Cooperative transmission control scheme using erasure coding for vehicular delay-tolerant networks

Abstract

Transmission control is a challenging problem in vehicular delay-tolerant networks because the network has a high vehicle mobility which leads to a dynamic and unreliable network connectivity. In this paper, we propose a COoperative Transmission control Scheme using erasure coding (COTS) to improve the transmission efficiency. In this scheme, the cooperative message distribution algorithm uses delivery capacities to decide the transmission direction and traffic. Besides, the cooperative task scheduling algorithm sets the transfer order for messages from both sides. This algorithm uses a comprehensive parameter, the number of data blocks to send, to simplify the computation of transmission priority. After analyzing the vehicle transmission behavior under different storage conditions, we apply local deleting and creating behaviors instead of sending and receiving behaviors in specific states to decrease communication overhead. Simulation results show that COTS, compared with other well-known schemes, not only increases the delivery ratio but also decreases the delivery latency and the transmission overhead.

Appendix

Proposition 1

In the cooperative message distribution algorithm, the expected number of coded blocks carried by node 1 in Eq. (2) is accurate.

Proof

Assume node 1 and node 2 are two meeting vehicles in the cooperative message distribution algorithm. Let $\mathrm{CD}_1$ and $\mathrm{CD}_2$ be their capacities of delivering a given data message, respectively. Considering the positiveness (or negativeness) of the weight $w_i$ in Eq. (1) shows the positive (or negative) correlation with the delivery capacity, $\mathrm{CD}_1$ and $\mathrm{CD}_2$ may also be positive or negative. We compute the expected number of coded blocks according to the signs of these capacities below.

We use the delivery capacities and the current storage states in both sides to compute the expected storage states. The current numbers of data blocks in nodes 1 and 2 are $\mathrm{Count}_1$ and $\mathrm{Count}_2$, respectively. Take the expected number of coded blocks of this message in node 1, $\mathrm{Count}_1^{'}$, as an instance. We analyze different cases in detail below. The computation of $\mathrm{Count}_2^{'}$ for node 2 can be done in a similar way.

• 1. When $\mathrm{CD}_1=CD_2=0$, nodes 1 and 2 are independent with the delivery of this data message. As zero is better than negative values, it is still used in the block distribution. For these two nodes have the same capacity to deliver the blocks, we distribute the data blocks equally in the neighborhood, expressed as $\mathrm{Count}_1^{'}=\frac{1}{2}(Count_1+Count_2)$.

• 2. When $\mathrm{CD}_1>0$ and $\mathrm{CD}_2 \ge 0$, since the sum of these two capacities is positive, the data blocks are distributed in proportion to each node’s delivery capacity. Thus node 1 gets its part at the ratio of $\mathrm{CD}_1$ to the sum capacity, as $\mathrm{Count}_1^{'}=\frac{\mathrm{CD}_1}{\mathrm{CD}_1+\mathrm{CD}_2}(\mathrm{Count}_1+\mathrm{Count}_2)$.

• 3. When $\mathrm{CD}_1 \ge 0$ and $\mathrm{CD}_2 <0$, it implies that node 2 interrupts the delivery of this data message, while node 1 does well to deliver the message. In order to avoid negative effects of node 2, we distribute all the blocks in the neighborhood to node 1. That is, $\mathrm{Count}_1^{'}=\mathrm{Count}_1+\mathrm{Count}_2$.

• 4. When $\mathrm{CD}_1<0$ and $\mathrm{CD}_2 \ge 0$ or $\mathrm{CD}_1=0$ and $\mathrm{CD}_2>0$, node 1 is not helpful to delivery this message ($\mathrm{CD}_1=0$) or even interrupts the delivery ($\mathrm{CD}_1<0$), while node 2 does well. In order to avoid negative effects of node 1, all the blocks are distributed to node 2. In other words, node 1 gets no blocks, shown as $\mathrm{Count}_1^{'}=0$.

• 5. When $\mathrm{CD}_1<0$ and $\mathrm{CD}_2<0$, both nodes 1 and 2 disturb the data delivery. However, the interruptions have different extents. The smaller the capacity is, the stronger the negative impact is. Thus less blocks should be distributed to the node having a smaller capacity. We distribute blocks at the reverse ratio of the capacities as $\mathrm{Count}_1^{'}=\frac{\mathrm{CD}_2}{\mathrm{CD}_1+\mathrm{CD}_2}(\mathrm{Count}_1+\mathrm{Count}_2)$.

To sum up, these cases have covered all the possibilities of the capacities. It works well to compute $\mathrm{Count}_1^{'}$ and $\mathrm{Count}_2^{'}$ in nodes 1 and 2. Comparing the current and expected storage states, we get $\mathrm{Count}_1^{'}+\mathrm{Count}_2^{'}=\mathrm{Count}_1+\mathrm{Count}_2$. Thus the total blocks in the neighborhood are distributed at two sides simultaneously. Therefore, Eq. (2) is accurate to compute the expected number of blocks carried by node 1 in the cooperative message distribution algorithm. $\square$

Proposition 2

$\mathrm{TCount}$ is a suitable substitute for the local and neighbor parameters Prob and Count in the cooperative task scheduling algorithm.

Proof

As shown in Eq. (5), we construct the mathematical model of transmission priority of a given data message. Let node 1 and node 2 be two meeting vehicles. Assume $\mathrm{TCount}_1>0$, which means that node 1 should send $\mathrm{TCount}_1$ blocks of this message to node 2. Other cases when $\mathrm{TCount}_2>0$ can be analyzed similarly. Denote the parameters from node 1 as $\mathrm{Prob}_1$ and $\mathrm{Count}_1$, and those from node 2 as $\mathrm{Prob}_2$ and $\mathrm{Count}_2$.

First, we qualitatively analyze the effects of $\mathrm{Prob}_1$, $\mathrm{Prob}_2$, $\mathrm{Count}_1$ and $\mathrm{Count}_2$ on the transmission priority of this message from node 1 to node 2.

Larger $\mathrm{Prob}_1$ indicates a higher probability for the sender node 1 to deliver these blocks by itself. Thus node 1 has a smaller chance to forward these blocks to its neighbor. In other words, $\mathrm{Prob}_1$ has a negative correlation with the transmission priority of this message from node 1 to node 2. Similarly, $\mathrm{Prob}_2$ shows a positive correlation since a larger probability of the receiver node 2 to deliver these blocks prompts the data transmission from node 1 to node 2.

Larger $\mathrm{Count}_1$ indicates that node 1 has more data blocks. As data dissemination is helpful for the data delivery, larger $\mathrm{Count}_1$ requires more data transfers to others, to improve the cover range of these blocks. Thus $\mathrm{Count}_1$ shows positive correlation with the priority. Similarly, $\mathrm{Count}_2$ has a negative effect on the priority, since sufficient blocks in node 2 prohibit the extra transmission from node 1 to node 2. Therefore, it is concluded that the weights of $\mathrm{Prob}_2$ and $\mathrm{Count}_1$ in Eq. (5) should be positive, while those of $\mathrm{Prob}_1$ and $\mathrm{Count}_2$ should be negative.

Next we analyze Eq. (9) to check out the sign of each parameter. Note that Eq. (9) can be simplified as $\mathrm{CT}=a \times \mathrm{TTL} +b \times \mathrm{TCount}$ where $a>0, b>0$. By Eq. (4), we get

$$\begin{aligned} \mathrm{CT}&= a \times \mathrm{TTL} +b \times (\mathrm{Count}_1- \frac{\mathrm{Prob}_1}{\mathrm{Prob}_1+\mathrm{Prob}_2}(\mathrm{Count}_1+\mathrm{Count2})) \nonumber \\&= a \times \mathrm{TTL} +b \times \mathrm{Count}_1- \frac{b \times \mathrm{Prob}_1}{\mathrm{Prob}_1+\mathrm{Prob}_2}(\mathrm{Count}_1+\mathrm{Count}2) \nonumber \\&= a \times \mathrm{TTL} +b \times \mathrm{Count}_1-\frac{b}{1+{\mathrm{Prob}_2}/{\mathrm{Prob}_1}}(\mathrm{Count}_1+\mathrm{Count}_2)) \end{aligned}$$

(11)

$$\begin{aligned}&= a \times \mathrm{TTL} +\frac{b \times \mathrm{Prob}_2}{\mathrm{Prob}_1+\mathrm{Prob}_2}\mathrm{Count}_1- \frac{b \times \mathrm{Prob}_1}{\mathrm{Prob}_1+\mathrm{Prob}_2}\mathrm{Count2}. \end{aligned}$$

(12)

From Eqs. (11), (12), we derive that $\mathrm{Prob}_2$ and $\mathrm{Count}_1$ have positive correlations with CT, while $\mathrm{Prob}_1$ and $\mathrm{Count}_2$ have negative correlations, which are in accordance with the previous theoretical analysis. Therefore, we conclude that $\mathrm{TCount}$ is a suitable substitute of the local and neighbor parameters Prob and Count in the cooperative task scheduling algorithm. $\square$