Stochastic Modelling and Scenario Generation for Cloud Workload and Network Traffic in OR Models

The focus in this study is on estimating the underlying weather index for pricing financial derivatives to hedge weather risks in crop production. Different index estimation methods for growing degree days (GDDs) are compared. In particular, daily average temperatures for deriving GDDs are simulated using an econometric model and a stochastic process that uses three methods to estimate the mean-reversion parameter. Finally, the historical approach based on a five-year moving average of GDDs is compared with the econometric and stochastic models. Results indicate that econometric model provides the best fit, followed by the the historical average method and then the stochastic process with a high mean reversion parameter. Premiums from the econometric model with sine function and historical average approaches are closer to those based on realized weather values compared with the stochastic approach. Therefore, the econometric model with sine function and the historical average approach provide better pricing estimates than other methods.

Current commercial software tools for transmission and generation investment planning have limited stochastic modeling capabilities. Because of this limitation, electric power utilities generally rely on scenario planning heuristics to identify potentially robust and cost effective investment plans for a broad range of system, economic, and policy conditions. Several research studies have shown that stochastic models perform significantly better than deterministic or heuristic approaches, in terms of overall costs. However, there is a lack of practical solution approaches to solve such models. In this paper we propose a scalable decomposition algorithm to solve stochastic transmission and generation planning problems, respectively considering discrete and continuous decision variables for transmission and generation investments. Given stochasticity restricted to loads and wind, solar, and hydro power output, we develop a simple scenario reduction framework based on a clustering algorithm, to yield a more tractable model. The resulting stochastic optimization model is decomposed on a scenario basis and solved using a variant of the Progressive Hedging (PH) algorithm. We perform numerical experiments using a 240-bus network representation of the Western Electricity Coordinating Council in the US. Although convergence of PH to an optimal solution is not guaranteed for mixed-integer linear optimization models, we find that it is possible to obtain solutions with acceptable optimality gaps for practical applications. Our numerical simulations are performed both on a commodity workstation and on a high-performance cluster. The results indicate that large-scale problems can be solved to a high degree of accuracy in at most two hours of wall clock time.

A novel method for efficient and accurate jet noise prediction is developed and tested in the framework of coupled LES and stochastic noise modeling. In the proposed method, the low frequency range of the acoustic spectrum, which corresponds to large turbulent structures, is resolved with an implicit LES model by employing higher-order spatial and temporal discretizations. The high frequency range, which corresponds to the fine-scale turbulence, is modeled via a stochastic broadband noise generation model. The inputs to the stochastic model are represented by statistics from an axisymmetric RANS jet simulation. The smaller synthetic scales are convected by larger scales, accounting for the effects of sweeping from the larger LES-resolved turbulent scales. The farfield acoustic data is obtained using either the Linearized Euler Equations, or an acoustic analogy based on the Ffowcs-Williams Hawkings method. The method is evaluated on cold and heated jets at different Reynolds numbers.

Fractional Brownian Motions, Fractional Noises and Applications

Accurately portraying the spatially linked network characteristics of digital infrastructure and exploring its energy-saving effects are highly valuable for enhancing the synergy in digital infrastructure development and expanding its network spillover effects on energy conservation. This paper uses panel data at the city level in China and employs a modified gravity model to calculate the centrality of digital infrastructure spatial correlation network nodes. Based on this, an econometric model is constructed, incorporating variables such as digital infrastructure spatial correlation network node centrality and urban green total factor energy efficiency. The model is used to analyze the effects and transmission paths of digital infrastructure network node centrality on urban green total factor energy efficiency. The analysis yields the following conclusions: (1) Digital infrastructure spatial correlation network node centrality significantly improves urban green total factor energy efficiency, with considerable variability due to city geographic location, city scale, and city attributes. (2) Nonlinear testing results indicate that as digital infrastructure construction advances, its impact on urban green total factor energy efficiency shifts from inhibitory to promotional. (3) The impact mechanism shows that digital infrastructure node centrality enhances urban green total factor energy efficiency through green technology innovation. Additionally, it promotes advanced industrial structures and reduces capital mismatch, further influencing energy efficiency. (4) Digital infrastructure node centrality not only boosts urban green total factor energy efficiency but also facilitates regional convergence, increasing the convergence rate from 0.094 to 0.170%. The findings of the research offer policy guidance for the government on advancing digital transformation initiatives and enhancing energy efficiency.

Stochastic Day-ahead operation of cascaded hydropower systems with Bayesian neural network-based scenario generation: A Portland general electric system study

Carbon emission causal discovery and multi-step forecasting for global cities

This study investigates the problem of outlier detection based on discrete wavelet transform in the context of time series data where the identification and treatment of outliers constitute an important component. An outlier is defined as a data point that deviates so much from the rest of observations within a data sample. In this work we focus on the application of the traditional method suggested by Tukey (1977) for detecting outliers in the closed price series of the Saudi Arabia stock market (Tadawul) between Oct. 2011 and Dec. 2019. The method is applied to the details obtained from the MODWT (Maximal-Overlap Discrete Wavelet Transform) of the original series. The result show that the suggested methodology was successful in detecting all of the outliers in the series. The findings of this study suggest that we can model and forecast the volatility of returns from the reconstructed series without outliers using GARCH models. The estimated GARCH volatility model was compared to other asymmetric GARCH models using standard forecast error metrics. It is found that the performance of the standard GARCH model were as good as that of the gjrGARCH model over the out-of-sample forecasts for returns among other GARCH specifications.

The combined impact of node architecture and workload characteristics on off-chip network traffic with performance/cost analysis has not been investigated before in the context of emerging cloud applications. Motivated by this observation, this paper performs a thorough characterization of twelve cloud workloads using a full-system datacenter simulation infrastructure. We first study the inherent network characteristics of emerging cloud applications including message inter-arrival times, packet sizes, inter-node communication overhead, self-similarity, and traffic volume. Then, we study the effect of hardware architectural metrics on network traffic. Our experimental analysis reveals that (1) the message arrival times and packet-size distributions exhibit variances across different cloud applications, (2) the inter-arrival times imply a large amount of self-similarity as the number of nodes increase, (3) the node architecture can play a significant role in shaping the overall network traffic, and finally, (4) the applications we study can be broadly divided into those which perform better in a scale-out or scale-up configuration at node level and into two categories, namely, those that have long-duration, low-burst flows and those that have short-duration, high-burst flows. Using the results of (3) and (4), the paper discusses the performance/cost trade-offs for scale-out and scale-up approaches and proposes an analytical model that can be used to predict the communication and computation demand for different configurations. It is shown that the difference between two different node architecture's performance per dollar cost (under same number of cores system wide) can be as high as 154 percent which disclose the need for accurate characterization of cloud applications before wasting the precious cloud resources by allocating wrong architecture. The results of this study can be used for system modeling, capacity planning and managing heterogeneous resources for large-scale system designs.

One of the factors leading to a decrease in the efficiency of polymer electrolyte membrane (PEM) electrolyzers is the blockage of water transport pathways through the porous transport layer (PTL). The oxygen bubbles generated from the electrochemical reaction at the catalyst layer accumulate in the PTL, impeding the transport pathways and reaction sites for the reactant water (1). An improved understanding of oxygen bubble accumulation and water transport behaviour in porous transport layers is essential to reduce mass transport losses in PEM electrolyzers. This study presents a method to stochastically generate a PTL composed of sintered titanium (Ti) powders and investigate the transport properties using pore network modeling. A microscale X-ray computed tomography (µ-CT) was performed for a sintered Ti powder PTL sample to obtain a 2D density map. The density map contains material content information, providing higher intensity at the positions with higher material content. With the density map as an input, a stochastic model of the PTL was generated by placing Ti powder particles at positions decided by the density map and a probability function until the model reached the target volume (2). Two critical parameters are considered in this model: the seeding parameter, α, and a filling radius, β. The seeding parameter controls the number of Ti powder “seeds” that act as nucleation sites. The second parameter, the filling radius, allows the model to mimic the morphology of the sintered regions. The structural properties of the stochastic model are investigated by comparing the pore size distribution, throat size distribution, and the porosity profile to the µ-CT reconstruction. Pore network modeling is an alternative to continuum modeling for simulating transport in porous media. Pore network modeling simplifies the solution of differential equations for mass transport by treating the pore space as a network of pores and narrow throats (3). Using pore network modeling as the analysis tool, the in-plane permeabilities of the µ-CT reconstruction and the stochastic model were compared. The stochastic modeling of PTLs will facilitate the detailed parametric studies of PTL structural property impacts on transport and provide novel insights into mass transport behavior in PEM electrolyzers.References H. Ito, T. Maeda, A. Nakano, Y. Hasegawa, N. Yokoi, C. M. Hwang, M. Ishida, A. Kato, and T. Yoshida, International journal of hydrogen energy 35(18), 9550-9560 (2010). A. Ebrahimi Khabbazi, J. Hinebaugh, A. Bazylak, Science Bulletin, 61(8), 601-611(2016).A. Putz, J. Hinebaugh, M. Aghighi, H. Day, A. Bazylak, and J. T. Gostick, ECS Transactions, 58(1), 79-86 (2013).

Interest in modeling the relationship between the macroeconomy and the agricultural economy has risen steadily since Schuh's 1974 article which illustrated the potential effects of macroeconomic policy shocks on the agricultural sector. A variety of authors has examined the effects of exchange rates, interest rate, money supply and general price level shocks on agricultural variables (prices, exports, etc.). A variety of techniques has also been used to examine these relationships. Both structural econometric models and time series approaches have been employed. In this study a new economietric technique, Vector Autoregressive (VAR) modeling, is used to investigate the impact of macroeconomic factors on the Canadian agricultural sector. Vector Autoregressive models (VARs) are dynamic simultaneous equation models. VAR models allow the data to provide a representation of the changes in the system without the restrictions on coefficients that are usually used in the estimation of simultaneous equation econometric models. VAR models focus on the dynamic paths of the variables in the system. They provide a concise summary of the dynamic interrelationships in an economic system. In this study, several forms of VAR models are used to examine the dynamic interaction of agricultural prices, exports and macroeconomic variables. There are a number of significant conclusions from the empirical analysis performed in this study. First, there appear to be significant macroeconomic impacts on the Canadian agricultural sector. Other studies of macroeconomic-sectoral linkages have found limited impact of macroeconomic factors. This study, however, using a relatively new methodology, has discovered a stronger integration. The strongest linkage appears to be between interest and exchange rates and agricultural output prices. There is little direct impact from domestic inflation. Such a result is not surprising given the international nature of Canadian agriculture. Input prices do not appear to be as significantly affected by macroeconomic shocks as are output prices. Such a result may be interpreted as providing support to the hypothesis that input and output prices in agriculture exhibit the fixed-price flex-price phenomenon. The methods used in this study are relatively new and they provide a flexible approach to modeling economic time series. It is apparent that the conditions assumed by the researcher significantly affect the empirical results. In this study we have modified existing techniques to provide more plausible identification restrictions on the model. The results indicate that the agricultural sector, in particular through agricultural output prices, is sensitive to exchange rate and interest rate variation. The techniques used here may be applied in future research to investigate the impact of macroeconomic variables on specific commodities and on regions of the country.

New technologies and digital infrastructures are enabling smart farming with high productivity levels across countries. Yet, there is dearth of evidence on how they are enabling smallholder farmers in Africa to increase their farm produce. By focussing on smallholder maize crop producers in South Africa and relying on a panel data for the period 2011–2021, this study applied a stochastic production frontier framework and Cobb–Douglas production function to estimate the relationship between variance of yield increase in relation to aggregate modern technologies adopted. The stochastic production frontier model was estimated using simple ordinary least square, maximum likelihood estimation and probit regressions. The analysis adopted a three-stage procedure which began with the specification of regression model, the calculation of least residuals squares of the explanatory variables and finally the estimation of the variances in the functional forms of output levels. The results revealed a positive relation between the application of digital agriculture technologies and increased crop performance for rural maize cultivators in South Africa. The policy inference from this study is that accelerating investment in digital agriculture infrastructure offers the promise of a quadruple return for South Africa’s agriculture sector.

The incidence of systemic and metabolic co-morbidities increases with aging. The purpose was to investigate a novel paradigm for modeling the orchestrated changes in many disease-related biomarkers that occur during aging. A hybrid strategy that integrates machine learning and stochastic modeling was evaluated for modeling the long-term dynamics of biomarker systems. Bayesian networks (BN) were used to identify quantitative systems pharmacology (QSP)-like models for the inter-dependencies for three disease-related datasets of metabolic (MB), metabolic with leptin (MB-L), and cardiovascular (CVB) biomarkers from the NHANES database. Biomarker dynamics were modeled using discrete stochastic vector autoregression (VAR) equations. BN were used to derive the topological order and connectivity of a data driven QSP model structure for inter-dependence of biomarkers across the lifespan. The strength and directionality of the connections in the QSP models were evaluated using bootstrapping. VAR models based on QSP model structures from BN were assessed for modeling biomarker system dynamics. BN-restricted VAR models of order 1 were identified as parsimonious and effective for characterizing biomarker system dynamics in the MB, MB-L and CVB datasets. Simulation of annual and triennial data for each biomarker provided good fits and predictions of the training and test datasets, respectively. The novel strategy harnesses machine learning to construct QSP model structures for inter-dependence of biomarkers. Stochastic modeling with the QSP models was effective for predicting the age-varying dynamics of disease-relevant biomarkers over the lifespan.

This paper presents a stochastic cost model and a solution technique for optimal scheduling of the generators in a wind integrated power system considering the demand and wind generation uncertainties. The proposed robust unit commitment solution methodology will help the power system operators in optimal day-ahead planning even with indeterminate information about the wind generation. A particle swarm optimization based scenario generation and reduction algorithm is used for modeling the uncertainties. The stochastic unit commitment problem is solved using a new parameter free self adaptive particle swarm optimization algorithm. The numerical results indicate the low risk involved in day-ahead power system planning when the stochastic model is used instead of the deterministic model.

Use of Lagrange Interpolating Polynomials in RLT. Systems in Series. Parallel Configurations. Spanning trees. Recycling. Split Cuts. Retrial Queues. Horse Racing. MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Dual simplex. History of CP. Procurement Contracts. MRP. Just in Time. Push and Pull Production. MULTIVARIATE INPUT MODELING. Operational Research Society. The M/G/1 Queue. Drama Theory. Hyper-heuristics. Antithetic Variates. Music. Edgeworth market games. Operational Risk. Queueing Notation. Environmental impact. Why variance is not risk. Conjugate gradient methods. Birth-and-Death Processes. Surgery Planning and Scheduling. Large-scale linear models. Standby Systems. Billiards/Pool. AXIOMATIC MEASURES OF RISK AND RISK-VALUE MODELS. Age Replacement Policies. PASTA and Related Results. Collaborative Procurement. LP projection algorithms. R&D risk management. Bioterrorism. Vendor-Managed Inventory. Gomory Cuts. Travel demand modeling. System Availability. Infinite horizon problems. Trust. Bayesian Network Classifiers. Integer Programming Duality. Queueing Disciplines. Stakeholder participation. Models and Basic Properties. Parametric LP analysis. Operations Research and Golfing. Ice Hockey. Clustering. Finite-Population Models. Batch Arrivals and Service. Optimal Monitoring Strategies. Basic Polyhedral Theory. Operations Research and Art. Managing portfolios of risks. Measures of risk equity. Branch and Bound Algorithms. Analytics in Retail. Variational Inequalities. Cross-Entropy Method. TSP heuristics. Capacity allocation. Control Variates. Cover Inequalities. Direct Search Methods. NLP Software. Bilinear optimization. Discrete-Time Martingales. Branch and Price. Column generation. IP Preprocessing. Optimal Reliability Allocation. Simplex-based LP solvers. Instance Formats. Clique generalizations. Availability in Stochastic Models. Evolutionary Algorithms. Basic CP theory: Search. Multimethodology. Branch and Cut. Memetic Algorithms. Urban mass transit. Coherent Systems. Subgradient optimization. Klimov's Model. Credit risk assessment. Branch-width and Tangles. Stochastic Hazard Process. Deterministic Global Optimization. Multistage (stochastic) games. Basis Reduction Methods. ACCIDENT PRECURSORS AND WARNING SYSTEMS MANAGEMENT: A BAYESIAN APPROACH TO MATHEMATICAL MODELS. Genetic Algorithms. Newsvendor models. Parallel Systems. Opportunities in Tennis. Job-shop scheduling. Simplex method and complexity. Geometric programming. Evacuation Planning. The Performance? Allocation Games. Scenario Generation. Robustness Analysis. Dynamic auctions. Neuroeconomics and game theory. Common Random Numbers. Selective Support Vector Machines. Semi-Markov Processes. Risk Averse Models. Sampling Methods. Domination problems. Simulation of Rare Events. Introduction to Tabu Search. Basic Interdiction Models. Introductory Concepts. Remanufacturing. PAUSE procedure. Wardrop equilibria. Mass customization. Ellipsoidal algorithms. Benders decomposition. Dynamic vehicle routing. Warranty Modeling. Design for Network Resiliency. Passenger rail transportation. Vehicle Routing Problem. Supply Chain Outsourcing. Lovasz-Schriver Reformulation. Hazard Rate Function. Lot-sizing. Differential games. Regenerative Processes. Guided Local Search. Preferences for repeated gambles. Percolation Theory. Simulated Annealing. Scoring Rules. Mixing Sets. Cricket. Prospect Theory. Combining Forecasts. Graph search techniques. Quasi-Newton methods. Random search algorithms. Supply chain coordination. Service Outsourcing. Markov Renewal Processes. K-out-of-n Systems.