Perfect Simulation for a Stationary Silo with Absorbing Walls

The objective of this work is to generate random samples of the unique stationary distribution associated to the stochastic model for grain storage in a finite bidimensional silo. The support of this measure is an unbounded and continuous state space and therefore a truncation was necessary to apply the CFTP perfect simulation scheme. The performance of the algorithm was measured by comparing the sample moments to the theoretical ones.     

Modelling the clogging of gas turbine filter houses in heavy-duty power generation systems

ABSTRACT

A prognostic approach based on a MISO (multiple inputs and single output) fuzzy logic model was introduced to estimate the pressure difference across a gas turbine (GT) filter house in a heavy-duty power generation system. For modelling and simulation of clogging of the GT filter house, nine real-time process variables (ambient temperature, humidity, ambient pressure, GT produced load, inlet guide vane position, airflow rate, wind speed, wind direction and PM10 dust concentration) were fuzzified using a graphical user interface within the framework of an artificial intelligence-based methodology. The results revealed that the proposed fuzzy logic model produced very small deviations and showed a superior predictive performance than the conventional multiple regression methodology, with a very high determination coefficient of 0.974. A complicated dynamic process, such as clogging phenomenonin heavy-duty GT system, was successfully modelled due to high capability of the fuzzy logic-based prognostic approach in capturing the nonlinear interactions.     

Inverse estimation of indoor airflow patterns using singular value decomposition

The fast pace in the development of indoor sensors and communication technologies is allowing a great amount of sensor data to be utilized in various areas of indoor air applications, such as estimating indoor airflow patterns. The development of such an inverse model and the design of a sensor system to collect appropriate data are discussed in this study. Algebraic approaches, including singular value decomposition (SVD), are evaluated as methods to inversely estimate airflow patterns given limited sensor measurements. In lieu of actual sensor data, computational fluid dynamics data are used to evaluate the accuracy of the airflow patterns estimated by the inverse models developed in this study. It was found that the airflow patterns estimated by the linear inverse SVD model were as accurate as those estimated by the nonlinear inverse-multizone model. For the zones tested, sensor measurements along on the walls and near the inlet and outlet provided the greatest improvement in the accuracy of the estimated airflow patterns when compared with the results using measurements from other locations.     

A disaster queue with Markovian arrivals and impatient customers

We consider a single server queueing system in which arrivals occur according to a Markovian arrival process. The system is subject to disastrous failures at which times all customers in the system are lost. Arrivals occurring during the time the system undergoes repair are stored in a buffer of finite capacity. These customers can become impatient after waiting a random amount of time and leave the system. However, these customers do not become impatient once the system becomes operable. When the system is operable, there is no limit on the number of customers who can be admitted. The structure of this queueing model is of GI/M/1-type that has been extensively studied by Neuts and others. The model is analyzed in steady state by exploiting the special nature of this type queueing model. A number of useful performance measures along with some illustrative examples are reported.     

Modelling the velocity of air through beds of cereal grains

The quality of cereal grains in storage will deteriorate toan unacceptable level if they are not kept dry and cool. Tomodel the drying and cooling process, an accurate knowledgeof the airflow distribution is required. In this paper, theequations used to model the air velocity are analysed. To study the flow of air through a typical drying system forstored grain, a two-dimensional rectangular bin is considered,with a single source of air on the bin floor. Two paths ofstudyare undertaken: the first is a linear analysis for low velocities,and following on from this is a nonlinear approach for largervelocities. The linear analysis is used to study a bin witha semi-infinite height, and the drying pattern is studied inthis bin using the air traverse time. Then bins with a finiteheight are analysed: it is shown that, for tall enough bins,the semi-infinite solution is accurate enough. A perturbationanalysis is used to study the semi-infinite bin when the airvelocity is too large for the linear analysis to be accu rate.It is shown that the effect of the nonlinearity is to move theair away from the high-velocity regions towards the areas oflower velocity.     

Dynamic load balancing in parallel queueing systems: Stability and optimal control

We consider a system of parallel queues with dedicated arrival streams. At each decision epoch a decision-maker can move customers from one queue to another. The cost for moving customers consists of a fixed cost and a linear, variable cost dependent on the number of customers moved. There are also linear holding costs that may depend on the queue in which customers are stored. Under very mild assumptions, we develop stability (and instability) conditions for this system via a fluid model. Under the assumption of stability, we consider minimizing the long-run average cost. In the case of two-servers the optimal control policy is shown to prefer to store customers in the lowest cost queue. When the inter-arrival and service times are assumed to be exponential, we use a Markov decision process formulation to show that for a fixed number of customers in the system, there exists a level S such that whenever customers are moved from the high cost queue to the low cost queue, the number of customers moved brings the number of customers in the low cost queue to S. These results lead to the development of a heuristic for the model with more than two servers.     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

Perishable Inventory System at Service Facilities with N Policy

Abstract

This article presents a perishable stochastic inventory system under continuous review at a service facility in which the waiting hall for customers is of finite size M. The service starts only when the customer level reaches N (< M), once the server has become idle for want of customers. The maximum storage capacity is fixed as S. It is assumed that demand for the commodity is of unit size. The arrivals of customers to the service station form a Poisson process with parameter λ. The individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. The items of inventory have exponential life times. It is also assumed that lead time for the reorders is distributed as exponential and is independent of the service time distribution. The demands that occur during stock out periods are lost.The joint probability distribution of the number of customers in the system and the inventory levels is obtained in steady state case. Some measures of system performance in the steady state are derived. The results are illustrated with numerical examples.     

Everywhere Regularity of Solutions to a Class of Strongly Coupled Degenerate Parabolic Systems

A class of strongly coupled degenerate parabolic system is considered. Sufficient conditions will be given to show that bounded weak solutions are Hölder continuous everywhere. The general theory will be applied to a generalized porous media type Shigesada-Kawasaki-Teramoto model in population dynamics.     

Markovian Imperfect Software Debugging Model and Its Performance Measures

Abstract

This paper considers a Markovian imperfect software debugging model incorporating two types of faults and derives several measures including the first passage time distribution. When a debugging process upon each failure is completed, the fault which causes the failure is either removed from the fault contents with probability p or is remained in the system with probability 1 ? p. By defining the transition probabilities for the debugging process, we derive the distribution of first passage time to a prespecified number of fault removals and evaluate the expected numbers of perfect debuggings and debugging completions up to a specified time. The availability function of a software system, which is the probability that the software is in working state at a given time, is also derived and thus, the availability and working probability of the software system are obtained. Throughout the paper, the length of debugging time is treated to be random and thus its distribution is assumed. Numerical examples are provided for illustrative purposes.     

Scheduling just-in-time part supply for mixed-model assembly lines

With increasing cost competition and product variety, providing an efficient just-in-time (JIT) supply has become one of the greatest challenges in the use of mixed-model assembly line production systems. In the present paper, therefore, we propose a new approach for scheduling JIT part supply from a central storage center. Usually, materials are stored in boxes that are allotted to the consumptive stations of the line by a forklift. For such a real-world problem, a new model, a complexity proof as well as different exact and heuristic solution procedures are provided. Furthermore, a direct comparison with a simple two-bin kanban system is provided. Such a system is currently applied in the real-world industrial process that motivates our research. It becomes obvious that this policy is considerably outperformed according to the resulting inventory- and α-service levels. Moreover, at the interface between logistics and assembly operations, strategic management implications are obtained. Specifically, based on the new approach, it is the first time a statistical analysis is being made as to whether widespread Level Scheduling policies, which are well-known from the Toyota Production System, indeed facilitate material supply. Note that in the literature it is frequently claimed that this causality exists.     

Logging damage and injured tree mortality in tropical forest management

Using insights from the forest ecology literature, we analyze the effect of injured trees on stand composition and carbon stored in above‐ground biomass and the implications for forest management decisions. Results from a Faustmann model with data for a tropical forest on Kalimantan show that up to 50% of the basal area of the stand before harvest can consist of injured trees. Considering injured trees leads to an increase in the amount of carbon in above‐ground biomass of up to 165%. These effects are larger under reduced impact logging than under conventional logging. The effects on land expectation value and cutting cycle are relatively small. The results suggest that considering injured trees in models for tropical forest management is important for the correct assessment of the potential of financial programs to store carbon and conserve forest ecosystem services in managed tropical forests, such as reducing emissions from deforestation and forest degradation and payment for ecosystem services. Recommendations for Resource Managers

• Considering the role of injured trees is important for managing tropical forests
• These trees can cover up to 50% of basal area and contain more than 50% of the carbon stored in above‐ground biomass
• Reduced impact logging leads to a larger basal area of injured trees and more carbon stored in injured trees than conventional logging
• Injured trees play an important role when assessing the potential for carbon storage in the context of payment for forest ecosystem services.

     

Statistical Modeling of a Pharmacokinetic System

Abstract

The aim of the article is to investigate the drug concentration behavior in a three-compartment open pharmacokinetic model which describes the disposition of an antibiotic drug used in Lyme disease, coumermycin A ₁.

We study a system of random differential equations representing this model. The three rate constants that are used in the system of differential equations are simulated using the trivariate truncated normal probability distribution. The initial values of the rate constants that are used in the simulation are calculated from the pharmacokinetic profile of coumermycin A ₁ determined in four human subjects based on the serum level data obtained from the report of a clinical study. The extensive numerical solutions for the system of random differential equations under different combinations of the covariance structure and the initial conditions are developed.

Numerical comparisons of the deterministic characterizations of the drug concentration as a function of time of the individual compartments to study the effect of various combinations of the covariance structure and the initial conditions on these characterizations are presented. A similar comparison between the deterministic and the stochastic characterizations is also presented.     

Markov Decision Processes with Variance Minimization: A New Condition and Approach

Abstract

This article deals with the limiting average variance criterion for discrete-time Markov decision processes in Borel spaces. The costs may have neither upper nor lower bounds. We propose another set of conditions under which we prove the existence of a variance minimal policy in the class of average expected cost optimal stationary policies. Our conditions are weaker than those in the previous literature. Moreover, some sufficient conditions for the existence of a variance minimal policy are imposed on the primitive data of the model. In particular, the stochastic monotonicity condition in this paper has been first used to study the limiting average variance criterion. Also, the optimality inequality approach provided here is different from the “optimality equation approach” widely used in the previous literature. Finally, we use a controlled queueing system to illustrate our results.     

On Lévy-driven vacation models with correlated busy periods and service interruptions

This paper considers queues with server vacations, but departs from the traditional setting in two ways: (i) the queueing model is driven by Lévy processes rather than just compound Poisson processes; (ii) the vacation lengths depend on the length of the server’s preceding busy period. Regarding the former point: the Lévy process active during the busy period is assumed to have no negative jumps, whereas the Lévy process active during the vacation is a subordinator. Regarding the latter point: where in a previous study (Boxma et al. in Probab. Eng. Inf. Sci. 22:537–555, 2008) the durations of the vacations were positively correlated with the length of the preceding busy period, we now introduce a dependence structure that may give rise to both positive and negative correlations. We analyze the steady-state workload of the resulting queueing (or: storage) system, by first considering the queue at embedded epochs (viz. the beginnings of busy periods). We show that this embedded process does not always have a proper stationary distribution, due to the fact that there may occur an infinite number of busy-vacation cycles in a finite time interval; we specify conditions under which the embedded process is recurrent. Fortunately, irrespective of whether the embedded process has a stationary distribution, the steady-state workload of the continuous-time storage process can be determined. In addition, a number of ramifications are presented. The theory is illustrated by several examples.     

A two-fluid storage model with Lévy inputs and alternating outputs

In this paper we consider a storage model with two types of inputs and outputs that are subject to seasonal switching. Inputs are assumed to occur in a fluid fashion whereas outputs occur at a unit rate so long as the corresponding storage is non-empty. The distribution properties of the storage levels {Z ₁(t),Z ₂(t)} are derived at finite time as well as in stationary regime. We first investigate this process embedded at the successive switching points. This process is Markovian with independent components. In continuous time the components {Z ₁(t),Z ₂(t)} are also independent for each finite t, but are dependent in stationary regime.      

A NOTE ON SUBCATEGORIES OF REACHABLE MACHINES

Abstract

Given a category K. a state-behaviour process X: K → K and an image factorization system (E,M) for K, it is shown that under mild conditions the full subcategory with objects all reachable machines is coreflective. A corresponding result is obtained for coequalizer-reachable machines if X is only an input process.     

Weakly Convex and Concave Random Maps with Position Dependent Probabilities

Abstract

A random map is a discrete‐time dynamical system in which one of a number of transformations is randomly selected and applied in each iteration of the process. In this paper, we study random maps with position dependent probabilities on the interval. Sufficient conditions for the existence of absolutely continuous invariant measures for weakly convex and concave random maps with position dependent probabilities is the main result of this note.     

CFD studies on burner secondary airflow

In many fossil power plants operating today, there is insufficient means to assure the proper balancing of the secondary airflows between the individual burners of wall-fired units. This mismatch leads to decreased boiler efficiency and increased emissions. In this study, a computational fluid dynamics (CFD) modeling of a fossil power plant wind box was performed. The model solved the three-dimensional Reynolds averaged Navier–Stokes equations with the k–ε turbulence model. The CFD results were validated by the experimental data taken from a 1/8th scale model of a wall-fired fossil unit. Simulations under various mass flow rates specified at inlet, various baffle positions and two opening conditions of the burners were obtained to identify the optimum design in terms of the equalization of the secondary airflow through the burners. This study demonstrated that the combination of experimental and CFD approach can be an effective tool in the research of burner secondary airflow balancing.     

Traveling fronts in diffusive and cooperative Lotka–Volterra system with nonlocal delays

This paper is concerned with a diffusive and cooperative Lotka–Volterra model with distributed delays and nonlocal spatial effect. By using an iterative technique recently developed by Wang, Li and Ruan (Traveling wave fronts in reaction-diffusion systems with spatio-temporal delays, J. Differential Equations 222 (2006), 185–232), sufficient conditions are established for the existence of traveling wave front solutions connecting the zero and the positive equilibria by choosing different kernels. The result is an extension of an existing result for Fisher-KPP equation with nonlocal delay and is somewhat parallel to the existing result for diffusive and cooperative Lotka–Volterra system with discrete delays.