State-dependent Rates Research Articles

Reliability and MTTF prediction ofK-out-of-ncomplex systems with components subjected to multiple stages of degradation

In some environments the components may not fail fully but can degrade, and there may be multiple stages of degradation. In such cases, the efficiency of the system may decrease. In this study we present a model for predicting the reliability of k-out-of-n: G systems assuming that components are subjected to several stages of degradation as well as catastrophic failures. In the analysis we consider the state-dependent transition rates for the catastrophic failures and degradation processes. We also present the expressions to determine the reliability and mean time to failure (MTTF) of the k-out-of-n systems. Reliability and M TTF expressions for a special case of the model without catastrophic failures are also presented. Several numerical examples are given to illustrate the results.

Dissociative attachment of low-energy electrons to state-selected diatomic molecules

The dissociative attachment process in low-energy collisions [Na{sub 2}({ital v}{sup {double_prime}},{ital j}{sup {double_prime}})+{ital e}{sup {minus}}{r_arrow} Na + Na{sup {minus}}, with electron energies {lt}1.0 eV] is studied as a function of vibrational excitation over a broad range of excited levels. We employ a crossed electron-molecule beams arrangement and two optical methods for preparing vibrationally excited states: Franck-Condon pumping (FCP) as well as the efficient and highly state-specific technique of stimulated Raman scattering with adiabatic passage (STIRAP). Both methods are capable of preparing vibrational levels with energies up to about 60{percent} of the Na{sub 2}{ital X}{sup 1}{Sigma}{sub {ital g}}{sup +} binding energy ({ital v}{sup {double_prime}}{le}30). Analysis of the FCP data shows an increase of more than three orders of magnitude in the state-dependent dissociative attachment rate as a function of the vibrational level up to {ital v}{sup {double_prime}}=12. For {ital v}{sup {double_prime}}{approx_gt}12, which is close to the exoergic threshold, no further increase with {ital v}{sup {double_prime}} is observed. The dissociative attachment rates measured for single rovibronic states using the STIRAP technique confirm the validity of the conclusions drawn from our analysis of the FCP measurements. The potential curve of the Na{sub 2}{sup {minus}}{ital A}{sup 2}{Sigma}{sub {ital g}}{sup +} state, which is essentialmore » for the dissociative attachment process, has been determined from variational valence shell multireference configuration interaction calculations in its bound region but by imposing Feshbach projection in its resonance region. The crossing of this potential with that of the Na{sub 2}({ital X}) state is found between {ital v}{sup {double_prime}}=11 and {ital v}{sup {double_prime}}=12, in full agreement with the conclusions from analysis of the experimental data. (Abstract Truncated)« less

Generalised erlang loss formula

A teletraffic model for a full availability loss system with a generalised Poisson input stream is proposed. The idea is based on the analytic continuation of the Poisson distribution and the erlang-B formula. The authors use techniques based on birth and death processes and state-dependent arrival rates. The advantages of simplicity and uniformity in representing both peaked and smooth traffic make the model attractive for modelling traffic in network analysis and synthesis.

Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates

We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.

Mean-value analysis of multi-facility blocking models with state-dependent arrivals

A new mean-value type of algorithm is developed for analyzing multi-facility blocking models with state-dependent arrival rates. It can be applied to a broad class of blocking systems with simultaneous resource possession including, for example, circuit-switched networks. The underlying recursion is cast in terms of blocking probabilities and marginal state probabilities. The developments made here generalize previous results that were restricted to the case of constant arrival rates.

Computing steady state probabilities in λ( n)/G/1/ K queue

In this paper a recursive method is developed to obtain the steady state probability distribution of the number in system at arbitrary and departure time epochs of a single server state-dependent arrival rate queue λ( n)/G/1/ K in which the arrival process is Markovian with arrival rates λ( n) which depend on the number of customers n in the system and general service time distribution. It is assumed that there exists an integer K such that λ( n) > 0 for all 0 ⩽ n < K and λ( n) = 0 for all n ⩾ K. Numerical results have been presented for many queueing models by suitably defining the function λ( n). These include machine interference model, queues with balking, queues with finite waiting space and machine interference model with finite waiting space. These models have wide application in computer/communication networks.

Traffic overflow in closed queueing models

We consider a generalized birth death process that represents a multiserver (closed or open) overflow queueing system with n primary servers and c-n secondary servers. An arrival to the system joins a server of the primary group, if available, otherwise it overflows to the secondary group. If all servers are busy, arrivals are queued, provided the queue buffer is not full, and served as servers become free. Arrivals that find the queue buffer full are lost. Our overflow model differs from models in the open literature in that it combines state dependent arrival rates with group dependent service rates. We present a general formulation that allows a simple derivation of the joint stationary probabilities of i busy primary servers and j busy secondary severs. This main result easily lends itself to an efficient iterative algorithm to evaluate the joint probabilities. We apply our basic theorem to produce new results for several overflow models. A distinctive feature of our approach is that it uses transform-free analysis.

Computational analysis of M( n)/ G/1/ N queues with setup time

An efficient iterative algorithm is developed for computing the stationary queue length distribution in M/ G/1/ N queues with setup time and arbitrary state dependent arrival rates. The overall computation of the algorithm is O( N 2) in complexity. Our numerical investigations demonstrate the strength of the algorithm.

Using state-dependent processing rates to emulate SPT queue discipline in an FCPS queueing network

Using the ‘shortest processing time’ queue discipline results in long queues being quickly reduced as the short jobs are quickly pushed through the system. We approximate this effect under the ‘first-come, first-served’ queue discipline by having the service rate increase with the queue length. That is, instead of picking the shortest job, the server instead picks the first job, but then processes it at a higher rate. This new load-dependent queue is compared with the original queue both individually and within open queueing networks.

Rejection rules in theM/G/1 queue

We consider aM/G/1 queue modified such that an arriving customer may be totally or partially rejected depending on a r.v. (the barricade) describing his impatience and on the state of the system. Three main variants of this scheme are studied. The steady-state distribution is expressed in terms of Volterra equations and the relation to storage processes, dams and queues with state-dependent Poisson arrival rate is discussed. For exponential service times, we further find the busy period Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associated birth-death process.

An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates

The algorithm developed in Choudhury et al. (1994) for computing (exact) steady-state blocking probabilities for each class in product-form loss networks is extended to cover general state-dependent arrival and service rates. This generalization allows to consider, for the first time, a wide variety of buffered and unbuffered resource-sharing models with non-Poisson traffic, as may arise with overflows in the context of alternative routing. As before, the authors consider noncomplete-sharing policies involving upper-limit and guaranteed-minimum bounds for the different classes, but in the present paper both bounds are discussed simultaneously. These bounds are important for providing different grades of service with protection against overloads by other classes. The algorithm is based on numerically inverting the generating function of the normalization constant, which is derived in the present paper. Major features of the algorithm are: dimension reduction by elimination of nonbinding resources and by conditional decomposition based on special structure, an effective scaling algorithm to control errors in the inversion, efficient treatment of multiple classes with identical parameters and truncation of large sums. The authors show that the computational complexity of the inversion approach is usually significantly lower than the alternative recursive approach. >

Detonation Wave Structure of Gases at Elevated Initial Pressures

ABSTRACT The characteristic “structure” of gaseous detonation waves, defined here as the spatial variation of the pressure, temperature, density, species concentrations, and velocity within the detonation wave is examined theoretically at elevated initial pressures. The approach taken in this work is to extend the Zel'dovich-von Neumann-Doering (ZND) theory of gas-phase detonation to use real-gas equations of state, Chemkin Real Gas, a computer program capable of calculating real-gas thermodynamic properties and chemical kinetic reaction rates, is used to describe the P-V-T behaviour of the gaseous mixtures in this investigation. The mathematical model for a ZND detonation wave is presented in an equation of state independent form and integrated numerically for a hydrogen-oxygen system to determine the structure of the detonation wave. The ZND model is used to characterize the thermodynamic states and reaction zone length scales present in the detonation wave. The variation of the reaction zone length parameters is examined as a function of the initial pressure, temperature, and composition. The distance from the shock front to the maximum temperature derivative is shown to be a reproducible reference location in the detonation wave structure. The numerical calculations exhibit sensitivity to equation of state dependent constants and pre-exponential rate coefficients in the elementary reaction mechanism.

The CH 3 3p z2A 2″ ← X̃ 2A 2″ 0 00 band at temperatures up to 1700 K investigated by REMPI spectroscopy

The 0 0 0 band of the CH 3 3p z 2A 2″ ← X̃ 2A 2″ Rydberg transition has been recorded using the (2 + 1) resonance-enhanced multi-photon ionization (REMPI) of CH 3 at 333 nm. CH 3 was generated in a discharge flow reactor at room temperature and in a hot-filament-assisted chemical vapor deposition (HFCVD) reactor at temperatures of 820 to 1700 K. By means of spectral simulation the rotational constants, B 0′ and C 0′, and the rotational state-dependent predissociation rates of the 3p z 2A 2″ state were determined. Based on these constants and the well-known rotational and vibrational ground-state constants, relative intensities of the CH 3 REMPI spectra were calculated for temperatures up to 2300 K. These spectra were used to evaluate relative CH 3 concentrations from measured REMPI peak intensities of the dominant Q branch.

Gaussian white noise as a many-particle process: the Kardar-Parisi-Zhang equation

A new approach is proposed to derive a stochastic differential equation from a master equation. Starting from the Liouvillian in a Fock space formulation and using a functional integral representation in terms of coherent states the authors get the corresponding Langevin equation. As examples aggregation and segregation processes with different probability rates are analyzed. In the case of a state dependent growth rate it results in a generalized Kardar-Zhang equation including the kind of noise which is a purely Gaussian one in this model.

Optimal Control and Replacement with State-Dependent Failure Rate: Dynamic Programming

A class of stochastic control problems where the payoff depends on the running maximum of a diffusion process is described. The controller must make two kinds of decision: first, he must choose a work rate (this decision determines the rate of profit as well as the proximity of failure), and second, he must decide when to replace a deteriorated system with a new one. Preventive replacement is a realistic option if the cost for replacement after failure is larger than the cost of a preventive replacement. We focus on the profit and replacement cost for a single work cycle and solve the problem in two stages. First, the optimal feedback control (work rate) is determined by maximizing the payoff during a single excursion of a controlled diffusion away from the running maximum. This step involves the solution of the Hamilton-Jacobi-Bellman (HJB) partial differential equation. The second step is to determine the optimal replacement set. The assumption that failure occurs only on the set where the state is increasing implies that replacement is optimal only on this set. This leads to a simple formula for the optimal replacement level in terms of the value function.

Smoothing for linear systems erxcited by point processes with state–dependent rates

Smoothing for a linear system driven by a marked point process with a rate that depends on the state of the system is considered. A linear combination of the states is observed in additive white Gaussian noise. A smoother that uses estimation and detection is simulated on a computer and its mean squared error (MSE) is compared with the theoretical MSE of the optimal linear smoother and filter. The falso alarm rate is shown to depend strongly on the region of support of the mark distribution. When false alarms are low, the estimation/detection scheme has lower MSE than the optimal linear smoother.

Charge transfer of N4+ with atomic hydrogen.

State-dependent cross sections and rate coefficients for the charge-transfer process N{sup 4+}+H{r arrow}N{sup 3+}(2{ital s}3{ital l})+H{sup +} for {ital l}={ital s},{ital p},{ital d} in the collision-energy range from 0.1 eV to 8 keV are presented. A close-coupled quantum-mechanical method is employed, and it is argued that the molecular-state expansion method without translation factors is a valid low-energy approximation for charge-transfer processes. We show that the method does not suffer from the electron-origin problem. The spin-coupled valence-bond method is used to construct both {ital ab} {ital initio} potential curves and adiabatic coupling elements. The calculated cross sections exhibit variations with energy, which we propose are a manifestation of Stueckelberg oscillations. The cross sections are compared with measured total cross sections for electron capture by N{sup 4+} ions in collisions with hydrogen. Agreement is excellent in the collision-energy range from 4.1 to 182 eV/amu.

Empirical Bayes estimation for queueing systems and networks

Empirical Bayes estimators are derived for standardM/M/1 queues,M/M/1 queues with state-dependent arrival and service rates, finite capacityM/M/1 queues with state-dependent rates and for open Jackson networks. The asymptotic properties of the empirical Bayes estimators are derived both with respect to the conditional distribution of the observations given the parameters, and with respect to the joint distribution of the observations and the parameters.

Transient error bound analysis for continuous-time Markov reward structures

Conditions are provided to conclude error bounds and comparison results when evaluating transient or cumulative reward structures for continuous-time Markov chains under slightly different system input values or protocols. Such results are of interest for: sensitive (perturbation), computational (truncation), or bounding (modification) purposes. A reliability network with state dependent breakdown rates is studied as illustration. An explicit error bound is derived for the effect of inaccuracies in breakdown and repair rates. Also, monotonicity results are established.

A mathematical model and computer simulation study of insulin sensitive glucose transporter regulation

A mathematical model of insulin sensitive glucose transporter regulation is developed. Model structure is based on experimental evidence from adipocytes and myocytes. Model parameters correspond with known cellular processes. As an example, computer simulation results are compared with data from rat adipocytes. Cellular processes explicitly represented in the model include state-dependent glucose transporter synthesis and degradation rates, insulin sensitive glucose transporter translocation rates, and a glucose transporter endocytosis rate. Most of these processes are represented as first-order events. Using more complex representations of the model structure (e.g. higher order rate constants or saturable pathways) or alternative structures did not result in qualitatively better results. The model is able to accurately simulate the insulin sensitive, insulin concentration dependent, reversible translocation of glucose transporters observed in normal adipocytes. The model is also able to accurately simulate the changes in regulation of glucose transporter translocation observed with increases in cell surface area. Finally, the model can simulate pathogenic states which induce impairment of glucose transporter regulation (e.g. altered glucose transporter regulation in adipocytes from rats on high fat diets, rats with streptozotocin induced diabetes, and fasted rats). Since the structure of our model is sufficient to explain glucose transporter regulation in both normal and pathological states, it may aid in understanding the post-receptor components of insulin resistance (decreased sensitivity or responsiveness to insulin) seen in pathological states such as obesity and diabetes mellitus.