Automated analysis of phased-mission reliability

A method for automated analysis of phased mission reliability which considers the problem in terms of the construction of a continuous-time discrete-state Markov model and uses a standard Markov-chain solution technique that is adapted to the problem of phased missions is presented. The resulting state space is the union of the states in each independent phase, rather than the sum. This results in a model that can be substantially smaller than those required by other methods. A unified framework which is used for defining the separate phases using fault trees and for constructing and solving the resulting Markov model is discussed. The usual solution technique is altered to account for the phased nature of the problem. The framework is described for a previously published, simple three-component, three-phase system. An example in which a hypothetical two-phase application involving a fault-tolerant parallel processor is considered is given. The approach applies where the transition rates (failure and repair rates) are constant and where the phase change times are deterministic     

Recursive estimation of parameters in Markov-modulated Poissonprocesses

A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. Recursive algorithms can be used to estimate parameters in mixed distributions governed by a Markov regime. The authors derive a recursive algorithm for estimation of parameters in a Markov-modulated Poisson process also called a Cox point process. By this the authors mean a doubly stochastic Poisson process with a time dependent intensity that can take on a finite number of different values. The intensity switches randomly between the possible values according to a Markov process. The authors consider two different ways to observe the Markov-modulated Poisson process: in the first model the observations consist of the observed time intervals between events, and in the second model they use the total number of events in successive intervals of fixed length. They derive an algorithm for recursive estimation of the Poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study. The estimates of the switch intensities are based on the observed conditional switch probabilities     

Phased-mission system reliability under Markov environment

The authors show how to determine the reliability of a multi-phase mission system whose configuration changes during consecutive time periods, assuming failure and repair times of components are exponentially distributed and redundant components are repairable as long as the system is operational. The mission reliability is obtained for 3 cases, based on a Markov model. (1) Phase durations are deterministic; the computational compact set model is formulated and a programmable solution is developed using eigenvalues of reduced transition-rate matrices. (2) Phase durations are random variables of exponential distributions and the mission is required to be completed within a time limit; the solution is derived as a recursive formula, using the result of case 1 and mathematical treatment-a closed-form solution would be prohibitively complex and laborious to program. (3) Phase durations are random variables and there is no completion time requirement; the solution is derived similarly to case 1 using moment generating functions of phase durations. Generally, reliability problems of phased-mission systems are complex. The authors' method provides exact solutions which can be easily implemented on a computer     

Computationally-efficient phased-mission reliability analysis forsystems with variable configurations

Several techniques and a software tool for reliability analyses that generally apply to fault-tolerant systems operating in phased-missions are given. Efficient models, using Markov chains without an explosion of the state space, are provided for missions consisting of multiple phases, during which the system configuration or success criteria can change. In different phases, the failure rates and the fault and error handling models can also change, and the duration of any phase can use deterministic or random models. An efficient reconfiguration procedure that is computationally more efficient than any existing technique is developed. The technique is demonstrated using a numerical example to show the effects of mission phases on the system reliability     

Modular solution of dynamic multi-phase systems

Binary Decision Diagram (BDD)-based solution approaches and Markov chain based approaches are commonly used for the reliability analysis of multi-phase systems. These approaches either assume that every phase is static, and thus can be solved with combinatorial methods, or assume that every phase must be modeled via Markov methods. If every phase is indeed static, then the combinatorial approach is much more efficient than the Markov chain approach. But in a multi-phased system, using currently available techniques, if the failure criteria in even one phase is dynamic, then a Markov approach must be used for every phase. The problem with Markov chain based approaches is that the size of the Markov model can expand exponentially with an increase in the size of the system, and therefore becomes computationally intensive to solve. Two new concepts, phase module and module joint probability, are introduced in this paper to deal with the s-dependency among phases. We also present a new modular solution to nonrepairable dynamic multi-phase systems, which provides a combination of BDD solution techniques for static modules, and Markov chain solution techniques for dynamic modules. Our modular approach divides the multi-phase system into its static and dynamic subsystems, and solves them independently; and then combines the results for the solution of the entire system using the module joint probability method. A hypothetical example multi-phase system is given to demonstrate the modular approach.     

A note on optimum checkpointing policies

In this paper, we treat checkpointing policies. We derive the total expected loss time and obtain the optimum checkpointing policy which minimizes that expected loss time. We further present the numerical examples using the exponential and the Weibull distributions. First, we discuss the model in which the intervals between checkpointing completion times may vary, and secondly the model with constant intervals.     

Analysis of Stochastic Petri Net model with non-exponential distributions using a generalized Markov Renewal Process

Stochastic Petri Nets have been developed to model and analyze systems involving concurrent activities. However, the firing times of a Stochastic Petri Net model are always exponentially distributed. This paper presents an aggregate approach on how to analyze Stochastic Petri Net model with non-exponential distributions using a generalized Markov Renewal Process. Therefore, the modeling flexibility of Petri Net and the analyzing power of Markov Renewal Process are fully exploited. Moreover, an Abstract Partial Reachability Graph is introduced to simplify the Markov solution. Furthermore, the aggregate approach is applied to evaluate performance of a parallel operation system.     

Computationally efficient method for analyzing guard channel schemes

Call admission control (CAC) is important for cellular wireless networks in order to provide quality of service (QoS) requirements to users. Guard channel scheme is one of the CAC schemes. There are different computational models for analyzing the guard channel scheme which make unrealistic assumption of exponential distribution for both call holding duration and cell residence time for computational tractability. On the other hand, there are some more realistic models for guard channel schemes which capture general distributions of call holding duration and cell residence time by phase type distributions but are computationally cumbersome to implement. The state-spaces of the Markov chains for those models make the computation intractable. In this paper, we develop a tractable computational model to analyze guard channel scheme with general cell residence time and call holding duration captured by phase type distributions. We make our mathematical model computationally tractable by keeping track of the number of calls in different phases of the channel holding time instead of the phase of the channel holding time of individual calls.     

Closed-Form Solution for System Availability Distribution

Highly reliable systems with long mission time, that can tolerate no down time, have motivated the study of system reliability. The emergence of fault-tolerant computing systems, where small down times may be tolerable, and preventive and corrective maintenance permitted, motivates a revisit to measures like mean availability. Vendors of computer systems are being required to specify the level of availability that will be met by their systems over a finite time interval, and pay a penalty for non-compliance. Since no closed-form solution has been reported in the literature, numerical approaches have often been used to compute systems availability over a finite time, even for simple Markov models. We report a Laplace transform solution for the distribution of availability over a finite interval, for a semi-Markov model. The transform of the distribution is analytically inverted to obtain a closed-form solution for the corresponding Markov model.     

Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach

A quantitative reliability model for a phased mission system is developed using a Markov process. Two cases for the mission-phase change times are assumed: 1) to be known in advance and 2) to be random variables. A method of solution is presented and illustrated by examples. The solution of phased-mission systems is equivalent to solving a sequence of uni-phase systems with appropriate initial conditions.     

Quantum mechanical simulation of charge transport in very smallsemiconductor structures

A quantum-mechanical simulation method of charge transport in very small semiconductor devices is presented that is based on the numerical solution of the time-dependent Schrodinger equation (coupled self-consistently to the Poisson equation to determine the electrostatic potential in the device). Carrier transport is considered within the effective mass approximation, while the effects of the electron-phonon interaction are included in an approximation that is consistent with the results of the perturbation theory and gives the correct two-point time correlation function. Numerical results for the transient behaviour of a planar ultrasubmicrometer three-dimensional GaAs MESFETs (gate length of 26 nm) are also presented. They indicate that extremely fast gate-step response times (switching times) characterize such short-channel GaAs devices     

Reliability Analysis of a Two-Unit Standby-Redundant System with Preventive Maintenance

We consider a standby-redundant model of two units, where we assume that one unit is operative and the other unit is in standby at time t = 0. If the operative unit fails, a unit in standby is put into preventive maintenance policy of the operative unit to maintain our the preventive maintenance policy of the operative unit to maintain our system with high reliability. Our concern for the system is the time to the first system-down. The Laplace-Stieltjes transform of the time distribution to the first system-down and the mean time to the first system-down are derived by applying the relationship between Markov renewal processes and signal flow graph. Further, the behavior after the system-down is investigated by using the results of Markov renewal processes. Finally, numerical examples are presented for the k-Erlang failure time distributions. The optimal preventive maintenance time is discussed.     

Rainbow Net analysis of VAXcluster system availability

A system modeling technique, Rainbow Nets, is used to evaluate the availability and mean-time-to-interrupt of the VAXcluster. These results are compared to the exact analytic results showing that reasonable accuracy is achieved through simulation. The complexity of the Rainbow Net implemented for the VAXcluster does not increase as the number of processors increases, but remains constant. This is unlike a Markov model which increases in size exponentially. The constancy is achieved by using tokens with identity attributes (items) that can have additional attributes associated with them (features) which can exist in multiple states. The time to perform the simulation increases, but this is a polynomial increase rather than exponential. With Rainbow Nets, there is no restriction on distributions used for transition firing times. This freedom allows real situations to be modeled more accurately by choosing the distribution which best fits the system performance. This eliminates the need to make the many simplifying assumptions that are typically required to keep analytic calculations from becoming intractable     

Hybrid analysis of response time distributions in queueing networks

A hybrid analytic/simulation methodology is formulated for evaluating end-to-end response time distributions in closed product-form queueing networks. The method combines Markov-Monte-Carlo simulation with analytical results pertaining to uniformized Markov chains and product-form queuing networks. A stratified sampling plan is incorporated as a variance reduction technique. The concept of importance sampling is used to reduce the computational requirements of the plan and make it realizable in practice. The most important consequence of applying uniformization is that it enables the characterization of the response time distribution as an infinite mixture of Erlangian distributions. An estimate of the entire response time distribution may then be obtained in each simulation trial. This circumvents the practical problems associated with estimating tail probabilities. A numerical example is provided to illustrate the theory     

Approximate Markov Modeling of High-Reliability Telecommunications Systems

The reliability model of a system with redundancy but only a single repairman is Markov only if the component failure rates and the repair rate are constants. This paper introduces a method with which a reliability analyst can formulate an approximate (time-homogeneous) Markov model for a system with 1-out-of-2 redundancy when repair is nonexponential (repair rate is time-dependent). This approximate model yields accurate steady-state predictions of system reliability when time-to-repair is orders of magnitude smaller than timeto-component-failure, as is typical in high-reliability telecommunications systems. Transition rates and error bounds for the approximate model are given based on the first three moments of the repair time distribution. An application of the method is shown for the system in which repair time is composed of a "next day" parts delivery phase followed by an on-site repair phase.     

Decomposition in Reliability Analysis of Fault-Tolerant Systems

Two important problems which arise in modeling fault-tolerant systems with ultra-high reliability requirements are discussed. 1) Any analytic model of such a system has a large number of states, making the solution computationally intractable. This leads to the need for decomposition techniques. 2) The common assumption of exponential holding times in the states is intolerable while modeling such systems. Approaches to solving this problem are reviewed. A major notion described in the attempt to deal with reliability models with a large number of states is that of behavioral decomposition followed by aggregation. Models of the fault-handling processes are either semi-Markov or simulative in nature, thus removing the usual restrictions of exponential holding times within the coverage model. The aggregate fault-occurrence model is a non-homogeneous Markov chain, thus allowing the times to failure to possess Weibull-like distributions. There are several potential sources of error in this approach to reliability modeling. The decomposition/aggregation process involves the error in estimating the transition parameters. The numerical integration involves discretization and round-off errors. Analysis of these errors and questions of sensitivity of the output (R(t)) to the inputs (failure rates and recovery model parameters) and to the initial system state acquire extreme importance when dealing with ultra-high reliability requirements.     

OLED器件寿命衰退模型的MATLAB分析计算

介绍了OLED器件寿命衰退模型的MATLAB分析计算方法.一般认为运动离子是驱动电压变化的原因之一.利用MATLAB求解了运动离子瞬态方程,得到了与时间相关的负指数形式分布函数.介绍了阳极为恒流离子源条件时模型的数值求解算法.根据模型可以计算出运动离子引入的驱动电压随时间的变化关系,其结果可用于与实验数据进行拟合比较.     

Performance of a nonblocking space-division packet switch in a timevariant nonuniform traffic environment

The authors study the performance of a nonblocking space-division packet switch, given that the traffic intensities at the switch not only are nonuniform but also change as a function of time. A finite-state Markov chain is used as an underlying process to govern the time variation of traffic for the entire switch. The packet arrivals at each input form an independent Bernoulli process modulated by the underlying Markov chain. The output address of each packet is independently and randomly assigned with probability distributions, which are also modulated by the Markov chain. Provided that the traffic on each output is not dominated by individual inputs the service time of each output queue for sufficiently large switches can be characterized by an independent Markov modulated phase-type process. A matrix geometric solution for the resultant quasi-birth-death type queuing process is presented. The maximum throughput is obtained at the system saturation. The performance of the switch is numerically examined under various traffic conditions. A contention priority scheme to improve the switch performance is proposed     

Performance analysis of RTS/CTS scheme in WLAN with the impact of bit errors

To estimate the system performance of RTS/CTS scheme in an error‐prone WLAN channel, this paper proposes a new three‐dimensional Markov model, which considers the impact of bit error on all kinds of frames, and both station short retry limit and long retry limit. The system performance parameters including saturation throughput, packet drop probability, drop time, and average delay are derived using the new Markov model. By comparing the numerical results with simulation results, the model is proved to be more accurate than previous work. The numerical results show that the channel bit error rate has a significant impact not only on system performance, but also on the sensitivity of other system parameters including network scale, channel data rate, and packet length. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of the TLM method to half-space and remote-sensingproblems

The problem of scattering and radiation in the presence of a material half-space is solved using the transmission line matrix (TLM) method. The TLM method is a general numerical method for obtaining an approximate solution to the time-dependent form of Maxwell's equations in the presence of complex environments. The method requires the discretization of the entire spatial domain of the problem and provides the transient response as well as (through discrete Fourier transform) the frequency domain response. The three-dimensional symmetric-condensed TLM node is applied. A total/scattered field formulation is applied to excite the space. The source used is an electrically short electric dipole and is described analytically in the time-domain. The method is used to calculate near field distributions (in both the time and frequency domain) and the change in source input impedance of a dipole radiator in the presence of a half-space. Numerical simulations relevant to the detection of buried objects are provided