Research on forest fire information propagation model based on IoV

In this section, we briefly review the recent research on forest fire monitoring and applications of IoV.

Traditional forest fire monitoring

The main purpose of forest fire monitoring is to detect fire in time, protect the natural environment and avoid threats to life and property safety.

Satellite remote sensing can obtain the heat radiation and optical characteristics of the surface by satellite sensors¹⁴, and detect the occurrence and spread of forest fires by comparing the images at different time points.

UAVs are equipped with equipment such as spray system and fire pump, which can directly carry out fire fighting operations to improve fire fighting efficiency and safety¹⁵. These applications help to improve the ability and effectiveness of fire fighting and reduce casualties and property losses.

Thermal imaging can capture heat source detection information and identify temperature changes within the monitoring range. Once the temperature rises and exceeds the preset threshold, a warning is triggered. This method is not limited by objective conditions such as light and weather within the monitoring range, and has a high recognition accuracy¹⁶.

Infrared imaging can capture the infrared radiation emitted, reflected, scattered, or absorbed by objects through infrared sensors and convert it into visible images¹⁷. Furthermore, it can further achieve the localization and tracking of hotspots.

As an advanced sensing and detection instrument, lidar possesses high precision and high spatiotemporal resolution capabilities¹⁸. Leveraging the interaction of light with matter to generate light scattering, lidar enables effective detection of the emission location trends and concentrations of atmospheric particulate matter. For example, in 2021, Salgueiro¹⁹ et al. discussed the results of measuring dense forest fire plumes and Saharan dust layers using multi-wavelength Raman lidar and sun photometer. They utilized parameters such as wavelength indices, black carbon con-centration, optical depth, and linear depolarization ratio to distinguish the aerosol microphysics and optical characteristics of smoke layers, dust layers, and mixed layers in the atmosphere.

In addition, with the rapid development of artificial intelligence, computer vision-based forest fire monitoring technology has been widely applied. This forest fire monitoring technology can utilize deep learning algorithms such as Faster RCNN, YOLO, SSD, etc., to detect and identify fire targets in images or videos²⁰. Zhao²¹ et al. proposed an improved fire-YOLO deep learning algorithm for detecting small targets, fire-like objects, and smoke-like objects in forest fire images, as well as for fire detection under different natural lighting conditions.

Applications of IoV for fire monitoring

IoV has been increasingly explored for fire monitoring due to its real-time communication capabilities and wide-area coverage. Compared to traditional fixed monitoring systems, IoV can provide dynamic and adaptive sensing solutions. Recent studies have explored various IoV-based fire detection and management approaches.

For instance, Singh²² et al. proposed an IoT- and IoV-based disaster management system to enhance real-time earthquake and fire detection by integrating vehicle and building-mounted sensors. This system enables rapid data collection and analysis, facilitating quicker emergency responses and optimized evacuation routes.

Recent advancements in IoV-based fire monitoring have demonstrated the feasibility of deploying lightweight, real-time fire detection models in connected vehicles. For instance, FlameNet, a neural network specifically designed for fire detection in IoV environments, has shown high computational efficiency and accuracy while operating on resource-constrained embedded devices²³.

In addition, IoV has significant potential in enhancing emergency response through V2X communication. For example, Nair and Tanwar²⁴ proposed an AI-based accident severity detection scheme that utilizes machine learning to predict accident severity and dispatch emergency services in real time. This highlights the capability of IoV to facilitate rapid decision-making and improve public safety in critical situations, further supporting its application in fire monitoring.

IoV also holds significant potential in enhancing disaster management and public safety. For example, Umaeswari²⁵ et al. proposed an IoT and IoV-based safety system for remote real-time monitoring and detection of seismic activity and fires. The system integrates sensors in buildings and vehicles to detect earthquakes and fires, utilizing advanced data analytics and IoV technology to enhance emergency response and optimize evacuation routes.

These studies demonstrate that IoV has the potential to revolutionize fire monitoring by providing real-time, scalable, and adaptive sensing solutions. However, while existing research has explored various IoV applications for fire monitoring, few studies have focused on analyzing its communication capabilities, which are critical for ensuring the effectiveness of large-scale IoV-based fire detection systems.

Comparison of IoV with traditional fire monitoring methods

Traditional fire monitoring methods, including satellite monitoring, UAV-based surveillance, and thermal imaging, have been widely employed. However, these approaches exhibit inherent limitations in scalability, cost-effectiveness, and real-time applicability. The Internet of Vehicles (IoV) addresses several of these challenges, positioning it as a promising alternative.

Satellite-based fire detection offers extensive coverage but is constrained by temporal resolution, as satellites may take several hours or even days to revisit the same location²⁶. In contrast, IoV operates continuously through a network of connected vehicles, ensuring real-time monitoring without temporal gaps. Similarly, UAVs provide flexible coverage but are limited by flight duration and battery life, whereas IoV can sustain continuous monitoring by leveraging existing vehicle networks.

Satellite-based fire monitoring systems involve substantial operational costs, including expenses related to satellite launch and maintenance. UAV-based systems also require dedicated personnel for deployment and maintenance, further escalating operational costs²⁷. In contrast, IoV utilizes existing vehicular infrastructure, significantly reducing deployment costs while providing continuous monitoring capabilities.

Thermal imaging and infrared detection offer high-accuracy fire detection. However, they are often limited by fixed-location sensors, which restrict their coverage²⁸. IoV enhances real-time applicability by leveraging Vehicle-to-Everything (V2X) communication, enabling the instant sharing of fire alerts across multiple vehicles and emergency response units. This facilitates a faster, more coordinated firefighting response.

Given these considerations, we focus on the unique advantages of IoV in terms of communication efficiency, ensuring timely and reliable data transmission for fire monitoring. Unlike traditional methods, IoV’s mobility and connectivity make it particularly effective in dynamic environments where rapid situational awareness is essential.

System scenario and communication connectivity matrix

System scenario

Due to the consideration of protecting the natural environment, the infrastructure construction in the forest is not comprehensive enough, so the communication base stations and other roadside units are relatively few, and it is difficult to cover the whole forest. If a fire occurs, due to the lack of full coverage of the communication network, it may be difficult to accurately and timely transmit the fire to the monitoring center, which will lead to a greater disaster. In this case, using the dynamic topological characteristics of IoV can help build a full-coverage communication network. Therefore, this paper assumes that intelligent vehicles traveling in the forest constitute IoV, as shown in Fig. 1. Vehicles interact with each other’s location information through Vehicle to Vehicle (V2V) communication. Environmental parameters such as humidity, temperature, and visibility are exchanged between the vehicle and the roadside unit through Vehicle to Infrastructure (V2I) communication²⁹. Once the roadside unit or vehicle detects the source of the fire through its own sensors, the information can be transmitted to the monitoring center in the form of a broadcast.

Fig. 1

System scenario of IoV for forest fire.

We assume that each vehicle is an independent station for sending and receiving data packets, and the signal transceiver devices of all vehicles are installed in the middle of the vehicle. Then in the communication network, the vehicle can be seen as a point, and the location of the signal transceiver is the location of the vehicle²⁹. It is assumed that each vehicle has the same broadcast range, exchanging information such as speed, location, and some non-safety information to nearby vehicles. In addition, all vehicles follow the IEEE 802.11p protocol rules.

Communication connectivity matrix

Communication connectivity indicates the connectivity of links between nodes on a network. If nodes in the network can communicate through a path, it can be determined that the two nodes are connected. In this paper, the communication mode inside IoV is V2X communication. Under this communication mode, the judgment basis of whether the nodes are connected to each other is whether they exist in the communication range of the other side. If they exist, they can communicate directly, otherwise they cannot. The connectivity of the whole network needs to consider the connectivity between any two nodes. Since there are many nodes in the scene and the connectivity between them is complicated, this paper adopts the adjacency matrix to simplify the connectivity description.

We assume that there are total N vehicles in the system and the communication range of each vehicle is uniformly R_c. The position of each vehicle is positioned by constructing a coordinate system. Thus the communication connectivity matrix can be defined as $\:H\left(t\right)$. $\:H\left(t\right)$ is a $\:N\times\:N$ matrix that can be expressed as

$$H\left( t \right)=\left[ {\begin{array}{*{20}{c}} {{h_{1,1}}\left( t \right)}& \cdots &{\begin{array}{*{20}{c}} {{h_{1,i}}\left( t \right)}& \cdots &{{h_{1,N}}\left( t \right)} \end{array}} \\ {\begin{array}{*{20}{c}} \vdots \\ {{h_{i,1}}\left( t \right)} \\ \vdots \end{array}}&{\begin{array}{*{20}{c}} \vdots \\ \cdots \\ \vdots \end{array}}&{\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} \vdots \\ {{h_{i,j}}\left( t \right)} \\ \vdots \end{array}}&{\begin{array}{*{20}{c}} \vdots \\ \cdots \\ \vdots \end{array}}&{\begin{array}{*{20}{c}} \vdots \\ {{h_{i,N}}\left( t \right)} \\ \vdots \end{array}} \end{array}} \\ {{h_{N,1}}\left( t \right)}& \cdots &{\begin{array}{*{20}{c}} {{h_{N,j}}\left( t \right)}& \cdots &{{h_{N,N}}\left( t \right)} \end{array}} \end{array}} \right],$$

(1)

where

$${h_{i,j}}\left( t \right)=\left\{ \begin{gathered} 1,\sqrt {{{\left[ {{x_i}\left( t \right) – {x_j}\left( t \right)} \right]}^2}+{{\left[ {{y_i}\left( t \right) – {y_j}\left( t \right)} \right]}^2}} \leqslant {R_c} \hfill \\ 0,\sqrt {{{\left[ {{x_i}\left( t \right) – {x_j}\left( t \right)} \right]}^2}+{{\left[ {{y_i}\left( t \right) – {y_j}\left( t \right)} \right]}^2}} >{R_c} \hfill \\ \end{gathered} \right.,$$

(2)

where $\:\left({x}_{i}\left(t\right),{y}_{i}\left(t\right)\right)$ represents the position of vehicle i at time t. $\:{h}_{i,j}\left(t\right)=1$ indicates that the distance between vehicle i and vehicle j is less than the communication range R_c at time t, that is, the two vehicles can communicate with each other at time t. On the contrary, $\:{h}_{i,j}\left(t\right)=0$ means that the distance between the two vehicles is greater than the communication range R_c at time t, that is, the two vehicles cannot communicate with each other at time t. For vehicle i, the number of vehicles within its communication range can be expressed as

$$N_{{rc}}^{i}
(3)

We set $\:\text{∆t}$ as a very small time interval, then the behavior of vehicle i within $\:\text{∆t}$ can be approximated as a uniformly variable linear motion. When the state parameter of vehicle i is given at the initial time t₀, the position of the vehicle at any time t can be obtained by iterative method. We define $\:{v}_{i}\left(t\right)$ as the speed of vehicle i at time t. Compared to urban streets, vehicles in forest areas are typically fewer in number and more sparsely distributed. Therefore, we assume that all vehicles are traveling at a constant speed at the initial time t₀. Note that, the initial speed of each car is different.

From Fig. 1, we can find that vehicle i may not travel in a straight line in the forest, so we need to calculate the real-time position of vehicle i according to $\:{\theta\:}_{i}\left(t\right)$, which is the direction of vehicle i. Therefore, the real-time position of vehicle i can be expressed as

$$\left\{ \begin{gathered} {s_i}(\Delta t)={v_i}(t – \Delta t)\Delta t \hfill \\ {x_i}
(4)

where $\:{s}_{i}\left(\varDelta\:t\right)=0$ represents the distance traveled by vehicle i within $\:\text{∆t}$.

Since the initial speed of each vehicle is different, two vehicles traveling in the same direction in the same lane may collide. Therefore, the safety distance between vehicles is set as $\:{s}_{e}$ according to Intelligent Driving car-following Model (IDM)³⁰.

$${s_e}=\frac{{{s_0}+{v_{i – 1}}{T_0}}}{{\sqrt {1 – {{\left( {\frac{{{v_{i – 1}}}}{{{v_0}}}} \right)}^4}} }},$$

(5)

where $\:{s}_{0}$ indicates the minimum vehicle distance, $\:{v}_{0}$ indicates the maximum allowable speed on the road, $\:{v}_{i-1}$ indicates the speed of the front vehicle, and $\:{T}_{0}$ indicates the minimum headway. When vehicle i detects that the distance from the front vehicle is less than $\:{s}_{e}$, it needs to slow down immediately to avoid rear-end collision with the front vehicle. At this time, the acceleration of vehicle i can be calculated as

$${a_i}
(6)

where

$$^{{\text{*}}}{S_{i,i – 1}}
(7)

In the above equations, $\:\varDelta\:{S}_{i,i-1}\left(t\right)$ represents the distance between vehicle i and the front vehicle i-1; $\:{{}^{*}S}_{i,i-1}\left(t\right)$ represents the ideal spacing to the front vehicle; $\:\varDelta\:{v}_{i,i-1}\left(t\right)$ represents the speed difference between the two vehicles; a and b represent, respectively, the maximum uniform acceleration and an appropriate deceleration for all vehicles specified by the system.

When the vehicle is slowing down, the distance traveled during the time period $\:\text{∆t}$ in Eq. (4) should be rewritten as

$$S_{i}
(8)

Communication performance analysis model

In this paper, considering the dynamic mobility characteristics of the terminal, semi-Markov decision process theory³³ is used to model and analyze the service scheme decision of the system in this scenario, and analyze its service response capability.

802.11p EDCA mechanism

IEEE 802.11p is a wireless network standard specifically designed for V2V and V2I communications, commonly utilized in vehicular communication systems³⁰. EDCA is a mechanism within the IEEE 802.11p standard aimed at adjusting access to the wireless radio channel. EDCA aims to enhance the efficiency and performance of wireless networks in the Medium Access Control (MAC) layer. The implementation involves prioritizing data frames at different priority levels. EDCA introduces four Access Categories (AC0 to AC3), each with distinct transmission opportunities and contention windows. Higher-priority data frames have a greater chance of being transmitted during contention windows. AC0 queue transmits the background traffic; AC1 queue transmits the best effort traffic; AC2 queue transmits the video traffic; AC3 queue transmits the voice traffic. Once a fire is detected, the relevant information is identified as an emergency message and transmitted through the AC0 queue to ensure a quick response by the relevant authorities.

Each AC has an independent transmission queue. In order to distinguish the priority of different AC, EDCA assigns different competition parameters to each AC, including minimum competition window $\:{CW}_{min}$, maximum competition window $\:{CW}_{max}$ and Arbitration Inter-Frame Space (AIFS)³⁰. AIFS also represents the idle time of the channel that must be waited for to obtain the transmission opportunity, and the value is determined by the Arbitration Inter-Frame Space Number (AIFSN). Table 1 provides information about the relevant competition parameters.

Table 1 EDCA contention parameters.

The standard specifies the limits on the size of the competition window for $\:{AC}_{m}$ as follows:

$$CW_{{max}}^{m}={2^{{M_m}}}(CW_{{min}}^{m}+1) – 1,$$

(9)

where $\:{M}_{m}$ is defined as the number of retransmissions when the competition window of $\:{AC}_{m}$ queue does not increase.

The relationship between AIFS and AIFSN can be expressed as

$$AIF{S_m}=AIFS{N_m} \times \delta +SIFS,$$

(10)

where SIFS indicates the Short Inter Frame Space, and $\:\delta\:$ indicates a time slot. For ease of calculation, $\:{A}_{m}$ is defined as the number of extra slots that the $\:{AC}_{m}$ queue must wait for monitoring the idle channel compared to $\:{AC}_{0}$, i.e.,

$${A_m}=AIFS{N_m} – AIFS{N_0}.$$

(11)

The EDCA mechanism specifies the transmission process of each AC queue as shown in Fig. 2.

We define $\:{W}_{m,n}$ as the size of the competition window for $\:{AC}_{m}$ at the nth retransmission, $\:{M}_{m}$ as the maximum retransmission stage, and $\:{M}_{m}^{lim}$ as the maximum retransmission limit.

$${W_{m,n}}=\left\{ \begin{gathered} {2^n}(CW_{{\hbox{min} }}^{m}+1),n \in [0,{M_m}] \hfill \\ {2^{{M_m}}}(CW_{{\hbox{min} }}^{m}+1),n \in ({M_m},M_{m}^{{\lim }}] \hfill \\ \end{gathered} \right.$$

(12)

Once a packet is transmitted from the $\:{AC}_{m}$ queue at a station, the backoff process is initialized. Firstly, the backoff counter of $\:{AC}_{m}$ queue takes a random value in $\:\left[0,{W}_{m,0}-1\right]$. If the channel is detected to be idle for one slot time $\:\delta\:$, the backoff counter is immediately reduced by one. If the channel is detected as busy medium, the backoff counter enters the frozen state until the channel is detected as idle for a duration of $\:{AIFS}_{m}$. When the backoff counter is reduced to 0, $\:{AC}_{m}$ begins to attempt to transmit packets. If there is no other station and no queue with a priority higher than $\:{AC}_{m}$ simultaneously sending a packet, the packet is transmitted successfully and the backoff counter is reset to a random value in $\:\left[0,{W}_{m,0}-1\right]$. Otherwise, a collision occurs. At this time, the packet begins to enter the retransmission process, the number of retransmissions plus one, and the backoff counter is randomly specified in $\:\left[0,{W}_{m,1}-1\right]$. It should be noted that when multiple ACs at the same site transmit packets at the same time, only the $\:{AC}_{m}$ with highest priority will be successfully transmitted, and other queues will be retransmitted. In this paper, $\:{M}_{m}^{lim}={M}_{m}+{L}_{m}$ is defined as the maximum retransmission limit, where $\:{L}_{m}$ represents the limit of retransmission times when the retransmission stage reaches $\:{M}_{m}$. When the number of retransmissions exceeds $\:{M}_{m}^{lim}$, the packet is discarded and no further transmission attempt is made.

Markov model

Markov model is a probabilistic model based on state transitions, widely used to describe systems with stochastic and dynamic characteristics. In vehicular communication networks, due to the high-speed movement of vehicles, dynamic changes in network topology, and the complexity of the communication environment, traditional deterministic models often struggle to accurately capture the behavior of the system. Markov model, by abstracting the network state into a discrete set of states and defining transition probabilities between these states, can effectively describe stochastic processes in vehicular communications, such as channel contention, packet transmission, and network congestion³⁰. In this paper, we utilize Markov chains to model the communication behavior under the 802.11p EDCA mechanism, as shown in Fig. 3. By analyzing the state transition processes of different priority queues (e.g., AC0-AC3), we quantify the transmission performance of fire-related information in high-priority queues, particularly suitable for emergency communication scenarios requiring low latency and high reliability.

We assume that the packet arrives at the $\:{AC}_{m}$ queue in the MAC layer at the rate of $\:{\lambda\:}_{i,m}\left(t\right)$, and $\:{\lambda\:}_{i,m}\left(t\right)$ follows the Poisson distribution³¹. Then the probability $\:{p}_{i,m}^{a}\left(t\right)$ can be expressed as:

$$p_{{i,m}}^{a}
(13)

According to the Markov process^32,33 shown in Fig. 3, the internal transmission probability $\:{w}_{i,m}\left(t\right)$ can be defined as the probability that the $\:{AC}_{m}$ backoff counter of vehicle i decreases to 0, i.e.,

$${w_{i,m}}=\left\{ {\begin{array}{*{20}{l}} {{{\left[ {\frac{{{W_{0,0}}+1}}{{2\left( {1 – p_{{i,m}}^{{busy}}
(14)

where $\:{p}_{i,m}^{c}\left(t\right)$ indicates the probability of a collision occurring inside the station (vehicle); $\:{p}_{i,m}^{busy}\left(t\right)$ represents the probability of backoff freezing; $\:{p}_{i,m}^{a}\left(t\right)$ represents the probability that a packet will reach the $\:{AC}_{m}$ queue of vehicle i; $\:{\rho\:}_{i,m}\left(t\right)$ represents the probability that the $\:{AC}_{m}$ queue of vehicle i is not empty.

The external transmission probability $\:{\tau\:}_{i,m}\left(t\right)$ can be defined as the probability that no queue of higher priority than $\:{AC}_{m}$ is transmitted simultaneously when the $\:{AC}_{m}$ queue of vehicle i is transmitted. Therefore, $\:{\tau\:}_{i,m}\left(t\right)$ can be expressed as

$${\tau _{i,m}}
(15)

Because the 802.11p EDCA mechanism stipulates that there are only four AC queues in a vehicle, for the target vehicle i, the total transmission probability at time t can be expressed as

$${\tau _i}
(16)

According to the definition of $\:{p}_{i,m}^{c}\left(t\right)$ (the probability that there are other queues in a station besides $\:{AC}_{m}$ transmitting packets at the same time), we can achieve

$$p_{{i,m}}^{c}
(17)

According to the definition of $\:{p}_{i,m}^{busy}\left(t\right)$ (the probability that a channel remains busy until it is detected as idle for m duration, i.e., the probability that there are multiple vehicles transmitting at the same time or there is a queue with a higher priority than $\:{AC}_{m}$ trying to transmit a packet), we can achieve

$$p_{{i,m}}^{{busy}}
(18)

where $\:{N}_{rc}^{i}\left(t\right)$ represents the number of vehicles within the communication range of target vehicle i, which can be calculated according to Eq. (3).

Transmission delay and delivery ratio

In this paper, we convert the service process of MAC layer to Z domain for modeling and deducing the delay calculation method. Since the influence of the physical layer on the data transmission delay is much smaller than that of MAC layer, this paper considers the ideal channel in the model. Under this condition, the packet loss is only caused by the MAC layer. Therefore, in this paper, the packet transmission delay $\:{PTD}_{i,m}\left(t\right)$ is the service time of MAC layer, and can be expressed as

$$PT{D_{i,m}}
(19)

where $\:{\mu\:}_{k,i,m}\left(t\right)$ represents the service rate of the $\:{AC}_{m}$ queue in vehicle i.

In this paper, the probability generating function (PGF) method is used to transform the typical Markov model for describing 802.11p EDCA mechanism in the time domain into the Z domain. The PGF of packet transmission delay can be expressed as

$$P_{{i,m}}^{{ptd}}(z){\text{=}}\left\{ {\begin{array}{*{20}{c}} {B_{{i,m}}^{0}(z){T_{tr}}(z)}&{m=0} \\ {(1 – p_{{i,m}}^{c}
(20)

where $\:{T}_{tr}\left(z\right)$ represents the PGF of the transmission time, and $\:{B}_{i,m}^{j}\left(z\right)$ represents the PGF of the time that the backoff counter of $\:{AC}_{m}$ queue in vehicle i decreases to 0 when the number of retransmissions is j.

The PGF of the transmission time $\:{T}_{tr}\left(z\right)$ can be expressed as

$${T_{tr}}=\frac{{PH{Y_H}}}{{{R_b}}}+\frac{{MA{C_H}+E[P]}}{{{R_d}}}+\sigma ,$$

(21)

where $\:{PHY}_{H}$ and $\:{MAC}_{H}$ represent the head length of the physical layer and MAC layer respectively; $\:{R}_{b}$ and $\:{R}_{d}$ represent the basic rate and data rate of the channel respectively; $\:\sigma\:$ stands for propagation delay; E[P] indicates the size of the packet.

The PGF of the backoff time $\:{B}_{i,m}^{j}\left(z\right)$ can be expressed as

$$B_{{i,m}}^{j}(z)=\left\{ {\begin{array}{*{20}{l}} {\frac{1}{{{W_{0,0}}}}\sum\limits_{{k=0}}^{{{W_{0,0}} – 1}} {{{\left[ {{H_{i,m}}(z)} \right]}^k},m=0} } \\ {\frac{1}{{{W_{m,j}}}}\sum\limits_{{k=0}}^{{{W_{m,j}} – 1}} {{{\left[ {{H_{i,m}}(z)} \right]}^k},m=1,2,3,j \in [0,{M_m} – {\text{1}}]} } \\ {\frac{1}{{{W_{m,{M_m}}}}}\sum\limits_{{k=0}}^{{{W_{m,{M_m}}} – 1}} {{{\left[ {{H_{i,m}}(z)} \right]}^k},m=1,2,3,j \in [{M_m},M_{m}^{{\lim }}]} } \end{array}} \right.,$$

(22)

where $\:{H}_{i,m}\left(z\right)$ represents the PGF of the time that the backoff counter decreases one. $\:{H}_{i,m}\left(z\right)$ consists of the backoff freezing time $\:{F}_{m}\left(z\right)$ and the time slot $\:\delta\:$ required for the backoff counter decreasing one when the channel is idle. According to the 802.11p EDCA mechanism, once the channel is detected to be occupied by another vehicle or a high-priority queue within the same vehicle, the backoff freezing is activated and lasts the time of $\:{T}_{tr}+{AIFS}_{m}$. Therefore, $\:{F}_{m}\left(z\right)$ can be expressed as

$${F_m}(z)={z^{{T_{tr}}+AIF{S_m}}}.$$

(23)

Considering the continuous backoff freezing, $\:{H}_{i,m}\left(z\right)$ can be solved by Mason’s formula³² as

$$H_{{i,m}} (z) = \frac{{(1 – p_{{i,m}}^{{busy}}
(24)

To sum up, we can use the $\:{p}_{i,m}^{busy}\left(t\right)$ and $\:{p}_{i,m}^{c}\left(t\right)$ obtained before to calculate $\:{P}_{i,m}^{ptd}\left(z\right)$. Then the inverse transformation of the Z-domain model can calculate the actual transmission delay $\:{PTD}_{i,m}\left(t\right)$ in the time domain.

$$PT{D_{i,m}}
(25)

In order to ensure that the information can be fully received within the delay tolerance range, 802.11p protocol also has strict requirements on packet delivery ratio³⁴. Utilizing $\:{N}_{rc}^{i}\left(t\right)$ and $\:{\tau\:}_{i,m}\left(t\right)$ obtained before, we can calculate packet delivery ratio $\:{PDR}_{i,m}\left(t\right)$ as follows

$$PD{R_{i,m}}
(26)

Network throughput

Network throughput, defined as the amount of data successfully transmitted per unit time, is one of the key metrics for evaluating the performance of communication systems. In IoV, throughput directly reflects the data transmission capability of the system under high-load and dynamic network conditions. For forest fire monitoring scenarios, the level of throughput significantly impacts the efficiency and real-time performance of fire-related information transmission. High throughput ensures that a large volume of sensor data (e.g., temperature, humidity, and gas concentration) as well as high-definition images and video streams can be transmitted to the command center quickly and reliably, thereby providing strong support for early fire warning and rapid response.

In this paper, the network throughput can be expressed as³⁵

$$\begin{aligned} {C_i}
(27)

where $\:{p}_{i}^{c}\left(t\right)$ represents the collision probability of vehicle i; $\:{p}_{i}^{s}\left(t\right)$ represents the successful transmission probability of vehicle i; $\:{p}_{i}^{idle}\left(t\right)$ represents the probability of an idle time slot; $\:{T}_{s}$ represents the time duration of a successful transmission; $\:{T}_{c}$ represents the time duration of a collision. $\:{p}_{i}^{c}\left(t\right)$, $\:{p}_{i}^{s}\left(t\right)$ and $\:{p}_{i}^{idle}\left(t\right)$ can be separately calculated as

$$p_{i}^{c}
(28)

$$p_{i}^{s}
(29)

$$p_{i}^{{idle}}
(30)