Showing papers on "Renewal theory published in 1990"

Urban Renewal: Theory and Practice

Abstract: Aspects of the historical development of urban renewal economic theory for urban renewal social aspects for urban renewal management and organizational theory for urban renewal urban design for urban renewal. Appendix: some facts and figures of government performance.

Cumulative shock models

Abstract: We show that a theory for stopped two-dimensional random walks is well suited to describe cumulative shock models. Limit theorems for the lifetime/failure time of a system are provided.

A Queue with Service Interruptions in an Alternating Random Environment

Abstract: This paper considers a single server queue that operates in a random environment defined by an alternating renewal process with states 1 and 2. When the random environment is in state ii = 1, 2, the arrivals occur at a mean rate of λi and the distribution of service-time for these arrivals is Bit. The server is working when the random environment is in state 1 and not working when the state is 2. This model is applicable to situations in manufacturing, computer and telecommunications problems when the server is subject to random breakdown. It is also useful in modeling some priority and cyclic server queues. We analyze the problem by first examining the steady-state distribution of work in the system. We show that the work in the system is closely related to the waiting time in a special GI/G/1 queue. For the special case when the off-period is exponentially distributed, exact closed-form expressions are obtained for the performance measures of interest. For other cases, we propose an approximation and show that it works well when compared with simulations.

Structural Load Modeling and Combination for Performance and Safety Evaluation

Abstract: 1. Introduction. Benefit versus risk of engineering facilities. Uncertainties in demand and capacity of engineering facilities. Treatment of uncertainty in design of engineering facilities. Objectives and emphasis. Organization of subject materials. 2. Basic Random Variable and Random Process Models. Commonly used load occurrence models. Bernoulli sequence. Poisson process. Renewal process. Polya process. Multi-variate point process. Commonly used load intensity models. Uni- and multi-variate normal distribution. Lognormal distribution. Gamma and exponential distribution. Extreme value distribution. Continuous Gaussian process. Point process with deterministic shape response function. Generation of random load intensity and random load process on digital computer and Monte-Carlo method. Generation of random variables. Generation of random processes. Convergence of Monte-Carlo method. 3. Modeling of Time Varying Load and Load Effect. Fluctuation of load and load effect. Loadings with macro-scale time variability only. Loadings with both macro- and micro-time variability. Pulse process. Poisson pulse process. Generalization. Other pulse process. Intermittent continuous process. Examples of load and load effect as pulse and intermittent processes. Appendix 3-A: Input-Output relationship of linear systems. Under dynamic random excitation. 4. Combination of Loads and Load Effects. Linear combination. Load coincidence (L.C.) method. Method of point crossing. Method of upcrossing rate. Other methods. Nonlinear combination. Outcrossing rate analysis. Resistance uncertainty. Load coincidence method. First and second order methods. Point crossing method. 5. Modeling and Effect of Load Dependencies. Within-load dependencies. Dependence between intensity and duration. Occurrence dependence (clustering). Intensity dependence. Between-load dependencies. Occurrence clustering among loads. Intensity dependence between loads. General case. Duration of coincidence of dependent loadings. Appendices: Monte-Carlo simulation and combination of dependent pulse processes. Sum of two independent Gauss-Markov processes. Derivation of function h 12 (3) (t,t'). Integration of Eq. 5.50. 6. Load Combination Rules. Risk consistency of current rules. Load reduction factor method (LRF). SRSS rule. Companion action factor method (CAF). Turkstra's rule (TR). Accuracy of load combination rules. Appendices: Derivation of joint distribution function of lifetime maximum value, R, and arbitrary-point-in-time value, S, of a pulse or intermittent process. Derivation of nonexceedance probability according to Turkstra's rule. Index.

A simple approximation to the renewal function (reliability theory)

Abstract: The authors present a simple, easy-to-understand approximation to the renewal function that is easy to implement on a personal computer. The key idea is that, for small values of time, the renewal function is almost equal to the cumulative distribution function of the interrenewal time, whereas for larger values of time an asymptotic expansion depending only on the first and second moment of the interrenewal time can be used. The relative error is typically smaller than a few percent for Weibull interrenewal times. The simple approximation methods works very well with one term if not too much accuracy is required (e.g. in the block replacement problem) or if the interrenewal (failure) distribution is not exactly known (e.g. only the first two moments are known). Although the accuracy of the simple approximation can be improved by increasing the number of terms, this strategy is not advocated since speed and simplicity are lost. If high accuracy is required, it is better to use another approximating method (e.g. power series expansion or cubic splines method). >

Approximation techniques for computing packet loss in finite-buffered voice multiplexers

Abstract: The three performance models studied differ primarily in the manner in which the superposition of the voice sources (i.e. the arrival process) is modeled. The first approach models the superimposed voice sources as a renewal process. The second approach is based on modeling the superimposed voice sources as a Markov modulated Poisson process (MMPP). The choice of parameters for the MMPP captures aspects of the long-term correlation in the arrival process in a more intuitive manner and computes loss more accurately than previous approaches for computing the MMPP parameters. A fluid flow approximation for the superposition is evaluated on the basis of the technique of D. Anick et al. (1982). For all three approaches, the case of multiplexing voice sources over a T1-rate link is considered. Both the new MMPP model and the fluid flow approximation can provide accurate loss predictions for parameter ranges of practical interest. The modeling of buffer overflow for general arrival processes is addressed, and modeling approaches for analyzing finite-buffer multiplexers with general arrival and service processes in a network environment are outlined. >

Stochastic Methods in Reliability Theory

Abstract: Preliminaries. Elements of Stochastic Processes. Markovian Systems. Extended Markov Models. Applications of Renewal Theory. Semi--Markov Models. Stochastic Point Process in Reliability Theory. Special Methods in Reliability Theory. Monto Carlo Method in Reliability Analysis. Two--Unit Parallel Redundant System----A Review. Author Index. Subject Index.

Diffusion approximation to the G/G/R machine repair problem with warm standby spares

Abstract: The G/G/R machine repair problem with M operating machines, S warm standby spares, and R repairmen is studied as a diffusion process. The steady-state equations are formulated as diffusion equations subject to two reflecting barriers. The approximate diffusion parameters of the diffusion equations are obtained (1) under the assumption that the input characteristics of the problem are defined only by their first two moments rather than their probability distribution function, (2) under the assumption of heavy traffic approximation, that is, when queues of failed machines in the repair stage are almost always nonempty, and (3) using well-known asymptotic results from renewal theory. Expressions for the probability density functions of the number of failed machines in the system are obtained. A study of the derived approximate results, compared to some of the exact results, suggests that the diffusion approach provides a useful method for solving complex machine-repair problems.

On the optimality of the (S — 1,S) policy

Abstract: The one-for-one (S - 1,S) inventory policy, which calls for a replenishment order after each demand equal in magnitude to the size of the demand, is often advocated for controlling the stock levels of expensive, slow-moving items. In particular, this policy has frequently been promoted for use in recoverable-item inventory systems. An important managerial question is: When is the (S - 1,S) policy optimal? Results in this article provide guidance for the selection of this policy. Conditions under which it is not economical to batch demands are developed, provided the renewal function of the renewal process of demand sizes is concave. This includes the important case of unit-sized demands. The inventory system considered is one with continuous review, constant lead times, general interarrival and discrete demand distributions, complete backlogging, and linear holding and penalty costs per unit per unit time. Examples are given for the special case when the demand process is Poisson and when the demand process is a particular compound Poisson distribution known as the stuttering Poisson distribution.

Examples for the Theory of Strong Stationary Duality with Countable State Spaces

Abstract: Let X1,X2,… be an ergodic Markov chain on the countable state space. We construct a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X. Examples include birth and death chains, queueing models, and the excess life process of renewal theory. This paper gives the first extension of the stopping time arguments of Aldous and Diaconis [1,2] to infinite state spaces.

The use of renewal theory for stochastic transport

Abstract: The class of statistics for which previously reported renewal equations constitute an exact description of stochastic time-independent linear transport in the absence of scattering is discussed.

Alternating renewal process models for electric power system loads

Abstract: Results are derived for a class of stochastic processes called alternating renewal processes that appear particularly suitable for modeling air-conditioning loads on electrical power systems. Expressions for the Laplace transforms of the nonstationary mean and the stationary autocorrelation function are obtained. If the on-duration and off-duration random variables have gamma distributions of the particular type known as Erlang-n, then the transforms will turn out to be rational functions. Therefore, this class of air-conditioning loads can be characterized by the poles and zeros of these functions. Moreover, pole and zero locations determined empirically under quasi-equilibrium conditions can be used to predict the payback transient. How these results permit the prediction of transient behavior after an outage based on measurements taken under nominal conditions is explained. >

Vacation queues with markov schedules

Abstract: This paper identifies a probability structure for queues that belong to the class of vacation systems operating according to Markov schedules, admitting a wide variety of server scheduling disciplines including most disciplines associated with those M/GI/1/L vacation systems reported in the literature. The conditions that define these schedules are identified, and it is shown that when these conditions are satisfied, queueing behavior is governed by an underlying Markov renewal/semiregenerative structure. A simple example is examined (the M/GI/1 vacation system with limited batch service) to demonstrate the usefulness and generality of the underlying probability structure.

Regenerative inventory systems : operating characteristics

Abstract: 1 Introduction- 2 Renewal Theory Background- 3 Operating Characteristics- 4 Optimality Conditions- 5 Optimal Policies and Approximations- 6 Extensions- References- Appendix 1: Optimal Policies and Approximations for Continuous Review Systems- Appendix 2: Optimal Policies and Approximations for Periodic Review Systems

Excess-time Renewal Theory with Applications

Abstract: In this paper, the renewal theory is investigated from the point of view of the excess-time (non-excess-time) renewal intervals. Useful results are derived, and applications to several renewal models are given.

A renewal look at switching rules in the MIL-STD-105D sampling system

Abstract: A sampling system, MIL-STD-105D, used in quality control consists of three sampling plans with different acceptance probabilities used in turn for lot inspection. The decision to switch plan is based on the history of the lot acceptance records and a set of stopping rules. We derive the performance measure, average outgoing quality (AOQ), of this sampling system from a renewal process in which AOQ is expressed in terms of the moments of the stopping times. The renewal approach is simpler than that of the Markov chain generally used in computing AOQ for an infinite sequence of lots; it also provides a formula for AOQ for a finite sequence of lots.

Semimarkov walk on the composition of two renewal processes

Abstract: For a semi-Markov random walk on the composition of two renewal processes under the assumption that the positive jumps of the walk are distributed by an exponential law, an analytic expression is obtained for the generating function of the times of reaching level zero.

Markovian interval processes I: Nonparametric inference

Abstract: Consider a p-variate counting process N = (...) with jump times {...}. Suppose that the intensity of jumps ... of ... at time t depends on the other components, i. e. ..., where the ... are unknown, nonrandom functions. From observing one single trajectory of the processes N over an increasing interval of time we estimate nonparametrically the functions ... The estimators are shown to be uniformly consistent over compact sets. We derive a nonparametric asymptotic test for the hypothesis that ... does not depend on ... i. e. that ... is a renewal process. In Part II the results obtained are applied in the analysis of simultaneous neuronal spike train series.

Optimal random replacement policies for repairable systems

Abstract: For a stationary renewal process with preventive repair optimal policies of preventive repair are established within the class of age-dependent replacement policies with random repair time, provided the expected number of renewals for a fixed time period is given. Under certain conditions the distribution of the random preventive repair time is the degenerate one. Nevertheless, there exist conditions that yield optimal replacement policies with nondegenerate repair time distributions, i.e. random replacement times

Economic Theory for Urban Renewal

Abstract: To discuss urban renewal processes from an economic viewpoint requires contributions from a number of different strands of economic theory. The general demand for buildings derives from the needs of producers and consumers for urban space and their ability to pay for such space. Urban renewal comes about through action within the construction and development industries and will only occur under conditions which those industries find satisfactory or are prepared to tolerate. The urban renewal decision results from a view being taken about the economic life of existing buildings and the potential earnings or utility to be gained from a refurbished or replacement building. The value of existing and potential buildings depends upon the nature and workings of the urban land market at given points in time. Thus it is pertinent to examine in turn: the demand for construction; the supply of construction; the urban land market, the economic life of a building and the renewal decision. In this section the reasons and possibilities for state intervention in the renewal process and the economics of regeneration are also examined.

Estimating the Change in a Renewal Process When the Data are Counts

Abstract: Let X 1, …, X n be the interarrival times of a renewal process. A change-point is said to occur in this sequence if X 1, …, X τ have a common distribution F while X τ +1, … X n have distribution G, with F ≠ G. Usually τ is unknown, and must be estimated from the data. In a renewal process, it is sometimes not possible to observe the renewal times accurately. Instead, the data consist of counts of renewals in successive time intervals. This paper investigates methods of estimation of the change-point when the only data available are these counts. Examples and simulations are included.

A Multi-type Critical Emigration Branching Process

Abstract: A multi-type age-dependent Bellman-Harris process is defined such that each cell is subject to emigration in accord with a simple renewal process, independent of other cells, with the renewal process depending only on its type. This age-dependent emigration process may be made to act similar to a critical multi-type Bellman-Harris branching process. Limit theorems analogous to those for critical multi-type Bellman-Harris processes are given. A multi-type critical emigration-immigration model is also considered.