Age-of-Information-Based Transmission Protocol in Vehicular Network ^†

Abstract

With the development of the Internet of Things (IoT) and communication networks, the concept of a smart city emerged spontaneously. In the traffic control of a smart city, the vehicular network plays an important role. If the driving information of vehicles can be collected from the vehicular network and then aggregated into a smart city system, traffic control facilities can be adjusted in real time to improve traffic or increase traffic safety. This study is based on WAVE/DSRC under the IEEE 802.11p and IEEE 1609 standards. When the vehicle is moving, the On-Board Unit (OBU) on the vehicle and the Roadside Unit (RSU) transmit data through the 5.9 GHz (5.85–5.925 GHZ) frequency band to establish vehicle-to-vehicle communication (V2V) and vehicle-to-infrastructure communication (V2I). The immediacy of the transmission of beacon messages is also discussed over a vehicular network. A beacon message is essential for communication in a vehicular network, including various safety messages, such as driving directions, driving speed, and location. We introduce the Age-of-Information (AoI) indicator to reflect the immediacy of information. AoI is used for the elapsed time after the sender samples the message until the receiver receives the message. We propose a centralized AoI-based protocol and a decentralized AoI-based protocol. By using Random-Walk and SUMO, we simulate driving dynamics and various RSU setting scenarios. Finally, we verify the performance of the proposed AoI-based protocol through experimental simulations.

1. Motivation

This research aims to design a transmission protocol that enables the vehicle and the RSU to receive the most real-time driving information. When the received information has the minimum average AoI, it is the most real-time driving information. If the vehicle information can be collected from the vehicular network and then aggregated into a smart city system, traffic control facilities can be adjusted in real time to improve traffic and increase traffic safety. Traffic control is associated with many real-time applications, and the quality of applications is based on whether the information is collected in real time. For applications that need to be predicted or monitored, outdated information does not match reality, resulting in poor quality. In order to continuously monitor and control the traffic system, it is necessary to constantly collect real-time information from the vehicular network, not simply the minimum delay or maximum throughput. The transmission period proposed by Baiocchi [1] has a functional relationship with the average AoI of the vehicular network in a known network topology, and an optimal value exists. We thus design a decentralized vehicular network transmission protocol that dynamically adjusts the transmission period. Ni [2] proposed a centralized vehicular network, and its experimental design, context setting, and control group are all references for this study. The difference in the channel connection status between this study and Ni’s research is that we assume that the vehicular network is variable, and the channel connection status is unstable. In Kaul’s work [3] the vehicular network employed the CSMA model and adjusted the contention window and broadcast period. It was experimentally proven that AoI is mainly affected by the broadcast period instead of the contention window. Kadota [4] proposed a design strategy for wireless communication networks, and we refer to the max-weight strategy of Kadota’s work and design a centralized vehicular network transmission protocol.

2. Methodology

2.1. Network Architecture

The network topology of the vehicular network proposed in this study is divided into two types: centralized and decentralized. The centralized vehicular network includes the RSU, which receives the vehicles’ messages, transmits the collected information to the server for subsequent applications, or sends warning messages to the vehicles to maintain driving safety. However, deploying many RSUs in a wide area is expensive. The centralized vehicular network is only suitable for urban areas. The decentralized vehicular network consists only of vehicles, and the transmission is carried out through the vehicles among the network. This network architecture can be applied to most areas, but it lacks centralized equipment to collect driving information, making it challenging to develop more advanced applications. In addition, those areas with sparse vehicle density cannot support a decentralized vehicular network due to intermittent connection.

The vehicular network includes the OBU installed in the vehicle and the RSU installed on the roadside. The OBU generates beacon messages, including the vehicle’s speed, direction, and location. In addition, the OBU can transmit beacon messages with RSUs and other OBUs. The OBU records when the beacon message is transmitted. The RSU is responsible for managing the connection status between its channel and each OBU and it transmits beacon messages to the OBU. If the OBU obtains and exchanges the safety information of its vehicle with other vehicles, other vehicles and the RSU know the current state of the vehicle to prevent accidents and improve driving safety. The OBU records when the beacon message is received and subtracted from the current time to calculate the AoI. The connection state between the RSU’s channel and each OBU may change due to obstacles in the driving environment or other factors. The RSU constantly communicates with the OBU to obtain the vehicle’s driving information and keep the connection states updated for upcoming transmissions.

2.2. Traffic Model

The binomial equation [5,6] is used for the workload modeling of the vehicular network. The binomial represents the probability of the successful transmission of messages by applications in individual nodes, and the arrival function, $\lambda \left(x\right)$, represents the distribution function of the successful transmission of messages by applications, as shown in Equation (1).

$$\mathrm{P}[T_i\left(x\right)>t]={(1-p(x\left)\right)}^{\frac{t}{t_c}}=e^{-\lambda \left(x\right)t}$$

(1)

where $p\left(x\right)$ represents the probability that a node successfully transmits a message in each slot, $T_i\left(x\right)$ is the size of a single slot, $t$ is the time required to transmit a message, and $t_c$ is the maximum time needed to transmit a message, as shown in Equation (2).

$$t_c=\frac{maximum length of packets}{transmission rate}$$

(2)

Equation (3) can be obtained by taking the logarithmic operation on ${(1-p(x\left)\right)}^{\frac{t}{t_c}}$ ≌ $e^{-\lambda \left(x\right)t}$ in Equation (1).

$$\lambda \left(x\right)=\frac{1}{t_c}\ln \left(\frac{1}{1-p\left(x\right)}\right)$$

(3)

The main application in the vehicular network is the transmission of safety messages. We only consider the transmission based on the immediacy of messages. When a node transmits a message, it has its exclusive slot in each time frame, so the value of $p\left(x\right)$ is determined by the number of slots in the frame. The slot, $T_i\left(x\right)$, needs to be greater than $t_c$ to ensure that each message is successfully delivered. In Equation (4), there are 20 slots in each frame, and the $p\left(x\right)$ can be expressed as follows:

$$p\left(x\right)=\frac{length of a slot}{length of a frame}=\frac{1}{20}$$

(4)

By substituting $p\left(x\right)$ in Equation (4) into Equation (3), we can derive Equation (5).

$$\lambda \left(x\right)=\frac{0.051}{t_c} > \frac{0.051}{T_i\left(x\right)}=\frac{0.051}{slot }$$

(5)

The slot, $T_i\left(x\right)$, must be greater than $t_c$ and make the arrival rate $\lambda \left(x\right)<1$. If $\lambda \left(x\right)>1$, the slot size does not allow the application to transmit messages. Therefore, the slot size must be set appropriately so that $\lambda \left(x\right)<1$.

2.3. Age-of-Information-Based Transmission Protocol

2.3.1. Centralized AoI-Based Transmission Protocol

In the centralized AoI-based transmission protocol, the time allocated to the dedicated channel is based on the frame/slot structure. When the vehicle receives the update message, the AoI is updated, as shown in Figure 1.

In Figure 1, the frame is the period during which the vehicle generates the beacon message. Generally, a frame is about hundreds of milliseconds, and the length of the frame is fixed and does not change no matter how many vehicles there are in the RSU coverage. When the RSU or vehicle receives the beacon message during the frame, the vehicle’s driving information is updated, and the AoI reduces. The maximum time required for each slot to transmit the beacon message depends on the packet size of each beacon message and the transmission speed of the channel. In this study, the size of the beacon message is fixed. Therefore, after setting the transmission speed of the channel, the slot length is a fixed value. Because a frame consists of multiple slots, vehicles in a given frame broadcast beacon messages in a single RSU area by using the channel and the time allocated by the RSU to avoid collisions. At the beginning of each frame, there is a short time for the RSU to update the information of the vehicles in the coverage so that the RSU knows which vehicles exist in the coverage. The AoI-based protocol updates the RSU for the vehicles under the coverage, the combination of channels used, and the selected slot. Then, it publishes a message to notify those vehicles in the next frame that the beacon message can be broadcast. The actual length of the frame and slot is determined by the experiment. We assume that the vehicle sends the beacon message to all vehicles in the area and the centralized RSU through broadcasting. The relationship between the AoI of the beacon message received by the RSU and the AoI of the overall network is as follows: Let there be n vehicles, $v_1$, $v_2$, …, $v_n$. At time, t, the AoIs of the beacon messages of other vehicles stored by each vehicle can be represented by an n × n matrix, $V_t$.

$$V_t=\left[\begin{array}{ccc}{v}_{11\left(t\right)}& \cdots & v_{1n\left(t\right)}\\ ⋮& \ddots & ⋮\\ v_{n1\left(t\right)}& \cdots & v_{nn\left(t\right)}\end{array}\right]$$

(6)

where $v_{ij}$ represents the AoI obtained by vehicle $v_i$ observing vehicle $v_j$, which must satisfy the following properties.

$$\begin{array}{l}{v}_{ij\left(t\right)}=0,ifi=j\\ v_{ij(t+1)}^{}={(v}_{ij\left(t\right)}+1)\times u_i\\ u_i=\left\{\begin{array}{c}0 , if v_i updates \\ 1 , if v_i doesn’t update\end{array}\right.\end{array}$$

(7)

$v_{ii }$= 0 means that each vehicle always knows its information instantly, and $v_{ij(t+1)}^{}$ means $v_{ij}$ at the next time point. The AoI changes according to whether the vehicle transmits the beacon message. If $v_i$ is updated, the AoI is set to zero. Otherwise, the AoI increases with time. Next, we calculate the average AoI matrix M stored by each vehicle.

$$M=[m_1, m_2, \dots m_n] \mathrm{where} m_i=\frac{v_{1i}+v_{2i}+\dots +v_{ni}}{n}, 1\le \mathrm{i}\le \mathrm{n}$$

(8)

The RSU receives the driving information of each vehicle and records the AoI, but the RSU does not have the driving information to be transmitted. Therefore, the AoI of the RSU itself does not exist. Let the RSU record the 1 × n matrix X of the AoI of each vehicle at time t as

$$X_t=[x_{1\left(t\right)}, x_{2\left(t\right)}, \dots x_{n\left(t\right)}]$$

(9)

where $x_{i\left(t\right)}$ represents the AoI of the vehicle $v_i$ observed by the RSU.

$$x_{i(t+1)}^{}={(x}_{i\left(t\right)}+1)\times u_i,1\le \mathrm{i}\le \mathrm{n}$$

(10)

The AoI observed by the RSU is the same as the AoI observed by the vehicles, so the AoI obtained by the vehicles other than vehicle i and the RSU satisfy the following property:

$$\begin{array}{l}{x}_i=v_{1i}=v_{2i}=\dots =v_{ji}, 1\le j\le \mathrm{n},\mathrm{j}\ne \mathrm{i}\\ x_i=\frac{v_{1i}+v_{2i}+\dots +v_{ji}+\dots +v_{ni}}{n-1}\end{array}$$

(11)

Next, comparing $m_i$ and $x_i$, we obtain

$$x_i=\frac{n}{n-1}\times m_i$$

(12)

$$X=\frac{n}{n-1}\times M$$

(13)

From the above equations, we find the coefficient relationship between the AoI of the vehicle observed by the RSU and the average AoI of the overall vehicular network. In other words, we need to pay attention to the AoI observed by the RSU, which indicates the AoI of the whole network. When considering the centralized vehicular network, it is necessary to avoid message collision due to competing channels and transmission failure. When the information continues to fail to be transmitted and it is not updated for a long time, the AoI increases, and the immediacy of the vehicle information is lost. In this study, the channel assignment is performed by the RSU to avoid channel contention and packet collision. Due to the characteristics of vehicle movement, the connection status of each vehicle and channel changes dynamically, so we need to continuously update the channel connection information.

At the beginning of each frame, the RSU selects specific vehicles to update the driving information and thus knows the AoI of the vehicles and the channel–vehicle connection status. We denote the specific channel as $c_i$ and the vehicle as $v_i$, as shown in Figure 2. We make a graph of the connection between the channel and the vehicle. The points on the left and right represent the channel and the vehicle, respectively, and the individual AoI of the vehicle weights the edge connected between them. We use the maximum matching algorithm to select the channel–vehicle combination of the AoI with the maximum sum to assign the channel to a specific vehicle. As shown in Figure 3, the solid line represents the selected channel–vehicle combination this time.

The example in Figure 3 shows that the channel–vehicle combination selected for driving information update is ($c_1$,$v_1$), ($c_2$,$v_6$), ($c_3$,$v_2$), ($c_4$,$v_3$), ($c_5$,$v_4$). The updated AoI sum is 1997 + 1170 + 1575 + 1863 + 1014 = 7619 ms, which is the sum of the maximum matching of this channel–vehicle combination. The AoI of $v_5$ is 1544 ms, which is not the lowest, so it cannot be updated. We follow the above steps each time, picking the maximum matching channel–vehicle combination to obtain the maximum sum of the AoIs. The vehicles selected in the combination broadcast the beacon message and update the AoI that has not been updated for the longest time in the overall network. Based on this principle, we propose an AoI-based protocol that is suitable for centralized vehicular networks. The AoI-based protocol must be installed on the RSU and vehicle’s OBU. At the beginning of each frame, the RSU obtains the connection statuses of vehicles and then calculates the AoI of each vehicle as follows:

• For the vehicles that existed in the previous frame, use the current time minus the time of the previous vehicle’s beacon message update as the vehicle’s AoI.
• For the new vehicles that appear in the current frame, give the initial value as the vehicle’s AoI.

After calculating the AoI of the vehicles in each area, the RSU creates a channel–vehicle bipartite graph based on the previously obtained vehicle connection status. The calculated AoI selects the max matching to determine which vehicles broadcast the beacon message in the subsequent slots of the frame.

2.3.2. Decentralized AoI-Based Transmission Protocol

The proposed AoI-based protocol for decentralized vehicular networks is based on the concept of the work of Baiocchi [1]. Baiocchi improved the IEEE 802.11p (https://standards.ieee.org/ieee/802.11p/3953/ (accessed on 1 December 2023)) CSMA model and proposed a protocol to change the transmission period dynamically. Their work considers only periodic one-hop message exchange. In IEEE 802.11p CSMA, $T_{msg}$ is defined as the period for the vehicle to transmit messages periodically. $B_1$ and $B_2$ in Figure 4 and Figure 5 are the first and second message transmission times, respectively. $B_1$ and $B_2$ include the time spent transmitting the message, the time T spent in the DIFS (Distributed Inter-frame Spacing) process, and the time C spent returning the back-off counter to zero. Y represents the AoI of each message interval, which is defined as the current message arrival time minus the last message arrival time. $t_1$ and $t_2$ represent the arrival times of the first and second messages, respectively. Figure 4 shows that the node can successfully transmit the message in the transmission period ($T_{msg}$), and Figure 5 shows that the node cannot successfully transmit the message in the transmission period ($T_{msg}$).

The decentralized model uses updated processing to model the behaviors of generic nodes to transmit packets. We assume that the node sends beacon messages at times $t_1$ and $t_2$. At time $t_2$, the AoI is the current time minus the time $t_1$ when the last message was received, so AoI Y = $t_2-t_1$. Because the competition for the transmission channel keeps the channel busy, if the waiting time C for the back-off counter to return to zero is increased, the transmission time B increases. According to the length of the node transmission time B, we consider two cases: the regular transmission time ($T_{msg}$) is greater than the message transmission time ($B_1$), and the transmission is successful within the specified time (Figure 4), or the regular transmission time ($T_{msg}$) is less than the message transmission time ($B_1$), and it cannot be successfully transmitted within the specified time (Figure 5). When the periodic message transmission time ($T_{msg}$) is greater than the message transmission time ($B_1$), Y = $B_2$+ ($T_{msg}-B_1$), and when the periodic message transmission time is less than the message transmission time ($B_1$), Y = $B_2$. Therefore, the general equation for the relationship between AoI Y and B is as follows:

$$\mathrm{Y}=B_2+\mathrm{m}\mathrm{a}\mathrm{x}\{0,T_{msg}-B_1\}$$

(14)

Equation (14) implies that the minimum AoI $\mathrm{Y}=B_2+0$; that is, $T_{msg}$ and $B_1$ have the same value. Our goal is to minimize the AoI Y, and the AoI Y can be reduced by adjusting the values of C and back-off counter to make $T_{msg}$ close to $B_1$. The decentralized vehicular network is established under the IEEE 802.11p standard. When the nodes compete for the transmission channel and the node senses that the channel is not busy, it waits for a slot and subtracts it from the back-off counter. The slot’s length, δ, is the IEEE 802.11p back-off slot duration. When the node perceives that the channel is busy, it freezes the back-off counter and waits for a time, T, so that other nodes can complete the transmission. T is the time it takes to complete the transmission and the subsequent DIFS process, and we use ε to represent the length of time T. C is the sum of δ and ε and it is represented by Equation (15):

$$\mathrm{C}={\sum }_{j=1}^{N}X\left(j\right)$$

(15)

where N is a discrete random variable with uniform distribution with values in the range [0, $W_0-1$], and $W_0$ is the contention window size of IEEE 802.11p, where $W_0$ = 16. X(j) is generally a random variable of an independently identically distribution (iid), and it is defined as having the same distribution as X.

$$\mathrm{X}=\left\{\begin{array}{c}\delta \mathrm{with} \mathrm{probabilty} 1-\mathrm{b}\\ \epsilon \mathrm{with} \mathrm{probabilty} \mathrm{b} \end{array}\right.$$

(16)

where b is the probability that the node perceives that the channel is busy. Baiocchi proved the functional relationship between $T_{msg}$ and the AoI of adjacent vehicles by using the CSMA model mentioned above and Equations (10) and (11) and by using the adjacency matrix topology of the vehicular network. If the adjacency matrix of the vehicular network does not change, that is, when the relative locations of the vehicles do not change, there is a specific value $T_{msg}$, so that the average AoI of the entire vehicular network is minimum [1]. The function consists of a decreasing function and an increasing function, as shown in Figure 6.

In driving, the status regarding whether the vehicles are in the same area or connected with other vehicles changes randomly over time, which causes the adjacent matrix to change accordingly. With the proof of ref. [1], we use the protocol with a variable transmission period to increase or decrease the length of $T_{msg}$ to make the AoI minimal. If we increase $T_{msg}$ and find that the AoI is higher than the value obtained last time, then $T_{msg}$ decreases, and vice versa.

3. Experimental Simulations and Results

The experiment is simulated by NS-3 (network simulator-3). The vehicle density of the simulated environment is set to be between 50 and 400 vehicles/${\mathrm{k}\mathrm{m}}^2$, which means that the driving environments range from sparse to crowded. The frame size and slot sizes are 120 ms and 6 ms, respectively. The propagation loss model uses Friis, the vehicle speed uses the moving speed transmission module provided by NS-3 and is set to 40 km/h, and the time of each simulation is 40 s. The default value of the transmission period of the decentralized AoI-based protocol is set to 100 ms. The increase/decrease time to adjust the transmission period is set to 50 ms. We have two simulations to verify the proposed AoI-based transmission protocols. The first simulation uses Random Walk to simulate the mobility model of vehicles, and the second uses SUMO (Simulation of Urban Mobility) to simulate the urban vehicle mobility model. Because the simulation is limited by the number of vehicles and vehicle density that a single subnet can accommodate, we set the vehicle to roam in an area of 799 × 799 m. The vehicle density ranges from 50 to 400 vehicles/${\mathrm{k}\mathrm{m}}^2$. The number of RSUs is set to 0, 1, 2, and 4, respectively. By setting different numbers of RSUs, we simulate the performance of centralized, decentralized, and hybrid vehicular networks. Each experiment is carried out for 40 s, the AoI is sampled for all vehicles in the network every 0.5 s, and the average AoI is calculated. The control group includes Round Robin (in the centralized vehicular network only) and IEEE 802.11p default transmission (in both centralized and decentralized vehicular networks).

3.1. Simulation 1: Random Walk Mobility Model

The first experiment simulation uses Random Walk as the mobility model, assuming that the vehicles move randomly in the area. It is also assumed that each vehicle and RSU in the area install the proposed AoI-based protocol so that the vehicle roams freely and transmits beacon messages to other vehicles and RSUs. We have several scenarios in simulation 1. The first scenario has one RSU in the area as the centralized AoI-based protocol. In the second scenario, we set up four RSUs as the centralized AoI-based protocol applied in a multiple-RSU scenario, simulating the impact of handoff with vehicles passing through different RSUs. In the third scenario, we do not set up any RSUs as the decentralized AoI-based protocol. The last scenario sets up two RSUs as a hybrid vehicular network, enabling vehicles to switch between centralized and decentralized AoI-based protocols. Regarding the control group, Round-Robin is conducted in a single RSU and four RSU scenarios since it requires a centralized RSU for scheduling. The IEEE 802.11p default is conducted with the number of RSUs being 0, 1, 2, and 4. The simulation results are shown in

Table 1. Random Walk: AoI-based protocol improvement.

No. of RSU.	Avg. Improvement Compared with Round-Robin	Avg. Improvement Compared with 802.11p
RSU = 0	N/A	33.3%
RSU = 1	40.4%	56.9%
RSU = 2	N/A	38.5%
RSU = 4	30.0%	41.3%

.

3.2. Simulation 2: SUMO Simulates Vehicle Dynamics

SUMO is a traffic simulation software for microscopic traffic flow, which is highly portable and simulates continuous traffic flow and discrete-time traffic events for large-scale road networks. Simulation 2 uses SUMO and OSM (Open Street Map) to generate real driving dynamics. The OSM is used to extract “Sec. 2, Zhinan Rd., Wenshan Dist., Taipei City” in front of National Chengchi University as the central area for simulation, as shown in Figure 7. The same area corresponding to the Google map is shown in Figure 8.

In addition to basic street routes, SUMO also includes traffic control systems for traffic lights and intersections and has an actual driving dynamic simulation.

In simulation 2, we compare the performance of the proposed AoI-based protocol, Round-Robin, IEEE 802.11p default, and the AoI-based protocol [7].

Table 2. SUMO: AoI-based protocol improvement.

No. of RSU.	Avg. Improvement Compared with Round-Robin	Avg. Improvement Compared with 802.11p	Avg. Improvement Compared with AoI-Based Protocol [7]
RSU = 0	N/A	24.5%	N/A
RSU = 1	40.1%	57.8%	N/A
RSU = 2	N/A	34.85	N/A
RSU = 4	32.7%	51.1	19.7%

shows that the AoI-based protocol improves the AoI of the IEEE 802.11p default, Round-Robin, and AoI-based protocol [7] in various RSU scenarios.

4. Conclusions

The experimental simulations show that under the four RSU setting scenarios, the AoI-based protocol outperforms the average AoI of Round-Robin and IEEE 802.11p default. We also simulate the actual driving environment through SUMO and OSM to verify the practicability of the AoI-based protocol. We found that when using the AoI-based protocol in four simulation scenarios with RSU = 0, 1, 2, and 4, when the vehicle density is 50–400 vehicle/${\mathrm{k}\mathrm{m}}^2$, regardless of the Random Walk or SUMO simulations, there is a different degree of improvement, as shown in

Table 3. Vehicles’ overall AoI-based protocol improvement.

No. of RSU	Random Walk	SUMO	Average Improvement
RSU = 0	33.3%	24.5%	28.9%
RSU = 1	48.7%	41.0%	44.9%
RSU = 2	38.5%	34.9%	36.7%
RSU = 4	35.6%	41.9%	38.8%

.