Enhancing vehicular edge computing system through cooperative computation offloading

Abstract

Vehicular Edge Computing is the specific application of Mobile Edge Computing in vehicular scenarios. In this work, to efficiently provide on-demand computational resource access for Mission Vehicles, Road Side Units (RSUs) and Cooperative Vehicles are both mounted with edge servers. To further improve the performance of this system, we firstly study the dynamic and cooperative task caching between RSUs. Under the control of the central controller, our caching scheme fully utilizes edge servers’ storage resources. Then, we resort to Deep Deterministic Policy Gradient (DDPG) algorithm to adapt to the time-varying wireless environment. Moreover, we propose the DDPG-OCWB algorithm to improve the convergence performance of DDPG. Finally, numerical results verify the improved performance of our proposed algorithm. Based on a detailed comparison with existing research schemes, it is evident that our scheme dramatically reduces system delay while utilizing edge servers’ energy efficiently.

Appendix A

The optimization objective in the optimization problem P2 is a convex function, and the constraint conditions are linear. So P2 is a convex optimization problem. This implies that the first-order Kuhn-Tucker conditions are necessary and sufficient. For simplicity, this paper uses a function F(I,O) to express the objective function in P1, and the Lagrangian function is expressed as:

$$\begin{aligned}{} & {} F(I,O) + \gamma \left( - \sum \limits _{i = 1}^N {{I_i} + \sum \limits _{i = 1}^N {{O_i}} } \right) + \sum \limits _{i = 1}^N {{\mu _i}{I_i}} \nonumber \\{} & {} \quad + \sum \limits _{i = 1}^N {{\sigma _i}} {O_i}+ \sum \limits _{i = 1}^N {{\delta _i}({\phi _{i,1}+\phi _{i,2}} + {I_i} -{O_i})} \end{aligned}$$

(47)

The optimal solution satisfies the first-order KKT condition:

$$\begin{aligned}&\frac{{\partial L}}{{\partial {I_i}}} = W {d_i}(w_{i,1},w_{i,2}) + q_i\kappa slf_{i}^2- \gamma + {\delta _i} + {\mu _i}=0 \end{aligned}$$

(48)

$$\begin{aligned}&\frac{{\partial L}}{{\partial {O_i}}} = -p {d_i}({w _{i,1},w_{i,2}})- q_i\kappa slf_{i}^2 + W g(\lambda _1,\lambda _2 ) \end{aligned}$$

(49)

$$\begin{aligned}&\qquad + \gamma -\delta _i+\mu _i=0\end{aligned}$$

(50)

$$\begin{aligned}&\frac{{\partial L}}{\gamma } = - \sum \limits _{i = 1}^N {{I_i}} + \sum \limits _{i = 1}^N {{O_i}}=0 \end{aligned}$$

(51)

$$\begin{aligned}&\delta _{i}(\phi _{i,1}+\phi _{i,2}+I_{i}-O_{i})=0,\forall i\in \mathcal {N}\end{aligned}$$

(52)

$$\begin{aligned}&\phi _{i}+I_{i}-O_{i}\ge 0,\delta _{i}\le 0\end{aligned}$$

(53)

$$\begin{aligned}&I_{i}\ge 0,\mu _{i}I_{i}=0,\mu _{i}\le 0,\forall i\in \mathcal {N}\end{aligned}$$

(54)

$$\begin{aligned}&O_{i}\ge 0,\sigma _{i}O_{i}=0,\sigma _{i}\le 0,\forall i\in \mathcal {N} \end{aligned}$$

(55)

By summing up (48) and (49), $-Wg(\lambda _1,\lambda _2)=\mu _i+\delta _i, \forall i\in \mathcal {N}$ can be obtained. Since $g(\lambda _1,\lambda _2)>0$ and $W>0$, either $\mu _{i}<0$ or $\sigma _{i}<0$ (or both) can be determined. Through the analysis above, there are three conditions for $I_i$ and $O_i$:

Case I : $I_{i}=0, O_{i}=0$. From the equation $w_{i,1}+w_{i,2}=\phi _{i,1}+\phi _{i,2}+I_{i}-O_{i}$, we obtain:

$$\begin{aligned} (w_{i,1}+w_{i,2})^*=\phi _{i,1}+\phi _{i,2} \end{aligned}$$

(56)

It follows from (52) that $\delta _{i}=0$. In order to search optimal $(w_{i,1}+w_{i,2})^*$ for Neutral RSU, we substitute $\delta _{i}=0$ into (48) and (49). We obtain:

$$\begin{aligned} \begin{aligned}&\frac{\gamma +g(\lambda _1,\lambda _2)-q_i \kappa slf_i^2}{W}\ge d_i((w_{i,1}+w_{i,2})^{*})\\&\ge \frac{\gamma -q_i \kappa slf_i^2}{W} \end{aligned} \end{aligned}$$

(57)

In this case, RSU i belongs to Neutral RSU. Case II :$I_{i}=0,O_{i}>0$. It follows from (55) that $\delta _{i}=0$. The following two subcases are as follows:

Case II.1 : $\phi _{i,1}+\phi _{i,2}=O_{i}$. We obtain $w_{i,1}+w_{i,2}=0$ and substitute it into (48) and (49). We obtain:

$$\begin{aligned}{} & {} Wd_{i}(w_{i,1},w_{i,2})+ q_i \kappa slf_{i}^2=\gamma -\mu _i-\delta _i\ge \gamma \end{aligned}$$

(58)

$$\begin{aligned}{} & {} Wd_{i}(w_{i,1},w_{i,2})+q_i \kappa slf_i^2=\gamma +W g(\lambda _1,\lambda _2)-\delta _i\ge \nonumber \\{} & {} \quad \gamma +g(\lambda _1,\lambda _2) \end{aligned}$$

(59)

Case II.2 :$\phi _{i,1}+\phi _{i,2}>O_{i}$. It follows from (52) that $\delta _i=0$. We substitute this into (48) and (49). It can be obtained that:

$$\begin{aligned}{} & {} Wd_{i}(w_i)+ q_i\kappa slf_{i}^2=\gamma -\mu _i\ge \gamma \end{aligned}$$

(60)

$$\begin{aligned}{} & {} Wd_i(w_{i,1},w_{i,2})+ q_i\kappa slf_i^2=\gamma +Wg(\lambda _1,\lambda _2) \end{aligned}$$

(61)

Thus, it can be conclude as $Wd_{i}+q_i\kappa slf_i^2 \ge \gamma +Wg(\lambda _1,\lambda _2)$. In this case, RSU i belongs to Source RSU.

Case II : $I_{i}>0,O_{i}=0$. We obtain $w_{i,1}+w_{i,2}\ge \phi _{i,1}+\phi _{i,2}$. It follows from (54) that $\mu _{i}=0$. We substitute this into (48). we obtain:

$$\begin{aligned} Wd_{i}(w_{i,1}+w_{i,2})+ q_i\kappa slf_i^2<\gamma \end{aligned}$$

(62)

In this case, RSU i belongs to Sink RSU.