A reputation-based cooperative content delivery with parking vehicles in vehicular ad-hoc networks

Abstract

In recent years, vehicular ad-hoc network (VANET) is getting a growing interest due to its significant function in terms of vehicle information services and vehicular entertainment applications. In particular, VANET enables parking vehicles (PVs) and roadside units (RSUs) to share their contents with mobile vehicles (MVs), which improves the efficiency of content delivery. However, content delivery in VANET still confronts with several challenges. Due to the selfishness of the PVs, an incentive mechanism is needed to motivate them to contribute their cached contents. Moreover, MVs may be threatened by the trustless or even malicious PVs. In this paper, we propose a reputation-based cooperative content delivery mechanism to improve the efficiency and security of content delivery. We formulate the relationships among MVs, RSUs, and PVs as the two-layer auction game. With the auction game, MVs find the optimal PV and RSU for delivering contents and offering the optimized rewards. In addition, we present a dynamic reputation evaluation model. Based on the feature of content delivery, this model incentivizes these honest PVs and isolates malicious PVs, which improves the security of content delivery. Finally, simulation results show that the proposed mechanism can not only improve the effectiveness of content delivery in VANET, but also avoid the attacks of malicious PVs.

Appendices

Appendix A

Proof of Theorem 1

We assume that the bidding strategy $\left ({s_{i,j,q}^{*},r_{i,j,q}^{*}} \right )$ is not the optimal of PV j. Then, there must be another optimal bidding $\left ({{{s^{\prime }}_{i,j,q}},{{r^{\prime }}_{i,j,q}},{{p^{\prime }}_{i,j,q}}} \right )$ to maximize the utility of PV j. Here, $s_{i,j,q}^{*} \ne {s^{\prime }_{i,j,q}}$, $r_{i,j,q}^{*} \ne {r^{\prime }_{i,j,q}}$. Let

$$ \begin{array}{@{}rcl@{}} {\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta {-} {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - {{s^{\prime}}_{i,j,q}}}}{{{r_{cloud}}}} {+} \frac{{{{s^{\prime}}_{i,j,q}}}}{{{{r^{\prime}}_{i,j,q}}}}} \right) {+} {{\upbeta}_{i,q}}{f_{q}}{{s^{\prime}}_{i,j,q}}} \right] - {{p^{\prime}}_{i,j,q}}\\ {=} {\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta {-} {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - s_{i,j,q}^{*}}}{{{r_{cloud}}}} {+} \frac{{s_{i,j,q}^{*}}}{{r_{i,j,q}^{*}}}} \right) + {{\upbeta}_{i,q}}{f_{q}}s_{i,j,q}^{*}} \right] - p_{i,j,q}^{*}. \\ \end{array} $$

(26)

Therefore, we have

$$ \begin{array}{@{}rcl@{}} && {{p^{\prime}}_{i,j,q}} - {\xi_{i,j,q}}{\theta_{s}}{{s^{\prime}}_{i,j,q}} - {\xi_{i,j,q}}{\theta_{r}}{{r^{\prime}}_{i,j,q}} = p_{i,j,q}^{*} - \\ && {\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - s_{i,j,q}^{*}}}{{{r_{cloud}}}} + \frac{{s_{i,j,q}^{*}}}{{r_{i,j,q}^{*}}}} \right) + {{\upbeta}_{i,q}}{f_{q}}s_{i,j,q}^{*}} \right]\\ && + {\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - {{s^{\prime}}_{i,j,q}}}}{{{r_{cloud}}}} + \frac{{{{s^{\prime}}_{i,j,q}}}}{{{{r^{\prime}}_{i,j,q}}}}} \right) + {{\upbeta}_{i,q}}{f_{q}}{{s^{\prime}}_{i,j,q}}} \right] \\ && - {\xi_{i,j,q}}{\theta_{s}}{{s^{\prime}}_{i,j,q}} - {\xi_{i,j,q}}{\theta_{r}}{{r^{\prime}}_{i,j,q}} \leqslant p_{i,j,q}^{*} - \end{array} $$

(27)

$$ \begin{array}{@{}rcl@{}} &&{\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - s_{i,j,q}^{*}}}{{{r_{cloud}}}} + \frac{{s_{i,j,q}^{*}}}{{r_{i,j,q}^{*}}}} \right) + {{\upbeta}_{i,q}}{f_{q}}s_{i,j,q}^{*}} \right]\\ && {\text{ + }}{\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - s_{i,j,q}^{*}}}{{{r_{cloud}}}} + \frac{{s_{i,j,q}^{*}}}{{r_{i,j,q}^{*}}}} \right) + {{\upbeta}_{i,q}}{f_{q}}s_{i,j,q}^{*}} \right]\\ && - {\xi_{i,j,q}}{\theta_{s}}s_{i,j,q}^{*} - {\xi_{i,j,q}}{\theta_{r}}r_{i,j,q}^{*} \\ && = p_{i,j,q}^{*} - {\xi_{i,j,q}}{\theta_{s}}s_{i,j,q}^{*} - {\xi_{i,j,q}}{\theta_{r}}r_{i,j,q}^{*}. \end{array} $$

Obviously, Eq. (27) is contradictory to the initial assumption. Therefore, the bidding strategy $\left ({s_{i,j,q}^{*},r_{i,j,q}^{*}} \right )$ is optimal.

Equation 13 is a binary function denoted as f(s_{i, j, q},r_{i, j, q}). PV changes s_{i, j, q} and r_{i, j, q} to maximize this function. The maximum value can be obtained at the boundaries ${r_{i,j,q}}{\text { = }}r_{i,j,q}^{{\min \limits } }$, ${r_{i,j,q}}{\text { = }}r_{i,j,q}^{{\max \limits } }$, ${s_{i,j,q}}{\text { = }}s_{i,j,q}^{{\min \limits } }$, ${s_{i,j,q}}{\text { = }}s_{i,j,q}^{{\max \limits } }$ and the stagnation point of the function. By taking the first partial derivatives on the four boundaries of the function f(s_{i, j, q},r_{i, j, q}), we have

$$ \begin{aligned} \frac{{\partial f({s_{i,j,q}},r_{i,j,q}^{\min })}}{{\partial {s_{i,j,q}}}} = {\text{Re}}{{\text{p}}_{i,j}}\bigg[& - {\alpha_{i,q}}{f_{q}}\left( { - \frac{1}{{{r_{cloud}}}} + \frac{1}{{r_{i,j,q}^{\min }}}} \right) \\ &+{{\upbeta}_{i,q}}{f_{q}} \bigg] - {\xi_{i,j,q}}{\theta_{s}}, \end{aligned} $$

(28)

$$ \begin{aligned} \frac{{\partial f({s_{i,j,q}},r_{i,j,q}^{\max })}}{{\partial {s_{i,j,q}}}} = {\text{Re}}{{\text{p}}_{i,j}}\bigg[& - {\alpha_{i,q}}{f_{q}}\left( { - \frac{1}{{{r_{cloud}}}} + \frac{1}{{r_{i,j,q}^{\max }}}} \right) \\ &{+{\upbeta}_{i,q}}{f_{q}} \bigg] - {\xi_{i,j,q}}{\theta_{s}}, \end{aligned} $$

(29)

$$ \frac{{\partial f(s_{i,j,q}^{\min },{r_{i,j,q}})}}{{\partial {r_{i,j,q}}}} = \frac{{{\text{Re}}{{\text{p}}_{i,j}}{\alpha_{i,q}}{f_{q}}s_{i,j,q}^{\min }}}{{r_{i,j,q}^{2}}} - {\xi_{i,j,q}}{\theta_{r}}, $$

(30)

$$ \frac{{\partial f(s_{i,j,q}^{\max },{r_{i,j,q}})}}{{\partial {r_{i,j,q}}}} = \frac{{{\text{Re}}{{\text{p}}_{i,j}}{\alpha_{i,q}}{f_{q}}s_{i,j,q}^{\max }}}{{r_{i,j,q}^{2}}} - {\xi_{i,j,q}}{\theta_{r}}. $$

(31)

By taking the first partial derivative of the function f(s_{i, j, q},r_{i, j, q}), we can get the stagnation point

$$ \left\{ \begin{array}{ll} {{\tilde s}_{i,j,q}}{\text{ = }}{{{\text{Re}}{{\text{p}}_{i,j}}{\xi_{i,j,q}}{\theta_{r}}{\alpha_{i,q}}{f_{q}}r_{cloud}^{2}} {\left/ {\vphantom {{\operatorname{Re} {{\text{p}}_{i,j}}{\xi_{i,j,q}}{\theta_{r}}{\alpha_{i,q}}{f_{q}}r_{cloud}^{2}} {\left( {r_{cloud}^{2}\xi_{i,j,q}^{2}{\theta_{s}^{2}} - } \right.}}} \right.} {\left( {r_{cloud}^{2}\xi_{i,j,q}^{2}{\theta_{s}^{2}} } \right.}} \\ -2r_{cloud}^{2}{\text{Re}}{{\text{p}}_{i,j}}{\xi_{i,j,q}}{{\upbeta}_{i,q}}{f_{q}}\theta + r_{cloud}^{2}{\text{Rep}}_{i,j}^{2}{\upbeta}_{i,q}^{2}{f_{q}^{2}} \\ +\operatorname{Re} {\text{p}}_{i,j}^{2}\alpha_{i,q}^{2}{f_{q}^{2}} - 2{r_{cloud}}{\text{Re}}{{\text{p}}_{i,j}}{\xi_{i,j,q}}{\alpha_{i,q}}{f_{q}}{\theta_{s}}{\text{ }} \\ \left. {+2{r_{cloud}}{\text{Rep}}_{i,j}^{2}{\alpha_{i,q}}{{\upbeta}_{i,q}}{f_{q}^{2}}} \right), \\ {{\tilde r}_{i,j,q}}{ { = }}{{\text{Re} {{\text{p}}_{i,j}}{\alpha_{i,q}}{f_{q}}{r_{cloud}}} {\left/ {\vphantom {{\operatorname{Re} {{\text{p}}_{i,j}}{\alpha_{i,q}}{f_{q}}{r_{cloud}}} {\left( {\operatorname{Re} {{\text{p}}_{i,j}}{r_{cloud}}{{\upbeta}_{i,q}}{f_{q}}} \right. + }}} \right.} {\left( {{\text{Re}}{{\text{p}}_{i,j}}{r_{cloud}}{{\upbeta}_{i,q}}{f_{q}}} \right. }} \\ \left. { +{\text{Re}}{{\text{p}}_{i,j}}{\alpha_{i,q}}{f_{q}} - {r_{cloud}}{\xi_{i,j,q}}{\theta_{s}}} \right). \\ \end{array} \right. $$

(32)

Therefore, the optimal bidding strategy of PV j can be expressed as

$$ \begin{array}{@{}rcl@{}} && \left\{ {s_{i,j,q}^{*},r_{i,j,q}^{*}} \right\} = \\ && \underset{{{s_{i,j,q}},{r_{i,j,q}} \in {{\Delta}_{i,j,q}}}}{\arg \max } \left\{ {{\text{Re}}{{\text{p}}_{i,j}}\left[ {\delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - {s_{i,j,q}}}}{{{r_{cloud}}}}} \right.} \right.} \right. \\ && \left. {\left. {\left. {{ { + }}\frac{{{s_{i,j,q}}}}{{{r_{i,j,q}}}}} \right) + {{\upbeta}_{i,q}}{f_{q}}{s_{i,j,q}}} \right] - {\xi_{i,j,q}}{\theta_{s}}{s_{i,j,q}} - {\xi_{i,j,q}}{\theta_{r}}{r_{i,j,q}}} \right\}. \\ \end{array} $$

(33)

Here, ${{\Delta }_{i,j,q}}{\text { = }}\left \{ {\left ({s_{_{i,j,q}}^{1},r_{i,j,q}^{1}} \right ), {\ldots } ,\left ({s_{_{i,j,q}}^{5},r_{i,j,q}^{5}} \right )} \right \}$ is the set of candidate points on stagnation point and boundaries.

This completes our proof.

Appendix B

Proof of Theorem 2

When the optimal content size $s_{i,j,q}^{*}$ and transmission rate $r_{i,j,q}^{*}$ are determined by PV j, the utility of RSU i can be rewritten as

$$ \begin{array}{@{}rcl@{}} && \tilde u_{i,j,q}^{RSU} = \text{Re}\text{p}_{i,j}\bigg[ \delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - s_{i,j,q}^{*}}}{{{r_{cloud}}}} + \hfill \frac{{s_{i,j,q}^{*}}}{{r_{i,j,q}^{*}}}} \right) +\\ && \qquad\qquad\qquad{{\upbeta}_{i,q}}{f_{q}}s_{i,j,q}^{*} \bigg] - {p_{i,j,q}}. \end{array} $$

(34)

When the bidding price of PV j is equal to the cost price, the utility of RSU i can be maximized. The maximum utility of RSU i can be calculated by

$$ \begin{array}{@{}rcl@{}} {\varphi_{i,j,q}} = \text{Re}\text{p}_{i,j}\bigg[\delta - {\alpha_{i,q}}{f_{q}}\left( {\frac{{{S_{q}} - s_{i,j,q}^{*}}}{{{r_{cloud}}}} + \frac{{s_{i,j,q}^{*}}}{{r_{i,j,q}^{*}}}} \right) +\\ {{\upbeta}_{i,q}}{f_{q}}s_{i,j,q}^{*} \bigg] - {\xi_{i,j,q}}{\theta_{s}}s_{i,j,q}^{*} - {\xi_{i,j,q}}{\theta_{r}}r_{i,j,q}^{*}. \end{array} $$

(35)

Combining Eq. (34) and Eq. (35), the expected utility of PV j can be expressed as

$$ E\left\{ {u_{i,j,q}^{PV}} \right\} = {\mathbb{P}_{i,j}}({\varphi_{i,j,q}} - \tilde u_{i,j,q}^{RSU}), $$

(36)

where ${\mathbb {P}_{i,j}}$ is the probability that PV j wins the game. Note that RSU i wants to select the PV to obtain the maximum utility. Namely, we can obtain

$$ u_{i,j,q}^{RSU {\text{*}} } = \max \left\{ {\tilde u_{i,j,q}^{RSU}|j = 1,2, {\ldots} N} \right\}, $$

(37)

where N is the number of PVs with content q parked around RSU i. Thus, ${\mathbb {P}_{i,j}}$ also means that the probability of PV j to maximize the utility of RSU i. It can be calculated by

$$ {\mathbb{P}_{i,j}} = \prod\limits_{j^{\prime} = 1,j^{\prime} \ne j,{X_{i,j,q}} = 1}^{J} {P\left\{ {\tilde u_{i,j,q}^{RSU} > \tilde u_{i,j^{\prime},q}^{RSU}} \right\}}. $$

(38)

Let $\tilde u_{i,j,q}^{RSU} = {\omega _{i,j,q}}\left ({{\varphi _{i,j,q}}} \right )$ represent the relationship function between φ_{i, j, q} and $\tilde u_{i,j,q}^{RSU}$. The greater the φ_{i, j, q}, the higher the social welfare. It also means that PV j has more choices in its bidding price. Therefore, the function ${\omega _{i,j,q}}\left (\cdot \right )$ is an increasing function, we can have

$$ \begin{aligned} P\left\{ {\tilde u_{i,j,q}^{RSU} > \tilde u_{i,j^{\prime},q}^{RSU}} \right\} &= P\left\{ {{\varphi_{i,j,q}} > {\varphi_{i,j^{\prime},q}}} \right\} \\ &= P\left\{ {{\xi_{i,j,q}} < {\xi_{i,j^{\prime},q}}} \right\} \\ &= 1 - {\Phi} \left( {{\xi_{i,j,q}}} \right), \end{aligned} $$

(39)

where ${\Phi } \left (\cdot \right )$ is the probability distribution function of the cost parameter ${\xi _{i,j^{\prime },q}}$ of PV $j^{\prime }$. Therefore, the probability ${\mathbb {P}_{i,j}}$ can be rewritten as

$$ {\mathbb{P}_{i,j}} = {\left( {1 - {\Phi} \left( {{\xi_{i,j,q}}} \right)} \right)^{N - 1}}. $$

(40)

We set ${\mathbb {P}_{i,j}} = H\left ({{\varphi _{i,j,q}}} \right )$ to reflect the relationship between φ_{i, j, q} and the probability ${\mathbb {P}_{i,j}}$. Thus, we have

$$ {\mathbb{P}_{i,j}} = H\left( {{\varphi_{i,j,q}}} \right) = H\left( {{\omega_{i,j,q}}^{- 1}\left( {\tilde u_{i,j,q}^{RSU}} \right)} \right). $$

(41)

Then, the expected utility of PV j can be rewritten as

$$ E\left\{ {u_{i,j,q}^{PV}} \right\} = H\left( {{\omega_{i,j,q}}^{- 1}\left( {\tilde u_{i,j,q}^{RSU}} \right)} \right) \cdot ({\varphi_{i,j,q}} - \tilde u_{i,j,q}^{RSU}). $$

(42)

The first derivative of $E\left \{ {u_{i,j,q}^{PV}} \right \}$ with respect to ${\tilde u_{i,j,q}^{RSU}}$ can be calculated by

$$ \begin{array}{@{}rcl@{}} \frac{{\partial E\left\{ {u_{i,j,q}^{PV}} \right\}}}{{\partial \tilde u_{i,j,q}^{RSU}}} & = & \frac{{({\varphi_{i,j,q}} - \tilde u_{i,j,q}^{RSU}) \cdot \dot H\left( {{\omega_{i,j,q}}^{- 1}\left( {\tilde u_{i,j,q}^{RSU}} \right)} \right)}}{{{\omega '}_{_{i,j,q}}}\left( {{\varphi_{i,j,q}}} \right)}\\ && - H\left( {{\omega_{i,j,q}}^{- 1}\left( {\tilde u_{i,j,q}^{RSU}} \right)} \right). \end{array} $$

(43)

where $\dot H\left (\cdot \right )$ is the derivative of the function $H\left (\cdot \right )$ to $\tilde u_{i,j,q}^{RSU}$. Let $\frac {{\partial E\left \{ {u_{i,j,q}^{PV}} \right \}}}{{\partial \tilde u_{i,j,q}^{RSU}}} = 0$, we have

$$ \frac{{\partial \left[ {H\left( {{\varphi_{i,j,q}}} \right) \cdot {\omega_{i,j,q}}\left( {{\varphi_{i,j,q}}} \right)} \right]}}{{\partial {\varphi_{i,j,q}}}} = \dot H\left( {{\varphi_{i,j,q}}} \right) \cdot {\varphi_{i,j,q}}. $$

(44)

By solving Eq. (44), we can obtain

$$ {\omega_{i,j,q}}\left( {{\varphi_{i,j,q}}} \right) = \frac{1}{{H\left( {{\varphi_{i,j,q}}} \right)}}{\int}_{0}^{{\varphi_{i,j,q}}} {\dot H\left( x \right)} \cdot x \cdot dx. $$

(45)

By solving the integral equation in Eq. (45), we have

$$ {\omega_{i,j,q}}\left( {{\varphi_{i,j,q}}} \right) {=} \tilde u_{i,j,q}^{RSU} {=} {\varphi_{i,j,q}} {-} \frac{1}{{H\left( {{\varphi_{i,j,q}}} \right)}}{\int}_{0}^{{\varphi_{i,j,q}}} {H\left( y \right)} dy. $$

(46)

Substituting $\tilde u_{i,j,q}^{RSU}$ and φ_{i, j, q} into Eq. (45), we can obtain the optimal bidding price of PV j

$$ \begin{array}{@{}rcl@{}} p_{i,j,q}^{\text{*}} & = & {\xi_{i,j,q}}{\theta_{s}}s_{i,j,q}^{*} + {\xi_{i,j,q}}{\theta_{r}}r_{i,j,q}^{*}\\ && + \frac{1}{{H\left( {{\varphi_{i,j,q}}} \right)}}{\int}_{0}^{{\varphi_{i,j,q}}} {H\left( y \right)} dy, \end{array} $$

(47)

where $H\left ({{\varphi _{i,j,q}}} \right ) = {\mathbb {P}_{i,j}} = {\left ({1 - {\Phi } \left ({{\xi _{i,j,q}}} \right )} \right )^{N - 1}}$. Since ξ_{i, j, q} obeys the uniform distribution, we can obtain

$$ {\Phi} \left( {{\xi_{i,j,q}}} \right) = \frac{{{\xi_{i,j,q}} - \xi_{i,j,q}^{\min }}}{{\xi_{i,j,q}^{\max } - \xi_{i,j,q}^{\min }}}. $$

(48)

Therefore, the optimal bidding price of PV j is

$$ \begin{array}{@{}rcl@{}} p_{i,j,q}^{\text{*}} & = & {\xi_{i,j,q}}{\theta_{s}}s_{i,j,q}^{*} + {\xi_{i,j,q}}{\theta_{r}}r_{i,j,q}^{*}\\ && + \frac{{\left( {{\theta_{s}}s_{i,j,q}^{*} + {\theta_{r}}r_{i,j,q}^{*}} \right)}}{N}\left( {\xi_{i,j,q}^{\max } - {\xi_{i,j,q}}} \right). \end{array} $$

(49)

This completes our proof.