traffic setup of 60 veh/km/lane is below 0.92.
In LIMERIC, the gain saturation technique leads to a high beacon rate in low densities.Therefore, it only sets a beacon rate lower than 10 beacon/s if the traffic density is high, for example, when exceeds 50 veh/km/lane (see Fig. 15).If the beacon transmission rate is high, the impact of packet losses on the position error is lower.However, recurring packet losses eventually will lead to a higher position error, as shown in Fig. 17b.Note that the peaks of the maximum position error in LIMERIC are close to the peaks computed by ETSI DMG.This effect also can be observed in the traffic densities from 50 to 80 veh/km/lane, where the 95 % cut-off error achieved by LIMERIC increases up to 4 m (see Fig. 17a) and the mean PDR does not exceed 0.91 (see Fig. 18).For instance, it is expected that the maximum position error computed by LIMERIC be 1.4 m in the traffic density of 70 veh/km/lane (40 km/h).However, the 95 % cut-off maximum position error is almost three times higher than the expected value due to packet losses.
Fig. 18 shows that POSACC has also the best performance in terms of communication reliability, achieving a mean PDR higher than 0.95 for each traffic setup.The PDR achieved by LIMERIC decreases as traffic density increases.Since vehicles adjust the beacon rate to achieve fairness, it requires a great number of vehicles sharing the channel resources to set a low transmission rate.Fig. 15 shows that even in the more dense setups, the average beacon rate of LIMERIC is higher than 6 beacon/s.Consequently, more vehicles suffer from interference, leading to a higher packet collision rate, as shown in Fig. 19.This is critical in non-homogeneous scenarios where vehicles are moving at different speeds (e.g., a two-way highway in free flow and congested state).The interference generated by the congested section leads to a low position accuracy in the vehicles that move at high speed.ETSI DMG is also affected by vehicular density.We notice that controlling the beacon rate according to vehicle dynamics is not sufficient to guarantee a PDR higher than 0.95 on each traffic setup.
Fig. 20 shows that POSACC is able to regulate the channel load by adapting the beacon rate according to vehicle traffic dynamics.In this figure, the vertical lines also represent the 25th and 75th percentiles.As expected, ETSI DMG and LIMERIC measure the lower and higher CBR, respectively.ETSI DMG achieves a low CBR at the cost of reducing the position accuracy.Instead, LIMERIC maximizes channel utilization at the cost of reducing communication reliability.Whereas for POSACC, the measured CBR does not exceed 35 % of the channel capacity, and it is controlled by the relationship between the average velocity and traffic density (see [34]).Note that the CBR increases, then it remains stable and finally decreases.However, in the more dense traffic setups, the CBR measured by LIMERIC exceeds 50 % of channel capacity.In POSACC, the adaptive control of the minimum contention window provides a high position accuracy without significantly affecting communication reliability, as shown in Fig. 19.Note that POSACC and ETSI DMG compute a similar packet collision rate, but POSACC achieves a position accuracy two times higher.POSACC guarantees the priority metrics at the cost of increasing the end-to-end latency, as shown in Fig. 21.However, the 95 % cut-off end-to-end latency computed in all conditions are far away from the upper limit of 300 ms specified by ETSI for cooperative safety applications (see [10], [11]).In fact, the 95 % cut-off latency does not exceed 11 ms, and it is lower than 8 ms for N max = 500.We notice that both setups of N max achieve similar performance in terms of communication reliability (see Fig. 18); however, the setup of N max = 200 leads to an increase in the latency up to 3 ms.POSACC keeps a balance between the end-to-end latency and beacon interval in order to avoid packet losses due to expiration time reached.Note that an increase in the end-to-end latency also corresponds to an increase in beacon interval (see Fig. 15).Accordingly, POSACC provides the position accuracy and communication reliability required by cooperative safety applications with a 95 % cut-off latency that does not exceed 8 % of the beacon interval.

VI. CONCLUSION
In this paper, we proposed an adaptive beaconing algorithm, called POSACC, for cooperative vehicular safety systems.We designed three different control mechanisms to guarantee specific performance metrics.The performance of POSACC algorithm was evaluated in different traffic setups and compared against three different state-of-the-art beaconing algorithms; ETSI DMG, LIMERIC, and DC-BTR&P.Extensive evaluation results demonstrated that the design strategy was able to reduce the conflict between the required goals.The proposed control mechanisms proved their effectiveness to control the beacon transmission parameters in real-time.POSACC was able to limit the position error and improve communication reliability, while maintaining the warning distance, channel load, and end-to-end latency within the desired limits.POSACC outperformed the benchmark beaconing algorithms by guaranteeing the operational requirements of cooperative safety application in a wider range of traffic situations.POSACC achieved in each traffic setup a 95 % cut-off average position error of 1 m and PDR higher than 0.95, with a 95 % cut-off end-to-end latency that not exceeded 8 % of the beacon interval.
Regarding future work, we intend to study the benefits and limitations of controlling the values of CW max and N max in real-time according to the surrounding traffic situation, as well as using nonlinear functions in the contention window control mechanism.

FIGURE 2 .
FIGURE 2. Relevant time parameters that determine the position accuracy.

FIGURE 3 .
FIGURE 3. Numerical solutions of the beacon interval computed using (3) for b z = 378 bytes and R D = 6 Mbps [15], equivalent to a transmission delay of 500 µs.

FIGURE 5 .
FIGURE 5. Dynamic safety shield for the transmitting vehicle n i depending on its velocity v i and the safety time t s .

FIGURE 6 .
FIGURE 6. Probability of successful reception as a function of distance, using a carrier frequency of 5.89 GHz and antenna heights of 1.5 m.

FIGURE 7 .
FIGURE 7. Probability of packet collisions according to the contention window size for different numbers of contending vehicles.

FIGURE 9 .
FIGURE 9. Representation of the LDM database size dissemination process.

FIGURE 11 .
FIGURE 11.(a) Acceleration and (b) velocity developed by the vehicle during 100 s of simulation time with ρ = 70 veh/km/lane.

FIGURE 12 .
FIGURE 12. (a) Beacon interval and (b) beacon rate computed by the vehicle during 100 s of simulation time with ρ = 70 veh/km/lane.

FIGURE 13 .
FIGURE 13.(a) Communication range and (b) transmission power computed by the vehicle for different traffic situations.

FIGURE 14 .
FIGURE 14. Size of the minimum contention window computed in real-time by the vehicles on different traffic situations with POSACC.

FIGURE 15 .
FIGURE 15.Transmission parameters computed by the beaconing algorithms.

FIGURE 16 .
FIGURE 16.Probability-based histograms of the average and maximum position error achieved by the adaptive beaconing algorithms for (a) ρ = 50 veh/km/lane and (b) ρ = 10 veh/km/lane.

FIGURE 17 .
FIGURE 17.(a) 95 % cut-off and (b) peak values of the maximum position error achieved by the beaconing algorithms.

FIGURE 18 .
FIGURE 18. Packet delivery ratio computed by the beaconing algorithms on each traffic setup.

FIGURE 19 .
FIGURE 19.Packet collisions per second measured in the traffic setup of 60 veh/km/lane.

FIGURE 20 .
FIGURE 20.Channel busy ratio computed by the beaconing algorithms on each traffic setup.

TABLE 1 .
Operational requirements of LCRW and ICRW applications.
Transmission Power Control Mechanism Data: {v i , t s , r t , d w o , d c o } Result: {P T i } begin CR k − P SR (CR k )/P SR (CR k ); 1 d w i ← v i t s ; 2 if (d w i < d w o ) then