Social networking environments provide major platforms for the discussion and formation of opinions in diverse areas, including, but not limited to, political discourse, market trends, news, and social movements. Often, these opinions are of a competing nature, e.g., radical vs. peaceful ideologies, correct information vs. misinformation, and one technology vs. another. We study the battles of such competing opinions over evolving social networks. The novelty of our model is that it captures the exposure and adoption dynamics of opinions that account for the preferential and random nature of exposure as well as the persuasion power and persistence of different opinions. We provide a complete characterization of the mean opinion dynamics over time as a function of the initial adoption, as well as the particular exposure, adoption, and persistence dynamics. Our analysis, supported by case studies, reveals the key metrics that govern the spread of opinions and establishes the means to engineer the desired impact of an opinion in the presence of other competing opinions.

Predicting spreading patterns of information or virus has been a popular research topic for which various mathematical tools have been developed. These tools have mainly focused on estimating the average time of spread to a fraction (e.g.,$\alpha$) of the agents, i.e., so-called average$\alpha$-completion time$E(T_{\alpha})$. We claim that understanding stochastic confidence on the time$T_{\alpha}$rather than only its average gives more comprehensive knowledge on the spread behavior and wider engineering choices. Obviously, the knowledge also enables us to effectively accelerate or decelerate a spread. To demonstrate the benefits of understanding the distribution of spread time, we introduce a new metric$G_{\alpha, \beta}$that denotes the time required to guarantee$\alpha$completion (i.e., penetration) with probability$\beta$. Also, we develop a new framework characterizing$G_{\alpha, \beta}$for various spread parameters such as number of seeders, contact rates between agents, and heterogeneity in contact rates. We apply our technique to a large-scale experimental vehicular trace and show that it is possible to allocate resources for acceleration of spread in a far more elaborated way compared to conventional average-based mathematical tools.

A vehicle-to-vehicle (V2V) network is one type of mobile ad hoc network. Due to mobility, the topology in a V2V network is time-varying, which complicates the analysis and evaluation of network performance. In this paper, we model the network as geometric elements of lines and points and analyze the connectivity and capacity of the network using geometric probability. Under the assumption that n vehicles randomly arrive with a Poisson distribution, our analysis shows that the spatial distribution of vehicles within a given distance D, is uniform and that the average number of vehicles to be fully connected is approximately (1/a)(log (1/a) + log log (1/a)) for a = RT/D, where RT is the maximum transmission range of a vehicle. When a random access scheme is adopted, only (1/2)(1 - e-2)nof links comprised of two adjacent nodes are simultaneously activated, on average, so the expected network capacity increases in a way linearly proportional to (1/2)(1-e-2) as the number of vehicles increases. Through numerical studies and simulations, we verify the efficacy of our analytical results.

Smart mobile devices are generating a tremendous amount of data traffic that is putting stress on even the most advanced cellular networks. Delayed offloading has recently been proposed as an efficient mechanism to substantially alleviate this stress. The idea is simple. It allows a mobile device to delay transmission of data packets for a certain amount of time, while it searches WiFi (or similarly femtocell) networks to offload the data during the time. When the time expires, it completes the remaining portion of the delayed transmission through the cellular network that is available at the moment. In this paper, we develop an analytical framework using an embedded Markov process for the delayed offloading system. We provide a closed-form expression for estimating how much data generated by the users can be offloaded to WiFi networks from cellular networks even when there are non-Markovian data arrivals and service interruptions. We conduct extensive numerical studies with various ranges of delay, service interruption time, arrived data, and service rate. These numerical studies show that the current deployment of WiFi networks measured from a metropolitan city is capable of offloading about 80% of the generated data with 30 minutes of delay and 1 Mbps of WiFi data rate, but increasing the data rate does not help improve the amount of offloading. Further studies using this framework on two new deployment strategies of WiFi networks give guidance on how to upgrade WiFi networks by revealing that the amount of offloading for 30 minutes of delay and 1 Mbps of data rate can be drastically improved to about 90% or 98% according to the strategy.

A variety of mathematical tools have been developed for predicting the spreading patterns in a number of varied environments including infectious diseases, computer viruses, and urgent messages broadcast to mobile agents (e.g., humans, vehicles, and mobile devices). These tools have mainly focused on estimating the average time for the spread to reach a fraction (e.g., α) of the agents, i.e., the so-called average completion time E(Tα). We claim that providing probabilistic guarantee on the time for the spread Tαrather than only its average gives a much better understanding of the spread, and hence could be used to design improved methods to prevent epidemics or devise accelerated methods for distributing data. To demonstrate the benefits, we introduce a new metric Gα,βthat denotes the time required to guarantee α completion with probability β, and develop a new framework to characterize the distribution of Tαfor various spread parameters such as number of seeds, level of contact rates, and heterogeneity in contact rates. We apply our technique to an experimental mobility trace of taxies in Shanghai and show that our framework enables us to allocate resources (i.e., to control spread parameters) for acceleration of spread in a far more efficient way than the state-of-the-art.

Delay-capacity tradeoffs for mobile networks have been analyzed through a number of research works. However, Lévy mobility known to closely capture human movement patterns has not been adopted in such work. Understanding the delay-capacity tradeoff for a network with Lévy mobility can provide important insights into understanding the performance of real mobile networks governed by human mobility. This paper analytically derives an important point in the delay-capacity tradeoff for Lévy mobility, known as the critical delay. The critical delay is the minimum delay required to achieve greater throughput than what conventional static networks can possibly achieve (i.e., O(1/√n) per node in a network with n nodes). The Lévy mobility includes Lévy flight and Lévy walk whose step-size distributions parametrized by α ∈ (0,2] are both heavy-tailed while their times taken for the same step size are different. Our proposed technique involves: 1) analyzing the joint spatio-temporal probability density function of a time-varying location of a node for Lévy flight, and 2) characterizing an embedded Markov process in Lévy walk, which is a semi-Markov process. The results indicate that in Lévy walk, there is a phase transition such that for α ∈ (0,1), the critical delay is always Θ(n[1/2]), and for α ∈ [1,2] it is Θ(n[(α)/2]). In contrast, Lévy flight has the critical delay Θ(n[(α)/2]) for α ∈ (0,2].

In the literature, one of the key assumptions in characterizing the scaling laws for wireless mobile networks, is to assume that nodes do not communicate while being mobile. In other words, contact opportunities are not considered during the mobility process itself. However, we find that this assumption leads to an inflated estimate of the delay, even in an order sense. To address this issue, a new framework that allows nodes to communicate while being mobile is proposed in this paper. Under this framework, it is shown that delays to obtain various levels of throughput for i.i.d. mobility model are overestimated and a new tighter delay-capacity tradeoff is suggested. Also, the framework is used to analytically derive the delay-capacity tradeoff of Lévy flight model for various levels of throughput, where Lévy flight is a random walk of a power-law flight distribution with an exponent α ∈ (0, 2]. It is known as a mobility model which closely captures human movement patterns. The tradeoffs from the proposed framework between the delay (D̅) and per-node throughput (λ) indicate that D̅ = O(√(max(1,nλ3))) holds for i.i.d. mobility and D̅ = O(√(min(n1+αλ,n2))) holds for Lévy flight.

This paper analytically derives the delay-capacity tradeoffs for Lévy mobility: Lévy walks and Lévy flights. Lévy mobility is a random walk with a power-law flight distribution. α is the power-law slope of the distribution and 01/2) and for 1 ≤ α ≤ 2, is Θ(nα/2). In contrast, Lévy flight has critical delay Θ(nα/2) for 0 <; α ≤ 2.

In this paper, we propose an opportunistic downlink scheduling scheme that exploits multiuser diversity in a wireless network with threshold-based limited feedback. We assume that each user has its own ergodic rate requirement. The design objective of our scheme is to determine the values of thresholds with which heterogeneous ergodic rate requirements of all users are satisfied. In our analysis, we present a formula to check the feasibility of given ergodic rate requirements, and then obtain the feasible thresholds that realize them. We also obtain the optimal thresholds that maximize the ergodic sum-rate of the network while guaranteeing the ergodic rate requirements. Through numerical studies and simulations, we show the usefulness of our scheme and analysis.