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This paper aims to explore the impact of user behavior on information diffusion in D2D (Device-to-Device) communications. A discrete dynamical model, which combines network metrics and user behaviors, including social relationship, user influence, and interest, is proposed and analyzed. Specifically, combined with social tie and user interest, the success rate of data dissemination between D2D users is described, and the interaction factor, user influence, and stability factor are also defined. Furthermore, the state transition process of user is depicted by a discrete-time Markov chain, and global stability analysis of the proposed model is also performed. Finally, some experiments are examined to illustrate the main results and effectiveness of the proposed model.

The fast development of communication technologies, enhanced devices, and multimedia services will lead to a drastic change in the way of perceiving and interacting with the world around us [

As a key component of 5G systems, D2D communications are proposed as an effective paradigm to reduce information diffusion time [

In D2D communications, social network is an important carrier of information [

In social network, behavior characteristics of different users are crucial factors for information dissemination. Combined with proximity-based communication, rental work investigated the integration of communication and social domains based on user behaviors [

Information diffusion process can be decomposed into multiple end-to-end information transmission cases; each case involves three entities, namely, sender, receiver, and content (see Figure

Relationship of three entities in information diffusion process.

The subsequent materials of this paper are organized as follows: Section

In this paper, let a graph

Only within the scope of D2D communications can users establish communication links to transmit information.

Considering the interaction behavior which reflects the social relationship between users, and the latter determines the former in turn, an interaction factor is introduced to partly characterize the social relationship. Interaction factor reflects the subjective aspects to establish trustworthy feelings or experiences based on users’ historical interactions, and each interaction is judged by a numeric degree to signify the opinion of users. Then,

where

Obviously,

Stability factor manifests the numeric fluctuation of social tie between users. Then, it can be calculated based on the time slice aggregation as follows:

where

The reason for considering the interaction factor and stability factor is to adjust the scenario of this paper. In particular, information transmission over physical link requires reliability and stability to guarantee the successful rate. If the social tie between users is unstable, then the infection probability is accordingly decreased, which will lead to the failure of information transmission. On the contrary, strengthened and stable social tie indicates a reliable interaction and link status, resulting in an improvement of transmission efficiency.

The social tie strength

The success rate of data dissemination is proportional to the social tie strength and interest degree of user. Then, it can be expressed as

where

The state transition probability from

Based on the fact that user influence decays over time and inspired by attenuation models [

where

Before giving the mathematical expression of the model, let us first introduce some basic information diffusion rules.

If a node is in state

If a node is in state

If a node is in state

Collecting the foregoing assumptions and information diffusion rules, the state transition diagram of user

The state transition diagram of user

The equilibrium and its stability of system (

Assume that

According to the definition of equilibrium, one can get

From assumption (A6) and rule (R2), the probability that user stays in state

Note that

Hence, it suffices to consider the following system:

Define

Now, the main result of this paper can be derived as follows.

The equilibrium

At the stable point, the number of users that have received information (users in state

To validate the effectiveness of the proposed model, this section simulates the information diffusion process with MATLAB in a random network, in which each node represents a user. At each time point, users take the receiving or forwarding decision according to its own state and the system parameters. Meanwhile, the impact of user influence and information popularity on information diffusion is also illustrated. Here, let us introduce two important indexes in advance.

Consider system (

System convergence process.

The users state in different time points at t=2, 10, 18.

t=2

t=10

t=18

A comparison between awareness and no awareness.

The impact of user influence on information diffusion process.

AIN=0.87

AIN=0.92

AIN=0.94

Figure

Figure

Figure

Figure

Consider system (

The evolution of infected users over time under different destinations.

The evolution of recovered users over time under different destinations.

A comparison of

Figures

Figure

In this paper, with joint consideration of social tie, user influence, and user interest, a user behavior based information diffusion model for 5G systems has been proposed. By characterizing the state transition probability of each user, a discrete-time Markov chain system has been formulated. Furthermore, the global stability of the system has been proved. Finally, some experiments have been performed to illustrate the main results and effectiveness of the proposed model.

The provided insights can guide the development of information diffusion and D2D communications. The discovery of social attributes of user and information improves the effect of information diffusion, which is relevant to advertising, public opinion monitoring, and other scenarios.

In further work, the study can be continued in several directions. On the one hand, we shall apply the theory of discrete dynamics (e.g., [

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by Natural Science Foundation of China (Grants nos. 61702066 and 11747125), Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ1704080), Chongqing Research Program of Basic Research and Frontier Technology (Grants nos. cstc2017jcyjAX0256 and cstc2018jcyjAX0154), and Research Innovation Program for Postgraduate of Chongqing (Grants nos. CYS17217 and CYS18238).