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Vehicle-to-Everything (V2X) communications have been garnering massive interest across the academic and commercial bodies thanks to their potential to significantly promote the traffic safety [1].As such, the technologies take a central role in constitution of safety-critical applications in intelligent transportation system (ITS) and connected vehicle networks.Today, two major radio access technologies (RATs) enabling V2X communications have been attracting particular research interest: namely, Dedicated Short-Range Communications (DSRC) and cellular V2X (C-V2X).In 1999, the United States Federal Communications Commission (US FCC) allocated DSRC to the 5.9 GHz band (viz., 5.850-5.925GHz).Recently, however, C-V2X has been proposed to operate in the same band along with cellular operators' licensed bands [2].
Of the two RATs, DSRC has longer been deployed in many communities for as the key enabler technology for safety-critical applications owing to several merits.
The associate editor coordinating the review of this manuscript and approving it for publication was Oussama Habachi .
First, DSRC is a mature technology that has already been tested and deployed by a wide variety of stakeholders including car manufacturers and state governments in various aspects including not only technology but practical domains such as policy and deployment preparations [3].Second, DSRC does not require any paid subscription, which makes possible wider deployment at a lower cost [3].Third, the universal compatibility among IEEE 802.11 technologies leads to the spectrum versatility and easy operation [4], which could strengthen DSRC in the market of connected vehicles.
Based on these advantages, as of November 2018, more than 5,315 roadside units (RSUs) operating in DSRC were deployed in the United States (US) alone [5].In December 2016, the US National Highway Traffic Safety Administration (NHTSA) proposed to mandate DSRC for all new light vehicles [6].However, despite the advantages and widespread deployment, the technology has encountered an unprecedented obstacle: the 5.9 GHz band reallocation by the US FCC [7].
Therefore, according to this plan, DSRC is only allowed to use 10 MHz of spectrum (i.e., 5.895-5.905GHz) at maximum.It has never been studied nor tested if 10 MHz would suffice for operation of the existing DSRC-based transportation safety infrastructure.Many states in the US have already invested large amounts of fortune in the deployment of connected vehicle infrastructure based on DSRC [8].As such, it has become urgent to understand how much impact of the FCC's 5.9 GHz band reallocation will be placed on the performance of such connected vehicle infrastructure.
Another significant issue for DSRC is that it may need to experience coexistence with C-V2X users according to the FCC's proposition [7].The key technical challenge here is that the C-V2X standards adopt significantly different protocols, which makes the technology incompatible with DSRC-based operations.In fact, based on the author's recent investigation [9], DSRC may be severely interfered by C-V2X if the two disparate technologies coexist in a co-channel basis.Therefore, it has become crucial to lighten the load of a DSRC network while keeping the dissemination of packets operable, in order to suit the technology into such a competitive spectrum environment.

B. CONTRIBUTIONS
As shall be detailed in Section II, the current literature shows a key limitation to achieve the load lightening of a DSRC network: despite being a predominant factor determining the performance of a V2X network, the length of backoff time was allocated to each vehicle without considering ''semantic'' contexts that the vehicle is experiencing.
We would regard it more efficient from the system's point of view if vehicles being closer to a danger take higher chances to transmit.The rationale is that these vehicles in the closest proximity of a danger-causing object are the key nodes in the network for expedited propagation of basic safety messages (BSMs).That is, the other vehicles in the network will be able to receive the BSMs only after those being close to the danger source have successfully transmitted the BSMs.
To this line, this paper proposes a V2X networking scheme where a vehicle takes a transmission opportunity according to the distance to a danger source.Moreover, we clearly distinguish our contributions from the most relevant work [11].While the prior work focused on the stochastic geometry of a particular coexistence scenario between military and civilian vehicles in an urban area, this present paper significantly extends the scope of discussion to (i) a general two-dimensional geometry and (ii) detailed analysis on networking behaviors-viz., an exact backoff allocation method.
Overall, the technical contributions of this paper distinguished from the literature can be summarized as follows: 1) It proposes a method prioritizing a BSM according to the level of danger to which each vehicle is exposed.2) In order to measure the danger, it uses the ''distance to a danger source,'' which is a quantity that is easy to obtain by using the existing techniques and apparatus.3) Based on (i) key metrics-namely, latency, packet delivery rate (PDR), and IRT-and (ii) a generalized two-dimensional spatial model (not limited to certain road models), it provides a stochastic analysis framework characterizing a DSRC network's broadcast of BSMs.

II. RELATED WORK A. PERFORMANCE ANALYSIS SCHEMES 1) MATHEMATICAL ANALYSIS FRAMEWORK
Analysis frameworks based on stochastic geometry for DSRC have been provided recently [9]- [12].They commonly rely on the fact that uniform distributions of nodes on X and Y axes of a Cartesian-coordinate two-dimensional space yield a Poisson point process (PPP) on the number of nodes in the space [13].This paper distinguishes itself from the prior proposals in the sense that it applies the stochastic geometry framework for analysis of the temporal aspect of DSRC multiple access mechanisms.

2) PERFORMANCE EVALUATION METHOD
A recent proposal combines a packet-level simulation model with data collected from an actual vehicular network [14].It is critical to discuss the potential impacts of internal and external bandwidth contentions, which form a critical discussion point after the US FCC's recent 5.9 GHz band reallocation [7].The ''internal'' contention means the contention among DSRC vehicles themselves, while the ''external'' contention refers to the contention incurred by other RAT(s).
The limitation of the prior art lies in that the performance evaluation was performed without consideration of these bandwidth contentions, which might undermine its own generality.For instance, it is assumed that (i) safety messages and (ii) packets for non-safety applications are sent over separate DSRC channels [14], whereby no interference is generated between safety and Internet traffic.This assumption has become obsolete according to the US FCC's recent proposition where DSRC may not be able to utilize multiple channels any more [7].

3) CONGESTION IN DSRC NETWORKS
It has been found that a DSRC network is constrained by packet expirations (EXPs) and collisions over the air [36].An EXP refers to a packet ''drop'' as a result of not being able to (i) make it through the backoff process and hence (ii) be transmitted within a beaconing period.Since the IEEE 802.11p broadcast of BSMs does not support retry nor acknowledgement (ACK), an expired packet is dropped and the next packet with a new sequence number is generated [31]- [33].The reason of a packet not being able to go through a backoff process is finding the medium busy, which hinders the backoff counter from being decremented.
Meanwhile, a collision is composed of two types of cause: a synchronized transmission (SYNC) or a hidden node (HN).
The performance of a DSRC broadcast system in a high-density vehicle environment has been studied [16], yet the assumption was too ideal to be realistic, which means that the number of vehicles within a vehicle's communication range was kept constant.Another study proposed a DSRC-based traffic light control system [17], but it limited the applicability to the traffic lights only.

4) SAFETY-RELATED APPLICATION
Furthermore, we concentrate on DSRC's networking to support the safety-critical applications.In the related literature, a DSRC-based end of queue collision warning system has been proposed [18].However, it discusses a one-dimensional freeway model, which needs significant improvement for application to an intersection with two or more ways.

5) EXTERNAL BANDWIDTH CONTENTION
Lastly, the objective of our proposed protocol is to lighten the traffic load of a DSRC network to better suit in an environment of coexisting with a disparate technology (viz., C-V2X) according to the 5.9 GHz reallocation [7].The performance degradation of DSRC under interference from Wi-Fi has been studied [19]; however, it lacks consideration of coexistence with C-V2X.

B. PERFORMANCE IMPROVEMENT SCHEMES
Various modifications on the binary exponential backoff (BEB) algorithm have been proposed as a means to improve throughput and fairness in general carrier-sense multiple access (CSMA) in IEEE 802.11-related technologies.Specifically, adjustment of the contention window (CW) was often suggested to improve the performance of a vehicular communications network such as a recent work [20].More directly relevant to our work, a distance-based routing protocol has been found to perform better in vehicular ad-hoc networks (VANETs) [21].Also, in a general ad-hoc network, reduction of the length of a header can be a solution that is worth considering [22]; however, due to a centralized network structure, it shows a limit to be applied to a V2X network.A ''subjective'' user-end experience optimization is also worth consideration [23], wherein a one-bit user satisfaction indicator was introduced, which served as the objective function in a non-convex optimization.
Another method is the enhanced distributed channel access (EDCA), which divides the data to four queues according to priority: viz., voice, video, best effort and background.Using the default parameter values for EDCA protocol will lead to increasing the collisions in the wireless network and decreasing the capacity [15].More importantly, such application-specific differentiation of backoff counters cannot be directly applied to the situation that we are targeting to address.That is, we are trying to differentiate the backoff length according to the danger level of each vehicle, instead of the type of application.This makes a compelling case that urgent BSMs for safety-critical use cases need a more dedicated type of networking protocol than the existing EDCA.In this context, this paper proposes a protocol that guarantees to prioritize a BSM with a high urgency.

III. SYSTEM MODEL
This section describes the system model that this paper adopts for analysis.Note that Table 1 lists key abbreviations that are frequently used throughout this paper.Also, mathematical notations are summarized in Table 2.

A. GEOMETRY
A two-dimensional space R 2 is defined as a 2 km-by-2 km square, as illustrated in Figure 1.Once a vehicle reaches the end of the space, it bounces back into the space.This assumption is to maintain a fixed vehicle density and, hence, a same level of competition for the medium at any given time.
The distribution of the nodes follows a homogeneous PPP in R 2 .We define a general situation where a safety-critical application disseminates BSMs over a V2X network [24].That is, a source of ''danger'' exists (expressed as a large black square in Figure 1), which should be avoided by all the other vehicles.The danger source is located at the origin, i.e., the center of R 2 .It is noteworthy that the danger source is not expected to generate BSMs to inform the surrounding vehicles; rather, the vehicles approaching this danger source autonomously detects it.This assumption is practical based on the fact that a vehicle is likely equipped with various technologies (such as radar, lidar, etc.) enabling the vehicle to detect presence of a hazard.This way, any type of danger source can be detected even including those not being capable of transmitting BSMs, e.g., a construction site, wrecked vehicle, etc.
As shall be detailed in Section IV, our proposed algorithm prioritizes transmission of a BSM as a vehicle is closer to this danger source.This necessitates to measure the distance from the danger, which is denoted by d →dgr .Figure 1 demonstrates an example ''drop'' of vehicles with the density of λ = 20 km −2 , which is equivalent to 80 nodes over the defined space R 2 .The crash risk is quantified in categories (CATs) according to d →dgr as follows: CAT 1 (''Most dangerous'') : 0 ≤ d →dgr ≤ Th 1 CAT 2 (''Less dangerous'') : Th 1 < d →dgr ≤ Th 2 CAT 3 (''Far less dangerous'') : Th 2 < d →dgr ≤ Th 3 (1) In Figure 1, vehicles positioned within CATs 1, 2, and 3 are marked as red, yellow, and green circles, respectively.The vehicles that are sufficiently far and thus do not belong to any of the CATs are drawn as blue circles.As shall be depicted in Section IV, the proposed protocol does not allocate these vehicles not belonging to any of the three CATs.The rationale behind this is that these farthest located vehicles are within communications ranges of those belonging to CAT 3.That is, once vehicles in CAT 3 become able to transmit, the messages can be disseminated to these even further vehicles.
Notice, though, that the categorization into three CATs is only an example as an effort to show how the proposed protocol works.In other words, there could be a larger or smaller number of chunks than three; also, the values for each threshold can be set to any values to yield larger or smaller granularity.It means that, although this paper uses three CATs determined by {Th 1 , Th 2 , Th 3 } = {300, 500, 700} m as an example, the idea proposed in this paper can be extended to other numbers of CATs and other values for thresholds.

B. COMMUNICATIONS
We suppose that all the vehicles distributed in R 2 have the same ranges of carrier sensing and communication.Also, each vehicle broadcasts a BSM every 100 msec, which is denoted by T ibi -i.e., 10 Hz of the broadcast rate.Notice that we assume a BSM to be transmitted within a 50-msec control channel (CCH) according to the multi-channel operation defined by IEEE 1609.4 [25].
We remind that DSRC adopts distributed coordination function (DCF) as the basic access mechanism [26].This paper assumes that the DCF operates in a saturated-throughput scenario [27].The purpose of this assumption is to analyze a worst-case scenario (i.e., the heaviest possible network load), which can provide a conservative guideline for the performance evaluation of the proposed scheme in a DSRC network.
It is significant to note that the above-mentioned categorization into CATs 1-3 is mapped to categorization of backoff values, which is the central idea of the mechanism that is proposed in this paper.See Figure 2 for details of the mapping.We reiterate that the three-way categorization is only an example, while the idea can be extended to any other number of categories in terms of d →dgr (and hence CW as well).
Lastly, in accordance with the FCC's 5.9 GHz reallocation [7], this paper assumes the bandwidth of 10 MHz based on the operation in CCH as mentioned earlier.

IV. PROPOSED ALGORITHM
We propose a protocol that controls priority of a packet transmission according to d →dgr as a means to improve the performance of safety-critical messaging in DSRC.This section describes details of the proposed protocol.

1) KEY IMPROVEMENT FROM CONVENTIONAL CSMA
It has been noted that for contention resolution, the conventional BEB algorithm relies on the number of unsuccessful transmission attempts and Physical Layer (PHY)-related factors including packet retry limit, maximum and minimum values of CW size, header format, etc. [28].This specifically means that once the PHY-specific values are fixed, the future course of the BEB algorithm would be dictated by the number of unsuccessful attempts taken by a STA to successfully transmit the packet.In fact, the PHY parameters will likely remain constant since the current version of IEEE 802.11p does not support a link adaptation [34], [35].
We got motivated from a simple but critical curiosity: why must it be a uniform probability to choose a backoff time for all Txs competing for the medium?In other words, in the current CSMA scheme, if there are 50 vehicles on the road at a certain time instant and if they try to transmit a packet at the same time, all of them have an equal opportunity to choose for a backoff time randomly from a range of [0, CW-1].That is, a vehicle chooses a backoff time in a random manner regardless of the level of danger that the vehicle marks.For instance, the Tx STA being far away from a danger source (and thus at a lower risk of a crash) can be allocated a shorter backoff time compared to one being exposed to a higher risk.As an effort to make the protocol more efficient, we propose an idea of assigning a backoff time depending on d →dgr , the distance between a STA and the danger source.Specifically, a Tx STA with a smaller d →dgr (i.e., closer to the danger source) will have a shorter backoff time and vice versa.

2) DISTANCE CALCULATION METHOD
One significant discussion regarding the proposed algorithm is the rationale for d →dgr as the metric measuring the risk of a crash.While an accident can be caused by many factors including weather condition, road surface status, mechanical failures, etc., the dominating factor is the inborn reactive time limitation of the drivers [29].This makes it reasonable to consider the distance to a danger source as a key factor of an accident [30].
Furthermore, one understands that at the current level of technologies, it is not a difficult task to obtain a vehicle's exact distance from a danger source.Specifically, (i) each BSM contains information of the position of its transmitter vehicle based on commercially available techniques such as Global Positioning System (GPS); (ii) in this way, each vehicle is able to exchange each other's exact position; (iii) as such, each vehicle is able to calculate the distance from each other.

3) BACKOFF ALLOCATION ACCORDING TO d →dgr
Now, based on the aforementioned rationale, we propose a backoff allocation algorithm according to the distance to a danger.A flowchart for the proposed mechanism is provided in Figure 2. Unlike the traditional BEB scheme, the proposed protocol allocates a smaller backoff to the group of vehicles with a smaller d →dgr .Specifically, according to the threshold distance, Th i , the vehicles in R 2 are grouped in three categories-viz.,CATs 1, 2, and 3. A smaller CAT categorizes a smaller d →dgr , which, in turn, means a more urgent need for transmission.
Here is an elaboration on the relationship between CATs and CW.As presented in Section VI, this paper uses {300, 500, 700} m for {Th 1 , Th 2 , Th 3 }, representing the thresholds defining CATs 1, 2, and, 3, respectively, as have been shown in (1).The proposed protocol divides the entire range of CW into three chunks: for {Th 1 , Th 2 , Th 3 }, the backoff counter ranges of [0, (CW-1)/3], [(CW-1)/3, 2(CW-1)/3], and [2(CW-1)/3, CW-1] are allocated.Via this modification, a Tx STA belonging to CAT 1, which is at a higher crash risk due to a smaller d →dgr , has a higher probability of packet transmission only after a shorter backoff time.In contrast, a STA with a larger d →dgr is designed to hold a bit longer before a transmission.

V. PERFORMANCE ANALYSIS
This section formulates three metrics to measure the performance of the proposed backoff allocation scheme-namely, average latency, PDR, and IRT.
It is worth to notice that all the three quantities are defined with a BSM transmitted at a tagged vehicle.We emphasize that such an assumption keeps generality since the type of network being considered in this paper is distributed, in which every node has an equal characteristic and hence shows a consistent networking behavior.

A. AVERAGE LATENCY
We remind that this paper focuses on safety-critical applications, which makes the latency as one of the most significant metrics in the performance evaluation of a DSRC network.Further, reflecting the ''broadcast'' nature of a DSRC network, this paper defines an average latency among all the STAs across a network.
Let T denote an instantaneous total latency taken for a node to transmit a packet.Considering all possible results of a packet transmission (viz., expiration, success, and collision), an average latency can be computed as VOLUME 8, 2020 where P [•] and T [•] denote the probability and the time length of an event, respectively.Variables in (2) are defined as follows: τ denotes the probability that a tagged vehicle is able to transmit in a certain slot within a beaconing period [9]; P col gives the probability of a collision-viz., a SYNC or a HN [9]; T exp , T col , and T suc denote the time lengths taken for an expiration, a collision (viz., SYNC and/or HN), and a successful delivery, respectfully.Proof of (2): Each term in ( 2) is elaborated as follows: (1 − τ ) E T exp : We remind that τ is the probability of a tagged vehicle being able to (i) make it through a backoff process before expiration and thus (ii) transmit a packet.For calculation of τ , we modified a Markov chain for the DSRC backoff process [27] in order to reflect the impacts of packet expiration, which does not occur in classical IEEE 802.11DCF and hence was not reflected in the existing analysis models for DCF.Due to a long recursiveness in the computation process, it was more efficient to take a numerical approach to obtain τ instead of a closed-form derivation.
As shown in (3) below, E T exp is meant to express the average time length until a packet successfully completes a backoff process.Notice that the number of consecutive idle beaconing periods, N bcn , can be characterized as a geometric random variable [27].An EXP is modeled as a geometric random variable since it can be abstracted as a ''binary'' result about whether the packet was able to complete a backoff process within a beaconing period.Therefore, an average time taken for an expiration can be calculated as where T ibi denotes a beaconing interval (also known as ''inter-broadcast interval'' or IBI), and (1 − τ )τ −1 gives the mean of a geometric random variable with a success probability of τ in each trial.
The second term in (2) gives the length of time that is taken for a successfully delivered packet.We start derivation from computing the length of time taken for a backoff, which is given by where T slot is the length of a slot [27] (i.e., 66.7 µsec [9]).Also, in (4), N bo denotes the number of slots spent to go through a backoff process.This quantity can be displayed as a function of the number of STAs, denoted by N sta .Notice that mathematical details for this quantity is given in Section V.C of [36].We found that N bo does not act as a significant factor in determination of E T bo .Yet, here we report two noteworthy tendencies: (i) the proposed scheme consumes a smaller N bo as compared to the traditional CSMA, thanks to higher possibility of shorter backoffs; and (ii) a larger CW spends a larger N bo due to higher possibility of longer backoffs.
Regarding T suc in (2), the number of slots that are used by a successful delivery of a packet is formulated as T suc = (Time for a BSM) = Hdr + Pld + SIFS + T prop (5) where Hdr and Pld denote the lengths of a header and a payload, respectively.Also, T prop gives the propagation delay, which is assumed to be kept the same to all of the Rx vehicles within the tagged vehicle's communication range.P col T col : Now, upon transmission with the probability of τ , one needs to examine whether a packet survives from a collision.There are two types of packet collision: namely, SYNC and HN.A SYNC occurs when more than one vehicles happen to start a transmission in an exactly same time slot.
The assumption is that although the vehicles are in each other's carrier-sense range, they were unable to sense each other because they coincide to start in the same time slot.A HN occurs among vehicles being unable to sense each other.As such, the probability of a collision is formulated as Mathematical details and proofs for P sync and P hn are found in [36].See Figure 5 in Section VI for demonstration of P col between the proposed scheme (i.e., CAT 1) and the traditional CSMA.As inferred from Figure 1, the key reason that the proposed scheme achieves a lower P col is a dramatically smaller number of competing nodes.Now, T col gives the time length that has been taken while going through a collision.One most important note in DSRC is that there is no feedback from a receiver about a packet transmission.It means that no matter it was a SYNC or a HN or both, a vehicle needs to spend an entire transmission cycle, which is formulated as T col ≈ T suc .

B. PACKET DELIVERY RATE
Another metric that we use to assess the performance of the proposed scheme is PDR, which can be formally written as [36] where P col has been defined in (6).Also, τ has been mentioned after derivation of (2) as well.

C. INTER-RECEPTION TIME
Lastly, we define the IRT as the time taken between two given successful packet reception events.Notice that the unit of a quantity of IRT is ''the number of beaconing periods.''As such, one can multiply a beaconing time (e.g., 100 msec in this paper) when wanting to display an IRT in the unit of time (i.e., seconds).

3.
Values for key parameters.
Now, the that N bcn failures follow a successful delivery is modeled to follow a geometric distribution, which can be formally written as Proof of (8): For formulation of an ''IRT,'' we start from a successful reception, and then measure how many beaconing periods are expended until the next successful reception.That is, the first beaconing period is set to have the probability of PDR, and thereafter the possibility is left open between PDR and 1 − PDR depending on occurrence of a successful delivery or a failure, respectfully.

VI. NUMERICAL RESULTS
In this section, we evaluate the performance of the proposed backoff algorithm compared to the traditional CSMA (i.e., BEB) [26].As summarized in Table 3, each Tx STA is assumed to have a fixed payload length of 40 bytes [24].Also, for our numerical analysis, we set the spatial setting being consistent with what was shown in Figure 1.
One thing to note commonly in Figures 3 through 6 is that, regardless in the proposed or the traditional CSMA, the performance of a DSRC network predominantly depends on a packet's (i) EXP and (ii) collision over the air (viz., SYNC and/or HN).This justifies that we ignore impacts of small-scale link-level fluctuations such as Rayleigh and Nakagami fading.
It is noteworthy that plots representing the proposed scheme in Figures 3 through 6 are ''stepped'' rather than smooth.It is because of rounding the number of STAs to the nearest integer for calculation of binomial coefficients between the number of all STAs and the number of CAT 1 STAs, i.e., ''N all sta choose N cat 1 sta '' in calculation of τ .(Notice that the rounding comes from A (CAT 1) / R 2 where A (•) denotes the area of a space.)As such, all the subsequent quantities-viz., τ , P col and PDR-are also affected by the approximation since they are based on τ .See (3) for the relationship between E T exp .Meanwhile, see Section V.D of [36] for derivations of P col and PDR in terms of τ .
A. AVERAGE LATENCY Figure 3 demonstrates the average length of time taken for successful reception of a packet, E T , versus the number of STAs, N sta , according to the CAT and CW.We remind from ( 2) that E T is composed of three parts: i.e., (i) time taken for an EXP, (ii) that for a successful packet transmission and reception, and (iii) that for a successful packet transmission but a collision.It means that, as N sta grows, all of the three quantities increase, which results in a higher E T .This relationship is shown in (i) both traditional and proposed schemes as Figure 3a presents and (ii) commonly on all CW sizes as Figure 3b depicts.
The key rationale of the proposed protocol's outperformance is higher τ as displayed in Figure 4a.While it entails a negative margin compared to the traditional scheme in terms of P col as shown in Figure 5, the positive margin from τ is larger and, as a consequence, yields the outperformance in E T .
The same rationale is behind the positive coupling between E T and N sta with respect to CW size, which is described in Figure 3b: a smaller CW size favors in terms of E T in spite of disfavor in terms of P col 's.Although slight, each curve in Figures 3a and 3b shows an inflection point that transitions from a downtrend to an uptrend.It is interesting to observe the downtrend since it means E T decreases as N sta increases, which is against one's normal intuition.Soon enough, however, the tendency is reversed back to form an upward trajectory, and proceeds to increasing further thereafter.The quantitative rationale is given as below: • Although not explicitly displayed in the figure, we discovered that initially (i.e., with N sta ≈ 0), T exp T bo + T suc + T col and the weight for T bo + T suc + T col is greater than that for T exp since τ is large with a small N sta , as shown in Figure 4.
• Soon after, with N sta being still relatively small, we found that while still T exp < T bo + T suc + T col , T exp grows far faster than T bo + T suc + T col .Now, the weight for T exp is greater than that for the other since τ gets smaller due to N sta being greater.
• Eventually, however, with N sta being large enough, both the quantity and weight get bigger in T exp > T bo +T suc + T col and (1 − τ ) > τ as τ gets far smaller due to N sta getting very large.

B. PACKET DELIVERY RATE
Our next metric, PDR, also depends dominantly on τ and P col as shown in (7).Refer to Figures 4 and 5 for understanding the result displayed in Figure 6. Figure 4 presents τ , the probability that a STA transmits in an arbitrary slot within a beaconing period L bcn , versus the number of STAs competing for the medium, N sta .The figure provides two-fold comparisons: (i) between the proposed and traditional schemes and (ii) according to CW.
Figure 4a does the former: it compares τ between the proposed and traditional CSMA schemes for the most dangerous vehicles (i.e., CAT 1 from Figure 1) with CW = 63.It is straightforward that a larger N sta causes a lower τ .Also, the level of τ is significantly improved in the proposed scheme in comparison to the traditional CSMA.It highlights the principle of the proposed scheme: vehicles being closer to a danger source take higher chances of transmissions in a backoff process.As such, the semantic message prioritization is accomplished, which this paper's proposition aims at.
Figure 4b compares τ according to CW. Commonly with the proposed and traditional schemes, a larger CW results in a lower τ due to a longer backoff process.From this, one can infer that the EXP is one of the main causes limiting the performance of a DSRC network.Now, Figure 5 presents that two-fold comparisons on the other key factor for PDR: the probability of collision, P col .
It is interesting to observe the downside of the proposed scheme in Figure 5a: the result shows that the proposed scheme yields a higher P col .It is inevitable because the proposed scheme allows vehicles to transmit a packet with a higher probability by letting them succeed through a backoff process more easily.Also, one can obviously observe that a larger N sta yields a higher P col .
Figure 5b gives a comparison among different CW sizes.It matches one's intuition that a larger CW size yields a lower P col since the STAs can be distributed on a wider window of backoff counter values.This tendency is common in both proposed and traditional schemes.
As a result of the observations of τ and P col , we can demonstrate PDR as shown in Figure 6.We remind from (7) that PDR is directly proportional to τ , which yields that Figure 6 shows a similar overall tendency to what Figure 4 did.Meanwhile, it is critical to understand that the proposed scheme yields higher PDRs compared to the traditional scheme, despite higher P col s.The reason is, as observed from Figures 4 and 5, positive margins in τ being larger than negative margins in P col .We reiterate that an IRT represents the average length of time that is spent between two successful BSM receptions.

C. INTER-RECEPTION TIME
As such, the results displayed in Figure 7 translate to the probability that a vehicle is able to transmit with a certain length of delay between successful BSM receptions.Notice that an IRT is measured in the number of time slots.It means that an IRT can also be measured in terms of the number of seconds by multiplying a slot time, T slot = 50 µsec, as has been mentioned in Table 3. Intuitively speaking, applying the IEEE 1609.4 [25] as this paper assumes, each failed transmission takes an additional 100 msec since an entire beaconing period is wasted when an EXP occurs.This leads to an interpretation that the unit can always be translated to the length of time, i.e., 100 msec of IRT per beaconing period that is wasted.
In what follows, we discuss the implications of the results in detail.First, both PMF and CDF describe that the proposed scheme consumes fewer beaconing periods compared to the traditional CSMA, regardless of CW and N sta .(We note that CDF is a better mark for observation of this statement.)The rationale behind the phenomenon is that the proposed multiple access mechanism yields a higher PDR as has been presented in Figure 6.We remind that the outperformance of the proposed scheme in terms of PDR is mainly attributed to a higher packet transmission probability, τ , as has been demonstrated in Figure 4.
Regarding the outperformance of the proposed scheme more specifically, Figure 7 also depicts that the margin of outperformance achieved by the proposed protocol gets greater with N sta increased.This serves as a concrete evidence that the proposed scheme results in a higher efficiency as the DSRC network gets more congested.
Second, it is also suggested from both PMF and CDF that a larger N sta leads to a higher probability of experiencing a longer IRT.The main reason of the tendency is a lower PDR that is induced by a higher P col as N sta is incremented.
Third, a larger CW yields a smaller IRT.Akin to the previous discussions, the relationship between IRT and CW is also attributed to PDR as has been presented in (8).That is, from Figure 6, one can find that a larger CW yields a higher PDR.As a direct consequence, the IRT gets lower as CW is increased, which is observed from comparison of CWs through 31, 63, and 255 in Figure 7.

VII. CONCLUSION
This paper proposed a protocol prioritizing the transmission of a BSM for a vehicle with a higher level of accident risk.
Our results showed that this protocol effectively improved the performance of vehicles with higher risk, measured in terms of key metrics-viz., average latency, throughput, and IRT.This paper also provided a generalized (i) analytical framework and (ii) spatial system model for evaluating the performance of the proposed scheme according to key factors such as the number of competing STAs and CW.We remind that the contribution of this paper is to lighten the networking load of a DSRC system.It will let DSRC suit better in coexistence scenarios with C-V2X, which are likely to happen considering that both of the two technologies have strengths that will have to be adopted in future connected vehicle networks.
Thanks to the generality, this work can be extended in multiple directions.For instance, based on the general model of node distribution (as opposed to previous work limiting the models to ''road'' environments), this paper's findings can be applied to other types of transportation network such as unmanned aerial vehicles (UAVs) for building a stochastic geometry-based framework analyzing latency and throughput performances.
It will be a meaningful attempt to extend this work if one (i) considers multiple factors potentially causing an accident and (ii) finds an explicit relationship among them to quantify the accident risk.For instance, it will be easy to identify a number of risk factors; but the hard part will be to characterize the exact impact on the accident risk as a result of the factors in concert.

FIGURE 2 .
FIGURE 2. Flowchart for the proposed algorithm.
only +P HN only +P [Both SYNC and HN] = P sync (1 − P hn ) + P hn 1 − P sync + P sync P hn .

FIGURE 4 .
FIGURE 4. Probability of packet transmission vs. number of STAs.

FIGURE 5 .
FIGURE 5. Probability of collision vs. number of STAs.

Figure 7
Figure 7 presents the probability mass function (PMF) and cumulative distribution function (CDF) of random variable N bcn , respectfully, versus N sta .Each row of two subfigures demonstrates a different CW size.We reiterate that an IRT represents the average length of time that is spent between two successful BSM receptions.