Types Of Functional Units Research Articles

The influence of the Functional Unit on the comparability of life cycle assessments in the construction sector: A Systematic Literature Review and attempt at unification for Reinforced Concrete

This article explores the potential for unifying Functional Units (FU) for all LCAs in any given product category in the construction sector. To this end, a Systematic Literature Review (SR) has been conducted. Due to the significant environmental impact of Reinforced Concrete (RC) and its ubiquitous global utilization, it is taken as an exemplary model for a unified FU.. The results of this SR show a significant heterogeneity in the choice and definition of FUs in the construction sector. FUs were extracted from the source material and categorized by the authors into five primary categories. The literature review found Reference Flows (RF) to be the most commonly named type of FU (75%), although FU and RF are not defined in the same way according to the LCA norm. The authors suggest a feasible standardized FU for RC structures. FUs for RC must include Reference Service Life (RSL), strength requirements, durability, and basic material specifications to achieve reasonable functional equivalence. Given the context of LCA as a support to decision-makers (DM), a standardized property FU for RC is most appropriate. This might be defined as 1 m3 of concrete normalized by the 28-day compressive strength and the RSL, including exposure class, specific concrete, and type and percentage of reinforcement. Lastly, the authors argue that a standardized FU is not enough to produce reliable and comparable LCA results. Data limitations, methodological issues, and a questionable practicality of implementation must also be addressed. Short-, mid-, and long-term measures to this end are suggested.

A practice‐based framework for defining functional units in comparative life cycle assessments of materials

AbstractIn comparative life cycle assessment (LCA) studies of materials, there is a mismatch between the current practice and existing guidelines regarding functional unit definition. The purpose of this study is to develop a practice‐based framework for defining functional units in comparative LCAs of materials and provide guidance regarding in which situations different functional unit types are relevant. A literature review of comparative LCAs of materials identified three types of functional units: (i) the reference flow functional unit, (ii) the property functional unit, and (iii) the performance functional unit. These functional unit types, of which only the latter strictly complies with LCA guidelines, represent varying degrees of functional equivalence and technological maturity. The most relevant functional unit type depends on the goal of the study. We suggest that screening assessments of whether materials have comparable environmental impacts can apply reference flow functional units. Material comparisons for certain application areas with some important properties can apply property functional units. For comparisons of end products, performance functional units can be applied. However, even in such cases, complete functional equivalence can hardly be achieved due to more or less relevant product differences. The applicability of the framework is demonstrated for the case of comparing cemented carbide and polycrystalline diamond hard materials.

A universal and facile approach for building multifunctional conjugated polymers for human-integrated electronics

<h2>Summary</h2> Polymer semiconductors have shown distinct promise for the development of human-integrated electronics, owing to their solution processability and mechanical softness. However, numerous functional properties required for this application domain face synthetic challenges to being conveyed onto conjugated polymers and thus combined with efficient charge-transport properties. Here, we develop a "click-to-polymer" (CLIP) synthesis strategy for conjugated polymers, which uses a click reaction for the facile and versatile attachment of diverse types of functional units to a pre-synthesized conjugated-polymer precursor. With four types of functional groups, we show that functionalized polymers from this CLIP method can still retain good charge-carrier mobility. We take two realized polymers to showcase a photopatternable property and a biochemical sensing function, both of which advance the state of the art of realizing these two types of functions on conjugated polymers. We expect that the expanded use of this synthesis approach can largely enrich the functional properties of conjugated polymers.

Motivational factors of nurses in a group of primary health centres in the city of Lisbon: qualitative study

Introduction Professionals motivation, as a determinant of the behaviour in organisations, is an important factor for their efficiency. Managing people while keeping them motivated to work is not an easy task and because of that it is considered one of the most difficult and complex functions of the manager [1]. Because of that, the knowledge based on causes that move or influence nurses’ motivation is considered important as a management instrument [2]. Sensitivities to this topic and considering the current conjuncture, in which Portuguese nurses have been confronted with low salaries [3] and work overload due to the low number of nurses per 1000 inhabitants [4], the starting point of this study is about the question: which factors can motivate nurses from a Lisbon primary care units? The aim is meeting the motivational factors of nurses from a Lisbon primary care unit. Specific aims are: understanding which factors motivate nurses from primary care unit in Lisbon, understanding motivational influence due to nursing practice and nursing management. Materials and methods Qualitative case study, exploratory and descriptive approach. The data collection was based on a semi-structured interview based on a predefined script performed with 9 nurses from a Lisbon primary care unit, from 18 January to 5 February 2019, who agreed to participate in the study. The number of participants was determined following the response saturation criteria [5]. In order to increase data variety, interviews were conducted with nurses working in different types of Functional Units. The age of the subjects ranged between 33 and 46 years old, with an average professional practice time of 17 years. Interviews were recorded, fully transcribed and analysed according to Bardin [6] content analysis. The study started after obtaining approval from the Executive Director of the Group of Primary Care Units, and the Health Ethics Committee of the respective Regional Health Administration and informed consent signed by the participants. Results Study results indicate that the main motivational factor of nurses is: rewards, career development, recognition, workplace/practice environment, financing based on performance, leadership and professional achievement. Career development was the factor in which participants attributed greater importance and on the other hand, financing based on performance was considered the less important as a motivational factor. Discussion and conclusions Despite of participants’ motivational factors being identical, it was verified that their importance and meaning are different to which one of them. According that, context indicators emerged with contradictory meaning. This enhances the individuality of each participant while being unique and motivated by their own needs. It was noticed that motivation is not maximum on most of the participants and that there is also dissatisfaction with the measures that could work as motivators. Managers should take into account scientific evidence concerning nurses’ motivational factors in order to improve their motivation. Further studies should be developed, particularly in primary health care, where the lack of scientific content is notorious.

Environmental consequences of wheat-based crop rotation in potato farming systems in galicia, Spain

Intensive agricultural farming systems have negative impacts on the ecosystem. Therefore, the use of crop rotation emerges as an opportunity to improve the environmental sustainability of agricultural systems. In the region of Galicia in north-western Spain, potato and wheat are important commodities and essential foods in the diet. Hence, it is interesting to investigate the environmental profile of these crops to improve the understanding of local agrosystems. This study evaluated three agricultural crops managed under a crop rotation system and following a conventional arable farming: the main rotation crop, which is the potato in the first year (cP), followed by a second year of commercial wheat (cW) and autochthonous Galician wheat (GcW) in the third year. The Life Cycle Assessment (LCA) methodology was performed using four types of functional units: in terms of productivity (kg−1); land management (ha−1∙year−1); a financial function (euros €−1 of income from sales) and energetic value (MJ−1). The environmental indicators selected are Climate Change (CC), Particulate Matter (PM), Terrestrial Acidification (TA), Freshwater Eutrophication (FE), Marine Eutrophication (ME), Human Toxicity (HT), Land Use (LU) and Fossil Depletion (FD).The figures show that the GcW has the lowest environmental impact when the functional units refer to land management, financial function and energetic value. However, if analysed in terms of productivity, cP is presented as the best crop due to its comparatively higher yield, reaching a production ratio 10 times higher than wheat. In the specific case of wheat, compared to a previous study in the same region, the environmental impacts are lower when grown in a crop rotation system in contrast to monoculture. This article demonstrates the relevance of using LCA for diverse stakeholders (e.g., farmers, consumers and researchers) to understand the environmental impacts of regional agricultural systems. In addition, it serves as a basis for future work aimed at comparing rotational agricultural systems in this region, integrating economic and social aspects.

Functional unit influence on building life cycle assessment

The building sector is one of the most relevant sectors in terms of environmental impact. Different functional units (FUs) can be used in life cycle assessment (LCA) studies for a variety of purposes. This paper aimed to present different FUs used in the LCA of buildings and evaluate the influence of FU choice and setting in comparative studies. As an example, we compared the “cradle to grave” environmental performance of four typical Brazilian residential buildings with different construction typologies, i.e., multi-dwelling and single dwelling, each with high and basic standards. We chose three types of FU for comparison: a dwelling with defined lifetime and occupancy parameters, an area of 1 m2 of dwelling over a year period, and the accommodation of an occupant person of the dwelling over a day. The FU choice was found to bias the results considerably. As expected, the largest global warming indicator (GWi) values per dwelling unit and occupant were identified for the high standard dwellings. However, when measured per square meter, lower standard dwellings presented the largest GWi values. This was caused by the greater concentration of people per square meter in smaller area dwellings, resulting in larger water and energy consumption per square meter. The sensitivity analysis of FU variables such as lifetime and occupancy showed the GWi contribution of the infrastructure more relevant compared with the operation in high and basic standard dwellings. The definition of lifetime and occupancy parameters is key to avoid bias and to reduce uncertainty of the results when performing a comparison of dwelling environmental performances. This paper highlights the need for adequate choice and setting of FU to support intended decision-making in LCA studies of the building sector. The use of at least two FUs presented a broader picture of building performance, helping to guide effective environmental optimization efforts from different approaches and levels of analysis. Information regarding space, time, and service dimensions should be either included in the FU setting or provided in the building LCA study to allow adjustment of the results for subsequent comparison.

On the Design of Minimal-Cost Pipeline Systems Satisfying Hard/Soft Real-Time Constraints

Pipeline systems provide high throughput for applications by overlapping the executions of tasks. In the architectures with heterogeneity, two basic issues in the design of application-specific pipelines need to be studied: what type of functional unit to execute each task, and where to place buffers. Due to the increasing complexity of applications, pipeline designs face a bundle of problems. One of the most challenging problems is the uncertainty on the execution times, which makes the deterministic techniques inapplicable. In this paper, the execution times are modeled as random variables. Given an application, our objective is to construct the optimal pipeline, such that the total cost of the resultant pipeline can be minimized while satisfying the required timing constraints with the given guaranteed probability. We first prove the NP-hardness of the problem. Then, we present Mixed Integer Linear Programming (MILP) formulations to obtain the optimal solution. Due to the high time complexity of MILP, we devise an efficient (1+ε)-approximation algorithm, where the value of ε is less than 5 percent in practice. Experimental results show that our algorithms can achieve significant reductions in cost over the existing techniques, reaching up to 31.93 percent on average.

Life cycle assessment of a residential building in Egypt: A case study

The present study discussed the significant environmental impacts of a residential building located in New Cairo, Egypt. This covered all life cycle steps from cradle to cradle with a projected 60-year life span: (i) an inventory of all the construction materials were analysed, covering the building structure as well as the energy consumption; (ii) three types of functional units were defined; (iii) the two top building materials were examined, and a sensitivity analysis was conducted to investigate the impact associated with the choice of building materials. The result shows that two life cycle phases concerning, manufacturing and operation, were more significant in all of the impact categories. It also shows that building structure and flooring result in most of the environmental loads. In terms of the sensitivity analysis, it was found the structural concrete had the largest impact, dominating all selected impact categories except ODP. Finally, limitations and challenges are discussed to explore better design decisions for selecting buildings’ structural systems in future studies.

A queuing model for CPU functional unit and issue queue configuration

In a superscalar processor, instructions of various types flow through an execution pipeline, traversing hardware resources which are mostly shared among many different instruction types. A notable exception to shared pipeline resources is the collection of functional units, the hardware that performs specific computations. In a trade-off of cost versus performance, a pipeline designer must decide how many of each type of functional unit to place in a processor’s pipeline. In this paper, we model a superscalar processor’s issue queue and functional units as a novel queuing network. We treat the issue queue as a finite-sized waiting area and the functional units as servers. In addition to common queuing problems, customers of the network share the queue but wait for specific servers to become ready (e.g., addition instructions wait for adders). Furthermore, the customers in this queue are not necessary ready for service, since instructions may be waiting for operands. In this paper we model a novel queuing network that provides a solution to the expected queue length of each type of instruction. This network and its solution can also be generalized to other problems, notably other resource-allocation issues that arise in superscalar pipelines.

"제품의 기능단위 형태에 비례적 속성 가중치를 적용한 이차원 전형성 모델 추출 ; LED등기구 제품디자인 개발과정을 중심으로"

"제품의 기능단위 형태에 비례적 속성 가중치를 적용한 이차원 전형성 모델 추출 ; LED등기구 제품디자인 개발과정을 중심으로"

Particulate matter and heavy metal deposition on the leaves of Euonymus japonicus during the East Asian monsoon in Beijing, China.

Plants can be effectively used as bio-monitors of environmental pollution. However, how the particulate matter (PM) and heavy metal retention ability of plants changes in different areas with human disturbance along with monsoon has not yet been investigated in urban ecosystems. In this study, we measured the amount of PM and heavy metals such as Ni, Cr, Cu, Pb, and Zn accumulated by the leaves of Euonymus japonicus during the East Asian monsoon from different functional units in Beijing, China. A rinse-and-weigh method developed in our laboratory was used to determine the mass of the PM, and electro-thermal atomic absorption spectrometry was used for heavy metal analysis. We found that the types of functional units had little influence, whereas the monsoon had a significant effect on the deposition of PM: northwest areas during the monsoon had the lowest effect (with 0.005, 0.453, 0.643, and 1.569 g/m2 fine, coarse, large, and total PM, respectively), and the southeast areas during the monsoon had the highest effect (0.015, 2.687, 1.941, and 4.228 g/m2 for fine, coarse, large, and total PM, respectively). Notable, we found considerable variations in heavy metal accumulation across the functional units analyzed, that is, the accumulation level was higher in communities than in parks (P < 0.0001 for all heavy metals). Moreover, a positive relationship was found between PM retention and heavy metal accumulation by the leaves of E. japonicus. Taken together, our results suggested that the PM and heavy metal retention ability of E. japonicus was sensitive to human disturbance and monsoon in Beijing. Since E. japonicus is a widely distributed tree and has the ability of to purify the atmosphere, it is an ideal plant for mitigating urban environmental pollution.

Efficient utilization of imprecise computational blocks for hardware implementation of imprecision tolerant applications

Recently, it has been reported that exploiting imprecise arithmetic building blocks such as adders and multipliers significantly improves digital implementation costs as well as performance of an important category of systems named as Imprecision Tolerant (IT) applications. We have categorized this new type of functional units as Bio-inspired Imprecise Computational (BIC) blocks. To efficiently exploit BICs in an IT application, however, the traditional hardware design flow should also be customized based on unique features of this new type of computing blocks. The most significant modification on traditional design flow to maximize the cost-performance of BIC implementations is to verify that the application is capable of tolerating those types of errors which are inherently introduced by the selected BIC based on its internal structure. We call this “error-behavior compatibility matching” between the system and the selected BIC building blocks. In this paper, we introduce and explain a customized hardware design flow for BICs with the main focus on error-behavior compatibility matching process as the main difference between traditional and BIC design flows. Two different error-behavior compatibility matching strategies are also introduced and their applicability is verified by applying them to exploit BICs for hardware implementation of some significant case studies including a general multiply-accumulate (MAC) block as the basic building block of many signal processing applications as well as an Artificial Neural Network (ANN) as a critical instance of MAC-based IT applications.

Energy flows and greenhouses gases of EU (European Union) national breads using an LCA (Life Cycle Assessment) approach

Bread represents a staple food in many parts of the world including Europe. Depending on the region of origin and the respective cultural heritage bread is made with different ingredients and is consumed in various forms. This work consists of an environmental sustainability assessment of 21 different types of bread, representing a wide spectrum of typologies of such food consumed across the European Union, via a Life Cycle Assessment approach. The embedded energy and equivalent greenhouse gas emissions of each type of bread were estimated, from cradle to bakery gate, by considering a mass, a nutritional value and a price based functional unit. Overall, the results have highlighted the variability of the embedded energy and the equivalent GHG (greenhouse gas) emissions associated to the consumption of the 21 kinds of bread rooted in the cultural environment of 21 EU countries. When considering a functional unit of 1 kg of bread, the Cumulative Energy Demand results range from 9 MJ/kg to 32.9 MJ/kg. The Global Warming Potential indicator has a minimum value of 0.5 kgCO2eq/kg and a maximum of 6.6 kgCO2eq/kg. For a functional unit amounting to a 100 kcal provided by the consumption of bread, the Cumulative Energy Demand results vary from 0.33 MJ/100 kcal to 0.93 MJ/100 kcal whilst the Global Warming Potential indicator varies from 0.019 kgCO2eq/100 kcal to 0.135 kgCO2eq/100 kcal. For a functional unit amounting to the quantity of bread purchased with 1€ (weighted according to the purchasing price of each nation in the European Union), the Cumulative Energy Demand results vary from 1.197 MJ/€ to 3.708 MJ/€ whilst the Global Warming Potential indicator varies from 0.15 kgCO2eq/€ to 0.376 kgCO2eq/€.The study has pinpointed the importance of evaluating food, in terms of environmental sustainability, with more than one type of functional unit in order to account not only for the bread's nutritional purposes but also the need to satisfy social, cultural, hedonistic and other qualitative functions. Specifically, when using a mass based functional unit, the less impactful results involve bread types with simple recipes, based essentially on flour, yeast and water. By assessing the breads with an energy based functional unit, bread types which also contain vegetable oils and small amounts of animal based ingredients result as more carbon and energy friendly. The use of a price based functional unit indicates that the higher priced bread types, manufactured with more expensive ingredients that are produced in an environmentally efficient manner, are the more sustainable ones. Overall, for many types of bread, the energy consumption during the production phase, in particular the baking process, represents a hot spot and is dependent on the size and shape of the bread. Furthermore, the efficiency of ingredient production (in terms of material and energy use and in terms of the respective yields of each nation in the European Union), such as that of milk and flour, also influences the sustainability of the bread types.

Probabilistic Multiknob High-Level Synthesis Design Space Exploration Acceleration

One of the biggest advantages of C-based very large scale integration design over traditional register transfer level is its ability to automatically generate architectures with different area versus performance characteristics without the need of modifying the original behavioral description. Different knobs can be explored to obtain the dominating tradeoff curve (Pareto-front). So far previous works have only focused on exploring one set of knobs or combining all of them together without considering the underlying implications of each of these knobs. This paper presents the first method that accelerates the design space exploration (DSE) by first classifying these knobs and exploring them sequentially, thus reducing the design space to be explored considerably. In particular: 1) local synthesis directives in the form of pragmas inserted directly at the source code and 2) functional units (FUs) number and type. Second, we propose a probabilistic method to further accelerate the DSE by computing the probability of each micro-architecture generated after the pragma exploration stage, to lead to new dominating designs and in turn exploring only those with the highest probabilities. One additional contribution is that the explorer for both knobs are implemented using novel heuristics. The pragma based explorer is based on ant colony optimization, while the FU explorer explores the number and type of FUs in order to further maximize the total amount of resource sharing that can be extracted. Experimental results show that our proposed method finds Pareto-fronts of similar quality than an exploration method optimized for quality of their results, while accelerating the DSE by an average of $12.2 {\times }$ .

Self-assembly and modular functionalization of three-dimensional crystals from oppositely charged proteins.

Multicomponent crystals and nanoparticle superlattices are a powerful approach to integrate different materials into ordered nanostructures. Well-developed, especially DNA-based, methods for their preparation exist, yet most techniques concentrate on molecular and synthetic nanoparticle systems in non-biocompatible environment. Here we describe the self-assembly and characterization of binary solids that consist of crystalline arrays of native biomacromolecules. We electrostatically assembled cowpea chlorotic mottle virus particles and avidin proteins into heterogeneous crystals, where the virus particles adopt a non-close-packed body-centred cubic arrangement held together by avidin. Importantly, the whole preparation process takes place at room temperature in a mild aqueous medium allowing the processing of delicate biological building blocks into ordered structures with lattice constants in the nanometre range. Furthermore, the use of avidin–biotin interaction allows highly selective pre- or post-functionalization of the protein crystals in a modular way with different types of functional units, such as fluorescent dyes, enzymes and plasmonic nanoparticles.

Life cycle assessment of a single-family residential building in Canada: A case study

The present study quantified the significant environmental impacts of a two-story residential building located in Vancouver, Canada, with a projected 60-year life span: (i) an inventory of all the construction materials was analyzed, covering the building structure and exterior and interior envelopes as well as the energy consumption; (ii) four types of functional units were defined; (iii) the five top building materials were examined, and a sensitivity analysis was conducted to investigate the impact associated with the choice of building materials. Two life cycle phases, manufacturing and operation, were more significant in all of the impact categories, and two building assemblies, the walls and the roof, bore most of the environmental loads. In terms of the sensitivity analysis, the roofing asphalt had the largest impact, dominating three of the seven selected impact categories. Despite different definitions of functional units, the function of the dwelling buildings is always the same, to provide protection and housing for their habitants. Additionally, to improve the performance of an existing building, several strategies were proposed for the building renovation and maintenance, including alternative replacement materials regarding the building components with high environmental burdens, good patterns of the occupants’ consumption behaviors as well as considerations of the financial and environmental cost. Finally, limitations and challenges are discussed to explore better design decisions in future studies.

A multi structure genetic algorithm for integrated design space exploration of scheduling and allocation in high level synthesis for DSP kernels

This paper presents an integrated design space exploration of scheduling and allocation problem in high level synthesis using the heuristic based multi structure genetic algorithm. A cost function based on a combination of power consumption and pipelined execution time as well as a scheme to select functional unit type in case of multiple versions is proposed that can guide the genetic algorithm to near-optimal/optimal solution. The cost function model takes the functional units, registers, multiplexers and demultiplexers into consideration. The encoding process of the parent chromosome incorporates a special seeding process that enables the genetic algorithm to search for an optimal solution. This type of seeding process was specifically incorporated because the optimal solution to a problem always lies between the maximum serial and parallel implementation. Therefore it is always capable of finding a near-optimal/optimal solution to the combined problem of scheduling and allocation based on the provided user specified constraints. Results of the comparison with another recent genetic algorithm based exploration technique indicated considerable reduction of execution clock cycle as well as power consumption for almost all the benchmarks.

2011 ACM TODAES best paper award

In high-level synthesis for real-time embedded systems using heterogeneous functional units (FUs), it is critical to select the best FU type for each task. However, some tasks may not have fixed execution times. This article models each varied execution time as a probabilistic random variable and solves the heterogeneous assignment with probability (HAP) problem. The solution of the HAP problem assigns a proper FU type to each task such that the total cost is minimized while the timing constraint is satisfied with a guaranteed confidence probability. The solutions to the HAP problem are useful for both hard real-time and soft real-time systems. Optimal algorithms are proposed to find the optimal solutions for the HAP problem when the input is a tree or a simple path. Two other algorithms, one is optimal and the other is near-optimal heuristic, are proposed to solve the general problem. The experiments show that our algorithms can effectively reduce the total cost while satisfying timing constraints with guaranteed confidence probabilities. For example, our algorithms achieve an average reduction of 33.0% on total cost with 0.90 confidence probability satisfying timing constraints compared with the previous work using the worst-case scenario.

Size- and Shape-Selective Isostructural Microporous Metal–Organic Frameworks with Different Effective Aperture Sizes

Two isostructural metal-organic frameworks (MOFs) having micropores of the same "static aperture size" but different "effective aperture size" have been prepared using 5-(pyridin-3-ylethynyl)isophthalic acid as a ligand having two different types of functional units, an isophthalate (iph) unit and a pyridyl unit, simultaneously in a single ligand. The combination of iph unit and Cu (or Zn) ion led to two-dimensional layers of Kagomé (kgm) net topology, the layers being further pillared by the internal auxiliary pyridyl unit to form a three-dimensional microporous framework having two different types of cage-like pores, cage A and cage B, with different aperture sizes and shapes. (1) The MOFs can distinguish the adsorbates (N(2)/Ar) not based on the widely used kinetic diameters of the adsorbates but based on the minimum diameters of the adsorbates, which are more shape dependent. While cage A with a sufficiently large aperture size compared with the size of the adsorbates does not show any size selectivity, cage B with an approximate size match between the adsorbates and the pore apertures shows shape selectivity for the adsorbates. The smaller but spherically shaped Ar atom is not allowed into the pore with the oval-shaped aperture; however, the larger linear N(2) molecule is allowed into the pore with the oval-shaped aperture. (2) Even though the two isostructural MOFs have the same static aperture size of cage B, they show different size selectivity for the adsorbates based on the effective aperture size, which reflects the different extents of the framework flexibility.

Cost minimization while satisfying hard/soft timing constraints for heterogeneous embedded systems

In high-level synthesis for real-time embedded systems using heterogeneous functional units (FUs), it is critical to select the best FU type for each task. However, some tasks may not have fixed execution times. This article models each varied execution time as a probabilistic random variable and solves heterogeneous assignment with probability (HAP) problem. The solution of the HAP problem assigns a proper FU type to each task such that the total cost is minimized while the timing constraint is satisfied with a guaranteed confidence probability. The solutions to the HAP problem are useful for both hard real-time and soft real-time systems. Optimal algorithms are proposed to find the optimal solutions for the HAP problem when the input is a tree or a simple path. Two other algorithms, one is optimal and the other is near-optimal heuristic, are proposed to solve the general problem. The experiments show that our algorithms can effectively reduce the total cost while satisfying timing constraints with guaranteed confidence probabilities. For example, our algorithms achieve an average reduction of 33.0% on total cost with 0.90 confidence probability satisfying timing constraints compared with the previous work using worst-case scenario.