Performance Of Mathematical Model Research Articles

Session details: The tenth workshop on mathematical performance modeling and analysis (MAMA 2008)

Session details: The tenth workshop on mathematical performance modeling and analysis (MAMA 2008)

Adaptive wireless thin‐client model for mobile computing

AbstractThe thin‐client computing model has the potential to significantly increase the performance of mobile computing environments. By delivering any application through a single, small‐footprint client (called a thin client) implemented on a mobile device, it is possible to optimize application performance without the need for building wireless application gateways. We thus present two significant contributions in the area of wireless thin‐client computing. Firstly, a mathematical performance model is derived for wireless thin‐client system. This model identifies factors that affect the performance of the system and supports derivation and analysis of adaptation strategies to maintain a user‐specified quality of service (QoS). Secondly, a proxy‐based adaptation framework is developed for wireless thin‐client systems, which dynamically optimizes performance of a wireless thin client via dynamically discovered context. This is implemented with rule‐based fuzzy logic that responds to variations in wireless link bandwidth and client processing power. Our fuzzy inference engine uses contextual data to dynamically optimize tradeoffs among different quality of service parameters offered to the end users. Additionally, our adaptation framework uses highly scalable wavelet‐based image coding to provide scalable QoS that can degrade gracefully. Our thin‐client adaptation framework shields the user from ill effects of highly variable wireless network quality and mobile device resources. This improves performance of active applications, in which the display changes frequently. Further, active application behaviour may produce high transmission latency for screen updates, which can adversely affect user perception of QoS, resulting in poor interactivity. We report measured adaptive performance under realistic mobile device and network conditions for several different clients and servers. Copyright © 2008 John Wiley & Sons, Ltd.

Performance of schizophrenia and bipolar patients on verbal and figural working memory tasks.

Working memory (WM) was studied in 82 healthy volunteers, 43 schizophrenia patients, and 81 bipolar patients. Schizophrenia patients were impaired on verbal and figural WM tasks that possessed similar test discriminating power. Bipolar patients performed similarly to healthy volunteers. A mathematical model of WM performance revealed a primary role for reduced WM span in accounting for the impaired verbal WM of schizophrenia patients and a primary role for diminished attention in accounting for impaired figural WM. Although WM impairment in schizophrenia is due neither to the general effects of severe mental illness nor to the specific type of material studied, the microarchitecture of abnormal WM in schizophrenia may depend on the stimulus material presented.

An accurate mathematical performance model of partially adaptive routing in binary n-cube multiprocessors

Although several analytical models have been proposed in the literature for different interconnection networks with different routing algorithms, there is only one work [M. Ould-Khaoua, An approximate performance model for partially adaptive routing algorithm in hypercubes, Microprocessors and Microsystems 23 (1999) 185–190] dealing with partially adaptive routing. It is not accurate enough especially in heavy traffic regions due to the rough approximation of assuming equal traffic rate over network channels. We show, however, such an approximation can greatly affect the accuracy of the model. This paper proposes an accurate analytical model to predict the average message latency in wormhole hypercube networks using partially adaptive routing. Our model accurately formulates the traffic rate over individual network channels and the results obtained from simulation experiments confirm that the proposed model exhibits a significant accuracy for various network sizes and under different operating conditions even in moderate to heavy traffic regions, the regions for which the model in [M. Ould-Khaoua, An approximate performance model for partially adaptive routing algorithm in hypercubes, Microprocessors and Microsystems 23 (1999) 185–190] fails to exhibit acceptable accuracy.

Session details: Special issue on the Workshop on MAthematical performance Modeling and Analysis (MAMA2007)

Session details: Special issue on the Workshop on MAthematical performance Modeling and Analysis (MAMA2007)

An accurate mathematical performance model of adaptive routing in the star graph

Analytical modelling is indeed the most cost-effective method to evaluate the performance of a system. Several analytical models have been proposed in the literature for different interconnection network systems. This paper proposes an accurate analytical model to predict message latency in wormhole-switched star graphs with fully adaptive routing. Although the focus of this research is on the star graph but the approach used for modelling can be, however, used for modelling some other regular and irregular interconnection networks. The results obtained from simulation experiments confirm that the proposed model exhibits a good accuracy for various network sizes and under different operating conditions.

Developing Mathematical Models of Neurobehavioral Performance for the “Real World”

Work-related operations requiring extended wake durations, night, or rotating shifts negatively affect worker neurobehavioral performance and health. These types of work schedules are required in many industries, including the military, transportation, and health care. These industries are increasingly using or considering the use of mathematical models of neurobehavioral performance as a means to predict the neurobehavioral deficits due to these operational demands, to develop interventions that decrease these deficits, and to provide additional information to augment existing decision-making processes. Recent advances in mathematical modeling have allowed its application to real-world problems. Developing application-specific expertise is necessary to successfully apply mathematical models, in part because development of new algorithms and methods linking the models to the applications may be required. During a symposium, "Modeling Human Neurobehavioral Performance II: Towards Operational Readiness," at the 2006 SIAM-SMB Conference on the Life Sciences, examples of the process of applying mathematical models, including model construction, model validation, or developing model-based interventions, were presented. The specific applications considered included refining a mathematical model of sleep/wake patterns of airline flight crew, validating a mathematical model using railroad operations data, and adapting a mathematical model to develop appropriate countermeasure recommendations based on known constraints. As mathematical models and their associated analytical methods continue to transition into operational settings, such additional development will be required. However, major progress has been made in using mathematical model outputs to inform those individuals making schedule decisions for their workers.

A simple mathematical model of performance for proton exchange membrane fuel cells

Mathematical modeling is a powerful tool for improving the performance of fuel-cell stacks. In the present work, a mathematical model has been developed to study the performance of a proton exchange membrane fuel cell (PEMFC) at different operation variables. The effects of different operating para-meters on the performance of PEMFC have been studied using pure hydrogen on the anode side and air on the cathode side. Results with different fuel-cell operating temperatures, different operating pressures and various combinations of these parameters have been obtained. The possible mechanisms of the parameter effects and their inter-relationships are discussed. The modeling results compare well with the available experimental results. The comparison shows good agreement between the modeling results and the experimental data.

Review: On Mathematical Modeling of Circadian Rhythms, Performance, and Alertness

Mathematical models of neurobehavioral performance and alertness have both basic science and practical applications. These models can be especially useful in predicting the effect of different sleep-wake schedules on human neurobehavioral objective performance and subjective alertness under many conditions. Several relevant models currently exist in the literature. In principle, the development and refinement of any mathematical model should be based on an explicit modeling methodology, such as the Box modeling paradigm, that formally defines the model structure and calculates the set of parameters. While most mathematical models of neurobehavioral performance and alertness include homeostatic, circadian, and sleep inertia components and their interactions, there may be fundamental differences in the equations included in these models. In part, these may be due to differences in the assumptions of the underlying physiology. Because the choice of model equations can have a dramatic influence on the results, it is necessary to consider these differences in assumptions when examining the results from a model and when comparing results across models. This article presents principles of mathematical modeling and examples of how such procedures can be applied to the development and refinement of mathematical models of neurobehavioral performance and alertness. This article also presents several methods of testing and comparing these models, suggests different uses of the models, and discusses problems with current models.

On a particular Emden–Fowler equation with non-positive energy [formula omitted]: Mathematical model of enterprise competitiveness and performance

In this paper we work with the ordinary equation u ″ − u 3 = 0 and obtain some interesting phenomena concerning blow-up, blow-up rate and life-span of solutions to those equations under negative energy.

Altitude Training for the Marathon

For nearly 40 years, scientists and elite endurance athletes have been investigating the use of altitude in an effort to enhance exercise performance. While the results of many early studies on the use of altitude training for sea level performance enhancement have produced equivocal results, newer studies using the 'live high, train low' altitude training model have demonstrated significant improvements in red cell mass, maximal oxygen uptake, oxygen uptake at ventilatory threshold, and 3000m and 5000m race time. For the marathoner looking to add altitude training to their peak performance plans, residence at an altitude of 2000-2500m, a minimum of 20 hours per day, for 4 weeks, appears to hold the greatest potential for performance enhancement. Based on published mathematical models of marathon performance, a marathoner with a typical or average running economy who performed 'live high, train low' altitude training could experience an improvement of nearly 8.5 minutes (or approximately 5%) over the 26.2-mile race distance.

Mathematical modeling of the transmission performance of 2K–H pin cycloid planetary mechanism

A mathematical model of transmission performance of 2K–H pin-cycloid planetary mechanism with one tooth difference is proposed based on static analysis of actual meshing transmission process between gear pairs considering friction. Computer program for the output moment calculation is developed and is used to analyze the effects of the kinematics parameters on the transmission performance. With the theoretical guidance, the self-locking performance of the seat angle adjustment mechanism of an automobile is improved. The presented mathematical model also provides a basis for further investigations such as the effects of tooth profile and machining error on the transmission performance.

Modelling of aerobic and anaerobic energy production in middle-distance running

A mathematical model of performance describing aerobic and anaerobic energy production during exercise was applied to middle-distance running data from world records (WR) and from a group of elite runners (NL). The model is based on the assumption that, above a critical power (Pc), a continuous rate of anaerobic energy production occurs, until the entire anaerobic stores (W') are depleted. The fraction of metabolic power above Pc provided by anaerobic metabolism is denoted alpha. A second power threshold (Pt) sets the limit above which any further increase in power is met exclusively by anaerobic sources. The oxygen uptake kinetics was described by a monoexponential equation with time constant tau. The results show that the model successfully fits the WR over 1,500-5,000 m. However, in the range of distances from 800 to 5,000 m the performance over 800 and 1,000 m were overestimated. Contrary to Pc and the anaerobic contribution at steady state oxygen uptake, the estimate of W' was sensitive to the value assigned to tau in the range from 0 to 30 s. Using best performances from 1,500 to 5,000 m in NL resulted in Pc estimates not significantly different from the metabolic power at the lactate threshold. The anaerobic contribution at steady state oxygen uptake increased from zero at Pc to 8.3% (WR) and 7.8+/-3.1% (NL) at Pt. This suggests that a substantial contribution of anaerobic processes occurs in the range between Pc and Pt, even though the exercise does not elicit maximal aerobic power.

Seasonal Deterioration of Unsurfaced Roads

Seasonal deformation of unsurfaced roads was observed over several years and was studied using pavement deterioration models and finite-element analysis. The Mathematical Model of Pavement Performance is a model designed for pavement deterioration prediction and was successfully used for seasonal deterioration modeling because of its flexibility in defining the pavement structure, properties, and seasonal impact. However, these types of models are designed for highways and are somewhat limited in soils characterization and manipulation of the forces at the road–tire interface. Therefore, a three-dimensional dynamic finite-element model of a wheel rolling over soil was applied to simulate local vehicle traffic on a secondary unpaved road. These simulations were used to study the effects of vehicle speed, load, suspension system, wheel torque, and wheel slip on rutting and washboard formation. Modeling results are compared to field measurements and observations.

Integrated design methodology of ball-screw driven servomechanisms with discrete controllers. Part II: Formulation and synthesis of the integrated design

In order to acquire high-speed and high-precision performances in ball-screw driven servomechanisms, an integrated design methodology has been proposed. Based on strict mathematical modeling and analysis of servomechanism performance according to design and operating parameters, a nonlinear constrained optimization problem including the relevant subsystem parameters of a ball-screw driven servomechanism is formulated. A multi-objective function and nondimensional variables are introduced in the design process. Constraints for the mechanical and control subsystems render the integrated design problem accurate. Optimum design results of the mechanical and control subsystems are obtained according to the design parameters specified by designers through the integrated design process. Motors are optimally selected from the servo motor database according to the iteration process. Both geometric errors due to Abbe offset and contour errors are minimized while required constraints such as stability and saturated conditions are satisfied. This design methodology not only optimizes the dynamic performance of the servomechanism, but also improves quality of the design process to achieve the required performance for ball-screw driven servomechanisms.

Continuous Hydrogenation of 2-Butyne-1,4-diol to 2-Butene- and Butane-1,4-diols

Continuous catalytic hydrogenation of 2-butyne-1,4-diol (B 3D) was carried out in a fixed-bed reactor over 1% Pt/CaCO3 catalyst to give 2-butene-1,4-diol (B 2D) and butane-1,4-diol (B1D) without formation of any other side products. In case of continuous hydrogenation, higher selectivity (66%) to B2D could be obtained and the selectivity pattern was completely different from that found in case of batch slurry operation in which B 1D selectivity was very much higher (83%) than the B2D selectivity (17%). Another interesting feature was that by varying the contact time, the selectivity to both B 2D as well as B1D could be varied over a wide range which is an attractive option to obtain the desired products mix of B 1D and B2D, depending on the fluctuation in the market demand. Further, a mathematical model for reactor performance was also developed on the basis of the kinetic data obtained previously in a batch slurry reactor. The predicted values of conversion, selectivity, and rate of hydrogenation were found to agree with the experimental data over a wide range of conditions.

Calibrating a side-stream membrane bioreactor using Activated Sludge Model No. 1

Membrane bioreactors (MBRs) are attracting global interest but the mathematical modeling of the biological performance of MBRs remains very limited. This study focuses on the modeling of a side-stream MBR system using the Activated Sludge Model No. 1 (ASM1), and compares the results with the modeling of traditional activated sludge processes. ASM1 parameters relevant for the long-term biological behaviour in MBR systems were calibrated (i.e. Y(H) = 0.72 gCOD/gCOD, Y(A) = 0.25 gCOD/gN, b(H) = 0.25 d(-1), b(A) = 0.080 d(-1) and f(p) = 0.06), and generally agreed with the parameters in traditional activated sludge processes, with the exception that a higher autotrophic biomass decay rate was observed in the MBR. Influent wastewater characterization was proven to be a critical step in model calibration, and special care should be taken in characterizing the inert particulate COD (X(I)) concentration in the MBR influent. It appeared that the chemical-biological method was superior to the physical-chemical method. A sensitivity analysis for steady-state operation and DO dynamics suggested that the biological performance of the MBR system (the sludge concentration, effluent quality and the DO dynamics) are very sensitive to the parameters (i.e. Y(H), Y(A), b(H), b(A) micro(maxH) and micro(maxA), and influent wastewater components (X(I), S(s), X(s) and S(NH)).

Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)

The complexity of computer systems, networks and applications, as well as the advancements in computer technology, continue to grow at a rapid pace. Mathematical analysis, modeling and optimization have been playing, and continue to play, an important role in research studies to investigate fundamental issues and tradeoffs at the core of performance problems in the design and implementation of complex computer systems, networks and applications.

Three-Dimensional Catalytic Regeneration Modeling of SiC Diesel Particulate Filters

Increasingly stringent diesel particulate emissions standards have reestablished international interest in diesel filters, whose first series application dates back to 1985. Modern diesel engine technology, with computerized engine management systems and advanced, common rail injection systems, needs to be fully exploited to support efficient and durable diesel filter systems with catalytic aids, as standard equipment in passenger cars. Efficient system and components’ optimization requires the use of mathematical models of diesel filter performance. The three-dimensional model for the regeneration of the diesel particulate filter presented in this paper has been developed as an engineering tool for the detailed design optimization of SiC diesel filters of modular structure. The 3-D modeling is achieved by interfacing an existing 1-D model to commercial finite element method software for the computation of the 3-D temperature field within the whole filter assembly, including the adhesive of the filter blocks, the insulation mat, and the metal canning. The 3-D model is applied to real-world component optimization studies of diesel filter systems.

Exploiting NIC architectural support for enhancing IP-based protocols on high-performance networks

While a number of user-level protocols have been developed to reduce the gap between the performance capabilities of the physical network and the performance actually available, their compatibility issues with the existing sockets-based applications and IP-based infrastructure has been an area of major concern. To address these compatibility issues while maintaining a high performance, a number of researchers have been looking at alternative approaches to optimize the existing traditional protocol stacks. Broadly, previous research has broken up the overheads in the traditional protocol stack into four related aspects, namely: (i) compute requirements and contention, (ii) memory contention, (iii) I/O bus contention and (iv) system resources’ idle time. While previous research dealing with some of these aspects exists, to the best of our knowledge, there is no work which deals with all these issues in an integrated manner while maintaining backward compatibility with existing applications and infrastructure. In this paper, we address each of these issues, propose solutions for minimizing these overheads by exploiting the emerging architectural features provided by modern Network Interface Cards (NICs) and demonstrate the capabilities of these solutions using an implementation based on UDP/IP over Myrinet. Our experimental results show that with our implementation of UDP, termed as E-UDP, can achieve up to 94% of the theoretical maximum bandwidth. We also present a mathematical performance model which allows us to study the scalability of our approach for different system architectures and network speeds.