Resolving the Unfairness of Distributed Rate Control in ... - IEEE Xplore

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Resolving the Unfairness of Distributed Rate Control in the IEEE WAVE Safety Messaging Byungjo Kim, Member, IEEE, Inhye Kang, Member, IEEE, and Hyogon Kim, Member, IEEE

Abstract—In the IEEE Wireless Access in Vehicular Environment (WAVE), the periodic broadcast of the basic safety message (BSM) enables proximity awareness in the vehicle-to-vehicle (V2V) context. To maximize the level of awareness and consequently the driving safety, the BSM transmission at the highest allowed rate is desired in principle. A caveat, however, is controlling the BSM traffic within the given channel capacity because otherwise it can actually lower the delivery probability due to message collisions. To avoid such a congestion situation, a traditional mode of control is regulating the frequency of the BSM transmission based on the channel load. In this paper, we shed light on the pitfalls that lurk in exercising adaptive rate control based on an observed global state such as the channel load. Specifically, we show that straightforward threshold- or hysteresis-based controls can irrevocably render the rate assignments irrelevant to the given vehicle density pattern. As a solution, we show that distributed but coordinated control provably leads to stability and relevance to the given vehicle density pattern. Index Terms—Anomaly, basic safety message (BSM), congestion control, vehicle-to-vehicle (V2V) communication, Wireless Access in Vehicular Environment (WAVE).

I. I NTRODUCTION

I

N the vehicle-to-vehicle (V2V) context in the IEEE Wireless Access in Vehicular Environment (WAVE) [1]–[3], periodic broadcasts of the Basic Safety Message (BSM) [4] enables proximity awareness. The BSM from each vehicle reports its position, speed, heading, acceleration, steering wheel angle, brake status, and vehicle size among others. To maximize the level of awareness and consequently driving safety, the BSM transmission at the highest allowed rate is desired in principle. Although the WAVE standard suite does not stipulate the rate, most safety applications, e.g., as defined in the VSC-A implementation, require 10 Hz [5], [6]. A caveat in periodic BSM transmission, however, is not putting more BSM traffic than the wireless channel can digest. Otherwise, consequent message collisions can actually make the number of successfully delivered BSMs smaller than when the rate is lower. To avoid the congestion situation, the traditionally considered mode of

Manuscript received November 30, 2012; revised May 9, 2013, July 12, 2013, and September 14, 2013; accepted November 6, 2013. Date of publication January 2, 2014; date of current version June 12, 2014. This work was supported by the Mid-Career Researcher Program through the National Research Foundation under Grant 2011-0028892 funded by the Ministry of Education, Science, and Technology of Korea. The review of this paper was coordinated by Dr. J. Pan. B. Kim and H. Kim are with Korea University, Seoul 136-701, Korea (e-mail: [email protected]). I. Kang is with the University of Seoul, Seoul 130-743, Korea. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2013.2290373

control has been reducing the frequency [7]–[10] or the power [11], [12] of the BSM transmission based on the channel load such as channel utilization or the number of BSMs heard in the given monitoring interval. In this paper, we shed light on the pitfalls that lurk in exercising the aforementioned adaptive control based on an observed global state. Specifically, we argue that the rate assignment made in each vehicle through a straightforward congestion control can easily become irrelevant to the given vehicle density, which in turn can adversely affect the proximity awareness and eventually traffic safety. We will show that the pathology stems from positing that neighboring vehicles would see a single consistent picture of the global congestion state so that their individual reactions to the state will be identical and lead to convergence. However, the assumption is only roughly true, and the fine difference in the perceived global state by neighboring vehicles can occasionally trigger opposite adjustments on them. Once such apparently minor events takes place; however, it can start an irrevocable process of polarization even between close neighbors. The reason for the pathological behavior is that the global state is the sum of the rate adjustments made by possibly many vehicles, and the contribution from a single vehicle cannot quickly change it. Moreover, the opposite remediary actions by the neighboring vehicles based on the perceived congestion state can fall in the vicious cycle that amplifies the difference in the rate without changing the global state much. Since controlling the perceived congestion states between neighbors is impractical, we instead propose adding explicit coordination in the distributed control as a solution. We will demonstrate that by piggybacking the rate information on the BSM, neighbors can coordinate their rate adjustments, thus avoiding the anomaly. II. BACKGROUND A. Safety Communication in WAVE The WAVE standard allocates seven 10-MHz channels in a 5.9-GHz band for communication between WAVE devices such as on-board unit (OBU) and road-side unit. The frequency band is often called the dedicated short-range communication (DSRC) band. Unlike in wireless LAN, WAVE communication can use two channels [3]. The central channel among the seven, called the control channel (CCH), is exclusively used by vehicular safety messages (e.g., BSM) and service announcements, and the services provided in the remaining six channels are called service channels. The WAVE standard allows for four different modes of channel usage based on the OBU capacity, but the recent trend is where the OBU is

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KIM et al.: RESOLVING UNFAIRNESS OF DISTRIBUTED RATE CONTROL IN IEEE WAVE SAFETY MESSAGING

equipped with dual radio and always stays on the CCH using one of them (“continuous mode”) [3], whereas the other radio is used for any WAVE service subscriptions.

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TABLE I S IMULATION S ETTING FOR C OMPARISON

B. Related Work on Congestion Control The congestion control problem for BSM traffic has been traditionally tackled from two angles. First, vehicles could cooperatively control their transmission power to affect the number of BSMs audible in their neighborhood. Second, they could explicitly control the BSM frequency. In the first category, Torrent-Moreno et al. [11] control the power to limit the BSM traffic to a maximum beaconing load (MBL) that the DSRC channel can allocate for the BSM traffic. This work discusses a power increment scheme that stops as soon as the MBL is reached. Mittag et al. [12] propose explicitly exchanging power information with neighboring vehicles because the local adaptation proposed by Torrent-Moreno et al. [11] could cause some vehicles to violate the MBL [12]. Yoon and Kim [13] further point out that without such communication, distributed power control based on the observable shared state such as in [11] can lead to extreme distortion and unfairness in terms of power setting [13]. Huang et al. [14] utilize the channel occupancy information from the clear channel assessment (CCA) reports to linearly control the communication range using power control. With the step size of 0.5 dBm, the power control converts the desired communication range into the transmission power. Based on the assumption that nearby vehicles perceive roughly the same channel occupancy, the algorithm expects that vehicles in proximity coordinate their transmission power. In the frequency control category, Xu and Barth [7] decrease the frequency upon channel congestion, observable by transmission attempt failures and low packet reception rates. Khorakhun et al. propose using channel utilization to regulate the BSM frequency [8]. If the channel busy time is below a threshold, the frequency is lowered. Drigo et al. [9] and Baldessari et al. [10] also take similar approaches. Park and Kim [15] estimate the number of neighboring vehicles from the number of BSMs to compute the optimal messaging rate. Power control or rate control, these distributed control approaches commonly assume that the congestion metric they use should compute similarly for neighboring vehicles and that distributed and independent adaptation by the vehicles naturally lead to power or rates fair and relevant to the given vehicle density pattern. In the next section, we show that such assumption is naive and can lead to unwarranted polarization even between neighbors, undermining fairness and proximity awareness that will negatively affect driving safety. III. E VALUATION E XPERIMENTS Here, we experiment with two generic versions of commonly used distributed control, namely, threshold-based and hysteresis-based, and expose their instability. We use the Qualnet 4.5 simulator, which we augmented to model capture effect more precisely. In order not to diffuse the focus, we employ the simplest adaptation mechanism in this paper, which is the additive-increase multiplicative-decrease (AIMD). We

TABLE II A LGORITHM PARAMETERS

consider both static and mobile scenarios, where in the former, the relative positions of vehicles remain largely static, and in the latter, the vehicular topology changes dynamically. The former scenario is meaningful because the static position relation happens in naturally formed platoons or slow-moving traffic due to heavy congestion. For the wireless channel, we explore both fading and nonfading channels. Although the instability problem is best shown with the most stable channel environments, we additionally show that the problem happens under fading as well. The power is set at 19 dBm so that the communication distance is approximately 300 m. The simulation configuration is summarized in Table I. Finally, we limit ourselves to the investigation of rate control, where the instability problem under power control is fundamentally similar and documented by Yoon and Kim [13] and more recently by Nasiriani and Fallah [16]. Table II shows the parameters used in the distributed congestion control algorithms. For the initial BSM rate, vehicles use Rinit = 10 Hz. They pick a random start time for the BSM transmission, which repeats every 100 ms until the rate change takes place. For the channel busy percentage (CBP, denoted by ρ), they perform the congestion metric measurement every T = 1 s to use it for the rate decision for the next interval. In this paper, we use the CBP as sensed by the CCA. Unless otherwise mentioned, we assume that the time instance of the channel load report is not necessarily synchronized among vehicles. For CCA, the energy detection (ED) mode is used, where the channel is marked busy whether or not the ongoing transmission is decodable as long as the energy on the channel is above the ED threshold. For the AIMD algorithms, we use

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the additive constant of 1 and the multiplicative constant of 0.8. Therefore, when the rate increase decision is made, it is incremented by 1 (Hz) per interval T . When the rate decrease is necessary, the current rate is scaled by 0.8. The rate is clamped between Rmin = 1 and Rmax = 25 Hz. For threshold-based control, the threshold θl is set to 0.4. Namely, an upward of 40% of channel activity during the last interval triggers the rate decrease. For hysteresis-based control, two thresholds are used in the generic simulation, i.e., θl = 0.4 and θh = 0.6. They are chosen by the European Telecommunications Standards Institute (ETSI) according to [17], where it is argued that the offered load should be between 40% and 60% for efficient channel usage. As long as the congestion metric stays between these two values, the rate is not changed. However, when the metric is either over θh or below θl , the rate is adjusted. A. Threshold-Based Control Algorithm 1 Threshold-based control 1: R = Rinit 2: for each period T do 3: if ρ < θ then 4: R = min(R + α, Rmax ) 5: else if ρ ≥ θ then 6: R = max(R × β, Rmin ) 7: end if 8: Transmit with rate R 9: end for First, we experiment with the threshold-based control. Here, the vehicles monitor the channel through CCA, and if the ED reports 40% or more activity, they multiplicatively reduce the BSM frequency. However, if the CBP is below the threshold, they additively increase the frequency. To show that the straightforward rate assignment based on a common observed congestion state such as the sensed CBP can fall into a pathology, we perform a simulation according to Algorithm 1. We place 300 vehicles equidistant on a single-lane circular racetrack of 3 km in radius and let them start with Rinit = 10 Hz. The equidistance configuration is to show that the anomaly takes place even for the most regular topology. As will be shown later, other more irregular spacings used between vehicles, such as exponential distribution, lead to qualitatively identical results. The racetrack topology is used to avoid the edge effect. Due to the uniform vehicle density, one would expect that the rate settings converge to comparable levels across all vehicles. However, the experimental result points otherwise. Fig. 1 shows the time evolution of the rate assignment made by vehicles and the resulting CBP according to Algorithm 1 (for clarity, we only show 200 out of the total 300 vehicles). We can see that the rate adaptation deviates from the even vehicle pattern almost as soon as the system starts. Note that such distortion inevitably affects the proximity awareness as some vehicles get to transmit BSM at the lowest frequency of 1 Hz. We later show that the sustainable BSM rate given the vehicle density is approximately 6 Hz under the threshold of

Fig. 1. Anomaly in generic threshold-based rate control. (a) Adjusted rate. (b) CBP.

Fig. 2.

Undesirable feedback cycle between neighboring vehicles A and B.

θl = 0.4. Notice that the CBP is over θl where the vehicles use the lowest rate Rmin , whereas it is much lower where the rate is higher, as schematically shown in Fig. 2. This is an obscure but crucial dynamic that most distributed control proposals gloss

KIM et al.: RESOLVING UNFAIRNESS OF DISTRIBUTED RATE CONTROL IN IEEE WAVE SAFETY MESSAGING

over, which arises from two aspects of distributed control based on a “common” global state. 1) Inevitable microscopic perturbation of the channel utilization around the given target threshold is frequently classified and acted upon differently by neighboring vehicles (see Fig. 2). The microscopic movements can be triggered by many “minor” factors, i.e., randomness [e.g., from medium access control (MAC) contention resolution algorithm] and/or unreliability (e.g., from channel fading) in the WAVE communication, the granularity of control parameters, or the time-varying vehicular topology. 2) Once close vehicles take opposite actions, they may end up repeatedly applying the same measure as the channel utilization does not change much even after the remediary actions. This is first because the channel state is a collective state difficult to change single-handedly and second because opposing rate adjustments made by neighboring vehicles can cancel out each other’s effect on the channel utilization. As a consequence of these aspects, the vehicles can diverge further away from each other. It can eventually lead to the complete polarization of rate assignments by neighboring vehicles while looking at almost identical channel utilization, as shown in Fig. 1. To shed light on this dynamic in more detail, we pick out two relatively close vehicles from the previous simulation and see how their perception of the channel load and their corresponding action change over time. The two vehicles with ID = 20 and 40 in Fig. 1 are approximately 150 m away from each other within mutual communication range. Initially up to t = 5, they agree on the state of the channel (i.e., CBP over θ or below it) although their numeric readings of CBP almost always differ. Occasionally, however, their judgments do disagree because the threshold θ happens to come between their numeric readings. The first such instance comes at t = 6 (see Fig. 3(b), marked by the leftmost arrow) and t = 7. Based on these individual judgments, these two vehicles take opposite actions, e.g., vehicle 20 lowers the rate and vehicle 40 raises it at t = 6 [see Fig. 3(a)]. Another disagreement comes at t = 16, and every time such an incident repeats, their perceived CBP increasingly deviates [see Fig. 3(b)], exactly in the opposite direction of their intended control [see Fig. 3(a)]. This is what we predicted in Fig. 2, i.e., minor differences in the perceived channel utilization pushing neighbor vehicles toward opposite rate extremes while the channel state largely stays around the target threshold. Almost all existing works pay attention to the latter, but they gloss over the unfairness among vehicles, the cause, and its safety implications. B. Hysteresis-Based Control From the experiments in the previous section, one might conclude that the threshold should not be so “fine” that it sets apart neighbors with similar perceptions of the channel utilization. Namely, one might propose enlarging the boundary between the congested and the noncongested regimes. This idea essentially advocates hysteresis. A recent standard from the ETSI indeed employs it in the distributed congestion control for vehicular safety messaging [18]. Here, we perform a simulation

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Fig. 3. How the rate polarization is triggered and amplified. (a) Rate polarization over time. (b) Channel utilization.

experiment to check whether or not hysteresis eliminates the problem discovered in the previous section. To tell the conclusion first, unfortunately, it does not, and we demonstrate it below. 1) Generic Hysteresis-Based Control: A generic algorithm based on the idea of hysteresis is shown in Algorithm 2. Notice that the hysteresis-based control is the same as the thresholdbased control except that two thresholds are used instead of a single threshold. The behavior of the algorithm is the same when the CBP is over θh or below θl . However, when the perceived CBP stays between θh and θl , the rate is left unchanged. Algorithm 2 Hysteresis-based control 1: R = Rinit 2: for each period T do 3: if ρ < θl then 4: R = min(R + α, Rmax ) 5: else if ρ > θh then 6: R = max(R × β, Rmin ) 7: end if 8: Transmit with rate R end for Fig. 4 shows how the rate and the CBP change according to Algorithm 4. We notice that the hysteresis-based control generally appears more stable. However, some vehicles suffer a drastic rate drop, most conspicuously the vehicle with ID = 158, whereas the CBP is not visibly anomalous. To understand how the pathology develops, again we examine the rate and CBP dynamics for two vehicles in and around the collapse, with ID = 157 and 158, respectively. In Fig. 5, it is shown that the two vehicles initially start with the same rate for a couple of seconds. However, the rate on

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Fig. 5. Anomaly in generic hysteresis-based rate control. (a) Adjusted rate. (b) CBP.

Fig. 4. Anomaly in hysteresis-based rate control. (a) Adjusted rate. (b) CBP.

vehicle 158 suddenly dips to very low values, never to recover. Around this incident, we notice that the CBP at vehicle 158 temporarily goes beyond θh . For vehicle 157, on the other hand, the CBP is maintained below θh albeit close to it. Although transiently and to a minor degree, the two vehicles opposite each other cross θh and a few breaches over θh are enough to reduce the rate of vehicle 157 close to 2 Hz. A peculiarity of the hysteresis-based control is that the vehicle cannot begin to grow the rate again, unless its perceived CBP goes below θl . Therefore, once lowered, the rate has to stay low until there is a large disruption in the vehicle topology such as a drop in traffic density. This experiment tells us that putting a buffer zone between congested and noncongested regimes is not the solution to the anomalous rate adaptation behavior among vehicles. Rather, the result reaffirms the analysis of the previous section that minor fluctuations [see the y-axis scale in Fig. 5(b)] and consequent opposing classifications of the channel state are enough to trigger and aggravate the extensive rate adjustment deviations among neighbors. 2) ETSI-Style Rate Control: Recently, ETSI standardized a decentralized congestion control (DCC) algorithm for vehicular

Fig. 6. Rate transition diagram derived from the ETSI DCC access state machine. Required conditions are marked on arcs.

traffic [18]. To control congestion, it employs a state machine with three states, namely, relaxed, active, and restrictive. These states assign different power, messaging rate, channel sensitivity, and PHY transmission modes. Among them, we limit ourselves to the messaging rate control aspect to put it in perspective with other control schemes considered in this paper. Fig. 6 shows the rate control state machine derived from the ETSI DCC. In the ETSI specification, the rate increase decision is made when the given condition on CBP holds for 5 s (= NDL_timeUp). Likewise, the rate decrease is made when the required condition holds for 1 s (= NDL_timeDown) [18]. Fig. 7 shows the simulation results of the state machine, with all parameters set identically with the threshold- and hysteresisbased experiments. In Fig. 7(a), we notice that the unfairness in the rate setting is severe among neighboring vehicles. Still, the CBP, as shown in Fig. 7(b), does not show correspondingly wild deviations although it shows some differences. To understand the dynamics behind the rampant polarization between the rates, we pick and investigate two neighboring vehicles that are pushed to different extremes, i.e., vehicles 46 and 47. Fig. 8(a) shows that these two vehicles indeed take radically different

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Fig. 8. Analysis of ETSI-derived hysteresis. (a) Adjusted rate. (b) CBP.

Fig. 7.

Anomaly in ETSI-derived rate control. (a) Adjusted rate. (b) CBP.

rate adjusting steps. However, Fig. 8(b) hardly exhibits any clue that would lead to such pathology. This is one of the important points that this paper makes. If we only focus on the average packet delivery ratio and average channel load, the pathological rate polarization (which has no justification whatsoever) and its potential issues go unnoticed. The microscopic examination of the CBP [see Fig. 8(b)] explains why the polarization takes place. First, we notice that the channel assessment timing for vehicle 46 is behind that of vehicle 47. (Recollect that the CBP measurement time instances are not synchronized among vehicles.) According to the ETSI DCC, the rate can go up only when the low channel utilization is maintained for at least 5 s. Indeed, the two vehicles observe less than 15% CBP initially for five consecutive observations. This leads to the rate increase to 2 Hz for vehicles 47 and 46 at time t = 4.06 and t = 4.98, respectively. The low CBP condition persists another 5 s for node 47 until when it takes the channel measurement at t = 9.06. Accordingly, vehicle 47 reflects the result to its rate adjustment, raising it to 25 Hz. However, at t = 9.98, when it is vehicle 46’s turn to take the channel assessment, the CBP is no longer below 15% partly

because its neighbor vehicle 47 (and also some others now shown here for clarity) jumped their rates to 25 Hz. Therefore, only by a split-second difference, the CBP readings by the two neighbor vehicles can be on different sides of a threshold and lead to exactly opposing reactions. The same course of action repeats at around t = 16, where the fifth consecutive readings of lower than 15% CBP push the rates of both vehicles by one notch to 25 and 2 Hz, respectively. However, as a consequence of the rate increase by the vehicles, the CBP first jumps to near 40% and eventually hovers just above 25%. Interestingly, this condition holds both vehicles in their current state (see Fig. 6); hence, the neighboring vehicles end up having radically different BSM rates although their readings of CBP are almost identical. From the previous experiment, one might think that the polarization between neighbors stems from the time difference between their CBP observations and that synchronized CBP readings may cure the pathology previously demonstrated. Indeed, synchronization may be relatively easily achieved using the GPS time in the IEEE WAVE. However, our further investigation shows that, at best, it causes another undesirable problem of oscillation, which leads to repeated episodes of high packet loss rates [19] on the condition that all vehicles start at the same time. Under a more realistic assumption that the start times of the vehicles are all different, however, the pathological property resurfaces even if the CBP readings are tightly synchronized. In the next section, we will present a very simple yet robust solution that yields neither rate polarization nor oscillation. C. Anomaly in Real-Life Rate Control Schemes Although we have limited ourselves to generic rate control schemes to avoid diffusing the focus of our concern, the anomalous rate adaptation results in the previous sections can be shown to occur with more complex rate control schemes proposed recently. First, we investigate the PULSAR scheme

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using binary control that suffers from the pathological rate assignment anomaly, it proposes using linear control. Although the original theory requires that vehicles know the number of neighboring vehicles, it instead linearly adapts with respect to the difference between the target aggregated messaging rate and the observed rate on the channel. Again, we use the same parameters from the paper (particularly α = 0.1 and β = 1/150), but for all wireless and topology parameters used in the previous simulations. Fig. 9(b) shows the result. In essence, the problem eventually manifests itself if the vehicles are left interacting with each other for a sufficient period of time, for both these schemes as in generic schemes that we experimented with in the previous section. In the next section, we develop a simple remedy to the rate control schemes whether generic or realistic, which exhibit the pathological unfairness problems. D. Mean-Checked Threshold-Based Control

Fig. 9. Anomalous rate evolution in PULSAR and LIMERIC. (a) PULSAR. (b) LIMERIC.

by Tielert et al. [20]. In this paper, the channel busy ratio is the global metric that determines the rate to be used by individual vehicles. The congestion felt at a vehicle is propagated up to two hops, and it forms the basis of the global channel busy ratio calculation at individual nodes. The local average messaging rate is used as the target rate, toward which the AIMD adaptation is accelerated in the approaching direction and decelerated in the departing direction from it. Using the same parameters from the work (particularly the additive increase and decrease constants of 0.1 Hz and 0.03) but with the topological and wireless channel parameters in previous simulations, we get the result shown in Fig. 9(a). Another difference from the reference is that we start the transmissions from each individual vehicle randomly in the first 10 s of the simulation to model the situation where vehicles merge to an existing platoon. Next, we investigate the rate adaptation scheme called the LIMERIC proposed by Kenney et al. [21]. In this paper, the channel utilization, called the channel busy function (CBF), is used as the global measure of congestion as well. To avoid

The key idea we put forth in this paper is that the congestion control should be not only distributed but also coordinated. Making the IEEE WAVE system behave so is simple. Specifically, in the BSM format [4], the rate information can be carried in Part II as a local content. By doing so, vehicles can inform on their BSM rate through each broadcast BSM so that the neighboring vehicles that receive the BSM can use it to obtain the average BSM rate of the neighborhood. Once the average is obtained, we can use it as an additional check whenever making a rate adjustment decision. We call this mean-checked rate control in this paper. Note that it is orthogonal to the rate control schemes previously discussed, and it can augment them to cure their pathology. Algorithm 3 is a version that augments the threshold-based control, as described in Section III-A. Note that the only difference in the algorithm compared with the original threshold-based control is that the rate assignments in one’s neighborhood N are additionally considered before the rate assignment is made (i.e., lines 4 and 8). The neighborhood is defined by the vehicles in one’s communication range, i.e., N = {v1 , v2 , . . . , vn }. In the next algorithm, we will call this mean-checked threshold-based control simply by the meanchecked control. Algorithm 3 Mean-checked rate control 1: R = Rinit 2: for each period T do 3: if ρ < θ then ¯ ) then 4: if R < R(N 5: R = min(R + α, Rmax ) 6: end if 7: else if ρ ≥ θ then ¯ ) then 8: if R ≥ R(N 9: R = max(R × β, Rmin ) 10: end if 11: end if 12: Transmit with rate R 13: end for

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Fig. 10. Vector field for the mean-checked control for two vehicles as dictated by Algorithm 3.

1) Dynamics: Although looking simple, the addition of two ¯ ) leads to checks against the neighborhood average rate R(N a significant change in the structure of the control. We can visualize this using the vector field in Fig. 10 that reveals the dynamics of the mean-checked control. The vector field is easily obtained by consulting the algorithm at a given rate under a given channel utilization level. For the sake of illustration, let us suppose that N = {v1 , v2 } and the desirable operating ¯ ) = 12.5 Hz. For convenience, point O∗ is reached with R(N let R1 = R(v1 ) and R2 = R(v2 ). Note that O∗ is where the two diagonals meet in the vector field. The diagonal from the top–left to the bottom–right corner represents the sum rate that yields the target channel load, whereas the diagonal that runs from the bottom–left to the top–right corner is the fair rate line satisfying R1 = R2 . Let us call the former “sum rate diagonal” denoted by Δs and the latter “equal rate diagonal” denoted by Δe . We remark that in the threshold- and hysteresisbased schemes previously discussed, there is no constraint that relates the BSM rates of neighbors other than the sum rate should not be very large as to overshoot O∗ . For instance, with R1 + R2 ≤ 25 Hz as the constraint, R1 and R2 can diverge in the opposite directions yet meet the sum rate constraint. Under the circumstances, no definite vector field can be formed. For instance, with N = {v1 , v2 }, one could move almost in any directions as long as the sum rate moves toward Δs . In the mean-checked control, the vector field is clearly de¯ ) < R2 fined. Below the sum rate diagonal Δs , if R1 < R(N (a condition that corresponds to the operating regime marked “C” in Fig. 10), the vector field pushes only R1 to increase. This will continue until the operating point reaches either Δe or Δs . Then, the vector field pushes both R1 and R2 along Δe or Δs , respectively, toward O∗ . Notice that it implies that the mean-checked control exercises an equalizing force on the rates instead of polarizing them. Similar convergence occurs ¯ ) < R2 (see “B” in for regime “D.” Over Δs , if R1 < R(N Fig. 10), R2 is pulled down while R1 holds until the operating point hits either Δe or Δs , along which the rates are pushed down toward O∗ . Since the rate decrease is multiplicative, the rate of convergence is proportional to the current rate of the vehicles over Δs . It is shown in Fig. 10 as larger arrow sizes for the positions farther from the center. On the other hand, the

Fig. 11. Rate movements of neighboring nodes in the threshold-based control and mean-checked control. (a) Mean-checked (threshold-based). (b) Thresholdbased. (c) Hysteresis-based. (d) Hysteresis-based (ETSI-style).

rate is constant under Δs since the rate increase is additive. The rate of convergence can be controlled by setting α and β differently. Actual vector field should be multidimensional, where the number of dimensions is determined by the number of vehicles in the communication range. As a matter of fact, Fig. 11(a) plots the rate adjustments made by randomly selected two neighbor vehicles in the mean-checked control as the multidimensional vector field forces them. The diagonal line plots Δe . The starting point (“start”) is apparently not sustainable, and as we previously discussed, the rates move down along Δe , as we predicted in Fig. 10. Although frequently thrown away from Δe , the operating point stays close to it, supposedly in the neighborhood of O∗ . In contrast, the threshold-based control shown in Fig. 11(b) drifts away from Δe (and obviously from O∗ as it is on Δe ). Fig. 11(b) is another representation of Fig. 3, and we can clearly see the difference in the control dynamics of these two schemes. As for hysteresis-based controls, we observe that they are also easily knocked out from the equilibrium

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respectively. Now, let us consider two consecutive steps at some point in the pathological evolution. From the figure, it is evident that for the (2i)th step (i.e., rate decrease by v2 ) to occur, we need an enabling condition (i−1) ¯ )|t=2i = C · R1 + iα + R2 β θ ≤ ρ = C R(N |N |

⇒

(i−1) θ ¯ )|t=2i = R1 + iα + R2 β ≤ R(N C |N |

(1)

from premises 1 and 2a. Here, the cardinality of the neighbor set |N | = |{v1 , v2 }| = 2. Moreover, from premise 2b, we should also have ¯ )|t=2i ≤ R(v2 ) = R2 β (i−1) . R(N Fig. 12. Pathological rate assignment process in the proposed algorithm.

and show less dynamics due to the suppressing effects of the hysteresis. 2) Proof: Here, we provide a mathematical proof that the mean-checked control prevents anomalous divergence of beaconing rates among neighboring vehicles. As in the previous section, we focus on two neighboring vehicles denoted by v1 and v2 and see if they can fall into an extended diverging process that leads to two extreme rates. Specifically, we will see if the anomaly is allowed to happen under the premises of the mean-checked control. Using the proof by contradiction, we first hypothesize that the rate divergence takes place with the mean-checked control and then show the contradiction results. Suppose that the two neighboring vehicles can fall into an irrevocable process of rate divergence, so that at an arbitrary point in the rate evolution, one can keep increasing while the other can keep decreasing without violating these three premises of the mean-checked control. 1) The CBP ρ is proportional to the average messaging rate ¯ ), where C is of the given neighborhood, i.e., ρ = C R(N the scaling constant. 2) The enabling conditions for rate decrease for a vehicle v are a) θ ≤ ρ; ¯ ) ≤ R(v). b) R(N 3) The enabling conditions for rate increase for a vehicle v are a) θ > ρ; ¯ ) > R(v). b) R(N Without loss of generality, suppose that the system is initially under the threshold (ρ < θ), and let v1 start the rate adaptation first. Seeing ρ < θ, it raises its rate. Since we have interest in the pathological movements around the threshold, we will assume that the initial move causes ρ to exceed θ. Now, v2 will try to lower ρ by decreasing its rate. To have the pathological condition that we observed in the previous experiments, these alternating opposite actions should reiterate. Namely, the rate assignments should proceed, as shown in Fig. 12, where the numbers on the arrows represent the order of the given transition. In the figure, v1 keeps increasing its rate while v2 keeps decreasing, where R1 and R2 are the initial rates of v1 and v2 ,

(2)

Likewise, for the ensuing rate increase by v1 in the (2i + 1)th step, we should have i ¯ )|t=2i+1 = R1 + iα + R2 β < θ R(N 2 C

(3)

from premises 1 and 3a and ¯ )|t=2i+1 R(v1 ) = R1 + iα < R(N

(4)

from premise 3b. Note that the two constant entities C and θ, hence θ/C as well, remain the same over the two consecutive steps. Therefore, combining inequalities (1), (2), (3), and (4) under the constraint, we should have R1 + iα < R2 β (i−1) for any i ≥ 1 in the evolution. However, it is obvious that this inequality cannot hold for an arbitrarily large i as the left-hand side is a monotonically increasing function and the right-hand side is a monotonically decreasing function of i. In particular, it is clearly a contradiction when we start from equal rates, i.e., for R1 = R2 . In conclusion, the system cannot evolve with the pathological alternating condition under the mean-checked control. 3) Performance: Fig. 13 shows the rate assignments made by the mean-checked control algorithm. With only a minor modification to the threshold-based algorithm, it successfully finds the rate equilibrium for neighboring vehicles while maintaining the target channel utilization. Next, we vary the vehicular traffic density along the road to check if the mean-checked algorithm successfully regulates the BSM rate, reflecting the given traffic pattern. We give the varying traffic density at 200 positions on the road track as in Fig. 14, where the density value is defined to be the number of neighboring vehicles in a 100-m radius. Fig. 15(a) and (b) compares the rate adaptation results based on the thresholdbased control and the mean-checked control, respectively. As we notice, the threshold-based control leads to anomalous rate assignments that are largely irrelevant to the given traffic pattern. In contrast, the mean-checked control converges to control that correctly reflects the density. The reason that there is relatively long perturbation at the beginning of the simulation

KIM et al.: RESOLVING UNFAIRNESS OF DISTRIBUTED RATE CONTROL IN IEEE WAVE SAFETY MESSAGING

Fig. 13. Mean-checked (threshold-based) rate control. (a) Adjusted rate. (b) CBP.

Fig. 14. Traffic density.

is that we let the vehicles start randomly within 50 s from the beginning of simulation. One might wonder if groups of vehicles can keep different rates (i.e., not moving in the converging direction) if the CBP is close enough to the target threshold. The answer is no, because even if the CBP is close (or even equal) to the threshold, not all vehicles can keep their current rate. No matter how

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Fig. 15. Adaptation under varying vehicle traffic density. (a) Rate evolution under threshold-based control (in hertz). (b) Rate evolution under meanchecked control (in hertz).

stable the CBP is, it should be either above or below the target threshold. Depending on which side the system is, some vehicles are always picked to adjust their rates. Then, among the picked vehicles, those who are lagging behind the ambient average rate movement actually adjust their rates. In essence, there are always some vehicles that make the adjustments. An undesirable “equilibrium” in which vehicles maintain unfair rates just because the CBP is close to the threshold is not allowed in the proposed algorithm. Last but not the least, we made a few simplifying assumptions to avoid diffusing the focus on the core dynamics of the uncoordinated distributed congestion control of the IEEE WAVE safety messages. We now relax them and investigate if more realistic assumptions significantly change the qualitative conclusion that we draw previously. For instance, we can assume a fading channel, significantly dispersed starting times for vehicles, using a running average of CBP over a longer period of time instead of 1-s interval, different rate adaptation constants, and uneven intervehicle distance distributions among others. In the next section, we experiment with all these cases

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Fig. 17. Rate incoherence between close neighbors under fading. (a) Rate adaptation. (b) CBP (in percentage).

Fig. 18. Vehicles randomly starting to adapt rates within 50 s. (a) Rate adaptation, threshold-based control. (b) Rate adaptation, mean-checked control.

Fig. 16. Rate evolutions with Rayleigh fading. (a) Threshold-based control. (b) Mean-checked control.

and demonstrate that they do not fundamentally change the dynamics we observed previously and that coordinated control is the only remedy to the pathology. It is only natural since the root cause of the pathology we discussed so far comes from none of these factors but from the fact that the inevitable microscopic perturbation of the channel utilization around the given target level is frequently classified differently by neighboring vehicles. IV. OTHER C ONDITIONS So far, we have used simplifying assumptions to avoid diffusing the core dynamics of the uncoordinated distributed congestion control of the IEEE WAVE safety messages. Here, we will relax them and investigate if more realistic assumptions significantly change the qualitative conclusion that we draw previously. a) Channel fading: Here, we let the wireless channel suffer Rayleigh fading. A consequence is that packet error more randomly occurs with a higher rate than in the reference scenario. First, the global rate adaptation proceeds, as shown

in Fig. 16. We can see that unfairness still develops for the threshold-based scheme [see Fig. 16(a)] although the feedback cycle becomes more dynamic due to the channel-induced message losses. In contrast, the mean-checked threshold-based control succeeds in homogenizing the rates among vehicles [see Fig. 16(b)]. To show the microscopic dynamics of the threshold-based case, we pick two neighboring vehicles suffer from rate divergence for no apparent reason in terms of the channel utilization. Again, a microscopic observation in Fig. 17(b) reveals that, around the time of rate divergence (t = 50), there are three occasions where the CBP measurements by the vehicles disagree on the channel state classification (twice between t = 46 and t = 48 and once between t = 48 and t = 50). However, these three incidents are enough to take the vehicles apart by a factor of two or more in their BSM transmission rates. b) Random start time: In the simulations so far, we have let the vehicles start to adapt their rates only a second after the simulation begins. One might wonder if the simulation results may be the artifact of such setting. To show that it is not so, here we let vehicles start randomly within the first 50 s of the simulated time. Fig. 18 shows how two randomly selected neighbor vehicles adjust rates when they start at very different times in the threshold-based control (above) and in the mean-checked

KIM et al.: RESOLVING UNFAIRNESS OF DISTRIBUTED RATE CONTROL IN IEEE WAVE SAFETY MESSAGING

Fig. 19. Adaptation under smoothed CBP estimation using a sliding window of 5 s. (a) Rate adaptation. (b) CBP (in percentage).

Fig. 20. More aggressive control with α = 2 and β = 0.5. (a) Rate adaptation, threshold-based control. (b) Rate adaptation, mean-checked control.

control (below). For the mean-checked control, vehicles with ID = 1 and ID = 200 are back-to-back neighbors since they are on the circular track. In both schemes, the neighbors start with a large time gap, but how they react to the almost identical channel load is drastically different. The vehicles in the meanchecked control still converge to comparable rates that reflect the CBP, whereas in the threshold-based control, they diverge to extremes. c) Sliding window for channel measurements: In the reference scenario, we assumed that the CBP is computed every second. Since it may draw too sensitive a reaction, here we let vehicles use the CBP averaged over the last 5 s although its measurement is done every second. Doing this, we get smoother CBP movements. Fig. 19 shows that the pathology still develops, however, which happens as long as the neighboring vehicles get to disagree on the channel state. d) Different adaptation constants: To investigate if the simulation results so far are the artifacts of the adaptation constants α and β in the AIMD control, here we attempt to change the values. Specifically, here we set α = 2 and β = 0.5, yielding a far more aggressive control. Fig. 20 shows the consequences on the threshold-based control Fig. 20(a) and the mean-checked control Fig. 20(c). We notice that the new control parameters do not change the pathology of the threshold-based control, as shown in Fig. 20(a) beyond t = 70.

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Fig. 21. Exponential intervehicle distance distribution (λ = 10 m). (a) Rate adaptation. (b) CBP (in percentage).

e) Uneven vehicle distribution: Here, we try changing the intervehicle distance to have the exponential distribution, with the average set at 10 m (see Fig. 21). Again, we notice that the pathology exists among neighboring vehicles. At round t = 20 where the pathology develops in a major scale is caused by a small difference in the observed channel utilization. This shows that the pathology is not a by-product of the regular vehicle topology used in the reference scenario. f) Random mobility pattern: Finally, we explore the impact of mobility on the anomaly and the performance of the proposed scheme. We let all vehicles randomly choose a speed in the interval of [11, 22] m/s. Then, we start the vehicles, and let them run at their randomly picked speed on the circular road track so that the vehicular topology constantly changes. After running the system for 50 s in order that the vehicles are completely mixed, we take a snapshot of the rate assignments by letting them report their current beaconing rate at their position. Fig. 22 shows the result. Note in the figure that the horizontal axis is no longer the vehicle ID, but the physical position, as the initial topology has been completely disturbed. The figure in particular shows a section of the circular road, from 1500 to 2000 m, to help the readers compare the assignments of nearby vehicles. We notice that the three compared schemes show highly variable assignments, whereas the mean-checked control succeeds in focusing them on a relatively narrow band of rates. Even with the dynamic topology evolution, the addition of simple mean-checking conditions leads to much more stable behavior in the distributed rate control. V. C ONCLUSION Most congestion control proposals in the IEEE WAVE context aim at regulating the BSM transmission rate in order to not exceed a certain channel utilization threshold. What these proposals have failed to grasp, however, is that individual rate settings of even closely neighboring vehicles can dramatically diverge while their perceived channel utilization is apparently identical to a first degree. Such pathology has a negative implication on the levels of awareness they will offer to ambient vehicles, raising a safety issue. In this paper, we first have uncovered the root cause of the pathology that the inevitable microscopic perturbation of

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actions, they can repeatedly apply the same measure as the channel utilization frequently does not change much first due to it being a collective state and second due to opposing rate adjustments made by the vehicles canceling each other out. As a consequence, the vehicles can diverge further away from each other. This eventually leads to the partial or even the complete polarization of rate assignments by neighboring vehicles while having almost identical channel utilization. We have proposed a remedy to the pathology, which is composed of two steps. First, each vehicle explicitly professes its current rate assignment in the BSM in the optional Part II. Second, using the averaged rate as a safeguard, they only change their rates if it does not violate the safeguard. This simple coordinative ingredient yields a provably stable control so that vehicles in the same neighborhood converge their rates. We have demonstrated the pathology and the effect of the proposed solution through extensive simulation. R EFERENCES

Fig. 22. Rate assignments under dynamically changing topology due to random vehicle speeds. (a) Threshold-based control. (b) Hysteresis-based control. (c) ETSI-style control. (d) Mean-checked threshold-based control.

the channel utilization around the given target is frequently classified differently by neighboring vehicles. The microscopic movements can be caused by the randomness (e.g., from MAC contention resolution algorithm) and/or unreliability (e.g., from channel fading) in the WAVE communication, granularity of rate adaptation parameters, or by the time-varying vehicular topology. The problem is that once close vehicles take opposite

[1] IEEE 802.11 WG, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Amendment 6: Wireless Access in Vehicular Environments, IEEE Std 802.11p-2010, 2010. [2] IEEE 1609 WG, IEEE Standard for Wireless Access in Vehicular Environments (WAVE)—Networking Services, IEEE Std 1609.3-2010, 2010. [3] IEEE 1609 WG, IEEE Standard for Wireless Access in Vehicular Environments (WAVE)—Multi-Channel Operation, IEEE Std 1609.4-2010, 2010. [4] SAE International, Dedicated Short Range Communications (DSRC) Message Set Dictionary, SAE J2735, Nov. 2009. [5] CAMP vehicle safety communications consortium, vehicle safety communications project task 3 final report: Identify intelligent vehicle safety applications enabled by DSRC, National Highway Traffic Safety Administration, U.S. Dept. Transp., Washington, DC, USA, Tech. Rep. DOT HS 809 859, Mar. 2005. [Online]. Available: http://www.its.dot.gov/ research_docs/pdf/59vehicle-safety.pdf [6] “Vehicle safety communications—Applications (VSC-A) final report,” National Highway Traffic Safety Administration, U.S. Dept. Transp., Washington, DC, USA, Tech. Rep. DOT HS 811 492A, Sep. 2011. [7] H. Xu and M. Barth, “A transmission interval and power level modulation methodology for optimizing inter-vehicle communications,” in Proc. ACM VANET, 2004, pp. 97–98. [8] C. Khorakhun, H. Busche, and H. Rholing, “Congestion control for VANETs based on power or rate adaptation,” in Proc. WIT, 2008, pp. 33–43. [9] M. Drigo, W. Zhang, R. Baldessari, L. Le, A. Festag, and M. Zorzi, “Distributed rate control algorithm for VANETs (DRCV),” in Proc. ACM VANET, 2010, pp. 119–120. [10] R. Baldessari, D. Scanferla, L. Le, W. Zhang, and A. Festag, “Joining forces for VANETs: A combined transmit power and rate control algorithm,” in Proc. Int. WIT, 2010, pp. 1–5. [11] T. Torrent-Moreno, P. Santi, and H. Hartenstein, “Fair Sharing of Bandwidth in VANETs,” in Proc. ACM VANET, 2005, pp. 49–58. [12] J. Mittag, F. Schmidt-Eisenlohr, M. Killat, J. Harri, and H. Hartenstein, “Analysis and design of effective and low-overhead transmission power control for VANETs,” in Proc. ACM VANET, 2008, pp. 39–48. [13] Y. Yoon and H. Kim, “Resolving distributed power control anomaly in IEEE 802.11p WAVE,” IEICE Trans. Commun., vol. 94-B, no. 1, pp. 290–292, Jan. 2011. [14] C. L. Huang, Y. P. Fallah, R. Sengupta, and H. Krishnan, “Adaptive intervehicle communication control for cooperative safety systems,” IEEE Netw. Mag., vol. 24, no. 1, pp. 6–13, Jan./Feb. 2010. [15] Y. Park and H. Kim, “Application-level frequency control of periodic safety messages in the IEEE WAVE,” IEEE Trans. Veh. Technol., vol. 61, no. 4, pp. 1854–1862, May 2012. [16] N. Nasiriani and Y. P. Fallah, “Performance and fairness analysis of range control algorithms in cooperative vehicle safety networks at intersections,” in Proc. IEEE LNC, 2012, pp. 848–855. [17] C2C-CC White Paper on Network Design Limits, C2008 2008. [18] ETSI, Intelligent Transport Systems (ITS); Decentralized Congestion Control Mechanisms for Intelligent Transport Systems Operating in the 5 GHz Range; Access Layer Part, ETSI TS 102 687, Jul. 2011.

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[Online]. Available: http://www.etsi.org/deliver/etsi_ts/102600_102699/ 102687/01.01.01_60/ts_102687v010101p.pdf [19] B. Kim and H. Kim, Avoiding the pitfalls of distributed congestion control in the IEEE WAVE safety messaging, Korea University, Seoul, Korea, Tech. Rep. [Online]. Available: http://widen.korea.ac.kr/wiki/ images/8/88/Anomaly-techreport.pdf [20] T. Tielert, D. Jiang, Q. Chen, L. Delgrossi, and H. Hartenstein, “Design methodology and evaluation of rate adaptation based congestion control for vehicle safety communications,” in Proc. IEEE VNC, 2011, pp. 116–123. [21] J. B. Kenney, G. Bansal, and C. E. Rohrs, “LIMERIC: A linear message rate control algorithm for vehicular DSRC systems,” in Proc. ACM VANET, 2011, pp. 21–30.

Byungjo Kim (M’13) received the B.E. degree from Hongik University, Seoul, Korea, in 2011 and the M.E. degree from Korea University, Seoul, in 2013, where he is currently working toward the Ph.D. degree. His research interests include network virtualization, multimedia networking, vehicular networking, software radio, cognitive radio, and mobile computing.

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Inhye Kang (M’08) received the Ph.D. degree from the University of Pennsylvania, Philadelphia, PA, USA, in 1997. Prior to joining the University of Seoul, Seoul, Korea, in 2002, she was a Senior Researcher with Samsung SECUI. She is currently a Professor with the University of Seoul. Her research interests include formal methods, software engineering, and security.

Hyogon Kim (M’12) received the B.E. and M.E. degrees from Seoul National University, Seoul, Korea, in 1987 and 1989, respectively, and the Ph.D. degree from the University of Pennsylvania, Philadelphia, PA, USA, in 1995. He is currently a Professor with Korea University, Seoul. Prior to joining Korea University, he was a Research Scientist with Bell Communications Laboratory (Bellcore). His research interests include Internet protocols and applications, vehicular networking, software radio, and network security.