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Minghua Chen

Publications and source records attributed to Minghua Chen.

At least 91 records · Page 5Linked to original sources
arXiv2017

Understanding Performance of Edge Content Caching for Mobile Video Streaming

Today's Internet has witnessed an increase in the popularity of mobile video streaming, which is expected to exceed 3/4 of the global mobile data traffic by 2019. To satisfy the considerable amount of mobile video requests, video service providers have been pushing their content delivery infrastructure to edge networks--from regional CDN servers to peer CDN servers (e.g., smartrouters in users' homes)--to cache content and serve users with storage and network resources nearby. Among the edge network content caching paradigms, Wi-Fi access point caching and cellular base station caching have become two mainstream solutions. Thus, understanding the effectiveness and performance of these solutions for large-scale mobile video delivery is important. However, the characteristics and request patterns of mobile video streaming are unclear in practical wireless network. In this paper, we use real-world datasets containing 50 million trace items of nearly 2 million users viewing more than 0.3 million unique videos using mobile devices in a metropolis in China over 2 weeks, not only to understand the request patterns and user behaviors in mobile video streaming, but also to evaluate the effectiveness of Wi-Fi and cellular-based edge content caching solutions. To understand performance of edge content caching for mobile video streaming, we first present temporal and spatial video request patterns, and we analyze their impacts on caching performance using frequency-domain and entropy analysis approaches. We then study the behaviors of mobile video users, including their mobility and geographical migration behaviors. Using trace-driven experiments, we compare strategies for edge content caching including LRU and LFU, in terms of supporting mobile video requests. Moreover, we design an efficient caching strategy based on the measurement insights and experimentally evaluate its performance.

cs.MM↗
arXiv2016

Online Offering Strategies for Storage-Assisted Renewable Power Producer in Hour-Ahead Market

A promising approach to hedge against the inherent uncertainty of renewable generation is to equip the renewable plants with energy storage systems. This paper focuses on designing profit maximization offering strategies, i.e., the strategies that determine the offering price and volume, for a storage-assisted renewable power producer that participates in hour-ahead electricity market. Designing the strategies is challenging since (i) the underlying problem is coupled across time due to the evolution of the storage level, and (ii) inputs to the problem including the renewable output and market clearing price are unknown when submitting offers. Following the competitive online algorithm design approach, we first study a basic setting where the renewable output and the clearing price are known for the next hour. We propose sOffer, a simple online offering strategy that achieves the best possible competitive ratio of O(log θ), where $θ$ is the ratio between the maximum and the minimum clearing prices. Then, we consider the case where the clearing price is unknown. By exploiting the idea of submitting multiple offers to combat price uncertainty, we propose mOffer, and demonstrate that the competitive ratio of mOffer converges to that of sOffer as the number of offers grows. Finally, we extend our approach to the scenario where the renewable output has forecasting error. We propose gOffer as the generalized offering strategy and characterize its competitive ratio as a function of the forecasting error. Our trace-driven experiments demonstrate that our algorithms achieve performance close to the offline optimal and outperform a baseline alternative significantly.

cs.GT↗
arXiv2016

High-speed real-time single-pixel microscopy based on Fourier sampling

Single-pixel cameras based on the concepts of compressed sensing (CS) leverage the inherent structure of images to retrieve them with far fewer measurements and operate efficiently over a significantly broader spectral range than conventional silicon-based cameras. Recently, photonic time-stretch (PTS) technique facilitates the emergence of high-speed single-pixel cameras. A significant breakthrough in imaging speed of single-pixel cameras enables observation of fast dynamic phenomena. However, according to CS theory, image reconstruction is an iterative process that consumes enormous amounts of computational time and cannot be performed in real time. To address this challenge, we propose a novel single-pixel imaging technique that can produce high-quality images through rapid acquisition of their effective spatial Fourier spectrum. We employ phase-shifting sinusoidal structured illumination instead of random illumination for spectrum acquisition and apply inverse Fourier transform to the obtained spectrum for image restoration. We evaluate the performance of our prototype system by recognizing quick response (QR) codes and flow cytometric screening of cells. A frame rate of 625 kHz and a compression ratio of 10% are experimentally demonstrated in accordance with the recognition rate of the QR code. An imaging flow cytometer enabling high-content screening with an unprecedented throughput of 100,000 cells/s is also demonstrated. For real-time imaging applications, the proposed single-pixel microscope can significantly reduce the time required for image reconstruction by two orders of magnitude, which can be widely applied in industrial quality control and label-free biomedical imaging.

cs.CV↗
arXiv2016

Convergence proof for the multigrid method of the nonlocal model

Recently, nonlocal models attract the wide interests of scientist. They mainly come from two applied scientific fields: peridyanmics and anomalous diffusion. Even though the matrices of the algebraic equation corresponding the nonlocal models are usually Toeplitz (denote a0 as the principal diagonal element, a1 as the trailing diagonal element, etc). There are still some differences for the models in these two fields. For the model of anomalous diffusion, a0/a1 is uniformly bounded; most of the time, a0/a1 of the model for peridyanmics is unbounded as the stepsize h tends to zero. Based on the uniform boundedness of a0/a1, the convergence of the two-grid method is well established [Chan, Chang, and Sun, SIAM J. Sci. Comput., 19 (1998), pp. 516--529; Pang and Sun, J. Comput. Phys., 231 (2012), pp. 693--703; Chen, Wang, Cheng, and Deng, BIT, 54 (2014), pp. 623--647]. This paper provides the detailed proof of the convergence of the two-grid method for the nonlocal model of peridynamics. Some special cases of the full multigrid and the V-cycle multigrid are also discussed. The numerical experiments are performed to verify the convergence.

math.NA↗
arXiv2016

On Stability and Sojourn Time of Peer-to-Peer Queuing Systems

Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current study on these models focuses on the stability condition, under exponential workload assumption. This paper extends existing result in two aspects. In the first part of the paper we relax the exponential workload assumption, and study the stability of systems with general workload distribution. The second part of the paper focuses on the job sojourn time. An upper bound and a lower bound for job sojourn time are investigated. We evaluate tightness of the bounds by numerical analysis.

cs.PF↗
arXiv2016

Cost Minimizing Online Algorithms for Energy Storage Management with Worst-case Guarantee

The fluctuations of electricity prices in demand response schemes and intermittency of renewable energy supplies necessitate the adoption of energy storage in microgrids. However, it is challenging to design effective real-time energy storage management strategies that can deliver assured optimality, without being hampered by the uncertainty of volatile electricity prices and renewable energy supplies. This paper presents a simple effective online algorithm for the charging and discharging decisions of energy storage that minimizes the electricity cost in the presence of electricity price fluctuations and renewable energy supplies, without relying on the future information of prices, demands or renewable energy supplies. The proposed algorithm is supported by a near-best worst-case guarantee (i.e., competitive ratio), as compared to the offline optimal decisions based on full future information. Furthermore, the algorithm can be adapted to take advantage of limited future information, if available. By simulations on real-world data, it is observed that the proposed algorithms can achieve satisfactory outcome in practice.

cs.DS↗
arXiv2015

Peak-Aware Online Economic Dispatching for Microgrids

By employing local renewable energy sources and power generation units while connected to the central grid, microgrid can usher in great benefits in terms of cost efficiency, power reliability, and environmental awareness. Economic dispatching is a central problem in microgrid operation, which aims at effectively scheduling various energy sources to minimize the operating cost while satisfying the electricity demand. Designing intelligent economic dispatching strategies for microgrids, however, is drastically different from that for conventional central grids, due to two unique challenges. First, the erratic renewable energy emphasizes the need for online algorithms. Second, the widely-adopted peak-based pricing scheme brings out the need for new peak-aware strategy design. In this paper, we tackle these critical challenges and devise peak-aware online economic dispatching algorithms. For microgrids with fast-responding generators, we prove that our deterministic and randomized algorithms achieve the best possible competitive ratios $2-β$ and $e/(e-1+β)$, respectively, where $β\in[0,1]$ is the ratio between the minimum grid spot price and the local-generation price. Our results characterize the fundamental \emph{price of uncertainty} of the problem. For microgrids with slow-responding generators, we first show that a large competitive ratio is inevitable. Then we leverage limited prediction of electricity demand and renewable generation to improve the competitiveness of the algorithms. By extensive empirical evaluations using real-world traces, we show that our online algorithms achieve near offline-optimal performance. In a representative scenario, our algorithm achieves $17.5\%$ and $9.24\%$ cost reduction as compared to the case without local generation units and the case using peak-oblivious algorithms, respectively.

eess.SY↗
arXiv2014

High order algorithms for the fractional substantial diffusion equation with truncated Lévy flights

The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the Lévy flights; and the equation is derived as the macroscopic limit of the continuous time random walk in unbounded domain and the Lévy flights have divergent second order moments. However, in more practical problems, the physical domain is bounded and the involved observables have finite moments. Then the modified equation can be derived by tempering the probability of large jump length of the Lévy flights and the corresponding tempered space fractional derivative is introduced. This paper focuses on providing the high order algorithms for the modified equation, i.e., the equation with the time fractional substantial derivative and space tempered fractional derivative. More concretely, the contributions of this paper are as follows: 1. the detailed numerical stability analysis and error estimates of the schemes with first order accuracy in time and second order in space are given in {\textsl{complex}} space, which is necessary since the inverse Fourier transform needs to be made for getting the distribution of the functionals after solving the equation; 2. we further propose the schemes with high order accuracy in both time and space, and the techniques of treating the issue of keeping the high order accuracy of the schemes for {\textsl{nonhomogeneous}} boundary/initial conditions are introduced; 3. the multigrid methods are effectively used to solve the obtained algebraic equations which still have the Toeplitz structure; 4. we perform extensive numerical experiments, including verifying the high convergence orders, simulating the physical system which needs to numerically make the inverse Fourier transform to the numerical solutions of the equation.

math.NA↗
arXiv2014

On Routing-Optimal Network for Multiple Unicasts

In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the whole rate region, and we refer to them as routing-optimal networks. We identify a class of routing-optimal networks, which we refer to as information-distributive networks, defined by three topological features. Due to these features, for each rate vector achieved by network coding, there is always a routing scheme such that it achieves the same rate vector, and the traffic transmitted through the network is exactly the information transmitted over the cut-sets between the sources and the sinks in the corresponding network coding scheme. We present more examples of information-distributive networks, including some examples from index coding and single unicast with hard deadline constraint.

cs.IT↗
arXiv2014

SUPER: Sparse signals with Unknown Phases Efficiently Recovered

Suppose ${\bf x}$ is any exactly $k$-sparse vector in $\mathbb{C}^{n}$. We present a class of phase measurement matrix $A$ in $\mathbb{C}^{m\times n}$, and a corresponding algorithm, called SUPER, that can resolve ${\bf x}$ up to a global phase from intensity measurements $|A{\bf x}|$ with high probability over $A$. Here $|A{\bf x}|$ is a vector of component-wise magnitudes of $A{\bf x}$. The SUPER algorithm is the first to simultaneously have the following properties: (a) it requires only ${\cal O}(k)$ (order-optimal) measurements, (b) the computational complexity of decoding is ${\cal O}(k\log k)$ (near order-optimal) arithmetic operations.

cs.IT↗
arXiv2014

Numerical algorithms for the forward and backward fractional Feynman-Kac equations

The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a Schrödinger equation in imaginary time. The functionals of no-Brownian motion, or anomalous diffusion, follow the fractional Feynman-Kac equation [J. Stat. Phys. 141, 1071-1092, 2010], where the fractional substantial derivative is involved. Based on recently developed discretized schemes for fractional substantial derivatives [arXiv:1310.3086], this paper focuses on providing algorithms for numerically solving the forward and backward fractional Feynman-Kac equations; since the fractional substantial derivative is non-local time-space coupled operator, new challenges are introduced comparing with the general fractional derivative. Two ways (finite difference and finite element) of discretizing the space derivative are considered. For the backward fractional Feynman-Kac equation, the numerical stability and convergence of the algorithms with first order accuracy are theoretically discussed; and the optimal estimates are obtained. For all the provided schemes, including the first order and high order ones, of both forward and backward Feynman-Kac equations, extensive numerical experiments are performed to show their effectiveness.

physics.comp-ph↗
arXiv2013

FRANTIC: A Fast Reference-based Algorithm for Network Tomography via Compressive Sensing

We study the problem of link and node delay estimation in undirected networks when at most k out of n links or nodes in the network are congested. Our approach relies on end-to-end measurements of path delays across pre-specified paths in the network. We present a class of algorithms that we call FRANTIC. The FRANTIC algorithms are motivated by compressive sensing; however, unlike traditional compressive sensing, the measurement design here is constrained by the network topology and the matrix entries are constrained to be positive integers. A key component of our design is a new compressive sensing algorithm SHO-FA-INT that is related to the prior SHO-FA algorithm for compressive sensing, but unlike SHO-FA, the matrix entries here are drawn from the set of integers {0, 1, ..., M}. We show that O(k log n /log M) measurements suffice both for SHO-FA-INT and FRANTIC. Further, we show that the computational complexity of decoding is also O(k log n/log M) for each of these algorithms. Finally, we look at efficient constructions of the measurement operations through Steiner Trees.

cs.NI↗
arXiv2013

Discretized fractional substantial calculus

This paper discusses the properties and the numerical discretizations of the fractional substantial integral $$I_s^νf(x)=\frac{1}{Γ(ν)} \int_{a}^x{\left(x-τ\right)^{ν-1}}e^{-σ(x-τ)}{f(τ)}dτ,ν>0, $$ and the fractional substantial derivative $$D_s^μf(x)=D_s^m[I_s^νf(x)], ν=m-μ,$$ where $D_s=\frac{\partial}{\partial x}+σ=D+σ$, $σ$ can be a constant or a function without related to $x$, say $σ(y)$; and $m$ is the smallest integer that exceeds $μ$. The Fourier transform method and fractional linear multistep method are used to analyze the properties or derive the discretized schemes. And the convergences of the presented discretized schemes with the global truncation error $\mathcal{O}(h^p)$$ (p=1,2,3,4,5)$ are theoretically proved and numerically verified.

math.NA↗
arXiv2013

When Backpressure Meets Predictive Scheduling

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead window prediction model, we first establish a novel equivalence between the predictive queueing system with a \emph{fully-efficient} scheduling scheme and an equivalent queueing system without prediction. This connection allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and can drive it to zero with increasing prediction power. We then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving optimal utility performance in such predictive systems. \textsf{PBP} efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that \textsf{PBP} can achieve a utility performance that is within $O(ε)$ of the optimal, for any $ε>0$, while guaranteeing that the system delay distribution is a \emph{shifted-to-the-left} version of that under the original Backpressure algorithm. Hence, the average packet delay under \textsf{PBP} is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling beats the known optimal $[O(ε), O(\log(1/ε))]$ tradeoff for systems without prediction.

math.OC↗
arXiv2013

WSLD operators II: the new fourth order difference approximations for space Riemann-Liouville derivative

High order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but for fractional operators the stencils for high order schemes and low order ones are the same. Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved. Using the fractional linear multistep methods, Lubich obtains the $ν$-th order ($ν\leq 6$) approximations of the $α$-th derivative ($α>0$) or integral ($α<0) [Lubich, SIAM J. Math. Anal., 17, 704-719, 1986], because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with $α\in(1,2)$ for time dependent problem. By weighting and shifting Lubich's 2nd order discretization scheme, in [Chen & Deng, arXiv:1304.7425] we derive a series of effective high order discretizations for space fractional derivative, called WSLD opeartors there. As the sequel of the previous work, we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich's 3rd and 4th order discretizations. In particular, we prove that the obtained 4th order approximations are effective for space fractional derivatives. And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.

math.NA↗
arXiv2013

WSLD operators: A class of fourth order difference approximations for space Riemann-Liouville derivative

Because of the nonlocal properties of fractional operators, higher order schemes play more important role in discretizing fractional derivatives than classical ones. The striking feature is that higher order schemes of fractional derivatives can keep the same computation cost with first-order schemes but greatly improve the accuracy. Nowadays, there are already two types of second order discretization schemes for space fractional derivatives: the first type is given and discussed in [Sousa & Li, arXiv:1109.2345; Chen & Deng, arXiv:1304.3788; Chen et al., Appl. Numer. Math., 70, 22-41]; and the second type is a class of schemes presented in [Tian et al., arXiv:1201.5949]. The core object of this paper is to derive a class of fourth order approximations, called the weighted and shifted Lubich difference (WSLD) operators, for space fractional derivatives. Then we use the derived schemes to solve the space fractional diffusion equation with variable coefficients in one-dimensional and two-dimensional cases. And the unconditional stability and the convergence with the global truncation error $\mathcal{O}(τ^2+h^4)$ are theoretically proved and numerically verified.

math.NA↗
arXiv2013

Online Energy Generation Scheduling for Microgrids with Intermittent Energy Sources and Co-Generation

Microgrids represent an emerging paradigm of future electric power systems that can utilize both distributed and centralized generations. Two recent trends in microgrids are the integration of local renewable energy sources (such as wind farms) and the use of co-generation (i.e., to supply both electricity and heat). However, these trends also bring unprecedented challenges to the design of intelligent control strategies for microgrids. Traditional generation scheduling paradigms rely on perfect prediction of future electricity supply and demand. They are no longer applicable to microgrids with unpredictable renewable energy supply and with co-generation (that needs to consider both electricity and heat demand). In this paper, we study online algorithms for the microgrid generation scheduling problem with intermittent renewable energy sources and co-generation, with the goal of maximizing the cost-savings with local generation. Based on the insights from the structure of the offline optimal solution, we propose a class of competitive online algorithms, called CHASE (Competitive Heuristic Algorithm for Scheduling Energy-generation), that track the offline optimal in an online fashion. Under typical settings, we show that CHASE achieves the best competitive ratio among all deterministic online algorithms, and the ratio is no larger than a small constant 3.

cs.OH↗