A Novel Video-Spreading Strategy Based on the Joint Estimation of Social Influence and Sharing Capacity in Wireless Networks

Abstract

In this paper, we propose a novel video-sharing strategy based on the joint estimation of social influence and sharing capacity in wireless networks (SSISC), which promotes the scale and efficiency of video spread and ensures the balance of supply and demand. SSISC designs an estimation model of video-sharing gains by investigating social influence levels, sharing capacities (including capacities of information dispatching and video delivery), and predicted expansion scale. Some social parameters (e.g., centrality of degree and betweenness, and average shortest distance) and some parameters of sharing performance (e.g., number of forwarded messages and cached videos, the average time of transmission and freeze) are used to evaluate social influence, capacities of information dispatching, and video delivery; video interest levels, social relationship levels, and historical push success rates are used to predict video proliferation scale. A video-spreading strategy based on the assistance of spread nodes is designed, which controls the process of video push according to available bandwidth and push priority to balance supply and demand and ensure user experience quality. Extensive tests show how SSISC achieves much better performance results in comparison with other state-of-the-art solutions.

1. Introduction

Video applications make use of the mobile internet to provide visual content to mobile users carrying handheld terminal devices, and depend on excellent technologies of wireless communication to support a high-definition and smooth viewing experience [1,2,3,4,5,6]. The target of the videos’ release focuses on the large-scale popularity over the internet [7,8,9,10]. The excellent content and convenient access attract mass users, but a large number of videos have short and small-scale popularity [11,12,13]. This is because the traditional video expansion mode uses a request–response method on overlay network limits to increase the scale of videos [14]. Further, the single shared channels and rigid distribution mechanisms of the traditional spreading mode only passively handle various video requests, which results in the coexistence of redundant copies of unpopular videos and a scarce supply of popular videos. The integration of video sharing and social networks opens a new channel for video-spreading [15]. Nodes in social networks not only employ the broadened spread channels (active request and passive receive push) to share videos, but also depend on interest similarity and social relationships to efficiently share videos, which enriches the video-sharing processes and expands the video-sharing user scale. However, large-scale video-sharing between users with a high user quality of experience (QoE) requires the video applications to provide adequate supplies of video resources. The dynamic and diverse video demand of users promotes the complexity of the video supply. The economical balance between supply and demand with low-level copy redundancy and the effective guarantee of user QoE have become a significant challenge for the scalable social-based video-spreading in wireless networks [16,17]. The controllability of the video-spreading process is very important for supporting the large-scale scalable social propagation of video copies [18,19]. Controllable video-spreading can rely on social nodes to orderly promote copy scales according to available bandwidth and possible acceptance rates, avoiding the squeeze of available bandwidth caused by the disorderly explosion and bandwidth waste caused by invalid push and effectively ensure user QoE. The social-based video-spreading solutions should consider control methods of video copy dissemination.

The traditional social-based spreading methods mainly investigate interest similarity and social relationships to regulate video copy distribution to meet video requests, and heuristically push videos based on interest prediction [20,21]. Abundant supply and heuristical push promote the scale of video spread, but autonomous spread needs to pay a large number of costs of bandwidth, computation, and storage to maintain the overall balance between the relation of supply and demand and dissemination scale. This is because the accurate control of node-centric dissemination in the social-based spread modes is neglected by the traditional methods [22,23,24]. There are big differences for nodes in social networks, such as interest preference, social influence levels, and sharing capacities. The discriminate control of node-centric dissemination in social networks focuses on estimating contributions of nodes for video spread in the performance-related aspects such as resource-distribution capacities and expected spread scale whilst making use of advantages of each node in video distribution, social influence, and information dispatching to disseminate videos with the dynamic balance of supply and demand and low-cost cascade replication [25,26]. The effective estimation for spread contributions of nodes can implement accurate spread control such as video push with a high success rate, video caching with the balance of supply and demand, and precise video-request dispatching. Numerous researchers focus on social-based video spread [27,28,29,30,31,32]. For instance, Niu et al. propose a multiple-source-driven asynchronous information diffusion model based on substantial video diffusion traces, which makes use of the measurement results of contributions of multiple potential sources to promote video-spreading scale [31]; Wu et al. propose an effective pricing-based multicast video distribution based on grid clustering, which offloads and alleviates the base station traffic load caused by the rapidly growing video demand [32]. However, most of the existing methods neglect the node-level dissemination control without the consideration of metrics of spread contributions or the difficulty of obtaining a high accuracy of spread contributions to support effective node-level control. Therefore, an efficient method of node-centric social-based video-spreading control which can accurately estimate spread contributions of nodes using spread contribution metrics and scalable video copy diffusion with the dynamic balance of supply and demand and high QoE should be considered.

In this paper, we propose a novel video-spreading strategy based on the joint estimation of social influence and sharing capacity in wireless networks (SSISC). By investigating social influence levels and sharing capacities and by predicting scale levels of video spread, SSISC calculates weight gains of video-spreading brought by candidate spread nodes in social networks, which makes use of spread nodes to control the spread process and promote spread scale for the balance between supply and demand of video resources and high user QoE. Some distinct contributions of SSISC are as follows.

(1)

SSISC designs an estimation model of video-spreading gains based on social influence levels and sharing capacities. The node degree centrality (NDC) and average shortest distance (ASD) from the current node to other nodes are used to estimate social influence levels of nodes because NDC and ASD denote social resource levels and relative location (edge or center) of current nodes in social networks, respectively. The sharing capacities of nodes rely on information dispatching and data delivery for the spread of video content. The information dispatching capacity investigates several forwarded video-related messages and node betweenness centrality, which evaluates the capacities of nodes that converge and distribute video-related information in social networks. The delivery capacity of video data makes use of several cached videos, the average transmission time of video data, and average freeze time of videos to estimate service levels of nodes for other request nodes. The social influence and sharing capacity of nodes are considered the gains of video spread. The higher (lower) levels of social influence and sharing capacity are, the stronger (weaker) the video-spreading capacities of nodes are. The nodes which have strong capacities of video-spreading capacities can speed up video spread and promote the scale of video spread, so they should be preferentially selected as the video spread nodes.

(2)

SSISC designs an estimation method for the weight of video-spreading gains. Three parameters (video interest levels, social relationship levels, and historical push success rate) are used to evaluate the probability of nodes for current popular videos and calculate several nodes which may accept pushed videos. Moreover, the average number of nodes that received supply data is calculated in terms of historical information on video supply. The predicted spread scale of current popular videos can be calculated and used as the weight of spread gains. The weighted gains of video spread can be used as the evaluation basis for selecting video spread nodes.

(3)

SSISC designs a video spread strategy based on the assistance of spread nodes. The nodes which have the largest weighted gains are selected as the video spreaders. By message exchange with neighbor nodes, the spread nodes estimate the interest levels of neighbor nodes for current popular videos in terms of deviation between real and forecasted of acceptation results for the pushed videos. The spread nodes formulate precedence of video push according to estimation results of interest levels of neighbor nodes. Moreover, the spread nodes control the spreading scale in terms of the owned bandwidth to balance supply and demand and ensure efficient sharing.

The rest of the paper is organized as follows. Section 2 describes the related works of video-spreading strategy based on joint social influence and sharing capacity; Section 3 suggests the detailed design of SSISC, which includes an estimation model of weight gains of video spread based on social influence, sharing capacity, and predicted spreading scale, and describes a video-spreading strategy based on the assistance of spread nodes; Section 4 evaluates the performance of SSISC with the comparison of other solutions through a comparative experiment, and simulation results show how SSISC achieves much better performance results in comparison with other state-of-the-art solutions.

2. Related Work

Some researchers continuously focus on video propagation in social networks. For instance, Li et al. presents a cost-effective social network-aware cloud assistance module for video sharing [33]. The cloud assistance module is set between video-sharing sites and an online social network which improves the video access experience of users with the assistance of cloud resources and edge servers. The cloud assistance module makes use of dynamic management and updating of videos to respond to the dynamics of access behaviors of users, and promotes the efficiency of video cache replacement with minimized cache misses. However, the cost of cache copy and replacement, such as bandwidth and storage and balance of supply and demand, are not considered, which does not ensure cloud utilization efficiency. Roy et al. designed a transfer learning framework by analysis of social streams to estimate sudden popularity bursts in online content [34]. The designed transfer learning algorithm builds a model of video-spreading levels in social networks, which promotes the prediction accuracy of video popularity by learning topics in social streams. For data comprising a large number of videos, the social prominence of video context is the main factor of the sudden rise of video popularity. However, the designed video popularity model without consideration of the integration of the video context and social environment does not ensure the prediction accuracy of video popularity. Xu et al. propose a social-based forecast method of video popularity levels, which implements the trade-off between accuracy and timeliness of popularity prediction [35]. Context awareness results without a training phase and prior knowledge determine the prediction accuracy of video popularity, which can describe the variation and evolution of propagation patterns of videos in social networks. Sublinearity is proven as the bound of prediction performance loss of video popularity when the number of videos reaches a threshold value, which can be used to promote the prediction accuracy of video popularity during a short-term period. However, the designed model of video popularity does not the monitor levels of correlation and influence among video number, popularity levels, and prediction performance, and so does not ensure the prediction accuracy of video popularity. Wang et al. propose a solution of multiple cloud providers for social video-content sharing, which attempts to address the problems of inter-cloud social propagation with the low substantial operational cost of inter-cloud traffic [36]. The multi-cloud hosting of an instant social video system is formulated as an optimization problem. A heuristic algorithm with acceptable complexity with the effective trade-off between satisfying users with their ideal cloud providers is designed, which is used to solve the optimization problem. However, the designed solution neglects social influence with the mutual effect of users, so the dynamic variation of social video propagation among users increases the cost of inter-cloud traffic scheduling.

Some researchers continuously focus on propagation control methods in social networks. For instance, Chen et al. convert the node selection problem of social spread nodes as a bi-objective optimization problem to find a subset of blocked nodes which attempts to achieve the maximized spread control effect with minimized control cost [37]. An ant colony optimization algorithm is designed which divides the bi-objective problem into a set of single-objective subproblems. Each subproblem is optimized by an ant, where the pheromone and heuristic information of dimension size selection is incorporated into the node selection. The optimization algorithm generates an adaptive dimension size set of candidate selection nodes under the multiobjective evolutionary algorithm framework. However, the dynamic propagation process is influenced by multiple factors, so the single consideration of candidate spread nodes does not ensure the minimized control cost of video propagation. Zhang et al. review socially aware routing in mobile opportunistic networks [38]. The motivations behind socially aware routing are discussed. According to the various social metrics such as design principles, evaluation metrics, taxonomy, relay selection, and message distribution, the existing socially aware routing schemes are described. The emerging challenges and open issues for social metrics, social perception, privacy and security, emerging applications, and experiments are outlined. Kilanioti et al. investigate the association between the predictability of video sharing and the initial sharing of videos within the context of the media platform [39]. User-centric data from Twitter with video-centric data from YouTube are combined and are used as social network and media service datasets. A prediction model of video popularity is designed which defines time-related social influence fluctuation levels of users and calculates the distance of content interests among users. The prediction results of video popularity can be incorporated into the video-sharing mechanism, which effectively promotes video-delivery performance and improves user QoE. However, the integration between sociability and interests of users such as social influence and interaction is considered so that the accuracy of prediction results of video popularity cannot be ensured. Wang et al. propose an influence spread framework for geo-social networks based on multiobjective optimization, which finds the optimal Pareto solutions for decision makers [40]. By the construction of a reverse-influence sampling model, a similarity matching-based method of reverse influence sampling is designed for diverse social users. The formulated original problem is transformed into a weighted coverage problem and is solved by the greedy-based approximation approach and heuristic-based particle swarm optimization approach. However, the variation of social influence caused by the interaction of users is not considered by the built problem of multiobjective optimization, so the estimation accuracy of the influence spread scale can not be ensured. Nayak et al. propose an opinion maximization model to find a set of influential nodes for fast content dissemination in social networks. The regular nodes with heterogeneous social learning abilities are required to spread information from multiple sources to neighbor nodes via gossip-based smart and random information spreading [41]. By constructing of dynamic Bayesian network for social interactions and opinion evolution, opinion maximization is formulated as a sequential decision problem. The approximate solutions for the formulated problem are obtained by centralized and decentralized algorithms. However, heterogeneous social learning abilities are important for the selection of influential nodes, so the incomplete estimation of abilities introduces a negative influence onto the upper and lower bound of the set of influential nodes.

Some researchers continuously focus on video propagation based on the assistance of spread nodes in social networks. For instance, Yang et al. formulate a maximized content-spreading problem for incremental marginal gains of node connectivities [42]. The lower and upper bounds of the designed objective function are proved by the marginal increment-based algorithm, which guarantees a data-dependent factor. A scalable content-spreading maximization algorithm is designed based on the influence ranking of a single node, which achieves an accurate estimation of spread gains and maximizes the scale of content spread. However, the relation between spread content and social influence is not considered in the designed objective function, so the performance of the content-spreading algorithm is negatively influenced. Zhou et al. design a multilayer geo-social network including an online social network and a geographic co-location weighted network [43]. By calculation of mutual influence between users and by analyzing the influential spreaders on the geo-social network, the social relationships and individual behaviors of nodes are calculated and used to estimate influential nodes. In the built susceptible–infected–recovered model, the ability of spread nodes is evaluated, which effectively detects strong levels of social and geographic influence. However, the inaccurate estimation of the mapping relation between social influence and geographic co-location brings a negative influence on the measurement of the ability of spread nodes and results in the low accuracy of the selected set of spread nodes. Sharma et al. design a hybrid filter-based approach by employing multiple centrality measures to filter spreaders of information or content which can maximize and track the influence and spread of particular information [44]. However, estimation without the consideration of important factors such as betweenness and spreading-ability difficulty ensures the performance of information spread. Tulu et al. propose a content-spreading efficiency algorithm by investigating the degree and number of contact times of nodes with neighbor nodes and friends of neighbor nodes [45]. The topological position of nodes is used to estimate the efficiency with that the nodes spread content in networks and the effect of how the selected important nodes spread content is demonstrated. However, the relation and interaction of performance and cost of content spread are not accurately measured, which may result in the low efficiency of the spread content of nodes. Wang et al. propose an effective influence assessment model based on the total valuation and variance of the valuation of neighbor nodes which effectively handles the possibility of unreliable communication channels [46]. A discrete moth–flame optimization method is designed, which can search for influence-maximizing node sets by making use of a local crossover and mutation evolution scheme. A search-area selection scheme based on a degree-based heuristic is employed which can accelerate the convergence of the search-selection process and effectively address the problem of influence maximization. However, the influence assessment model should investigate more factors to further improve the accuracy of influence assessment and speed up the convergence of the search process.

3. SSISC Detailed Design

Social networks always are denoted by the graph $G=(V,E)$ where E is the set of nodes in G and V is the set of edges between nodes in G. All notations of SSISC are listed in

Table 1. Notations used in SSISC.

Notations	Descriptions
$C_D\left(n_i\right)$	node degree centrality of $n_i$
$N{S}_i$	neighbor set of $n_i$
$S{D}_A\left(n_i\right)$	average shortest distance between $n_i$ to other nodes
$I_S\left(n_i\right)$	social influence of $n_i$
$B_C\left(n_i\right)$	betweenness centrality level of $n_i$
$N{N}_H\left(n_i\right)$	normalized value of message relay levels of $n_i$
$C_F\left(n_i\right)$	capacity of information dispatching of $n_i$
$N{N}_V\left(n_i\right)$	normalized value of cached video number in $n_i$
$VS$	video set in social networks
$T_{ij}$	transmission time of video data of $n_i$
$A{T}_N\left(n_i\right)$	average transmission time of all videos of $n_i$
$N{F}_{ij}$	normalized value of freeze time of $n_i$
$A{T}_F\left(n_i\right)$	average transmission time of all videos of $n_i$
$D{C}_D\left(n_i\right)$	video delivery capacity of $n_i$
$G_S\left(n_i\right)$	video spread gains brought by selecting $n_i$
$\alpha$, $\beta$, $\lambda$	regulatory factors
$I{L}_{v{s}_k}\left(n_h\right)$	interest levels of $n_h$ for video $v{s}_k$
$S{I}_{hi}$	social influence of $n_i$ for $n_h$
$P_{hi}\left(v_j\right)$	probability that $n_h$ accepted $v_j$ pushed by $n_i$
$R_{hi}^p$	historical success rate that $n_i$ pushes videos to $n_h$
$N_i^a$	average number of nodes receiving data transmitted by $n_i$
$W_i$	predicted capacity of video spread of $n_i$
$W{G}_S^j\left(n_i\right)$	weighted gains generated by selecting $n_i$
$W{P}_{hi}$	interest levels of neighbor nodes of $n_i$

. The process of video spread in social networks is shown by the dynamic variation of node state, such as the epidemic model. For instance, the nodes which do not store data on popular videos in the local buffer can be considered as the susceptibles; the nodes which have stored data on popular videos or have requested data on popular videos can be considered as the infectors; the nodes have watched popular videos can be considered as immune. The target of video spread focuses on the scale of infected nodes. However, the initial seed nodes are unable to bear the task of the mass epidemic in social networks. The assisted spread of other nodes in social networks is very important for the target of the mass epidemic. The assisted spread nodes which have a strong social influence, abundant social resources, and a superior ability of video-sharing can infect more nodes with a low consumption of network resources and a balance between supply and demand of video resources. Figure 1 illustrates the design of SSISC architecture which includes the two components weight gains of video spread and spread strategy with the assistance of spread nodes.

(1)

The component “weight gains of video spread” consists of social influence, capacities of video sharing, and the weight of video spread. The three factors in addition to social influence and capacities of video sharing are used to estimate video-spread gains. The node degree centrality and average shortest distance are used to estimate social influence levels of nodes; capacities of video-sharing mainly investigate the capacities of information dispatching and video delivery. The two parameters of several forwarded messages and node-betweenness centrality are used to evaluate information-dispatching capacity. The video-delivery capacity considers three factors: number of cached videos, the average transmission time of video data, and average freeze time of videos. Levels of node interest and social relationship and push success rate are used to predict the spreading scale of candidate spread nodes, which also is considered as the weight of video spread gains.

(2)

The component “spread strategy with the assistance of spread nodes” includes priority measurement of video push, gain-based selection of spread nodes, and spread control based on gain prediction. The priority measurement of video push considers the spread gains brought by the candidate spread nodes and the predicted scale of nodes infected by the candidate spread nodes. The gain-based selection of spread nodes focuses on the global search of optimal spread nodes with the largest gains. The spread control based on gain prediction implements the regulation of video resources according to dynamic balance levels between supply and demand.

3.1. Estimation of Video-Spreading Gains

3.1.1. Node Social Influence

The social influence means that the nodes have a scale of neighbor nodes and the scale of nodes that are accessed by current nodes in social networks so that the nodes can make use of the resources of bandwidth, computation, and storage of neighbor nodes, and exert influence on fetching videos for neighbor nodes. The node degree centrality and the average shortest distance between the current node to other nodes denote the direct or indirect scale of neighbor nodes, respectively. The node degree centrality of any node $n_i$ can be defined as [47]:

$$C_D\left(n_i\right)=\frac{|N{S}_i|}{n-1}$$

(1)

where $N{S}_i$ is the set of neighbor nodes of $n_i$ and $|N{S}_i|$ returns the number of items in $N{S}_i$. n is the number of all nodes in social networks. $C_D\left(n_i\right)$ denotes the resource control levels of neighbor nodes of $n_i$ in social networks. Moreover, the average shortest distance between $n_i$ and other nodes in G can be defined as [48]:

$$S{D}_A\left(n_i\right)=\frac{{\displaystyle \sum _{j=1}^n}S{D}_{ij}}{n-1}$$

(2)

where $S{D}_{ij}$ is the shortest distance between $n_i$ and any node $n_j$; n is the number of all nodes in the social networks. If $n_i$ has the large value of $S{D}_A\left(n_i\right)$, $n_i$ is located at the edge of social networks and is far away from the center of social networks, which results in high-cost interactions with other nodes and low control levels of information and resources in social networks. Otherwise, if $n_i$ has the small value of $S{D}_A\left(n_i\right)$, $n_i$ is located at the center of social networks, which enables $n_i$ to have more opportunities of collecting and fetching video information and can quickly and conveniently interact with other nodes. If $n_i$ has high node-degree centrality and a low average shortest distance, the abundant social resources result in a strong social influence of $n_i$. Therefore, the social influence of $n_i$ can be defined as:

$$I_S\left(n_i\right)=\frac{C_D\left(n_i\right)}{S{D}_A\left(n_i\right)},I_S\left(n_i\right)\in [0,1]$$

(3)

$C_D\left(n_i\right)\in [0,+\infty )$ and $S{D}_A\left(n_i\right)\in [1,+\infty )$, so $I_S\left(n_i\right)\in [0,+\infty )$. Moreover, $C_D\left(n_i\right)$ and $S{D}_A\left(n_i\right)$ have the proportional and inverse relationship with $I_S\left(n_i\right)$, respectively. The larger the value of $I_S\left(n_i\right)$ is, the higher the social influence level of $n_i$ is.

3.1.2. Capacity of Information Dispatching

The nodes in social networks receive and handle messages forwarded by neighbor nodes. For instance, when a node $n_i$ receives the video lookup messages forwarded by the neighbor nodes, $n_i$ needs to forward the received messages to other neighbor nodes which have a high probability of supplying the requested videos. When $n_i$ receives the videos pushed by neighbor nodes, $n_i$ decides on rejection or acceptation. The more messages received and handled by nodes, the more accurate and abundant the felt variation of video distribution and demand is. Moreover, except for the message scale, the control levels of nodes for the received messages are also very important. If a node $n_i$ is not on the passage path of the messages relay, there is a high probability of message detour to other paths. The shortest paths between nodes in social networks are the only route that must be passed for the interactive messages between nodes. The more that $n_i$ is included in the shortest paths, the higher the control levels of $n_i$ for the forwarded messages. The betweenness centrality and scale of collected messages are used to estimate the capacity of the information dispatching of nodes, which ensures control levels and scale of past messages. The betweenness centrality level of $n_i$ is defined as [49]:

$$B_C\left(n_i\right)=\sum _{j=1}^n\sum _{k=1}^n\frac{N_S^i(n_j,n_k)}{N_S(n_j,n_k)}$$

(4)

where $N_S^i(n_j,n_k)$ is the number of shortest paths containing $n_i$ between $n_j$ and $n_k$; $N_S(n_j,n_k)$ is the total number of shortest paths between $n_j$ and $n_k$. The normalized value of the betweenness centrality level of $n_i$ is defined as:

$$N{B}_C\left(n_i\right)=\frac{B_C\left(n_i\right)}{{\displaystyle \sum _{j=1}^n}{B}_C\left(n_j\right)},N{B}_C\left(n_i\right)\in [0,1]$$

(5)

where ${\displaystyle \sum _{j=1}^n}{B}_C\left(n_j\right)$ is the cumulative sum of betweenness centrality levels of all nodes in G. Further, the video-related messages mainly include two categories: $n_i$ receives video information forwarded or pushed by $n_i$′s neighbor nodes; $n_i$ needs to handle video requests forwarded by $n_i$′s neighbor nodes. The higher the number of received and handled messages, the more important the levels of message distribution of $n_i$ are. Let $N_H\left(n_i\right)$ be the number of messages handled by $n_i$, and the normalized value of message relay levels of $n_i$ can be defined as:

$$N{N}_H\left(n_i\right)=\frac{N_H\left(n_i\right)}{{\displaystyle \sum _{j=1}^n}{N}_H\left(n_j\right)},N{N}_H\left(n_i\right)\in [0,1]$$

(6)

where ${\displaystyle \sum _{j=1}^n}{N}_H\left(n_j\right)$ is the total sum of handled messages of all nodes in G. $N{N}_H\left(n_i\right)$ denotes the global proportion of information collection and control in G. The capacity of information dispatching of $n_i$ can be defined as:

$$C_F\left(n_i\right)=N{B}_C\left(n_i\right)\times N{N}_H\left(n_i\right),C_F\left(n_i\right)\in [0,1]$$

(7)

If $n_i$ has the large value of $C_F\left(n_i\right)$, $n_i$ has a strong capacity of information collection and control in G. If the nodes with a strong capacity for information collection and control are selected as the spreaders, they can depend on the owned information to promote the forwarding success ratio of video request messages and actively regulate video distribution according to variations of supply and demand based on the collected information.

3.1.3. Capacity of Video Delivery

The spread efficiency of video data is based on channels and resources of video spread provided by social influence, and information-dispatching capacity is also a key factor for the spread scale and effect. The video-spread efficiency determines the rate and scale of video copying and the QoE of nodes. If a node $n_i$ has a low capacity for video delivery, the long transmission time of video data reduces the limited scale of video spread. Furthermore, the severe distortion caused by the frequent loss of video data reduces the willingness that nodes request or accept videos, which also limits the scale of video spread. The capacity of video delivery is also a key factor for the estimation of video spreaders. The number of cached videos, the transmission time of video data, and the freeze time of videos are key factors of video-delivery capacity. The number of cached videos determines the probability that the nodes meet the demand for the requested videos. The higher the number of cached videos, the higher the probability of meeting the demand of request nodes. The normalized value of the number of videos cached by $n_i$ can be defined as:

$$N{N}_V\left(n_i\right)=\frac{N_V\left(n_i\right)}{\left|VS\right|},N{N}_V\left(n_i\right)\in [0,1]$$

(8)

where $N_V\left(n_i\right)$ is the number of videos cached by $n_i$ in local buffer; $VS$ is the set of videos in social networks; $\left|VS\right|$ returns the number of items in $\left|VS\right|$. The transmission time of video data and the freeze time of videos are the key factors of node QoE. The long time of data transmission and frame freeze of videos are caused by the high rate of video data loss. Because video data-loss results in data re-transmission and frame-freezing, the time of data transmission and frame-freezing of videos are lengthened. Therefore, the transmission time of video data of $n_i$ for a video $v_j$ can be defined as [50]:

$$T_{ij}=\frac{S_j}{\overline{B_i}(1-\overline{P_i})}$$

(9)

where $S_j$ is the size of $v_j$; $B_i$ and $P_i$ are bandwidth and packet-loss rate (PLR) of $n_i$, respectively; $\overline{B_i}$ and $\overline{P_i}$ are average bandwidth and average PLR of $n_i$ in the process of data transmission of $v_j$, respectively. The normalized value of $T_{ij}$ can be defined as:

$$N{T}_{ij}=\frac{L_j}{T_{ij}}$$

(10)

where $L_j$ is the length of $v_j$. If the transmission rate of video data is always equal to the video playback rate and the PLR value is 0, the data transmission time is equal to the length of $v_j$. If the transmission rate of video data is always equal to the video playback rate and the PLR value is greater than 0, the data transmission time is greater than the length of $v_j$; $T_{ij}\ge L_j$ and $N{T}_{ij}\in (0,1]$. The average transmission time of all videos of $n_i$ can be defined as:

$$A{T}_N\left(n_i\right)=\frac{{\displaystyle \sum _{c=1}^{\left|VS\right(n_i\left)\right|}}N{T}_{ic}}{\left|VS\right(n_i\left)\right|}$$

(11)

where $VS\left(n_i\right)$ is the set of videos delivered by $n_i$; $\left|VS\right(n_i\left)\right|$ returns the number of items in $VS\left(n_i\right)$. The large value of $A{T}_N\left(n_i\right)$ denotes the strong delivery performance of $n_i$. The larger the value of $A{T}_N\left(n_i\right)$, the stronger the efficiency of video data transmission is. Similarly, the normalized value of freeze time of $n_i$ for the video $v_j$ can be defined as:

$$N{F}_{ij}=\frac{F{T}_{ij}}{L_j}$$

(12)

where $F{T}_{ij}$ is the total sum of freeze time. We assume that the value of $F{T}_{ij}$ is less than that of $L_j$ and $N{F}_{ij}\in [0,1]$. Further, the average transmission time of all videos of $n_i$ can be defined as:

$$A{T}_F\left(n_i\right)=\frac{{\displaystyle \sum _{c=1}^{\left|VS\right(n_i\left)\right|}}N{F}_{ic}}{\left|VS\right(n_i\left)\right|}$$

(13)

The lower the value of $A{T}_F\left(n_i\right)$ is, the higher the QoE of the nodes is. According to the definition of the number of cached videos, the transmission time of video data, and freeze time of videos, the video delivery capacity of $n_i$ can be defined as:

$$D{C}_D\left(n_i\right)=N{N}_V\left(n_i\right)\times A{T}_N\left(n_i\right)\times (1-A{T}_F\left(n_i\right))$$

(14)

Because $D{C}_D\left(n_i\right)$ has a positive correlation relation with the values of $N{N}_V\left(n_i\right)$, $A{T}_N\left(n_i\right)$ and $(1-A{T}_F\left(n_i\right))$, the nodes which have large values of $D{C}_D\left(n_i\right)$ can achieve fast video delivery and ensure QoE of request nodes.

3.1.4. Calculation of Video-Spread Gains

According to the values of $D{C}_D\left(n_i\right)$, $C_F\left(n_i\right)$ and $I_S\left(n_i\right)$, the video-spread gains brought by selecting $n_i$ as spread nodes can be defined as:

$$G_S\left(n_i\right)=\alpha \times D{C}_D\left(n_i\right)+\beta \times C_F\left(n_i\right)+\lambda \times I_S\left(n_i\right)$$

(15)

where $\alpha$, $\beta$ and $\lambda$ are the regulatory factors of $D{C}_D\left(n_i\right)$, $C_F\left(n_i\right)$ and $I_S\left(n_i\right)$, are in the range [0,1] and $\alpha +\beta +\lambda =1$.

3.2. Weight of Video-Spreading Gains

The video-spreading gains keep relatively static due to parameter measurement based on a statistical analysis of historical spread information, which shows the spread gains by bringing the individual ability of candidate spread nodes. However, the measurement results of the individual ability of candidate spread nodes do not reflect the real gains in the scale of video copying at the current video spread round. The real gains are predicted increments of spread scale generated by activating candidate spread nodes, and can be considered as the weight of static spread gains of individual ability. The large scale of infected nodes by activating candidate spread nodes denotes the high popularity of videos and ensures a balance between the supply and demand of videos. Further, if the nodes infected by the selected spread nodes have a high individual ability in the aspects of social influence, information dispatching, and video delivery, they continue to infect more nodes, which continually promotes spread scale and lengthens popular period time.

The prediction method of infected nodes depends on the estimation of the probability that the nodes accept videos pushed by candidate spread nodes and the probability that the request nodes receive video data delivered by candidate spread nodes. Because the social neighbor relationship between the two nodes is the precondition of pushing videos, the successful video push relies on the interest preference of pushed objectives and social influence from candidate spread nodes. Let $VS=(v{s}_1,v{s}_2,\dots ,v{s}_m)$ be the set of video classification where an item $v{s}_k$ in $VS$ is a video category k; let $N_{v{s}_k}^p\left(n_h\right)$ be the number of videos in $v{s}_k$ played by $n_h$, and $N_t^p\left(n_h\right)$ be the total number of all videos played by $n_h$. The interest levels of $n_h$ for $v{s}_k$ can be defined as:

$$I{L}_{v{s}_k}\left(n_h\right)=\frac{N_{v{s}_k}^p\left(n_h\right)}{N_t^p\left(n_h\right)},I{L}_{v{s}_k}\left(n_h\right)\in [0,1]$$

(16)

Similarly, the interest levels of all video categories are calculated according to the above equation. On the other hand, let $N{S}_i$ be the set of neighbor nodes of $n_h$ where all nodes in $N{S}_h$ have direct social links with $n_h$; let $N_{hi}^v$ be the number of videos shared between $n_h$ and neighbor node $n_i$ of $n_h$. ${\displaystyle \sum _{c=1}^{|N{S}_h|}}{N}_{hc}^v$ is the total number of videos shared by $n_h$ and all neighbor nodes of $n_h$ where $|N{S}_h|$ returns the number of items in $N{S}_h$. The social influence of $n_i$ for $n_h$ can be defined as:

$$S{I}_{hi}=\frac{N_{hi}^v}{{\displaystyle \sum _{c=1}^{|N{S}_h|}}{N}_{hc}^v},S{I}_{hi}\in [0,1]$$

(17)

If $v_j$ is a popular video and $v_j\in v{s}_k$, $n_i$ is the social neighbor node of $n_h$ and pushes $v_j$ to $n_h$, the probability that $n_h$ accepted $v_j$ pushed by $n_i$ can be defined as:

$$P_{hi}\left(v_j\right)=S{I}_{hi}\times I{L}_{v{s}_k}\left(n_h\right),P_{hi}\left(v_j\right)\in [0,1]$$

(18)

Let $N_{hi}^s$ be the number of successful video pushes from $n_i$ to $n_h$ and ${\displaystyle \sum _{c=1}^{|N{S}_h|}}{N}_{hc}^s$ be the total number of successful video pushes from all neighbor nodes of $n_h$ to $n_h$. The historical success rate that $n_i$ pushes videos to $n_h$ can be defined as:

$$R_{hi}^p=\frac{N_{hi}^s}{{\displaystyle \sum _{c=1}^{|N{S}_h|}}{N}_{hc}^s},R_{hi}^p\in [0,1]$$

(19)

$R_{hi}^p$ denotes the capacity of push-based video-spread of $n_i$ to $n_h$ and is considered as the threshold value for evaluating successful video-pushing from $n_i$ to $n_h$. If $P_{hi}\left(v_j\right)\ge R_{hi}^p$, $n_h$ may accept $v_j$ pushed by $n_i$ when $n_i$ is selected as the spread node. All neighbor nodes of $n_i$ can be estimated according to the above process and the neighbor nodes which may accept $v_j$ pushed by $n_i$ form a subset $SN{S}_i\left(v_j\right)\in N{S}_i$. On the other hand, the nodes in $SN{S}_i\left(v_j\right)$ depend on the push-based mode to obtain videos, so the video spread mode where the nodes actively request videos also should be considered. $|SN{S}_i\left(v_j\right)|$ returns the number of items in $SN{S}_i\left(v_j\right)$ and is the number of nodes which are spread by $n_i$ via push mode. $IN{S}_i\left(v_j\right)$ is a set of nodes which are neighbor nodes of $n_i$ and have stored $v_j$ at the spread round of current video $v_j$. $SI{S}_i\left(v_j\right)=SN{S}_i\left(v_j\right)-SN{S}_i\left(v_j\right)\cap IN{S}_i\left(v_j\right)$ is the set of nodes which do not store $v_j$ in $SN{S}_i\left(v_j\right)$.

Let $SN{S}_i^s$ be the set of nodes that receive video data transmitted by $n_i$. The nodes in $SN{S}_i^s$ depend on the pull-based mode to obtain videos and receive the video data transmitted by $n_i$. The average number of nodes that receive the video data transmitted by $n_i$ every round of video spread can be defined as:

$$N_i^a=\frac{|SN{S}_i^s|}{nu{m}_i}$$

(20)

where $|SN{S}_i^s|$ returns the number of items in $SN{S}_i^s$; $nu{m}_i$ is the number of video-spread rounds participated in by $n_i$. $⌊N_i^a⌋$ is the lower bound of an integer value of $N_i^a$ and can be defined as:

$$⌊N_i^a⌋=\left\{\begin{array}{c}⌊\frac{|SN{S}_i^s|}{nu{m}_i}⌋,N_i^a\in (1,+\infty ]\hfill \\ 0,N_i^a\in [0,1]\hfill \end{array}\right.$$

(21)

$N_i^a\in (1,+\infty ]$ means that $n_i$ receives more request messages and may provide services of video data transmission for at least one node every video-spread round; $N_i^a\in [0,1]$ means that $n_i$ receives fewer request messages and does not provide more contribution for the scale of video-spreading. $⌊N_i^a⌋$ is considered as the number of nodes which are spread by $n_i$ via pull mode. $|SI{S}_i\left(v_j\right)|+⌊N_i^a⌋$ is the total number of nodes which are spread by $n_i$ via pull and push modes and are normalized:

$$W_i\left(v_j\right)=\frac{|SI{S}_i\left(v_j\right)|+⌊N_i^a⌋}{n-1},W_i\left(v_j\right)\in [0,1]$$

(22)

$W_i\left(v_j\right)$ denotes the predicted capacity of video spread of $n_i$ at the spread round of $v_j$. The higher (lower) the value of $W_i\left(v_j\right)$ is, the higher (lower) the capacity of video spread of $n_i$.

3.3. Video-Spreading Strategy Based on Spread Nodes

According to the calculation method of spread gain and a weight value, the weighted gains generated by selecting $n_i$ can be defined as:

$$W{G}_S^j\left(n_i\right)=G_S\left(n_i\right)\times W_i\left(v_j\right),W{G}_S^j\left(n_i\right)\in [0,1]$$

(23)

The weighted gains generated by all nodes in social networks at the spread round of $v_j$ can be calculated according to the above method and form a set $G{S}_j=(W{G}_S^j\left(n_a\right),W{G}_S^j\left(n_b\right),\dots ,$ $W{G}_S^j\left(n_k\right))$. The weighted gains are used as the metric basis of spread node selection. Let $CN{S}_j$ be the set of candidate spread nodes of $v_j$ and $DN{S}_j$ be the set of nodes that have been selected as spread nodes of $v_j$. The spread strategy of $v_j$ based on the spread nodes is shown in the following steps and the pseudocode of the spread process is described in Algorithm 1.

(1)

By state-message exchange between nodes, the nodes which have stored $v_j$ are removed in $CN{S}_j$. If the rejection mark values of the nodes in $CN{S}_i$ which do not store $v_j$ are equal to or greater than 1, the nodes are removed in $CN{S}_j$. If $CN{S}_j$ is an empty set and $|CN{S}_j|=0$, return to step 5; If $UN{S}_i$ is an empty set and $|UN{S}_i|=0$, return to step 2.

(2)

If the node $n_i\in CN{S}_j$ which has the largest value of weight gains among all items in $CN{S}_j$, $n_i$, is selected as the spread node, it is removed by $CN{S}_j$ and is added into $DN{S}_j$; return to step 3.

(3)

Let $UN{S}_i\in N{S}_i$ be the set of neighbor nodes of $n_i$ which do not store $v_j$. $n_i$ exchanges the state messages with neighbor nodes of $n_i$. $n_i$ adds the neighbor nodes which do not store $v_j$ into $UN{S}_i$. If $UN{S}_i$ is an empty set and $|UN{S}_i|=0$, return to step 1; If $UN{S}_i$ is not an empty set and $|UN{S}_i|\ne 0$, return to step 4.

(4)

$n_i$ first checks the current available bandwidth $B_i$. If $⌊\frac{B_i}{p{b}_j}⌋<1$, $n_i$ does not provide the service of video data transmission for other request nodes and does not push $v_j$ for neighbor nodes of $n_i$. The current spread process returns to step 1. If $⌊\frac{B_i}{p{b}_j}⌋\ge 1$, $n_i$ estimates the interest levels of neighbor nodes of $n_i$ for the pushed $v_j$ according to the following equation:

$$W{P}_{hi}\left(v_j\right)=lo{g}_2(1+R_{hj})\times P_{hi}\left(v_j\right)$$

(24)

$P_{hi}\left(v_j\right)$ is the probability that $n_h$ accepted $v_j$ pushed by $n_i$ according to Equation (18); $lo{g}_2(1+R_{hj})$ is the weight value of $P_{hi}\left(v_j\right)$ and $R_{hj}$ is defined as:

$$R_{hj}=\frac{N_{hj}^s}{N_{hj}^f+1}$$

(25)

where $N_{hj}^s$ and $N_{hj}^f$ are, respectively, the successful and unsuccessful number of pushes when $n_i$ is selected as spread node and $P_{hi}\left(v_j\right)\ge R_{hi}^p$. $R_{hj}$ is the result that $n_i$ learns the predicted and real results of pushing videos to neighbor nodes, which promotes predicted accuracy using $P_{hi}\left(v_j\right)$ based on historical statistical information. $n_i$ selects the neighbor node $n_h$, which has the largest value of $W{P}_{hi}\left(v_j\right)$ among $UN{S}_i$ as the preferential push objective. $n_i$ pushes $v_j$ to $n_h$. If $n_h$ accepts $v_j$ pushed by $n_i$, the value of $N_{hj}^s$ is increased by 1 and $n_h$ is added into the set $DN{L}_{ij}$. If $n_h$ rejects $v_j$ pushed by $n_i$, $n_i$ adds a push failure mark for $n_h$ and the value of rejection mark of $n_h$ is $S{I}_{hi}$. Moreover, if $n_i$ receives the request messages of $v_j$ from other nodes, $n_i$ forwards the request messages to an item in $DN{L}_{ij}$, which reduces the bandwidth load of $n_i$ to ensure the sustainable push. Return to step 3.

(5)

The spread process is terminated.

Algorithm 1: Spread process of $v_j$ with assistance of spread nodes.

1: k is rejection mark and $e=0,h=0$;   2: items of $CN{S}_j$ is sorted in descending order of $W{G}_S^j$;   3: while $|CN{S}_j|\ne 0$   4:  for (i = 0; $i<|CN{S}_j|$; i++)   5:    if $CN{S}_j.\left[i\right]$ stores $v_j$   6:      removes $CN{S}_j.\left[i\right]$ in $CN{S}_j$;   7:    else if $CN{S}_j.\left[i\right].k\ge 1$   8:      removes $CN{S}_j.\left[i\right]$ in $CN{S}_j$;   9:    end if   10:  end for   11:  $CN{S}_j.\left[h\right]$ is selected as spread node;   12:  while $CN{S}_j.\left[h\right].\left|UNS\right|\ne 0$   13:    if $CN{S}_j.\left[h\right].⌊\frac{B_i}{p{b}_j}⌋\ge 1$   14:     calculates $WP\left(v_j\right)$ of all nodes in $CN{S}_j.\left[h\right].UNS$;   15:     $CN{S}_j.\left[h\right]$ pushes $v_j$ to $CN{S}_j.\left[h\right].UNS.\left[e\right]$ with maximum $WP\left(v_j\right)$;   16:      if $CN{S}_j.\left[h\right].UNS.\left[e\right]$ rejects $v_j$   17:        $CN{S}_j.\left[h\right].UNS.\left[e\right].=CN{S}_j.\left[h\right].UNS.\left[e\right]+S{I}_{he}$;   18:      end if   19:    e++;   20:  end while   21:  h++;   22: end while

4. Testing and Test Results’ Analysis

4.1. Testing Topology and Scenarios

We compare the performance of the proposed solution SSISC with that of the two state-of-the-art solutions, OEISS [51] and OCP [52], which are deployed in a mobile network environment by making use of Network Simulator 3 (NS-3) [53]. The square scenario is set to a 2000 × 2000 area. The number of mobile nodes is set to 500. Each mobile node has random movement behaviors during a 500 s simulation time in the square scenario. Initially, the beginning position coordinate of each mobile node is set to a random value. After each mobile node is randomly assigned an ending position and a constant speed, it moves along the path consisting of beginning and ending positions at a constant speed. When the mobile nodes arrive at the assigned ending position, they are randomly assigned a new ending position and a constant speed, and continuously move to the new ending position using the new speed. The velocity range of mobile nodes is defined as [1, 30] m/s. The movement behaviors of mobile nodes with the setting of 0 s stay time can speed up the variation of network topology and promote the efficiency and risk of 5G-based data delivery.

There are 20 video categories in $VS$ and each video category includes 100 video files. Each mobile node has a log that includes the watched videos. The number of videos that belong to a video category in a log meets the normal distribution, which can ensure the prominent interests of mobile nodes for video content. The number of video categories corresponding to the prominent interests of mobile nodes meets the normal distribution, which can highlight different popularity levels of video categories. The watched logs can be used to calculate the probability that the mobile nodes request videos or accept pushed videos based on video content and estimate interest-based relationship levels between mobile nodes. The number of spread videos in each video category is set to 5. If the videos are included in the watched logs of mobile nodes, the videos are not requested by the mobile nodes. The popularity of all videos follows the Zipf distribution [54]. The initial probability is that the mobile nodes request videos during the whole simulation time according to the equation [55].

$$P\left(n\right)=\frac{{\displaystyle \sum _{i=1}^M}{i}^{{\rho }_i}}{r_n^{{\rho }_n}}$$

(26)

r is the popularity ranking and $r_n$ is the popularity ranking of the n-th video; $\rho \in (0,1)$ denotes the Zipf exponent that describes the skewness for the video-request behaviors of users. The larger the value of $\rho$ is, the more concentrated the video requests are. ${\rho }_n$ is the Zipf exponent of the n-th video. i is the popularity ranking of videos, M is the total number of videos, and M = 100 according to the settings of simulation. Each mobile node has a pushed video list that records the received information of videos pushed by other nodes. When the mobile nodes obtain the videos via pull or push modes, they are randomly assigned the playback time in terms of the interest levels of mobile nodes. The lower the interest levels of mobile nodes for video content, the shorter the assigned playback time of the mobile nodes is. After the mobile nodes finish the video playback according to the assigned playback time, they record the watched videos into the watched logs and continue to fetch videos via pull or push modes. If the pushed video list is empty, the mobile nodes request the new videos which are not included in the watched logs according to the maximum value of probabilities of requesting videos; If the pushed video list is not empty, the mobile nodes select the videos which are the first push items in the push list and decide on accepting the push videos. The communication logs between nodes are simulated and generated for the measurement of social relationships between them. Every video has 100 s length and 25 MB size. The playback bitrate of all videos is 2000 kbps. The number of source nodes that store initial video data for every spread video is set to 10. The number of videos cached by every mobile node is set to 10 or 20, which shows the variation of spread scale and user QoE in the different supply levels. In OEISS, the social relationships of four types between mobile nodes are defined as the social influence for video acceptance and the interest levels of mobile nodes for video content use Equation (26).

The simulation scenarios rely on the uniformly distributed 25 base stations which are used as the access points (APs) to transmit and forward video data. The physical and MAC layer and modulation schemes of network units are reset according to the 5G industrial standardization. The MAC protocol employs 802.11p and the MAC channel delay is 250 ms. The upper bound of the data rate is set to 20 Mbps. The maximum communication range is 250 m. The propagation loss model employs the Friis propagation loss model (FPLM) in NS-3 [53], which is designed for an unstructured clear path between receivers and transmitters to eliminate the performance degraded by random shadowing effects. The FPLM effectively erases the random effects caused by shadowing for the simulation results. The D2D settings of the 5G network follow the settings in the popular studies [56].

4.2. Performance Evaluation

We compare the performance of SSISC, OEISS, and OCP in terms of startup delay, caching hit ratio, packet-loss rate, average freeze time, and control overhead, respectively.

Startup delay: A node $n_i$ sends a request message at $t_s$ and receives the first video data at $t_r$. $t_r-t_s$ is considered as the startup delay of $n_i$, which includes the query time of video supply nodes and transmission time of the first data. The scale and geographical distribution of video copies are the main influence factors for the query time of video supply nodes. The stability and congestion levels of data transmission paths are the main influencing factors for the transmission delay of video data. The average values of startup delay during a period of 5 s are shown in Figure 2 and Figure 3.

As Figure 2 shows, the three curves corresponding to SSISC, OEISS, and OCP keep the obvious processes of a fall after a rise during the whole simulation time. The orange curve of SSISC has a fast fall from t = 25 s to t = 60 s after a fast rise from t = 0 s to t = 20 s; SSISC’s curve has also a fast increase from t = 65 s to t = 130 s; SSISC’s curve keeps the vibration at the stable levels from t = 130 s to t = 500 s. The red curve of OCP keeps the vibration at stable levels from t = 145 s to t = 300 s after a rise from t = 0 s to t = 145 s. OCP’s curve has the slight fall from t = 300 s to t = 500 s. The blue curve of OEISS also has a clear trend of a slight fall from t = 260 s to t = 500 s after a rise from t = 0 s to t = 260 s. The orange curve of SSISC is higher than those of OEISS and OCP from t = 0 s to t = 145 s and is lower than those of OEISS and OCP from t = 150 s to t = 500 s.

As Figure 3 shows, the three curves corresponding to SSISC, OEISS, and OCP maintain a fall after rising during the whole simulation time. The orange curve of SSISC has a slight rise from t = 0 s to t = 270 s and keeps falling slowly from t = 275 s to t = 500 s. The red curve of OCP has a clear trend of falling from t = 300 s to t = 500 s after a rise from t = 0 s to t = 295 s. The blue curve of OEISS also has a clear trend of a slow fall from t = 260 s to t = 500 s after a rise from t = 0 s to t = 260 s. The orange curve of SSISC is lower than those of OEISS and OCP for most of the simulation time.

The video playback time of the mobile nodes is randomly allocated. When the mobile nodes finish the playback of all videos, they do not request a video again. The decrease in the number of request nodes relieves the pressure of video supply, which reduces the average startup delay. Moreover, a high enough supply of video resources can reduce the video lookup delay. Therefore, the three curves have a slight fall in the late simulation period.

SSISC depends on the selected spread nodes to propagate videos and supply video data for the request nodes. To promote propagation efficiency, SSISC estimates the video spread gains of nodes based on social influence levels and sharing capacities. The estimation of social influence levels relies on the investigation of NDC and ASD. NDC can reflect the social resource levels of nodes. The nodes with high NDC can not only use resources of bandwidth, computation, and storage of numerous neighbor nodes to provide the supply services of video resources for the request nodes, but also ensure a large base of successful video pushes. ASD denotes the reachability of nodes to other nodes in social networks. The nodes with low ASD can quickly communicate with the associated nodes with the lowest forwarding of messages, which reduces the transmission delay of messages in social networks and promotes the knowledge scale for the operation of social networks. The information dispatching and the data delivery for the spread of video content are the two estimation parameters of sharing capacities. The information dispatching capacity investigates the scale of forwarded messages and node betweenness centrality. The nodes with high capacities of information dispatching have strong capacities of converging and distributing video-related information in social networks, which promotes video-lookup success rate and reduces video-lookup delay. The delivery capacity of video data investigates the number of cached videos, the average transmission time of video data, and the average freeze time of videos. The nodes which strong delivery capacity have high service levels for the QoE of other request nodes. If the nodes with high social influence levels and strong sharing capacities are selected as the spread nodes, the spread nodes can speed up video lookup and data transmission, which increase the scale of video-spreading and reduce startup delay. SSISC predicts the spreading scale for the current popular videos when the candidate spread nodes are selected according to the probabilities that nodes fetch the current popular videos using video interest levels, social relationship levels, and historical push-success rates. The predicted spread scale is used as the weight value of video-spreading gains. The nodes with high-weighted video-spread gains can further ensure the large scale of video-spreading and low startup delay. SSISC designs a video-spreading strategy based on the assistance of spread nodes. The video spread nodes have high weighted gains and control the spreading scale in terms of the bandwidth supply capacities, which achieves an effective balance between supply and demand and ensures user QoE with efficient video-sharing. Initially, SSISC needs to estimate candidate video spread nodes and does not depend on the spread nodes to implement video push and distribution regulation of caching of video resources, so the average startup delay values of SSISC are higher than those of OEISS and OCP. After SSISC selects the video spread nodes, the spread nodes use video pushing to reduce the scale of video requests, which decreases the average startup delay.

OEISS defines the four types of social relationships for mobile users to evaluate the influences of social relationships on the information-spreading process in mobile social networks. OEISS defines a probability of two nodes encountering based on the assumption that the meeting times follow Poisson distribution. A degree of information-spreading is defined and is used to describe information-fetching probabilities of different social relationships. The multiobjective optimization problem based on the energy and delay of information transmission is formulated. Based on Pontryagin’s minimum principle and the Hamiltonian function, the optimal control under the objective function of information transmission is created. The mobile nodes can decide on information-spreading according to the objective function values of energy and delay of information transmission. The encounter-based information-spreading relies on the mobility of mobile nodes and makes use of one-hop information transmission to obtain low delays and energy loss. However, the encounter assumption of following the Poisson distribution difficulty adapts to the random movement model, namely, the movement behaviors of mobile nodes do not meet the encounter prediction of mobility based on the Poisson distribution. Therefore, the encounter-based video-pushing of OEISS in the process of simulation has a low success rate. The low effectiveness of push-based video-spreading control does not use efficient video pushing to meet the demand of video playback of mobile nodes, so a large number of mobile nodes send the request messages to fetch video data. Initially, OEISS uses the one-hop video push to obtain a low average startup delay. The average startup delay of OEISS with an increasing number of request nodes increases quickly and maintains high levels.

OCP collects and analyzes the state information of nodes to predict the demand variation of videos and requires the mobile nodes to cache and regulate video resources in terms of the variation of video demand. Although OCP does not employ video pushes to reduce the video lookup delay, enough video supply can promote the video lookup success rate, which also decreases the video lookup delay. Moreover, when the nodes cache and regulate local video resources, their video demand is also met by the locally cached videos with a certain probability, which also reduces the average startup delay. However, OCP does not use the video push to spread videos. The passive video spread via handling the video requests makes the real-time regulation of video caching to meet the various video demands difficult.OCP does not consider the social influence between users for the intention of fetching videos. The video demand is also difficult to accurately predict. If there are high difference levels between the predicted and real demand, the imbalance between supply and demand leads to a low video-lookup success rate and a high lookup delay. The same caching time via message broadcasting does not make the timely adjustments of local video caching, which makes it difficult to meet the various video demands. OCP has a low average startup delay at the initial simulation process, but the average startup delay of OCP quickly increases and maintains high levels in the middle and late stages of the simulation.

Caching hit ratio (CHR): A node $n_i$ stores a video $v_j$ and receives a request message of $v_j$ from another node $n_k$ for $v_j$. The event that $n_i$ handles the request of $n_k$ and delivers the data of $v_j$ to $n_k$ is a cache hit. The ratio between the number of successful cache hits and the total number of all video requests is defined as the caching hit ratio. To clearly show the CHR simulation results, the average values of CHR during periods of every 5 s are shown in Figure 4 and Figure 5.

As Figure 4 shows, the three curves corresponding to SSISC, OEISS, and OCP maintain the increase with drastic fluctuation during the whole simulation time. The orange curve of SSISC experiences a fast rise from t = 0 s to t = 220 s and maintains a stable fluctuation from t = 220 s to t = 500 s. The orange curve of OCP has an evident increase from t = 0 s to t = 160 s and slowly increases with a fluctuation from t = 160 s to t = 500 s. The blue curve of OEISS also quickly increases from t = 0 s to t = 70 s and maintains a slow rise from t = 70 s to t = 50 s. Although the CHR values of SSISC are less than those of OEISS and OCP during the initial simulation time from t = 0 s to t = 80 s, the orange curve of SSISC has higher CHR levels than those of curves of OEISS and OCP during most of the simulation time t = 80 s to t = 500 s.

As Figure 5 shows, the three curves corresponding to SSISC, OEISS, and OCP have similar variation processes during the whole simulation time. The orange curve of SSISC maintains a fast rise increase t = 0 s to t = 190 s and has a stable fluctuation from t = 190 s to t = 500 s. The red curve of OCP has an fast rise from t = 0 s to t = 150 s and increases slowly from t = 150 s to t = 500 s. The blue curve of OEISS also increases from t = 0 s to t = 80 s and increases slowly from t = 80 s to t = 500 s. Although the CHR values of SSISC are less than those of OEISS and OCP during the initial simulation time from t = 0 s to t = 90 s, the orange curve of SSISC has higher CHR levels than those of curves of OEISS and OCP during most of the simulation time from t = 90 s to t = 500 s.

The CHR reflects the effectiveness of video supply. The dynamic regulation of video distribution according to the variation of video demand can continuously supply the videos needed by the nodes to effectively promote the CHR. SSISC propagates videos and supplies video data with the assistance of the selected spread nodes. The selection of spread nodes relies on the measurement of video spread gains of nodes based on social influence levels and sharing capacities. The spread nodes push the videos to their social neighbor nodes by investigating interest preference and social influence, which promotes the push success rate. The selected spread nodes have high NDC, low ASD, and high node betweenness centrality, so they can use the video resources cached in the social neighbor nodes to help the request nodes quickly search the video supply nodes, which effectively promotes the CHR. SSISC calculates the probabilities that nodes fetch the current popular videos according to video interest levels, social relationship levels, and historical push success rate to predict the spreading scale of the popular videos. The spread nodes decide on video pushing and regulate video distribution according to the predicted spread scale. However, the spread nodes rely on the accuracy of prediction results of the spreading scale to regulate the video distribution and balance supply and demand. The fast variation of video demand results in the invalidation of caching regulation of the spread nodes and the imbalance between supply and demand. Therefore, the CHR values of SSISC do not have a rising trend in the middle and late stages of the simulation. OEISS uses the four types of social relationships for mobile users to implement video-sharing among social neighbor nodes. The video spread between nodes can prompt the dynamic regulation of locally cached videos of nodes. However, OEISS does not consider the regulation of video distribution based on video caching and neglects the control of the balance between supply and demand. Therefore, the CHR values of OEISS maintain low levels. OCP uses the collected state information of nodes to predict the demand variation of videos. The mobile nodes implement video caching and replace local useless videos in terms of the predicted video demand. The CHR values of OCP can keep the continuous rise trend. However, OCP does not consider the social influence between nodes, which results in the low accuracy of demand prediction. The unified video caching during the same period does not effectively handle the dynamic video demand of nodes. Therefore, the CHR values of OCP have a violent jitter and slow increase.

Packet loss rate (PLR): Let $N_l(\Delta t)$ be the amount of lost video data during a period $\Delta t$ and $N_s(\Delta t)$ the total amount of sent video data during $\Delta t$. $\frac{N_l(\Delta t)}{N_s(\Delta t)}$ is defined as the PLR. The PLR values of SSISC, OEISS, and OCP during $\Delta t$ = 10 s are shown in Figure 6.

As Figure 6 shows, the three curves of SSISC, OEISS, and OCP fall continuously during the whole simulation time. The orange curve of SSISC maintains a fast decrease from t = 0 s to t = 190 s and has a stable trend with a slight fluctuation from t = 190 s to t = 500 s. The red curve of OCP falls quickly from t = 0 s to t = 140 s and experiences a stable decrease from t = 140 s to t = 500 s. The blue curve of OEISS also falls quickly from t = 0 s to t = 160 s and maintains stable decrease from t = 160 s to t = 500 s. The PLR curve of SSISC is lower than those of OEISS and OCP.

Average freeze time (AFT): the interruption interval time in the process of video playback is defined as the freeze time. The average freeze time is the ratio between the total sum of freeze time and the number of freezes during a period $\Delta t$. The AFT values of SSISC, OEISS, and OCP during $\Delta t$ = 10 s are shown in Figure 7.

As Figure 7 shows, the orange curve of SSISC has a fast increase from t = 0 s to t = 170 s and keeps a slight decrease from t = 170 s to t = 500 s. The red curve of OCP has an fast increase from t = 0 s to t = 240 s and falls slowly from t = 240 s to t = 500 s. The blue curve of OEISS also has an increase from t = 0 s to t = 170 s, experiences a stable fluctuation from t = 170 s to t = 280 s, and decreases slowly from t = 280 s to t = 500 s. The orange curve of SSISC is lower than those of curves of OEISS and OCP during the whole simulation time.

The PLR and the AFT reflect the transmission performance of video data. The high stability and bandwidth of the transmission paths of video data can reduce the risk of data loss. Otherwise, the fast-changing paths and the scarce bandwidth result in a high probability of data loss. The video data loss leads to the interruption of playback, so the re-transmission delay of the video data increases the freeze time. SSISC investigates the sharing capacities of nodes such as the transmission time of video data and the freeze-time of videos. The selected spread nodes have strong capacities for video data delivery. To balance the supply and demand of popular videos in networks, the spread nodes control the amount of video pushing according to the predicted scale of video demand, avoiding the excessive consumption of bandwidth and reducing the redundancy levels of video supply. However, the historically strong capacities of video data delivery do not ensure the current performance of data transmission. The random mobility of nodes results in the fast change of data transmission paths. SSISC has a slight performance advantage in PLR and the AFT relative to OEISS and OCP. OEISS considers the mobility of nodes based on the assumption of the meeting times following a Poisson distribution. When the nodes encounter geographical one-hop distance, they share videos. The one-hop data transmission can reduce the negative influence of path variation. However, the mobility assumption is consistent with random movement settings. The random movement behaviors of nodes bring a severely negative influence on the one-hop data transmission. The PLR and the AFT of OEISS are higher than those of SSISC and OCP. OCP does not consider the mobility variation and delivery capacities of nodes. The selection of supply nodes of video data does not refer to the prior knowledge of mobility variation and delivery capacities. The variation of node mobility and path bandwidth brings a severely negative influence on the delivery performance of video data, so the PLR and the AFT of OCP cannot be effectively reduced. Enough bandwidth of nodes in the simulation settings effectively decreases the number of data loss, so that the PLR and the AFT of OCP maintain relatively low levels.

Control overhead (CO): The video-spreading needs to collect and share a large amount of information, such as node demand and available bandwidth. The message interaction also needs to consume the available bandwidth of mobile nodes. The bandwidth usage is used to communicate interaction.

As Figure 8 shows, the three curves corresponding to SSISC, OEISS, and OCP fall after a rise with the increasing simulation time. The orange curve of SSISC rises quickly from t = 0 s to t = 240 s and falls slightly from t = 240 s to t = 500 s. The red curve of OCP rises quickly from t = 0 s to t = 150 s and maintains a obvious fall from t = 150 s to t = 500 s. The blue curve of OEISS rises quickly from t = 0 s to t = 50 s, experiences a stable process from t = 50 s to t = 270 s, maintains an obvious fall from t = 270 s to t = 330 s, and shows a stable process with a slight fluctuation.

As Figure 9 shows, the orange curve of SSISC rises quickly from t = 0 s to t = 70 s, experiences a stable process from t = 70 s to t = 190 s, and maintains a slight fall from t = 190 s to t = 500 s. The red curve of OCP has a stable process with the high levels from t = 10 s to t = 130 s, maintains a slight fall from t = 130 s to t = 340 s, and experiences a stable process with low levels from t = 340 s to t = 500 s. The blue curve of OEISS rises quickly from t = 0 s to t = 70 s, and experiences a slight fall from t = 70 s to t = 500 s.

SSISC needs to collect a large number of information, such as interest preference, social relationships, and sharing capacities of nodes, to estimate the video-spreading gains of nodes. SSISC also needs to estimate the probabilities that the nodes fetch current popular videos to calculate the weight of spreading gains of nodes in the process of video-spreading, and controls the selection process of spread nodes according to the balance levels between the supply and demand of the popular videos. Moreover, the spread nodes use the message interaction with their social neighbor nodes to control the scale of video-spreading. Even if the scale of nodes that need to fetch the popular videos maintains a decreasing trend, SSISC still uses a large number of bandwidth resources to estimate the weighted spreading gains of nodes. Therefore, the CO values of SSISC are larger than those of OEISS and OCP. OEISS requires the nodes to exchange the current state information such as the geographical location and the played videos to search for the video-sharing objective nodes. The nodes also estimate energy and the delay of information transmission to decide on video-sharing. When the number of nodes that need to fetch the popular videos decreases, the consumption levels of bandwidth using the interaction of state information also keep the fall trend. Therefore, the CO values of OEISS are lower than those of SSISC and OCP. OCP collects the state information of nodes to predict the video demand of nodes and uniformly controls the video-caching of nodes. Moreover, OCP estimates the variation of video demand to further require the nodes to replace the local videos. The decreasing number of nodes that need to fetch the popular videos can reduce the control message scale for the caching and replacement of videos. Therefore, the CO values of OCP are less than those of SSISC.

5. Conclusions

In the paper, we propose a novel video-spreading strategy based on the joint estimation of social influence and sharing capacity in wireless networks (SSISC). By construction of the video-spreading gain model, SSISC makes use of the estimation of social influence levels and the sharing capacities and prediction of scale levels of video spread to calculate weight gains of video spread of candidate spread nodes in social networks, considering individual spread capability and expected spread gains of nodes to ensure gain-estimation accuracy. In the designed video-spreading strategy, the selected spread nodes formulate the priority of video-pushing based on learning deviation between real and forecasted results and the control process of video push according to available bandwidth, and adaptively dispatch the requested video traffic, which achieves the promotion of spread scale and the balance between supply and demand, and ensures high user QoE. Simulation results also show that SSISC obtains a lower startup delay, higher caching hit ratio, the lower packet-loss rate, lower average freeze-time, and higher control overhead than OEISS and OCP.