Delay-sensitive Task Offloading in Vehicular Fog Computing-Assisted Platoons

In recent years, some works designed the task offloading strategy in platoon to optimize various performances. In [16], Fan et al. designed the task offloading strategy in the mobile edge computing (MEC)-assisted platoon. They adopted the directed acyclic graph to model the task offloading process, and then employed the Lagrangian relaxation-based aggregated cost (LARAC) algorithm to minimize the cost of the task offloading. In [17], Ma et al. considered the change of vehicle velocity in the platoon and proposed a task offloading and task take-back strategy. The reinforcement learning is adopted to enhance the offloading efficiency and avoid the link disconnection resulting from task processing failures. In [18], Hu et al. designed the task offloading strategy in the MEC -assisted platoon under the stable condition of task queues. The Lyapunov optimization algorithm is employed to reduce the energy consumption of task execution and improve the offloading efficiency considering transmitting delay as well as computing delay. In [19], Du et al. considered the sensing, computation, communication and storage resources of a single autonomous vehicle and proposed a communication strategy for autonomous driving platoon. In addition, they adopted the genetic algorithm to design the offloading strategy to achieve the minimized processing delay. In [20], Zheng et al. proposed a platoon task offloading strategy based on the dynamic non-orthogonal multiple access (NOMA). The long-term energy consumption is minimized by optimizing the allocation of both the communication and computation resource based on the Lyapunov and block successive upper bound minimization (BSUM) methods. In [21], Xiao et al. considered a scenario where the requested vehicle offloads tasks to the vehicles in the platoon and proposed a resource allocation strategy based on the requested vehicle’s service pricing to effectively utilize the resources in the platoon. However, the computation resource in a platoon is limited. When the resources in the platoon are not enough to process the task, a potential threat will be posed for safety. In this situation, the vehicles driving near the platoon may form a VFC to provide computation resource.

Many works have studied task offloading in the VFC. In [22], Liao et al. considered the uncertain information and designed a task offloading strategy in the VFC to get the minimized total network delay. In [23], Zhou et al. considered a two-stage VFC framework and designed a task offloading strategy according to the price-based matching algorithm to minimize the long-term task offloading delay. In [24], Shi et al. proposed a task offloading strategy, where vehicles are likely to share idle computation resources by dynamic pricing strategy to maximize the utility of offloading tasks. In [25], Yadav et al. considered the vehicular node mobility and end-to-end latency deadline constraints and designed an energy-efficient dynamic computation offloading and resources allocation strategy (ECOS) in the VFC to minimize energy consumption and service latency. In [26], Xie et al. considered the parallel computation task offloading problem in the VFC and proposed an offloading strategy to reduce the service time and improve the amount of the finished tasks by using the hidden Markov model. In [27], Lqbal et al. designed an offloading strategy to improve the performance of queuing delay, end-to-end delay and task completion rate based on the computing capacity and the workload of vehicles in the VFC. In [28], Misra et al. proposed a task offloading strategy in a software-defined VFC network to reduce the task computing delay and minimize the control overhead in the network. In [29], Liu et al. considered the dynamic requirements and resource constraints in the two-layer VFC architecture and proposed a task offloading strategy to maximize the task service rate. In [30], Wang et al. proposed an online learning-based task offloading algorithm in the VFC to minimize the task offloading latency. In [31], Zhu et al. proposed an event-triggered dynamic task allocation framework in the VFC by using linear programming-based optimization and binary particle swarm optimization to minimize average service latency. In [32], Zhao et al. proposed a contract-based incentive mechanism that combines resource contribution and resource utilization in the VFC to improve the quality of service of vehicles. Moreover, they proposed a task offloading strategy based on the queuing model to enhance the performance of task offloading and resource allocation. In [33], Tang et al. considered the task deadline and proposed an offloading strategy in the VFC to enhance the offloading efficiency. In [34], Yang et al. considered the effective time of tasks in the VFC at the crossroads and proposed a low-cost offloading strategy to enhance the offloading efficiency among vehicles. In [35], Mourad et al. considered the intrusion detection tasks in the VFC and proposed a task offloading strategy to minimize the computation execution time and energy consumption and meanwhile maximize the offloading survivability. In [36], Liu et al. considered a two-layer VFC and proposed an adaptive task offloading mechanism to get the maximal tasks’ completion ratio. In [37], Cho et al. adopted the adversarial multi-armed bandit theory to propose an adversarial online learning algorithm with bandit feedback, which aimed to optimize the selection of vehicles in the VFC to minimize the offloading service costs including the delay and energy. In [38], Wu et al. considered directional vehicle mobility to propose a network model to minimize the average response time of the tasks. They further chose the neighboring vehicles to assist to process task based on a greedy algorithm. In [39], Huang et al. jointly considered the task type as well as the velocity of vehicle to propose the task offloading and resource allocation strategy, which decreases the vehicles’ energy cost and increases the income of the vehicles considering the delay constraint. In [40], Alam et al. developed a three-layer generic decentralized cooperative VFC system to overcome the lack of robustness against the high mobility environment. In [41], Fan et al. proposed a joint task offloading and resource allocation strategy for a VFC including devices and vehicles covered by a base station. In [42], Chen et al. focused on a energy-powered multi-server VFC system with cybertwin, where vehicles send the current status of network and unprocessed vehicular application tasks to the macro base station to get the efficient resources allocation. In [43], Chen et al. proposed a distributed multi-hop task offloading model to get a low delay for the task execution in the VFC. In [44], Lin et al. proposed an online task offloading strategy for the unknown dynamics heterogeneous VFC environment based on the online clustering of bandits (CAB) approaches to minimize the expectation of total offloading energy consumption while satisfy stringent delay requirements by learning the relationship between historical observations and rewards. In [45], Liu et al. considered the vehicle mobility and proposed a task offloading strategy by exploiting the computation resources of vehicles in the VFC to get the minimized weighted sum of execution delay as well as computation cost. In [46], Ma et al. proposed a traffic routing-based computation offloading strategy in the cybertwin-driven VFC for vehicle-to-everything applications to reduce latency. However, these works have not considered the platooning scenario.

The works mentioned above show that the strategy of task offloading in VFC has been studied intensively, but for task offloading in the VFC-assisted platoon, to mitigate the limited computation resource, has not been studied. This motivates us to conduct this work. Different from the existing works about task offloading in VFC or platoons, we jointly take into account several factors, i.e., the heterogeneous computation resources of vehicles in the platoon, the random arrival and departure of task, the random arrival and departure of the vehicles in the VFC, and the 802.11p DCF mechanism. Moreover, we adopt the SMDP to model the task offloading process and design the SMDP framework including state, action, reward and transition probability.

The states reflect the resource conditions of the system, which is influenced by the events including a task’s arrival and departure, a vehicle’s arrival and departure in the VFC. Hence, we formulate the states as the resource conditions when different events occur. The state set $\mathbb{S}$ is formulated as

where ${n_{i}}$ ($i=1,\ldots,N$) is a binary to indicate whether the resource of ${V_{i}}$ is occupied or not, i.e., ${n_{i}}=1$ indicates that the resource of ${V_{i}}$ is occupied and ${n_{i}}=0$ indicates that the resource of ${V_{i}}$ is available. ${B_{j}}$ ($j=1,\ldots,{N_{R}}$) is the number of the tasks that occupy $j$ RUs, ${N_{R}}$ is the maximum number of RUs that each task can occupy, $M$ is the total number of RUs in the VFC. Thus, the total number of occupied RUs is calculated as $\sum\nolimits_{r=1}^{{N_{R}}}{r{B_{r}}}$, where $r$ is the number of RUs a task occupies, and ${B_{r}}$ is the number of the tasks that occupy $r$ RUs. Then ${r{B_{r}}}$ represents the number of the occupied RUs for the tasks occupied $r$ RUs. The total number of occupied RUs should not exceed the total number of RUs in VFC, i.e., $\sum\nolimits_{r=1}^{{N_{R}}}{r{B_{r}}}\leq M$. $e\in\{A,{D_{1}},\ldots,{D_{N}},{L_{1}},\ldots,{L_{{N_{R}}}},{F_{+1}},{F_{-1}}\}$ is an event, where $A$ denotes that a task arrives at the system, ${D_{i}}$ denotes that a task occupying the resource of ${V_{i}}$ leaves the system, ${L_{j}}$ denotes that a task occupying $j$ RUs in the VFC leaves the system, ${F_{+1}}$ denotes that a vehicle arrives at the VFC, ${F_{-1}}$ denotes that a vehicle leaves the VFC.

The actions reflect the offloading decisions of the system, depending on different events. Specifically, when there is a task arriving, the system will make an offloading decision such as offloading to the platoon, offloading to the VFC or discarding the task, while the system will make no decision when other events occur. Thus, the action set $\mathbb{A}$ is formulated as

where $b_{i}^{p}$ indicates that vehicle ${V_{i}}$ in the platoon is allocated to process the offloaded task, $b_{j}^{vf}$ indicates that the system offloads the task to the VFC and allocates total $j$ RUs in the VFC to process the task, $b$ indicates that the system discards the task. ${b_{-1}}$ indicates that the system takes no action in the current moment.

The reward function reflects the benefit which is related to the offloading delay under different states and actions. The system will transit from the current state $s$ to the next state when an action $a$ is taken, thus it gets an income $U(s,a)$ when taking action $a$ under state $s$, and incurs a cost $G(s,a)$ during the duration from state $s$ to the next state. Hence, the reward function under state $s$ and action $a$ is calculated as

Next, we will formulate $U(s,a)$ and $G(s,a)$, respectively.

In this section, we will derive the state transition probability from the current state $s$ to the next state $s^{\prime}$ after taking action $a$. Let $e^{\prime}$ be the event at the next state $s^{\prime}$, $P(s^{\prime}|s,a)$ be the state transition probability from the current state $s$ to the next state $s^{\prime}$ after taking action $a$. The definition of $P(s^{\prime}|s,a)$ is discussed in the following six cases.

When a task arrives under the current state and the task is offloaded to vehicle $V_{i}$ in the platoon, the number of the tasks occupying vehicle $V_{i}$ is incremented by one. In this case, six kinds of different rates are listed as follows: the rate that tasks arrive at the system is $N{\lambda_{p}}$, the rate that tasks occupying vehicle $V_{i}$ depart the system is $\left({{n}_{i}}+1\right)\frac{{{f}_{i}}}{d}$, the rate that the tasks occupying vehicle $u$ ($u\neq i$) depart from the system is ${{n_{u}}\frac{{{f_{u}}}}{d}}$, the rate that the tasks occupying $j$ RUs depart the system is $j{{B_{j}}\frac{{{f_{v}}}}{d}}$, the rate that vehicles arrive and depart the VFC are $\lambda_{v}$ and $\mu_{v}$, respectively.

Therefore, the corresponding $P(s^{\prime}|s,a)$ are calculated respectively as follows:

1. (a)

   If the next event is a task arriving at the system, $P(s^{\prime}|s,a)$ is calculated as $\frac{{N{\lambda_{p}}}}{{\beta(s,a)}}$.

2. (b)

   If the next event is that a task occupying vehicle $V_{i}$ leaves the system, $P(s^{\prime}|s,a)$ is calculated as $\frac{{({n_{i}}+1)\frac{{{f_{i}}}}{d}}}{{\beta(s,a)}}$.

3. (c)

   If the next event is that a task occupying vehicle $u$ ($u\neq i$) leaves the system, $P(s^{\prime}|s,a)$ is calculated as $\frac{{{n_{u}}\frac{{{f_{u}}}}{d}}}{{\beta(s,a)}}$.

4. (d)

   If the next event is that a task occupying $j$ vehicles in the VFC leaves the system, $P(s^{\prime}|s,a)$ is calculated as $\frac{{{B_{j}}\frac{{j{f_{v}}}}{d}}}{{\beta(s,a)}}$.

5. (e)

   If the next event is a vehicle arriving at the VFC, $P(s^{\prime}|s,a)$ is calculated as $\frac{{{\lambda_{v}}}}{{\beta(s,a)}}$.

6. (f)

   If the next event is a vehicle leaving the VFC, $P(s^{\prime}|s,a)$ is calculated as $\frac{{{\mu_{v}}}}{{\beta(s,a)}}$.

Based on the above analysis, when $s=({n_{1}},\ldots,{n_{N}},{B_{1}},\ldots,{B_{{N_{R}}}},M,A)$ and $a=b_{i}^{p}$, the transition probability $P(s^{\prime}|s,a)$ is given by

Similarly, the transition probability $P(s^{\prime}|s,a)$ under other events and actions is calculated as Eqs. (18)-(22).

When $s=({n_{1}},\ldots,{n_{N}},{B_{1}},\ldots,{B_{{N_{R}}}},M,A),a=b_{j}^{vf}$:

When $s=({n_{1}},\ldots,{s_{N}},{B_{1}},\ldots,{B_{{N_{R}}}},M,{D_{i}}),a={b_{-1}}$:

When $s=({n_{1}},\ldots,{n_{N}},{B_{1}},\ldots,{B_{{N_{R}}}},M,{L_{j}}),a={b_{-1}}$:

When $s=({n_{1}},\ldots,{n_{N}},{B_{1}},\ldots,{B_{{N_{R}}}},M,{F_{+1}}),a={b_{-1}}$:

When $s=({n_{1}},\ldots,{n_{N}},{B_{1}},\ldots,{B_{{N_{R}}}},M,{F_{-1}}),a={b_{-1}}$: