Fair and stable joint beacon frequency and power control for connected vehicles
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Abstract
In vehicular communications, periodic onehop broadcast of beacons allows cooperative awareness for vehicles. To avoid congestion in the shared channel used for transmission of beacons, a joint beacon frequency and power control protocol based on game theory is presented in this paper. The existence, uniqueness and stability of the Nash Equilibrium (NE) of the game is proved mathematically. An algorithm is devised to find the equilibrium point in a distributed manner and its stability and convergence has been validated using simulation. The algorithm converges to the NE from any initial frequency and power and it can provide both fairness in power and weighted fairness in frequency. The protocol has per vehicle parameters, hence, every vehicle can control its share of the bandwidth according to its dynamics or safety application requirements while the whole usage of bandwidth is controlled at a desired level.
Keywords
Beacon frequency and power adjustment Channel congestion control Fairness Stability VANETs1 Introduction
In Vehicular Ad hoc Networks (VANETs), vehicles periodically broadcast their kinematic information in Basic Safety Messages (BSMs), also called beacons. The message broadcast enables vehicles cooperative awareness to support the safety applications in VANETs. In dense vehicular environments, uncontrolled broadcast of beacons results in channel congestion and consequently beacon loss, which degrades cooperative awareness and the accuracy of safety applications. The maximum level of awareness is obtained when the channel load is controlled around 0.65 [1]. Therefore controlling channel load around 0.65 was the main purpose for design of many congestion control mechanisms for VANETs [2, 3, 4, 5, 6, 7, 8, 9].
There are other important factors that should be considered in the design of congestion control mechanisms. Fair access to the wireless channel for vehicles creates awareness with respect to surrounding vehicles in a fair manner, which is necessary to make the safety applications of VANETs reliable. Fairness has significant impact on the performance of safety applications of VANETs. If some vehicles are assigned lower power or frequency, nearby vehicles would not be notified of them early enough and this might result in danger. Besides, a beaconing strategy should be able to assign more bandwidth to vehicles that are in more dangerous situations and require to create higher level of awareness; for example, those that have higher speed or are changing lane. The other important requirement of a congestion control mechanism is stability. This guarantees that vehicles can obtain and maintain the required transmission parameters for the application that they are running.
To address the problem of channel congestion, several solutions based on adaption of beacon transmission parameters such as transmission frequency, power and bit rate have been proposed [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. Many of these approaches just adapt one of the beacon transmission parameters, however, it is very likely that approaches that adapt more than one parameter are used in the future VANETs. In this paper, a fair and stable joint BSM frequency and power control algorithm called BFPC based on noncooperative game theory is proposed. The joint beacon power and frequency control mechanism is modeled as a noncooperative game in which the strategy spaces of the players (vehicles) are two dimensional (frequency and power). The existence, uniqueness and stability of the Nash Equilibrium (NE) of the game is proved mathematically. The algorithm converges to a stable beacon frequency and power from any initial point and it can provide both fairness in power and weighted fairness in frequency. The weighted fairness is useful in a congested situation where different vehicles require different beaconing frequencies. The algorithm has per vehicle parameters, therefore, every vehicle can control its share of the bandwidth (its beaconing frequency), while the whole usage of bandwidth is controlled at a desired level. The purpose of this paper is not to suggest any criteria (such as accuracy in tracking error) for adaption of beaconing frequency, however, the proposed algorithm has such capability without high computational burden, just by adapting the algorithm parameters. An advantage of the proposed approach is that it is overhead free, while most of the previous approaches rely on the exchange of extra information in beacons over one or two hops to obtain fairness.

The mechanism of beaconing congestion control has been modeled as a noncooperative game.

The proposed BFPC protocol can provide fairness in beacon power and weighted fairness in frequency.

BFPC has per vehicle parameters that can address individual vehicle beaconing requirements.

The protocol is stable, overhead free and computationally inexpensive.
2 Background and related work
2.1 Noncooperative game
A situation is referred to as a game when several entities are involved in the situation and the outcome of the situation for an entity depends not only on what the entity does but also what the other entities do. The entities are referred to as decisionmakers or players of the game. Game theory is a mathematical study of the interactions between the players who might have conflicting or common interests. Game theory deals with designing interaction models, studying the conditions that some outcome can be achieved and designing strategies to reach desired outcomes [23]. A noncooperative game is a game in which players take their actions without any agreement with other players.
2.2 Related work
In [14] a vehicle computes a target distance within that, beacons should be received. Then, the required power to cover the target distance is found using a lookup table. The beacon frequency is adapted in an allowed range to keep channel load under a maximum allowed level. The protocol lacks details for implementation and the performance of the approach was not evaluated. In [13] vehicles first decrease their beacon frequency until the minimum frequency is reached then reduce their power until collision rate and channel load are lower than some threshold levels. The frequency and power adaptation approach used in [13] results in unfair beaconing transmission frequency and power [8, 9].
ETSI proposed several techniques for DCC which are: (1) transmit frequency control, (2) transmit power control, (3) receiver sensitivity control, (4) transmit data rate control, and (5) transmit access control [25]. ETSI DCC can be implemented by applying one or a combination of several of these techniques. To implement ETSI DCC using the mentioned techniques, ETSI defines a State Machine (SM) that has three states: RELAXED, RESTRICTIVE and ACTIVE [12]. The ACTIVE state can have multiple substates. In each state, vehicles use different transmission or receiver parameters. The transition between the states happens based on measured channel load. Channel load is represented by Channel Busy Ratio (CBR), which is the ratio of the time that the channel is busy to the sampling time. Figure 1 shows the SM with one ACTIVE state in which \(CBR_{max}\) and \(CBR_{min}\) are threshold channel loads for changing states. If channel load passes a threshold and this condition continues for a specific time (1 second or 5 seconds as indicated in Fig. 1) the state changes.
Several studies have revealed that ETSI DCC suffers unfairness and oscillation [26, 27, 28]. In [26] a DCC that used methods (1) to (4) simultaneously was evaluated and it indicated that ETSI DCC is unstable and unfair. In [28] by adapting just transmit frequency control, the instability of the method was demonstrated. In [27] DCC techniques (1), (2) and (4) individually and also where the three techniques are simultaneously active, were evaluated. In all of them, instability in the state of vehicles was observed.
Adapting beaconing frequency based on PTE cannot always create the required awareness. There are situations where, although the PTE of vehicles is low, vehicles require high beaconing frequencies. For example, when vehicles are close to a junction even if they have low speed or are stationary [31]. Moreover, investigation in [30] revealed that considering information such as acceleration and speed instead of PTE to adapt beaconing frequency increases the performance of safety applications. In addition, the power control approach used in the algorithm results in unfairness in beacon transmission power [6].
In [18] beacon adaptation mechanism is relied on three parameters, the local density of vehicles, the CBR and the collision rate that are computed by vehicles. The local density of vehicles is predicted for short horizon of 100 ms. Then, if any of the above parameters is not in a predefined range, the beaconing adaption is triggered. If the parameter is higher than a defined threshold, first the beacon frequency is reduced until the frequency reaches a minimum level then, the transmission power is reduced. If the parameter is lower than a threshold, first the transmission power is increased to reach the highest level then the transmission frequency is increased. In this work, the beaconing requirements of safety applications has not been addressed. In addition, the mechanism creates overhead as vehicles require information on other vehicles outside their onehop neighborhood to be able to predict the local density of vehicles for near future. Vehicles provide this information for their neighbors by including a few excess bytes of information in their beacons.
In [20] a distributed beacon congestion control (DBCC) scheme was proposed so that vehicles with more neighbors and better link quality with its neighbors will have higher beacon frequency. In DBCC, machine learning was used to predict quality of links of vehicles with their neighbors then based on the predicted quality, a parameter called link weight is calculated for every vehicle. A maximization problem of the beacon frequency adaptation under a TDMA broadcast MAC is formulated and a greedy heuristic algorithm is proposed to solve the problem. Fairness and application requirements of beaconing have not been considered in DBCC. In addition, each vehicle broadcasts the information of link weights of itself and its onehop neighbors in its beacons.
MLCC [19] is a centralized congestion control strategy for junction areas in which, RSUs assign the beacon transmission parameters to vehicles. These parameters are data rate, transmission power and contention window size and AIFS of MAC protocol. Using unsupervised Kmean clustering algorithm, RSU classifies the received beacon messages in four clusters. Then the transmission parameters that minimize the communication delay for the centroid of each cluster is selected. RSU sends these parameters to the vehicles at the congested junction.
EPCR [21] is a combined power and frequency distributed congestion control algorithm. It adjusts the transmission power of beacons based on a desired target distance that beacons should reach at and adjusts beaconing frequency in order to control the channel load. To adapt transmission power each vehicle requires to estimate path loss exponent (PLE) of the wireless environment. To estimate PLE, vehicles need to know transmission power of their neighbors. Therefore, every vehicle should include its beacon transmission power in its beacon messages. The estimated PLE is used to compute the required transmission power so that the beacon messages reach to a desired distance which is set by application. For channel load control, beacon frequency is adapted by applying LIMERIC [3].
In [17] a Joint Adaptation of Transmission power and Bit rate (JATB) algorithm was presented. JATB presents a lookup table that vehicles can pick up the transmission power and bit rate based on the estimated number of their onehop neighbors. The lookup table was produced by solving an optimization problem that maximizes packet success rate and minimizes endtoend delay and busy time.
3 Noncooperative beacon frequency and power control (BFPC) game
The noncooperative beacon power and frequency control game is explained in this section. For easy reference, Table 1 lists the notation used in this paper.
Notations
\({\mathcal {N}}\)  The set of players (vehicles) 
N  The number of players 
\(p_i\)  The transmission power of player i 
\(r_i\)  The beacon frequency of player i 
\(x_i\)  Twotuple \(\left( p_i, r_i\right)\), strategy of player i 
\(\mathbf{x }\)  The vector of strategies of all players 
\({\mathbf{x }}_{i}\)  The vector of strategies of all players except player i 
\({\mathcal {X}}_i\)  The strategy set of player i 
\({\mathbf{X }}\)  The strategy space of all players 
\(U_i\)  The utility function of player i 
\(J_i\)  The price function of player i 
\({\mathcal {Q}}_i\)  The payoff function of player i 
\(CBR_{i}\)  Channel busy ratio that player i experiences 
m  Nakagami fading parameter 
\(T_{frame}\)  Required time to transmit a beacon message 
\(\lambda\)  Wavelength 
\(d_{ij}\)  Distance between players i and j 
\(\gamma\)  Path loss exponent 
\(C_{Tt}\)  Carrier sense threshold level 
\(c_i\), \(u_i\) ,\(w_i\)  Positive parameters of price, frequency and power utility 
Eq.(3) indicates the channel load that player i experiences is a weighted sum of beaconing frequencies of all the other players \(\left( \sum _{j=1}^{N}h_{ij} r_j \right)\). The weights \(\left( h_{ij}\right)\) are a function of beacon power of the players \(\left( p_j\right)\) and distance between players \(\left( d_{ij}\right)\).
It is worth noting that \(CBR_{i}\left( {\mathbf{x }}\right)\) is independent of \(p_i\) because \(d_{ii}\) in (4) is zero. Therefore, \(p_i\) has been considered as a coefficient in the price function so that for player i, the price of using network resources increases by increasing beacon power. In addition, it is easily verified that \(h_{ii}=T_{frame}\). Furthermore, the sum over all the nodes of the network in (3) does not mean that all the nodes should be in communication range of each other. For more information on the mathematical model used for \(CBR_{i}\left( {\mathbf{x }}\right)\) the reader is referred to [2].
3.1 Existence of Nash Equilibrium (NE)
3.2 Uniqueness of NE
Uniqueness of equilibrium point is very important for noncooperative games. In such games, players do not communicate their strategies with other players therefore, in case of existence of more than one equilibrium point the game might not converge to the desired point. In this section, it is proved that if the BFPC game has two equilibrium points these points should be the same.
3.3 Stability of NE under gradient dynamics
4 Simulation results
Simulations have been conducted to validate the stability and convergence of BFPC algorithm as well as to indicate its performance in different scenarios. For simulations, OMNeT++ [36] as network simulator and SUMO [37] as mobility generator were used. Simulation parameters are as indicated in Table 2.
4.1 Scenarios with stationary vehicles
Simulation parameters
Parameter  Value 

Carrier frequency  5.89 GHz 
Thermal noise  − 100 dBm 
Carrier sense threshold  − 90 dBm 
MAC protocol  IEEE 802.11p 
Bit rate  6 Mbps 
Beacon size  500 Bytes 
Sampling time  500 ms 
Propagation model  Nakagami \(m = 2.0\) 
\(r_{min}\), \(r_{max}\)  1, 10 Hz 
\(p_{min}\), \(p_{max}\)  1, 100 mW 
With \(u_i=4\) and 396 vehicles (track with 3 lanes), the vehicles contribute to congestion control simply by adapting their frequencies. By increasing the number of vehicles, the vehicles reduce both their power and frequency to control the channel congestion. With \(u_i=4\), the vehicles obtain lower beacon frequency in comparison with when \(u_i=10\). In addition, it is observed that with \(w_i=650\) and \(c_i=3.0\) for a range of \(u_i\) (the results are shown only for \(u_i=4\) and \(u_i=10\)), CBR is controlled in the desirable interval 0.4 to 0.8. This feature is used in the Section 4.2 to assign a higher frequency to the vehicles that need higher beaconing frequency e.g. due to higher speed or the beaconing requirement of a safety application. In all the presented configurations, good fairness in frequency and power is observed and the vehicles that are far enough from the edges of the track almost have the same beaconing frequency and power. In addition, the achieved beaconing frequency and power is stable.
Figure 4 also shows the results of experiment in condition 2 by applying JATB congestion control mechanism. JATB tunes the transmission parameters based on the number of neighboring vehicles. In this experiment, vehicles simply pick up the lowest transmission power in JATB look up table (4 mW) which results in waste of bandwidth because the CBR level is controlled around 0.2 which is far from desired level 0.65. Using very low power level although reduces the channel load, it decreases the awareness of vehicles too.
ETSI DCC states’ parameters [12]
Relaxed  Active  Restrictive  

Beacon frequency  25 Hz  2 Hz  1 Hz 
Transmit power  33 dBm  23 dBm  − 10 dBm 
Bit rate  3 Mbps  6 Mbps  12 Mbps 
Carrier sense threshold  − 95 dBm  − 85 dBm  − 65 dBm 
Figures 5 and 6 show the results of the experiment. States 0, 1 and 2 represent Relaxed, Active and Restrictive respectively. Figure 5 shows the state of vehicles over the track. It is observed that even vehicles very close together are in different states, e.g. in the middle of the track some vehicles are in Active and some are in Restrictive state. Vehicles in state 1 use beacon frequency and power of 2 Hz and 200 mW and vehicles in state 2 use beacon frequency and power of 1 Hz and 0.1 mW. These figures reveals clearly the unfairness in channel usages in ETSI DCC. Figure 6 shows the changes in state of a vehicle at position x = 334 m over the track. The xaxis shows the number of iterations of the DCC mechanism. The state of the vehicle keeps on changing and it does not converge to a state which signifies the instability of ETSI DCC. As ETSI DCC fails to provide a stable beaconing we do not provide its results in the next scenarios.
4.2 Scenarios with moving vehicles
The results of applying JATB is also indicated in 7. The power level is controlled in 4 mW and the CBR is around 0.1 which is far from 0.65. The other problem with JATB is that it assigns to all vehicles the same level of transmission parameters without considering their speed or other safety requirements.
Figure 7 shows that only the vehicles with speeds of 0 m/s and 10 m/s contribute to congestion control by adapting their frequencies and all the vehicles almost use the maximum power. In the next experiment, the number of stationary vehicles is increased to 946 vehicles (six lanes of stationary vehicles). Figure 8 shows the results in this case. By increasing the number of vehicles and consequently increasing the channel load, vehicles with speed of 15 m/s also contribute to congestion control by reducing their frequency. In addition, all the vehicles use lower power than the power they used in the experiment with less number of vehicles. Again, there is fairness in beacon power and weighted fairness in frequency and the CBR is controlled around 0.65.
5 Conclusion
The problem of channel congestion due to beaconing was addressed with joint adaptation of beacon frequency and power. An approach was proposed that is based on noncooperative game theory, in which the strategy spaces of the players are twodimensional. The existence, uniqueness and stability of the NE was proven mathematically, and an algorithm based on the gradient dynamics for solving the game was proposed. The stability and convergence of the algorithm was validated by simulation. Simulation results indicated that the algorithm converges to the NE from any initial point. It was seen that by selecting appropriate values for the parameters of the algorithm, fairness in beacon power and weighted fairness in beacon frequency is achieved, and CBR is controlled at an appropriate level. In addition, unlike other beaconing control algorithms fairness is obtained without control overhead. The fairness in BFPC is achieved based on the fairness of the NE. The algorithm has pervehicle parameters. So every vehicle by adapting them can gain beaconing that can meet its safety application requirements while fairness in beaconing between vehicles with the same requirement (parameter) is maintained.
Notes
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