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A kind of novel RSAR protocol for mobile vehicular Ad hoc network

  • De-gan Zhang
  • Xiao-huan Liu
  • Yu-ya CuiEmail author
  • Lu Chen
  • Ting Zhang
Regular Paper
  • 44 Downloads

Abstract

MVANET (Mobile Vehicular Ad hoc Network) as one part of Mobile Vehicular Ad hoc Network (MANET) has the feature: unreliable communication link and frequent change of network topology. In order to improve the communication link reliability and efficient routing, a kind of novel RSAR (rewarding smart Ad hoc routing) protocol for Mobile Vehicular Ad hoc Network is presented in this paper. Based on our suggested model, the reliability of the communication link is assessed and design a novel routing protocol according to the strategy of deep learning. As a kind of machine learning approach, the D-Learning (Deep-Learning) algorithm can be helpful to get the reliable routing path. The advantage of the RSAR protocol is evaluated by the simulator and tests of the practical applications. The experimental results show that RSAR exhibits good results at a delivery rate, end-to-end delay and average hops compared with SLBF, QLAODV and GPSR.

Keywords

Mobile vehicular Ad hoc networks Network topology Communication link Smart Deep learning 

1 Introduction

It is well known that MVANET (Mobile Vehicular Ad hoc Network) as one part of Mobile Vehicular Ad hoc Network (MANET) has the following feature: unreliable communication link and frequent change of network topology (Fukushima 2011; Weiss 2011; Liu 2019). MVANET is a very important topic on the problem of intelligent transportation system design. Nowadays, many research institutions have begun to focus on this research (Gao and Liu 2019; Seredynski et al. 2011; Al-Sultan et al. 2014; Lalitha and Rajesh 2014). In the intelligent transportation system, MVANET can achieve many security and non-security applications, such as security areas, safety information notification, road obstruction warnings, and accident avoidance applications, as well as applications such as in-car entertainment (Leung 2001; Liu et al. 2016; Abbasi et al. (2014); Wang and Song 2015), multimedia data sharing, remote controlling and telecommunications services in non-security areas. Routing protocols, as an important part of MVANET, which are a vital part of intelligent traffic. In order to meet the needs of different applications under different scenarios, it is a major problem to design a routing protocol that can adapt to different scenarios and has high reliability and low latency.

Because MVANET is a special MANET, many traditional MANET routing algorithms are used in the MVANET network. These routing algorithms can be divided into the following categories. Here are more representative of the four routing algorithms. They are respectively, active routing, reactive routing, geo-based beacon routing and geo-based beacon-less broadcast routing. Active routing algorithm, also known as table-driven routing algorithm, is more representative of the Destination node Sequence Distance Vector (DSDV) (Zhu 2012; Jerbi et al. 2009; Li et al. 2015; Eiza and Ni 2013) and Optimized Link State Routing (OLSR) (Yan and Olariu 2011; Zhang et al. 2014; Zhang 2012a, b; Chen et al. 2018) routing algorithm. This algorithm has a periodic routing packet broadcast, exchange routing information, and maintain a routing table containing routing information arriving at other nodes, regardless of whether there is a communication requirement. Reactive routing algorithm, also known as on-demand routing algorithm, is mainly worked by the route discovery and routing maintenance of the two processes. The representative algorithms are Ad hoc On-Demand Distance Vector (AODV) routing (Liu 2018; Tang 2019; Liu 2017) and Dynamic Source Routing (DSR) (Zhou 2018; Niu 2017; Zhang 2019; Zhang et al. 2014). Based on the geography-based routing algorithm, the researchers also proposed a beaconless broadcast routing algorithm based on geographical location. The representative algorithms are Self-adaptive and Link-aware Beaconless Forwarding protocol (SLBF), Timer Greedy Forwarding Algorithm (TGF) (Zheng and Zhang 2015; Zheng and Zhao 2016; Toutouh et al. 2012; Wu et al. 2010; Abboud and Zhuang 2014; Zhu et al. 2015; Chen et al. 2010; Beaulieu and Xie 2004; Cheng and Panichpapiboon (2012); Zhu and Li 2016) and so on.These routing protocols do not need to consider the topology changes, just using GPS to locate the destination node, and are designed by estimating traffic flow, but it does not consider the link reliability between nodes. Some reliable routing protocols are proposed, such as SLBF (Xue and Kumar 2004; Panichpapiboon et al. 2010) and EG-RAODV (Pascoe-Chalke et al. 2010; Darwish et al. 2018; Namboodiri and Gao 2007; Khasawneh et al. 2018). These protocols are designed by adding parameters as link reliability between nodes and packet error rate. It can improve the packet delivery ratio to a certain extent, but cannot guarantee the time delay.

In the aforementioned algorithms, the node also needs to use GPS to locate the destination node location. The sending node sends the data packet in the form of broadcast. The node does not need to maintain the neighbor table, but instead chooses the next hop forwarding node through the timer delay time, and becomes the node of the forwarding node and uses the broadcast form to suppress other node forwarding duplicate packets. Although this algorithm reduces the overhead by reducing the beacon packet, it takes the broadcast and timing so that it not only takes up many idle channels, wastes the transmission time, but also when the sending node increases and the amount of data is enlarged, it is easy to cause serious broadcast storm problems and difficultly guarantees the reliability of packet transmission.

In the literature (Wu et al. 2011; Ruiling et al. 2014), the authors proved by experiments that the distance between vehicles can be more consistent with real traffic flow and safety distance when it is lognormal distribution. Fully understanding of the traffic flow model and the motion characters of vehicles can help effectively evaluate the link reliability between nodes. In the literature (Sohail et al. 2018), the SL trust model, a subjective logic trust mechanism, was proposed, which reduced extra routing and computation overhead. The literature (Song et al. 2018) improved the current uneven clustering routing algorithm, which has a longer network life and better stability. The literature (Liu et al. 2018) presented a multi-source information fusion approach to detect bogus emergency messages, which can achieve a higher significantly detection rate. The literature (Qin et al. 2018) proposed a dynamic calculation method of the trust value of users, which has a better routing performance. With continuous researches of the routing protocol in recent years, some intelligent protocols (Zhang and Zhang 2018; Zhang et al. 2019; Zhang and Dong 2018; Zhu and Liu 2016; Hamed 2018; Ma 2017; Sujoy and Andrei 2014; Ahmed 2017; Liang and Ma et al. 2018) are applied in MVANET and have better results compared to traditional the routing protocols. As a self-learning algorithm, D-Learning (Deep -Learning) algorithm (Wu et al. 2010; Wu et al. 2011; Ruiling et al. 2014; Sohail et al. 2018; Song et al. 2018; Liu et al. 2018; Qin et al. 2018) can find the shortest path from the source node to the destination node through constant interaction with the outside environment. Based on this idea, a kind of novel rewarding smart Ad hoc routing protocol (RSAR) is proposed by using the D-Learning strategy in this paper. It can adaptively adjust D-Table with ensuring the reliability of each hop link to adopt such dynamic network topology as MVANET.

MVANET as a kind of mobile ad hoc network (MANET), its high-speed mobility of the nodes makes the network topology change frequently, and the transmission path can be easily interrupted, so the routing efficiency is lower. In order to improve the routing efficiency and traffic safety, and avoid the occurrence of traffic accidents (such as collision, rear-end), we present a reliable and adaptive routing protocol. The reliability of the whole link depends on the links between each hop. This paper establishes a reliable model of the link between nodes by a detailed study of the motion characteristics of vehicles. By calculating the probability of link reliability, the paper uses the result as a parameter in the D-Learning algorithm to design the RSAR protocol.

2 Modelling of MVANET

2.1 Interactive model of the vehicles

Considering a MVANET on a highway with no on or off ramps, all the vehicles in the road have the same transmission range, denoted by \( R \). Assuming that the transmission range is much longer than the width of the highway so that a node can communicate with any node within a longitudinal distance of less than \( R \) from it, therefore we ignore the width of the road (Abboud and Zhuang 2014; Zhu et al. 2015; Chen et al. 2010; Beaulieu and Xie 2004; Cheng et al. 2012; Zhu and Li 2016; Xue and Kumar 2004). The optimal route on the highway is also feasible. We still assume that there are acceleration, deceleration, changing lanes and overtaking on the road.

In a MANET, when choose the next hop forwarding node, we only need to consider the link quality and the distance between the two nodes. Analysis of the network topology model 2, when \( V_{S} \) send data to the \( V_{D} \), from the Fig. 1, we can easily know that \( V_{2} \) and send nodes \( V_{S} \) closer, and \( V_{ 3} \) near the broadcast edge of \( V_{S} \), \( V_{S} \) and \( V_{2} \) link quality significantly better than \( V_{ 3} \). However, it is easy to select \( V_{2} \) as the next hop forwarding node to ignore \( V_{ 3} \) if the quality of the link is only viewed from a unilateral basis, regardless of the effective neighbor density problem of the forwarding node. When \( V_{2} \) is selected as the forwarding node, it is obvious, because \( V_{ 4} \) is not within the hop of \( V_{2} \), this not only increases the number of hops, but also increases the delay time of packet transmission, but also makes the local maximization problem more prone to occur.
Fig. 1

An example of Vehicle model in MVANET

Assuming that the highway is in a steady traffic flow condition defined by a time-invariant vehicle density, it denotes the vehicle density on the lane under consideration by D in vehicles per kilometer (veh/km). Let μ and σ be the mean and the standard deviation of the distance headway in meters, respectively. Where μ =1000/D and σ are constant system parameters and take different values according to the vehicle density. Let
$$ X_{i} = \left\{ {X_{i} \left( m \right),m = 0,1,2, \ldots ,i = 1,2,3, \ldots } \right\} $$
(1)
be a discrete-time stochastic process of the ith distance headway, between node \( i - 1 \) and node \( i \), where Xi(m) is a random variable representing the distance headway of node i at the mth time step. At any time step, Xi(m)∈[α,Xmax] for all i ≥1, m ≥ 0. Where α and Xmax is the minimum and maximum inter-vehicle distances, respectively. Furthermore, assume that Xi is independent with identical statistical behaviors for all i ≥ 1. Besides, the distance headway between vehicles is log-normal distributed (Chen et al. 2010) and subject to XilogN (μi, δi). In Fig. 1, we regard node Vs as the reference node, then X represents the distance between Vs and any other node, where
$$ X = \sum\limits_{i = 1}^{m} {X_{i} } $$
(2)
so X is also log-normal distributed (Beaulieu and Xie 2004).
In a MVANET, let one lane’s width be W, the number of lanes be m, the transmission range be R and the node density be λ. Then, the probability of no nodes in the relay selection area is given by
$$ P_{n} = e^{ - \lambda g(x)} $$
(3)
where
$$ g(x) = x(2 - \sqrt {1 - x^{2} } ) - \arcsin x\begin{array}{*{20}c} {} & {x \in \left( {0,1} \right]} \\ \end{array} $$
(4)

Lemma 1

In a MVANET, let the inter-vehicle spacing be exponentially distributed with the parameter\( \lambda_{1} \)on\( {\text{Lane}}_{1} \)and\( \lambda_{2} \)on\( {\text{Lane}}_{2} \), respectively (Cheng et al. 2012). Let\( R' = \delta R \), where 0 < δ  1. Then, we have the following lemma:
  1. 1.
    The cumulative distribution function (CDF) F of the spacing between the reference node and its nearest intra-level node (i.e., \( {\text{X}}_{\text{near}} \)) is given by
    $$ {\text{F}}_{{{\text{X}}_{Near} }} \left( x \right) = 1 - e^{{ - \lambda_{1} x}} ,x \in \left( {0,\infty } \right) $$
    (5)
     
  2. 2.
    The CDF F of the spacing between the reference and its nearest inter-level node (i.e., \( {\text{Y}}_{\text{near}} \)) is given by
    $$ {\text{F}}_{{{\text{Y}}_{Near} }} \left( x \right) = 1 - e^{{ - \lambda_{2} y}} - \lambda_{2} yEi( - \lambda_{2} y),y \in \left( {0,\infty } \right) $$
    (6)
     

Proof

Let \( {\text{V}}_{2,0} \) and \( {\text{V}}_{2,1} \) are the nearest inter-level nodes of the reference \( {\text{V}}_{1,0} \). Thus, \( {\text{V}}_{1,0} \) can be seen as a node randomly distributed between \( {\text{V}}_{2,0} \) and \( {\text{V}}_{2,1} \) along the coordinate axis (Zhu and Li 2016). The horizontal distance between \( {\text{V}}_{1,0} \) and \( {\text{V}}_{2,1} \) is \( {\text{Y}}_{\text{near}} \), which uniformly distributes in \( \left( {0,S_{2,1} } \right) \). Thus, the CDF F of \( {\text{Y}}_{\text{near}} \) is given by
$$ \begin{aligned} F_{{Y_{Near} }} \left( y \right) &= \Pr \left\{ {Y_{Near} \le y} \right\} \hfill \\ &= \int\limits_{0}^{\infty } {\Pr \left\{ {Y_{Near} \le y|S_{2,1} = s} \right\}} f_{{S_{2,1} }} \left( s \right)ds \hfill \\ &= \int\limits_{0}^{y} {\lambda_{2} e^{{ - \lambda_{2} s}} } ds + \int\limits_{y}^{\infty } {\frac{y}{s}} \lambda_{2} e^{{ - \lambda_{2} s}} ds \hfill \\ &= 1 - e^{{ - \lambda_{2} y}} - \lambda_{2} yEi\left( { - \lambda_{2} y} \right),y \notin \left( {0,\infty } \right) \hfill \\ \end{aligned} $$
(7)

The proof is over.

2.2 Modelling of communication links

Absolutely, a vehicle can frequently change its speed and acceleration in the highway. However, it will not change its speed and acceleration all the time. When the surrounding vehicle is stable, the vehicle will maintain a certain speed for a period of time until it meets a diversion or obstacle and will consider changing its speed. When the surrounding road condition is wider than the open space, the vehicle can be selected to maintain the acceleration for a period of time. Therefore, it is of practical significance to assume that the vehicle will maintain a certain speed or maintain acceleration for a period of time in the link duration model.

The stability of the vehicle nodes is determined by the link stability in the learning process of the RSAR protocol. The criteria include the hop count, link quality and bandwidth between the nodes, and find the node with the highest link stability to forward information. If the current vehicle node link is disconnected or unstable, the learning process of the RSAR protocol will recalculate the link stability between the nodes, and select the vehicle node with the best link stability for information forwarding.

Taking into account that the movement of the vehicle is always in accordance with a fixed road, there are mainly two conditions when the link disconnected between two vehicle nodes. Assuming that in time t0=0, vehicle j is in the one-hop communication range of vehicle i, and the vehicle j is located in front of vehicle i. The initial distance between two vehicles is a random variable X. The maximum communication radius of the vehicle is constant R. At the initial moment, X meet 0 ≤ X < R According to the system model, there will be acceleration, deceleration and overtaking of vehicles in a highway. The maximum speed limit on the road is set to vm and all vehicles should move under or equal to vm. Assuming that the acceleration of any vehicle at the beginning of the vehicle is a(0) and its speed is v(0). When t  ≥ 0, the acceleration is defined as a(t) and the speed is defined as v(t).

Lemma 2

In a MVANET, let the inter-vehicle spacing be exponentially distributed with the parameter\( \lambda_{1} \)on\( {\text{Lane}}_{1} \)and\( \lambda_{2} \)on\( {\text{Lane}}_{ 2} \), respectively. Let\( R' = \delta R \), where 0 < δ  1. Then, we have the following lemma (Zhu and Li 2016).
  1. 1.
    The CDF F of the spacing between the reference node and its farthest intra-level neighbor (i.e., X) is given by
    $$ {\text{F}}_{\text{X}} \left( x \right) = \frac{{e^{{ - \lambda_{1} R}} \left( {e^{{ - \lambda_{1} x}} - 1} \right)}}{{1 - e^{{ - \lambda_{1} R}} }} $$
    (8)
     
  2. 2.
    The CDF F of the spacing between the reference node and its farthest inter-level neighbor (i.e., Y) is given by
    $$ {\text{F}}_{\text{Y}} \left( x \right) = \frac{{e^{{ - \lambda_{2} \left( {R' - y} \right)}} \left( {1 - e^{{ - \lambda_{2} y}} - \lambda_{2} yEi\left( { - \lambda_{2} y} \right)} \right)}}{{1 - e^{{ - \lambda_{2} R'}} - \lambda_{2} R'Ei\left( { - \lambda_{2} R'} \right)}} $$
    (9)
     
  3. 3.

    The CDF F of the second one-hop progress on Lane 1 (i.e., Z)is described by

    $$ {\text{F}}_{\text{Z|X}} \left( {z|x} \right) = \frac{{e^{{\lambda_{1} \left( {z - R} \right)}} - e^{{ - \lambda_{1} x}} }}{{1 - e^{{ - \lambda_{1} x}} }} $$
    (10)
    where \( x \in \left( {0,R} \right),y \in \left( {0,R'} \right),{\rm and} \)\( z \in \left( {R - x,R} \right). \)
     

Proof

Because distributions of inter-vehicle spacing are positive i.i.d. random variables (Zhu and Li 2016). Let the number of the reference node’s intra-level neighbors be N, where N is a non-negative integer. Then, the value of X is equal\( X = \sum\nolimits_{i = 1}^{N} {S_{1,i} } \). We have\( \sum\nolimits_{i = 1}^{N - 1} {S_{1,i} } < X \le R \)and\( \sum\nolimits_{i = 1}^{N + 1} {S_{1,i} } > R \). Let \( N_{{i,\left[ {a,b} \right]}} \) be the number of nodes in the range [a, b] on \( Lane_{i} \). Then, we can calculate the CDF F of X by
$$ \begin{aligned} F_{X} \left( x \right) &= \Pr \left( {X \le x} \right) \\&= \Pr \left( {\sum\nolimits_{i = 1}^{N} {S_{1,i} } \le x,\sum\nolimits_{i = 1}^{N + 1} {S_{1,i} } > R|x \le R} \right) \hfill \\ &= \frac{{\sum\nolimits_{n = 1}^{\infty } {\Pr \left( {\sum\nolimits_{i = 1}^{n} {S_{1,i} } \le x,\sum\nolimits_{i = 1}^{n + 1} {S_{1,i} } > R|x \le R} \right)} }}{{\Pr \left\{ {x \le R} \right\}}} \hfill \\ &= \frac{{\sum\nolimits_{n = 1}^{\infty } {\Pr \left( {N_{1,[0,x]} = n} \right)\Pr \left( {N_{1,[x,R]} = 0} \right)} }}{{1 - e^{{ - \lambda_{1} R}} }} \hfill \\ &= \frac{{\sum\nolimits_{n = 1}^{\infty } {\left( {\frac{{\left( {\lambda_{1} x} \right)^{n} }}{n!}e^{{ - \lambda_{1} x}} } \right)e^{{ - \lambda_{1} \left( {R - x} \right)}} } }}{{1 - e^{{ - \lambda_{1} R}} }} \hfill \\ &= \frac{{e^{{ - \lambda_{1} R}} \left( {e^{{\lambda_{1} x}} - 1} \right)}}{{1 - e^{{ - \lambda_{1} R}} }},x \in (0,R] \hfill \\ \end{aligned} $$
(11)
Assume the reference node has M inter-level neighbors, where M is a non-negative integer. Then, the distance between the reference and its farthest inter-level neighbor is given by \( Y = \sum\nolimits_{i = 1}^{M - 1} {S_{2,i} } \). We have \( \sum\nolimits_{i = 1}^{M - 1} {S_{2,i} } < Y \le R \) and \( \sum\nolimits_{i = 1}^{M + 1} {S_{2,i} } > R \). Thus, we can get the CDF F of Y by
$$ \begin{aligned} &F_{\text{Y}} \left( y \right) = \Pr \left( {Y \le y} \right) \\& = \Pr \left( {\sum\nolimits_{j = 1}^{M} {S_{2,j} } \le y,\sum\nolimits_{j = 1}^{M + 1} {S_{2,j} } > R'|y \le R'} \right) \\& = \frac{{\int_{0}^{y} {f_{{Y_{n} }} \left( s \right)\Pr \left\{ {\sum\nolimits_{j = 2}^{M} {S_{2,j} } \le y - s,\sum\nolimits_{j = 2}^{M + 1} {S_{2,j} } > R' - s,y \le R'} \right\}ds} }}{{\Pr \left\{ {Y_{n} \le R'} \right\}}} \\& = \frac{{\int_{0}^{y} {f_{{Y_{n} }} \left( s \right)\sum\nolimits_{m = 1}^{\infty } {\Pr \left\{ {Z_{{2,\left[ {0,y - s} \right]}} = m - 1} \right\}\Pr \left\{ {Z_{{2,\left[ {y - s,R'} \right]}} = 0} \right\}} ds} }}{{1 - \Pr \left\{ {Y_{n} > R'} \right\}}} \\& = \frac{{\int_{0}^{y} {f_{{Y_{n} }} \left( s \right)\sum\nolimits_{m = 1}^{\infty } {\left( {\frac{{\left( {\lambda_{2} \left( {y - s} \right)} \right)^{m - 1} }}{(m - 1)!}e^{{ - \lambda_{2} \left( {y - s} \right)}} e^{{ - \lambda_{2} \left( {R' - y + s} \right)}} } \right)} ds} }}{{1 - e^{{ - \lambda_{2} R'}} - \lambda_{2} R'Ei( - \lambda_{2} R')}} \\& = \frac{{e^{{ - \lambda_{2} \left( {R' - y} \right)}} \left( {1 - e^{{ - \lambda_{2} y}} - \lambda_{2} yEi( - \lambda_{2} y)} \right)}}{{1 - e^{{ - \lambda_{2} R'}} - \lambda_{2} R'Ei( - \lambda_{2} R')}},y \in (0,R'] \\ \end{aligned} $$
(12)
The proof is over.
We can calculate the instantaneous speed as follows:
  1. 1.
    If \( a\left( 0 \right) = 0 \), there is
    $$ v\left( t \right) = v\left( 0 \right) $$
    (13)
     
  2. 2.
    If \( a\left( 0 \right) > 0 \), there are
    $$ v\left( t \right) = \left\{ {\begin{array}{ll} {v\left( 0 \right) + a\left( 0 \right)t} & \quad {t \le \frac{{v_{m} - v\left( 0 \right)}}{a\left( 0 \right)}} \\ {v_{m} } & \quad {\text{else}} \\ \end{array} } \right. $$
    (14)
     
  3. 3.
    If \( a\left( 0 \right) < 0 \), there are
    $$ v\left( t \right) = \left\{ {\begin{array}{ll} {v\left( 0 \right) + a\left( 0 \right)t} & \quad {t \le \frac{ - v\left( 0 \right)}{a\left( 0 \right)}} \\ 0 & \quad {\text{else}} \\ \end{array} } \right. $$
    (15)
     
According to the definition above, the distance that any vehicle moves with the speed of v(x) at the time interval [0,t] is defined as:
$$ S\left( t \right) = \int\limits_{0}^{t} {v\left( x \right)dx} $$
(16)
According to the definition above, we can calculate the distance between vehicles i and j at time t. Assuming that the initial speed and acceleration of vehicles i and j are ai(0), vi(0), aj(0) and vj(0) respectively; the instantaneous speed and acceleration of vehicles i and j at time t are ai(t), vi(t), aj(t) and vj(t) respectively. We can get the distances of vehicles i and j at time interval [0,t] as follows:
$$ S_{i} \left( t \right) = \int\limits_{0}^{t} {v_{i} \left( x \right)dx} $$
(17)
$$ S_{j} \left( t \right) = \int\limits_{0}^{t} {v_{j} \left( x \right)dx} $$
(18)
When t = 0, the initial distance between vehicles i and j is X, that is the distance di,j(0) = X and the di,j(t) define is:
$$ d_{i,j} (t) = \left\{ {\begin{array}{*{20}c} {S_{j} \left( t \right) - S_{i} \left( t \right) + X} & {\text{at the same direction}} \\ {S_{j} \left( t \right) + S_{i} \left( t \right) + X{\kern 1pt} } & {\text{at opposite direction}} \\ \end{array} } \right. $$
(19)

From formula (19) we can see obviously that when di,j > R, the link is disconnected.

We first analyze the link duration which two vehicles move in the opposite direction. When two vehicles meet:
$$ S_{j} \left( t \right) + S_{i} \left( t \right) + X = R $$
(20)
We can calculate the maximum link duration t. Considering that
$$ S_{j} \left( t \right) + S_{i} \left( t \right) = \frac{1}{2}a_{r} t^{2} + v_{r} t $$
(21)
where \( a_{r} = a_{i} + a_{j} \) and \( v_{r} = v_{i} + v_{j} \). Put it into formula (20), the maximum link duration t is obtained as:
$$ t = \frac{{ - v_{r} + \sqrt {v_{r}^{2} + 2a_{r} \left( {R - X} \right)} }}{{a_{r} }} $$
(22)
While two vehicles move with the same direction, it is critical to determine whether vehicle i or j is in front. When
$$ S_{j} \left( t \right) - S_{i} \left( t \right) + X > 0, $$
(23)
vehicle j is located in front of vehicle i; On the contrary vehicle i is located in front of vehicle j. In order to effectively express that which vehicle is in front, we define a symbolic function as follows:
$$ I\left( {i, j} \right) = \left\{ {\begin{array}{ll} 1 & {S_{j} \left( t \right) - S_{i} \left( t \right) + X > 0} \\ { - 1} & {\text{else}} \\ \end{array} } \right. $$
(24)
When the link is in a critical state of disconnection, we have:
$$ S_{j} \left( t \right) - S_{i} \left( t \right) + X = R \cdot I\left( {i,j} \right) $$
(25)

At this time there are 2 cases to calculate the link duration.

When I(i, j) = 1, vehicle j is located in front of vehicle i. From formula (25) we know that
$$ S_{j} \left( t \right) - S_{i} \left( t \right) + X = R $$
(26)
Similar to formula (22), due to
$$ S_{j} \left( t \right) - S_{i} \left( t \right) = \frac{1}{2}a_{r} t^{2} + v_{r} t $$
(27)
where \( a_{r} = a_{j} - a_{i} \) and \( v_{r} = v_{j} - v_{i} \), we can get the time t as follows:
$$ t = \frac{{ - v_{r} + \sqrt {v_{r}^{2} + 2a_{r} \left( {R - X} \right)} }}{{a_{r} }} $$
(28)
Assuming that I(i, j) = − 1, vehicle i is located in front of vehicle j. From formula (25) we can get:
$$ S_{j} \left( t \right) - S_{i} \left( t \right) + X = - R $$
(29)
and calculate the link duration t as follows:
$$ t = \frac{{ - v_{r} + \sqrt {v_{r}^{2} - 2a_{r} \left( {R + X} \right)} }}{{a_{r} }} $$
(30)
Formula (22), (28) and (30) can be used to calculate the link duration of sending node and arbitrary node in one hop range.

3 Novel RSAR protocol

In MVANET, by ensuring the reliability of each hop to achieve the reliability of the whole routing path, our RSAR protocol chooses the next hop to forward the node, it is not blind to select only the node that is the farthest from the sending node, but it takes into account the distance calculation of the destination node, the link state between the nodes and the effective node degree of the next one-hop. The optimal route is established according to the link reliability in the random walk topology, and the link reliability between the nodes is calculated according to the link reliability model. The method evaluates the link reliability between the vehicle nodes through the link maintenance time. The higher the link reliability of the vehicle nodes, the higher the reward value it receives. Find the best route from the source node to the destination node in a dynamic network such as a random walk topology.

According to the related works, D-Learning strategy is unsupervised self-learning. Through continuous interacting with the external environment, it can adaptively adjust its value to find the optimal path to reach the destination. That makes it be able to respond well to the dynamic MVANET. This part will describe the routing and forwarding strategy of augmented D-Learning algorithm in MVANET.

3.1 Augmented D-Learning strategy

In MVANET, because most of the time to send packets from node passes through multiple hops to reach the destination node, and it is very important to evaluate each hop link in order to ensure the reliability of the whole link. In order to enable the quality of the inter-node link to meet the requirement of packet transmission, the accuracy of the package and the link maintenance time are used to evaluate the quality of the link. With these two measures, we can accurately evaluate the status of the link between the sending node and the forward node. When choosing the next hop forwarding nodes, we consider the packet transmission delay time of the node, such as local optimization problem. Joining the forwarding nodes effectively neighbor node density can effectively solve these problems.

Augmented D-Learning can be used to our RSAR protocol, because it is a heuristic learning method based on the learning Agent. Generally speaking, in augmented D-Learning algorithm, the learning process of the Agent is mainly composed of a three tuple {S,A,R}, where S = {s1,s2,s3….sn} represents the state space; A = {a1,a2,a3,….an} represents the activity space, and moving from one state to another is regarded as an effective activity; R represents the immediate reward for an activity, and the closer to the destination, the higher the reward of the activity was obtained. The detailed learning process is supported by Lemmas 1 and 2.

The MVANET environment may be full of the learning environment of the Agent. The learning Agent is each vehicle node. The state space S of an Agent is composed of other vehicle nodes in its one hop range. The beacon packet in activity space A is transmitted from one vehicle to another, which is defined as an activity. The immediate rewards R which the Agent carries out an activity and get. The important symbols for the design of the RSAR protocol are shown in Table 1.
Table 1

Important mathematical symbols

Symbols

Introduction

N d

One hop neighbor node set of destination node d

D s (d,x)

The D-Value to be updated

s

The Agent node

x

The neighbor node of s

d

The destination node

N x

The x’s neighbor node

R

The reward value

γ

The discount factor

r(l)

The reliability of inter-node links

n

The number of packets which the node send and receive

S B

The size of the packet and represented in a byte

T

The time interval

The value obtained by the Agent for an activity is called a rewarding value and its range is [0,1]. Because the one-hop neighbor nodes of a destination node can reach the destination node directly, the rewarding value is 1. Formula (31) defines the initial value R of the entire network as follows:
$$ R = \left\{ {\begin{array}{*{20}c} 1 & {s \in N_{d} } \\ 0 & {\text{else}} \\ \end{array} } \right. $$
(31)

The rewarding value of the activity for all the neighbor nodes of the destination node is one. In the learning process, the rewarding value that may be obtained from a state transition to another state is indicated by D-Value D(s,a), (s∈S,a∈A) and its range is [0,1].

Each learning Agent maintains a two-dimensional table that records the destination node address that it can reach and the D-Value of the one-hop neighbor node similar to a matrix. This two-dimensional table is named D-Table (Ruiling et al. 2014; Sohail et al. 2018; Song et al. 2018; Liu et al. 2018; Qin et al. 2018). The columns of the table represent all the destination nodes that it can be reached, which is expressed by Di; the rows of the table represent one-hop neighbor nodes, which is expressed by Ni. The D(D1,N1) represents the D-Value between itself and its neighbor node N1 when it reaches the destination node D1. D-Table is a two-dimensional table, whose size is determined by the number of the neighbor nodes and the number of the destination nodes. It is obvious that it has good scalability. The value in the D-Table is updated by periodically exchanging beacon packets among nodes. The task of learning is distributed to each node, which makes the algorithm quickly converge to the optimal path based on the Lemmas 1 and 2, and the changes of the network topology can be timely adjusted.

We suppose that there is a MVANET topology graph G = {V,E} as shown in the Fig. 2, where V = {A, B ,C,….H} represents the set of vehicle nodes. For vehicle node A, its state space SA is the set of all nodes that do not contain A; The edge set E represents a collection of nodes that can communicate directly in one hop range. We suppose A of the Fig. 2 is the source node and G is the destination node. Now we want to seek an optimal path from the sending node A to the destination node G through the way of D-Learning.
Fig. 2

Model of the learning process

The aforementioned learning tasks are assigned to each vehicle node (which is the Agent), and the learning process is mainly to update the parameters of the D-Table, that is, to update the pair of state activity of the D-Value D(s, a), (s∈S, a∈A). Based on our analysis, we know that the bigger the number of hops is, the smaller the rewarding value is. So the final rewarding value is based on the number of hops, link reliability and bandwidth. By adding the factors of link reliability, the optimal path from source node to destination node can be obtained in the MVANET.

In Fig. 2, node E and F are one-hop neighbor nodes of the destination node G. The rewarding value from node E and F to destination node G can be represented as DE(G,G) and DF(G,G) respectively. Considering the effects of link quality and bandwidth, we suppose that their final D-Value are 0.8 and 0.9 respectively. The neighbor nodes of D are A, B, C, E, F and H. When D receives the beacon packets sent from any neighbor, the data packets are parsed, and the maximum D-Value to the destination node G is got, such as node F,\( \mathop {\hbox{max} }\nolimits_{{y \in N_{F} }} D_{F} \left( {G,Y} \right) \). Calculate the corresponding D-Value (DD(G,F)), and update the D-Table. The DF(G,G) is the largest and its value is one, which can be recorded in the beacon packet. A similar process will be done with data packets from other neighbor nodes, then one certain column in the D-Table can be updated. Considering the bandwidth and link reliability, suppose that we get DD(G,F) = 0.6 and the D-Table of the other neighbor nodes are updated. With the constant receive beacon packets, the node D constantly updates its D-Table. Similarly, when the node D sends its beacon packet, it extracts a certain column in the D-Table, finds the maximum D-Value between the node D and its neighbor node to send out. When the node A receives the beacon packet sent from the node D, it extracts the maximum D-Value and carries on the computation to update the D-Value DA(G, D) in its D-Table. The same process will be done when it receives data packets from other neighbor nodes. Through the constant exchange of data packets, we will finally get the learning result. So we may easily find an optimal path from A to G, i.e., the path with the biggest D-Value of the node is the optimal path. That is to say, A → B → E → G is the path with the maximum D-Value, so it is the optimal path we want to choose. The process of dynamic update-and-save of the D-Table makes the strategy respond to the dynamic change of topology of MVANET quickly and ensure the reliability, and ensure good robustness of MVANET.

Of course, the link reliability could not totally represent the quality of the link of MVANET. The link reliability is only an index to measure link quality. The link reliability of the RSAR protocol proposed in this paper is not only a measure of the link quality between nodes but a combination of hop count, link quality and bandwidth to measure the link reliability. It is necessary to use it in an actual dynamic network topology. By determining the link reliability, link disconnection can be avoided, and the accuracy and efficiency of selecting the appropriate node to forward information are improved. Therefore, the application scenarios are still extensive.

3.2 The novel RSAR protocol

3.2.1 Main part of the protocol

The main part of the novel RSAR protocol involves the following 4 steps:
  1. 1.

    Firstly, when a source node of a MVANET sends a data packet, it looks for its own D-Table to see whether or not it has the next hop node to reach the destination which is based on Lemmas 1 and 2. If there is yes, then it chooses the neighbor node with the largest D-Value; if not, then it starts the route establishing process, which operates the following step of “Sub-process of route establishing”.

     
  2. 2.

    Secondly, after the route of a MVANET is established, a basic path from source node to destination node is obtained, and the D-learning of some vehicle nodes is completed which is based on Lemmas 1 and 2. In order to seek the optimal path of the whole network topology of a MVANET and solve the network segmentation problem, the route maintenance process is started to maintain the end to end path dynamically as the following step of “Sub-process of route maintaining”.

     
  3. 3.

    Thirdly, through the processes above the optimal path of the entire network topology of a MVANET is established. When a vehicle node receives or sends data packets, it implements the first step; otherwise, it will implement the second step.

     
  4. 4.

    Finally, check the aforementioned results of a MVANET, if it is OK, then EXIT; otherwise, goto the step 1.

     

3.2.2 Sub-process of route establishing

In a MVANET, while the source node want to send a data packet to the destination node, it checks the D-Table to see weather or not there is a next hop node to the destination node based on the formula (22), (28) and (30). If yes, it seeks a neighbor node with the maximum D-Value to the destination node, and forwards the data packet to it. If no, it starts the route discovery process which is based on Lemma 1. In the processing, the source node of MVANET sends a message R_REQ data packet by broadcasting to the entire network of a MVANET and starts a path request timer, where message R_REQ records all nodes’ id who has passed in the routing process. If the destination node receives the first R_REQ packet from the source node, it will store the packet, and the subsequently received packets are discarded. Using the message R_REQ data packet, the destination node can get the node id and then generate a R_REP data packet and write the reversed path into it. After waiting for a time slot, it will send the R_REP data packet to the nodes which are recorded in the reversed path id through the relative broadcast information. If a recorded node has received the data packet, it will modify the next hop node address, update the D-Table, and send out the data packet through the single hop broadcast mode, while the other non-destination nodes only modify the D-Table and drop the data packet if they receive it; until the message R_REP is sent to the destination node, i.e. When the source node receives the message R_REP packet, it will dismiss the request timer and update its D-Table. At this time, a path from the source node to the destination node can be found and updated the D-Table of the nodes on the path from the source node to the destination node.

3.2.3 Sub-process of route maintaining

In a MVANET, if the first routing path has been established, the D-Table of its neighbor nodes adjacent to this path will also be updated. Based on the goal of ensuring the effectiveness of the path in the dynamic change of MVANET, it is important to start the route maintaining process. The main work of the route maintaining process is to dynamically update the D-Table which is based on Lemma 1 or Lemma 2 and solve the relative problem of network segmentation. Each node of MVANET periodically broadcasts the beacon packets to update the D-Table of the neighbor nodes, where the beacon data packet includes the parameters of the position, speed and Max(D-Value) of the node based on the formula (22), (28) and (30). The Max(D-Value) is defined in the learning process. If we want to keep the effectiveness of the update work, the transmission delay of the beacon packet should be set to a random value between [0.55,1]. The effective threshold time of the destination node should be given for the D-Table. If the time of a destination node has exceeded the given threshold time, it means the destination node may be invalid and can delete its corresponding column data of the D-Table. Based on the Lemma 2, we can known that if there is the emergence of network partition due to the movement of vehicles of MVANET, the RSAR can use the carry-and-forward strategy (Zhu and Li 2016; Xue and Kumar 2004) at the dividing node. So it may start the timer of the path request to broadcast the message R_REQ packet. If it has NOT received the message R_REP packet which is sent from the destination node before the timer is over, it means the destination node may be unreachable and so the source node is informed to ignore the transmitted data, otherwise, it should establish the routing path again.

During the maintaining process, each node of MVANET periodically broadcasts the beacon packets to update the parameters such as position, speed and Max (D-Value). Each time, it is selected from the D-Table that the maximum D-Value is worth the neighbor as the next hop forwarding node. The D-Value is determined by three factors: hop count, link reliability and bandwidth. The higher the D-Value of the vehicle node, the better the link quality is. Therefore, choosing the maximum D-Value can ensure the high reliability of the link. When the maximum reward value is chosen, the source node can reach the destination node directly through the one-hop neighbor node, so the cost is the least. Consequently, when the beacon broadcasting selects the largest D-Value, it can guarantee the high reliability and low cost of the link.

3.3 Mathematical analysis of the complexity of the algorithm

The complexity of the RSAR algorithm are analyzed in this section and explained into two aspects: time complexity and space complexity.

Corollary 1

The time complexity of the RSAR algorithm is\( {\rm O}(n) \).

Proof

The time complexity of the RSAR algorithm is determined by exchanging Hello beacon packets periodically and handling link failure. Routing discovery is not required for every data transfer. This route discovery process can be considered as the basic operation of the \( {\text{N}} \) nodes of the MVANET. In this algorithm, the worst case is that there are N-2 nodes between the source and destination, and communication between two nodes must rely on all intermediate nodes, thus the worst time complexity of this algorithm is \( {\rm O}(n) \). In the route discovery process, the source node sends a R_REQ data packet by broadcasting to the entire network and starts a path request timer. When the intermediate node has a path to the destination or the destination receives the R_REQ packet, the worst time complexity of this process is \( {\rm O}(n_{1} ) \). The generated R_REP packet is forwarded to the source to form a forward path. The worst time complexity of this process is \( {\rm O}(n_{2} ) \). When the link fails, the worst time complexity of processing link failure is \( {\rm O}(n_{3} ) \). Let \( n = n_{1} + n_{2} + n_{3} \), thus the time complexity of the RSAR algorithm is \( {\rm O}(n) \).

Corollary 2

The space complexity of the RSAR algorithm is\( {\rm O}(n^{2} ) \).

Proof

In the MVANET, the frequent movement of nodes will generate the link and link disconnection constantly. Therefore, it is more suitable to utilize the adjacency matrix of the graph to represent the nodes. Each node in this algorithm stores the information and routing of neighbor nodes, thus the space complexity is \( {\rm O}(n^{2} ) \).

The RASR and the D-Learning algorithm have the same complexity. The RSAR algorithm improves packet transmission rate and reduces transmission delay by adding a reliability factor into D-Learning.

Although the performance improvement of the D-Learning algorithm is not reflected by complexity analysis, the improved RSAR protocol based on D-Learning algorithm shows better effect such as transmission rate, end-to-end delay and average hop count than D-Learning algorithm. In dynamic network topology, the D-Learning algorithm finds the shortest path from the source node to the destination node through dynamic continuous interaction with the surroundings. The RSAR protocol improves the D-Learning algorithm, adds a reliability factor to the algorithm, and adaptively adjusts to the D-Table to ensure the reliability of each hop link. The RSAR protocol increases the calculation of the link reliability probability than the D-Learning algorithm, which solves the problem of severe topology changes and unreliable links between vehicles. The RSAR protocol adds link reliability calculations, but does not increase the complexity of the algorithm, and is also a performance improvement of the D-Learning algorithm.

4 Real scene experiments

In this section, we use the real scene of a MVANET to verify the performance of the RSAR protocol or algorithm. The real environment parameters are illustrated in the table, and then we analyze the experiment results and give the conclusions.

4.1 Real scene parameters

The real scene of MVANET is used to carry out experiments. The 2000 × 2000 square road scene of vehicle movement is designed. The scene consists of intersections and straight roads, where each road is set to three two-way lanes, traffic lights are set in four intersections, and the change time of traffic lights is 6 s. In the above real scene of a MVANET, the basic parameters are shown in the Table 2. The whole network has 20 pairs of CBR data streams to send packets whose size is 1024 bytes, and the transmission layer uses UDP. The size of the beacon packet is computed according to the transmitted data. The MVANET in designed scenes have two kinds of situations, which can effectively test the performance of the RSAR protocol. The first situation is as follows: the number of nodes in the entire network of a MVANET is a fixed value 90, and the maximum speed of the vehicle is ranged from 20 to 80 km/h. In this case, we want to test the affection of vehicle speed on the routing protocol. The second situation is as follows: the maximum speed of the vehicle is a constant 60 km/h, and the number of nodes is changed from 50 to 130. In this case, we want to test the affection of vehicle density on the routing protocol. We suppose that the vehicle nodes of a MVANET are randomly distributed on the different roads and run on a given route. The practical time for each experiment is 600 s. Each case is done 30 times and we take the average value to access the results. The relative experimental results are as follows.
Table 2

Parameter of the MVANET

Parameters

Values

Size of topology (m)

2000 × 2000

MAC standard

IEEE 802.11 MAC (2Mbps)

Transmission range (m)

160

Propagation model

Two-ray ground

Practical time (s)

600

CBR packet size (byte)

1024

Data rate (packet/s)

20

4.2 The results of the tests

In order to test the research work of this paper, we have done many comparison experiments. For example, our RSAR protocol have been compared with the relative following protocols: GPSR (Cheng and Panichpapiboon 2012), SLBF (Li et al. 2015) and QLAODV (Wu et al. 2010). These three kinds of protocols are representative routing protocols. According to the comparisons, we can assess the advantages and disadvantages of our proposed RSAR protocol. In the relative different scenarios to do testing, considering the parameter comparisons of the end-to-end delay, the packet delivery ratio, and the number of hops, we have obtained the results as shown in the Figs. 3, 4, 5, 6, 7, where the Figs. 3, 4, 5 are comparisons in the first situation, and the Fig. 6, 7 are comparisons in the second situation. Max speed (km/h) in Figs. 3 and 5 refers to Maximum speed (km/h).
Fig. 3

Relationship between end-to-end delay and speed

Fig. 4

The relationship between routing length and speed

Fig. 5

The relationship between average route length and the number of nodes

Fig. 6

The relationship between the delivery rate of the package and the average speed

Fig. 7

The relationship between the delay time of the packet and the average speed

The Fig. 3 has shown the relationship between the end-to-end time delay and the speed in a MVANET, where the time delay only calculates the average value of time taken by the destination node of a MVANET to receive the valid data packets. We can see that with the increase of the speed of the vehicle node, the time delay of four protocols totally has a rising trend, among these trends, the time delay of our RSAR protocol is between that of GSPR and SLBF. If the maximum speed is greater than 70 km/h, the time delay of SLBF increases rapidly and is more than that of our RSAR, that is arouse by the influence of topology changes of MVANET, re-transmission data or re-calculation of the effective route path. But our RSAR protocol is less affected by the topology changes of MVANET, the path is based on the maximum D-Value, the shortest routing length and the most reliable link, so our RSAR protocol has the shortest time delay. The QLAODV protocol also uses machine learning model, but the increased speed makes it switch the path frequently in order to maintain the effective routing path, so the time delay of the packet delivery among the nodes is greatly increased.

The Fig. 4 has shown the relationship between the average route length and speed of a MVANET, where the route length is calculated by the average number of the hops which are taken from the valid data packets to the destination node. According to the results of the figure, we can see that the route length in our RSAR protocol is less than that of the QLAODV protocol, because it has NOT adopted the path transformation strategy in order to remain the whole path of a MVANET, and the decision of forwarding data is only used to select the node which has the maximum D-Value, so the time delay is much shorter than that of the QLAODV protocol. Our RSAR proposed has a stable route length because it has been embedded the storage-and-forwarding mechanism and the maximum D-Value selecting mechanism, so each selected path is the shortest path. Both the SLBF protocol and the GPSR protocol have been used the greedy strategy to forward the data packets, but if the speed of a MVANET is greater than 70 km/h, under the influence of the topology changes, the route length of the SLBF and the GPSR will increase.

The Fig. 5 has shown that the relationship between the average route length and the number of nodes of a MVANET. We can see from the results of the Fig. 5, with the increasing of the nodes of a MVANET, the average route length of the four protocols has shown a downward trend. The reason is which the number of effective forwarding nodes of a MVANET increases. The length of the route path of our RSAR protocol is much shorter than that of the QLAODV protocol. The reason of the very close length of RSAR, SLBF and GPSR is that the SLBF protocol and the GPSR protocol both use the greedy mechanism. With the increasing of the nodes of a MVANET, the next hop selected by our RSAR protocol is much closer to the farthest node of a MVANET.

From the Fig. 6, we can see that for different routing protocols, with the increase of the average speed, in the same topology environment of a MVANET, the routing protocol package delivery rate shows a downward trend. This is because with the increase of the average speed, the speed of the nodes becomes faster, so it results in a dramatic change in the network topology. It also makes the link extremely unstable and the delivery rate drop. For the different routing protocols, the delivery rate of the packets is reduced accordingly. GPSR reduced by about 19%, SLBF reduced by about 14%, RAR (which is our RSAR protocol in this paper) reduced by about 11%. In contrast, the RAR protocol has a smaller rate of decrease in the delivery rate of packets due to an increase in average speed.

From Fig. 7 we can see that the delay time of these three routing algorithms is relatively low, but we note that the algorithm in this paper is relatively stable delay time, and it is lower than the other two routing algorithms. For different protocols, the delay time of the packets increases correspondingly as the average speed increases. GPSR increased by about 66%, SLBF increased by about 23%, RAR (which is our RSAR protocol in this paper) increased by about 19%. In contrast, the RAR protocol has a smaller rate of delay for the packets caused by the increase in average speed.

As the speed and the number of the vehicle nodes of a MVANET increases, the quantified results of the relative performance of the packet delivery rate, delay time and average hops are shown in Tables 3 and 4.
Table 3

The performance of RSAR protocol (node speed increasing)

Performance

QLAODV

SLBF

GPSR

RSAR

Delivery rate

75.21%

70.96%

53.15%

93.15%

End-to-end delay

60.03%

51.28%

24.16%

38.94%

Average hops

77.48%

65.04%

53.86%

59.84%

Table 4

The performance of RSAR protocol (node number increasing)

Performance

QLAODV

SLBF

GPSR

RSAR

Delivery rate

87.30%

78.54%

72.99%

94.89%

End-to-end delay

11.55%

19.86%

07.04%

09.86%

Average hops

43.45%

34.68%

21.17%

26.18%

As the speed of vehicle nodes increases, the delivery rate of our RSAR protocol increases by 17.94, 22.19, and 40.00% compared with QLAODV, SLBF and GPSR respectively. The end-to-end delay of RSAR is reduced by 12.35% and 21.20% compared with SLBF and QLAODV respectively. The average hops of RSAR are reduced by 5.20% and 17.64% compared with SLBF and QLAODV respectively.

As the number of vehicle nodes increases, the delivery rate of the RSAR increases by 7.59, 16.35, and 21.90% compared with QLAODV, SLBF and GPSR respectively. The end-to-end delay of RSAR is reduced by 1.69% and 10.00% compared with QLAODV and SLBF respectively. The average hops of RSAR are reduced by 8.50% and 17.27% compared with SLBF and QLAODV respectively.

In addition, we have done many simulations and experiments based on many cases to study the performance of our proposed protocol, such as the performance on the computational complexity degree of the proposed method. We define the Scalar Transmission Overhead (STO) to analyze the complexity of the protocol and its cost. The complexity degree metrics of the protocol includes the data gathering overhead (Odg) of a MVANET, transmission overhead (Ot) of the data packet among nodes of a MVANET.
$$ STO = \sum\limits_{i = 1}^{MC} {\sum\limits_{j = 1}^{MC} {(\alpha O_{(i,j)}^{dg} + \beta O_{(i,j)}^{t} )} } $$
(32)
where MC is the vehicle node size number of each evaluation group in a MVANET, such as MC = 15, 25, 35, 45, 55, 65, 75, and so on, which means there are relative vehicle nodes in a certain evaluation group of a MVANET. Integer parameter i and j are node index of each evaluation group in a MVANET. Parameter \( \alpha ,\beta \) are weight real value, \( \alpha ,\beta \)∈ [0, 1] and \( \alpha + \beta = 1 \), such as the default real value is \( \alpha = 0.55,\beta = 0.45 \).are the scalar real values of the overhead of the vehicle node i and the vehicle node j of each evaluation group in a MVANET.

Based on the basic computational complexity analysis strategies (Zhang and Zhang 2018; Zhang et al. 2019; Zhang and Dong 2018), from the aforementioned formula of this paper, we can know the computational complexity degree of the proposed method belongs to O(n). According to the Eq. (32), after being compared with the existing protocols, we can see that our protocol has a much higher performance than that of the Ref. (Zhu and Liu 2016), Ref. (Hamed 2018), Ref. (Ma 2017), which guarantees much higher QoS (such as much lower overhead, much less complexity degree, much smaller delay and transmission reliability) of a MVANET. At the same time, we have done other relative comparisons with the protocols or methods of the Ref. (Sujoy and Andrei 2014), Ref. (Ahmed 2017), Ref. (Liang et al. 2018). The relative comparison figures are ignored because the effects are similar as the above figures. So according to the above results, we can see that our proposed protocol has certainly improved on routing overhead, transmission delay, the rate of packet delivery, the rate of losing a packet, throughput and other performances for a MVANET.

In the RSAR protocol, the link maintenance time model is established by analyzing the vehicle motion of a MVANET in the model establishment phase, and the link reliability evaluation method is given. But mainly for the highway to model, the link disconnection caused by the intersection still needs further research. Secondly, in the design stage of the RSAR protocol, since the learning task is allocated to each vehicle node in the learning process, the routing overhead of a MVANET is relatively large, and the routing overhead needs to be further reduced.

5 Conclusions

For the goal of solving the problem of dramatic topology change and unreliable link caused by the fast movement of the vehicles in a MVANET, a kind of novel RSAR protocol for Mobile Vehicular Ad hoc Network is presented in this paper. Based on our suggested model, the reliability of the communication link is assessed and design a novel routing protocol according to the strategy of deep learning. As a kind of machine learning approach, the D-Learning algorithm can be helpful to get the reliable routing path. The advantage of the RSAR protocol is evaluated by the simulator and tests of the practical applications. The experimental results show that RSAR exhibits good results at a delivery rate, end-to-end delay and average hops compared with SLBF, QLAODV and GPSR. So the RSAR protocol can be used in many applications of MVANET.

Notes

Acknowledgements

This research work is supported by National Natural Science Foundation of China (Grant No. 61571328), Tianjin Key Natural Science Foundation (No.18JCZDJC96800), CSC Foundation (No. 201308120010), Major projects of science and technology in Tianjin (No.15ZXDSGX00050), Training plan of Tianjin University Innovation Team (No.TD12-5016, No.TD13-5025), Major projects of science and technology for their services in Tianjin (No.16 ZXFWGX00010, No.17YFZC GX00360), Training plan of Tianjin 131 Innovation Talent Team (No. TD2015-23).

Compliance with ethical standards

Conflict of interest

Author De-gan Zhang, Xiao-huan Liu, Yu-ya Cui, Lu Chen and Ting Zhang declare that they have no conflict of interest.

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Copyright information

© China Computer Federation (CCF) 2019

Authors and Affiliations

  • De-gan Zhang
    • 1
    • 2
  • Xiao-huan Liu
    • 1
    • 2
  • Yu-ya Cui
    • 1
    • 2
    Email author
  • Lu Chen
    • 1
    • 2
  • Ting Zhang
    • 1
    • 2
  1. 1.Key Laboratory of Computer Vision and System and (Tianjin University of Technology), Ministry of EducationTianjinChina
  2. 2.Tianjin Key Lab of Intelligent Computing and Novel Software TechnologyTianjin University of TechnologyTianjinChina

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