Yoora Kim

Delay-capacity tradeoffs for mobile networks with Lévy walks and Lévy flights

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 0 < α ≤ 2. While in Lévy flight, each flight takes a constant flight time, in Lévy walk, it has a constant velocity which incurs strong spatio-temporal correlation as flight time depends on traveling distance. Lévy mobility is of special interest because it is known that Lévy mobility and human mobility share several common features including heavy-tail flight distributions. Humans highly influence the mobility of nodes (smartphones and cars) in real mobile networks as they carry or drive mobile nodes. Understanding the fundamental delay-capacity tradeoffs of Lévy mobility provides important insight into understanding the performance of real mobile networks. However, its power-law nature and strong spatio-temporal correlation make the scaling analysis non-trivial. This is in contrast to other random mobility models including Brownian motion, random waypoint and i.i.d. mobility which are amenable for a Markovian analysis. By exploiting the asymptotic characterization of the joint spatio-temporal probability density functions of Lévy models, the order of critical delay, the minimum delay required to achieve more throughput than Θ(1/√n) where n is the number of nodes in the network, is obtained. The results indicate that in Lévy walk, there is a phase transition that for 0 < α < 1, the critical delay is constantly Θ(n^1/2) and for 1 ≤ α ≤ 2, is Θ(n^α/2). In contrast, Lévy flight has critical delay Θ(n^α/2) for 0 < a ≤ 2.

An analytical framework to characterize the efficiency and delay in a mobile data offloading system

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.

Revisiting delay-capacity tradeoffs for mobile networks: The delay is overestimated

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.

Performance Analysis of M-QAM Scheme Combined With Multiuser Diversity Over Nakagami-

In this paper, we consider an M-ary quadrature amplitude modulation (M-QAM) scheme combined with multiuser diversity over Nakagami-m fading channels. Assuming that delayed but error-free signal-to-noise ratio (SNR) feedback is available, we derive closed-form formulas for the average transmission rate and the average bit error rate (BER), which are also shown to be generalizations of many previous results. Through numerical studies and simulations, we check the validity of our analysis. In addition, we investigate the impact of the Nakagami fading parameter m and feedback delay on system performance.

m

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].

Fading Channels

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.

On the critical delays of mobile networks under Lévy walks and Lévy flights

Social networking platforms are responsible 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 ideology, one technology vs. another. We study the battle 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 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 and adoption 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.

Threshold-based opportunistic scheduling for ergodic rate guarantees in wireless networks

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)n of 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.

Battle of opinions over evolving social networks

The wireless medium has a time-varying feature due to fading, and individual users experience different degrees of fading. Opportunistic scheduling exploits such diversity of fading across users to improve network performance. In this paper, we explicitly analyze the capacity of opportunistic scheduling in various fading environments. To that end, we use Nakagami-m fading as a fading channel model and analyze the multiuser diversity capacity when considering the number of users and fading parameters. Our analysis shows that the mean capacity is explicitly decomposed into three factors: the average signal-to-noise ratio (SNR), the number of users, and the capacity improvement that comes from diversity of fading across users. Our analytical results provide the precise impact of fading channels on multiuser capacity, which asymptotic analysis cannot capture. We verify the analytical results via simulations.

Analysis of Connectivity and Capacity in 1-D Vehicle-to-Vehicle Networks

Abstract In this paper, we consider opportunistic downlink scheduling in a cellular network that exploits multiuser diversity using one-bit feedback. To reduce the feedback overhead inherent in opportunistic scheduling, mobile stations are allowed to send one-bit information to the base station only when their channel quality exceeds a given threshold value. The objective of this paper is two-fold: (i) find the threshold value that can optimize queueing performance of the scheduler and (ii) investigate the relationship among capacity, fairness, and queueing performance. To this end, we first derive a formula for the sum-rate capacity as a function of the threshold. Next, we quantify the long-term and short-term fairness using Jain’s fairness index. Lastly, we develop a packet-level queueing model and derive QoS measures such as queueing delay and packet loss probability. Based on our analysis, we optimize the threshold value by considering both the traffic condition at the MAC layer and the temporal channel correlation at the PHY layer. Numerical results show that the optimized threshold can significantly reduce the average queueing delay and the packet loss probability. In addition, we find that there is a trade-off between short-term fairness and sum-rate capacity, whose control knob is the threshold. We show that, from a queueing performance perspective, supporting the sum-rate capacity (resp. the short-term fairness) is more important when the traffic is heavy (resp. light) or the wireless channel varies with low (resp. high) temporal correlation.