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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Discrete Deterministic and Stochastic Petri Nets

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

MATHEMATICAL MODELS↗
NASA NTRS1970

A Markovian reset problem

Optimal control of systems with time transitions described by finite state stationary Markov chain, noting resetting control

Kolesar, P.↗
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.↗