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At least 379 records · Page 21

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NASA NTRS1973

A unified method for analyzing mission reliability for fault tolerant computer systems.

For fault-tolerant computer systems consisting of multiple classes of modules, a unified method for analyzing mission reliability is proposed and evaluated. The analysis proceeds by generalizing the notions of standby and N modular redundancy into a concept called hybrid-degraded redundancy. The probabilistic evaluation of the unified redundancy concept is then developed to yield, for a given modular class, the joint distribution of success and the number of nonfailed modules from that class, at special times. With this information, a Markov chain analysis gives the reliability of an entire sequence of phases (mission profile).

Bricker, J. L.↗

NASA NTRS1974

Statistical analysis of flight times for space shuttle ferry flights

Markov chain and Monte Carlo analysis techniques are applied to the simulated Space Shuttle Orbiter Ferry flights to obtain statistical distributions of flight time duration between Edwards Air Force Base and Kennedy Space Center. The two methods are compared, and are found to be in excellent agreement. The flights are subjected to certain operational and meteorological requirements, or constraints, which cause eastbound and westbound trips to yield different results. Persistence of events theory is applied to the occurrence of inclement conditions to find their effect upon the statistical flight time distribution. In a sensitivity test, some of the constraints are varied to observe the corresponding changes in the results.

Graves, M. E.↗

NASA NTRS1973

An all digital phase locked loop for synchronization of a sinusoidal signal embedded in white Gaussian noise

An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.

Reddy, C. P.↗

NASA NTRS1975

On the effect of timing errors in run length codes

Many redundancy removal algorithms employ some sort of run length code. Blocks of timing words are coded with synchronization words inserted between blocks. The probability of incorrectly reconstructing a sample because of a channel error in the timing data is a monotonically nondecreasing function of time since the last synchronization word. In this paper we compute the 'probability that the accumulated magnitude of timing errors equal zero' as a function of time since the last synchronization word for a zero-order predictor (ZOP). The result is valid for any data source that can be modeled by a first-order Markov chain and any digital channel that can be modeled by a channel transition matrix. An example is presented.

Wilkins, L. C.↗

NASA NTRS1975

On the control, stability, and waiting time in a slotted ALOHA random-access system

This paper explores some of the boundaries in performance of slotted ALOHA systems by analyzing a simple and almost optimal centrally supervised control. The control results in a very simple Markov chain model and allows an examination of stability, conditional waiting time distribution of transmitting terminals, and many other system measures. The key to the simplicity is to have a probability of successful packet transmission that is independent of the number of transmitting terminals. In considering waiting time, we calculate the mean and other moments of the waiting time of a terminal when it enters the system to find (n - 1) other terminals already there competing for the channel. Under this control, the average time is proportional to n. The control requires exact knowledge of the number of terminals contending for the channel, and hence is not implementable, except as an approximation.

Ferguson, M. J.↗

NASA NTRS1977

Analysis of a first order phase locked loop in the presence of Gaussian noise

A first-order digital phase locked loop is analyzed by application of a Markov chain model. Steady state loop error probabilities, phase standard deviation, and mean loop transient times are determined for various input signal to noise ratios. Results for direct loop simulation are presented for comparison.

Blasche, P. R.↗

NASA NTRS1978

On reliable control system designs

A mathematical model for use in the design of reliable multivariable control systems is discussed with special emphasis on actuator failures and necessary actuator redundancy levels. The model consists of a linear time invariant discrete time dynamical system. Configuration changes in the system dynamics are governed by a Markov chain that includes transition probabilities from one configuration state to another. The performance index is a standard quadratic cost functional, over an infinite time interval. The actual system configuration can be deduced with a one step delay. The calculation of the optimal control law requires the solution of a set of highly coupled Riccati-like matrix difference equations. Results can be used for off-line studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.

Birdwell, J. D.↗

NASA NTRS1978

A general cratering-history model and its implications for the lunar highlands

Through analysis of a large number of Monte Carlo and Markov Chain simulations, a model for determining crater accumulation and crater obliteration histories has been derived. The model generally applies to populations of large craters. It predicts that the following relationships hold for subequilibrium-density crater populations: (1) the more negative the production function's exponent, alpha (N near D super alpha) the lower the crater density at which the population size-frequency distribution will significantly depart from its production function; (2) the more negative the production function's exponent, the less obliteration a crater population will sustain after a set number of impacts. Application of the model to the lunar highlands implies (1) the production function for the large craters is highly structured, resembling the observed size-frequency distribution and not the function N near D to the -2; (2) even the densely cratered highlands have not attained crater saturation or equilibrium. Direct simulations of the highlands' crater population supports the model's implications.

Woronow, A.↗

NASA NTRS1979

Numerical methods for problems involving the Drazin inverse

The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.

Meyer, C. D., Jr.↗

NASA NTRS1979

Extensions to the classical calculation of the effect of mutual shadowing in diffuse reflection

The classical method for accounting for the mutual shadowing among closely packed particles in multiple scattering calculations is extended in the following ways. (1) By modeling the particle distribution by a Poisson process with a varying density parameter, a 'Van der Waals' type approximation allows extension to a greater fractional volume density, D. In this case it is only required that D squared be much less than 1 instead of D being much less than 1. (2) In the case that the particle distribution is not uniform the classical calculation may be weighted by the pair correlation function of the distribution. (3) The use of the Markov chain formalism for radiative transfer allows inclusion of the effect of shadowing for two orders of scattering. For conditions such as might apply in Saturn's rings, the inclusion of this effect makes less than a 0.1% difference in the calculated phase curves, compared to previous calculations which have included shadowing only in the first scattering. The latter are thus shown to be quite accurate.

Esposito, L. W.↗

NASA NTRS1980

Use of generalized population ratios to obtain Fe XV line intensities and linewidths at high electron densities

A generalized method for obtaining individual level population ratios is used to obtain relative intensities of extreme ultraviolet Fe XV emission lines in the range 284-500 A, which are density dependent for electron densities in the tokamak regime or higher. Four lines in particular are found to attain quite high intensities in the high-density limit. The same calculation provides inelastic contributions to linewidths. The method connects level populations and level widths through total probabilities t(ij), related to 'taboo' probabilities of Markov chain theory. The t(ij) are here evaluated for a real atomic system, being therefore of potential interest to random-walk theorists who have been limited to idealized systems characterized by simplified transition schemes.

Kastner, S. O.↗

NASA NTRS1981

Investigation of air transportation technology at Ohio University, 1980

Specific configurations of first and second order all digital phase locked loops were analyzed for both ideal and additive gaussian noise inputs. In addition, a design for a hardware digital phase locked loop capable of either first or second order operation was evaluated along with appropriate experimental data obtained from testing of the hardware loop. All parameters chosen for the analysis and the design of the digital phase locked loop were consistent with an application to an Omega navigation receiver although neither the analysis nor the design are limited to this application. For all cases tested, the experimental data showed close agreement with the analytical results indicating that the Markov chain model for first and second order digital phase locked loops are valid.

Mcfarland, R. H.↗

NASA NTRS1981

A tutorial on the CARE III approach to reliability modeling

The CARE 3 reliability model for aircraft avionics and control systems is described by utilizing a number of examples which frequently use state-of-the-art mathematical modeling techniques as a basis for their exposition. Behavioral decomposition followed by aggregration were used in an attempt to deal with reliability models with a large number of states. A comprehensive set of models of the fault-handling processes in a typical fault-tolerant system was used. These models were semi-Markov in nature, thus removing the usual restrictions of exponential holding times within the coverage model. The aggregate model is a non-homogeneous Markov chain, thus allowing the times to failure to posses Weibull-like distributions. Because of the departures from traditional models, the solution method employed is that of Kolmogorov integral equations, which are evaluated numerically.

Trivedi, K. S.↗

NASA NTRS1982

On the delay analysis of a TDMA channel with finite buffer capacity

The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.

Yan, T.-Y.↗

NASA NTRS1983

Control of a heterogeneous two-server exponential queueing system

A dynamic control policy known as 'threshold queueing' is defined for scheduling customers from a Poisson source on a set of two exponential servers with dissimilar service rates. The slower server is invoked in response to instantaneous system loading as measured by the length of the queue of waiting customers. In a threshold queueing policy, a specific queue length is identified as a 'threshold,' beyond which the slower server is invoked. The slower server remains busy until it completes service on a customer and the queue length is less than its invocation threshold. Markov chain analysis is employed to analyze the performance of the threshold queueing policy and to develop optimality criteria. It is shown that probabilistic control is suboptimal to minimize the mean number of customers in the system. An approximation to the optimum policy is analyzed which is computationally simple and suffices for most operational applications.

Larsen, R. L.↗

NASA NTRS1983

Design of the hybrid automated reliability predictor

The design of the Hybrid Automated Reliability Predictor (HARP), now under development at Duke University, is presented. The HARP approach to reliability prediction is characterized by a decomposition of the overall model into fault-occurrence and fault-handling sub-models. The fault-occurrence model is a non-homogeneous Markov chain which is solved analytically, while the fault-handling model is a Petri Net which is simulated. HARP provides automated analysis of sensitivity to uncertainties in the input parameters and in the initial state specifications. It then produces a predicted reliability band as a function of mission time, as well as estimates of the improvement (narrowing of the band) to be gained by a specified amount of reduction in uncertainty.

Geist, R.↗

NASA NTRS1985

Vector computer memory bank contention

A number of vector supercomputers feature very large memories. Unfortunately the large capacity memory chips that are used in these computers are much slower than the fast central processing unit (CPU) circuitry. As a result, memory bank reservation times (in CPU ticks) are much longer than on previous generations of computers. A consequence of these long reservation times is that memory bank contention is sharply increased, resulting in significantly lowered performance rates. The phenomenon of memory bank contention in vector computers is analyzed using both a Markov chain model and a Monte Carlo simulation program. The results of this analysis indicate that future generations of supercomputers must either employ much faster memory chips or else feature very large numbers of independent memory banks.

Bailey, D. H.↗

NASA NTRS1984

Computer simulation of surface and film processes

All the investigations which were performed employed in one way or another a computer simulation technique based on atomistic level considerations. In general, three types of simulation methods were used for modeling systems with discrete particles that interact via well defined potential functions: molecular dynamics (a general method for solving the classical equations of motion of a model system); Monte Carlo (the use of Markov chain ensemble averaging technique to model equilibrium properties of a system); and molecular statics (provides properties of a system at T = 0 K). The effects of three-body forces on the vibrational frequencies of triatomic cluster were investigated. The multilayer relaxation phenomena for low index planes of an fcc crystal was analyzed also as a function of the three-body interactions. Various surface properties for Si and SiC system were calculated. Results obtained from static simulation calculations for slip formation were presented. The more elaborate molecular dynamics calculations on the propagation of cracks in two-dimensional systems were outlined.

Tiller, W. A.↗