Showing papers on "Renewal theory published in 1975"

On Approximate Computer System Models

Abstract: A new treatment of the boundary conditions of diffusion approximations for interconnected queueing systems is presented. The results have applications to the study of the performance of multiple-resource computer systems. In this approximation method, additional equations to represent the behavior of the queues when they are empty are introduced. This reduces the dependence of the model on heavy traffic assumptions and yields certain results which would be expected from queueing or renewal theory. The accuracy of the approach is evaluated by comparison with certain known exact or numerical results.

Exceptional Paper---Markov Renewal Theory: A Survey

Abstract: The objective is to survey the major results and applications in an informal setting. The exposition is restricted to finite state spaces; some real problems are modelled and the lines of attack are indicated; and an extensive bibliography is provided to get a further glimpse of the variety of applications. Throughout, the parallels with renewal theory are brought out, and the unity of thought afforded by the formalism of Markov renewal equations is stressed.

Nonlinear Analysis of Correlative Tracking Systems Using Renewal Process Theory

Abstract: A new method is presented which describes the behavior of an (N + 1) th-order tacking system in which the nonlinearity is either periodic [phase-locked loop (PLL) type] or a nonperiodic [delay-locked loop (DLL) type]. The cycle slipping of such systems is modeled by means of renewal Markov processes. A fundamental relation between the probability density function (pdf) of the single process and the renewal process is derived which holds in the transient as well as in the stationary state. Based on this relation it is shown that the stationary pdf, the mean time between two cycle slips, and the average number of cycles to the right (left) can be obtained by solving a single Fokker-Planck equation of the renewal process. The method is applied to the special case of a PLL and compared with the so-called periodic-extension (PE) approach. It is shown that the pdf obtained via the renewal-process approach can be reduced to agree with the PE solution for the first-order loop in the steady state only. The reasoning and its implications are discussed. In fact, it is shown that the approach based upon renewal-process theory yields more information about the system's behavior than does the PE solution.

Nonlinear analysis of correlative tracking systems using renewal process theory

Abstract: A new method is presented which describes the behavior of an (N + 1) th-order tacking system in which the nonlinearity is either periodic [phase-locked loop (PLL) type] or a nonperiodic [delay-locked loop (DLL) type]. The cycle slipping of such systems is modeled by means of renewal Markov processes. A fundamental relation between the probability density function (pdf) of the single process and the renewal process is derived which holds in the transient as well as in the stationary state. Based on this relation it is shown that the stationary pdf, the mean time between two cycle slips, and the average number of cycles to the right (left) can be obtained by solving a single Fokker-Planck equation of the renewal process. The method is applied to the special case of a PLL and compared with the so-called periodic-extension (PE) approach. It is shown that the pdf obtained via the renewal-process approach can be reduced to agree with the PE solution for the first-order loop in the steady state only. The reasoning and its implications are discussed. In fact, it is shown that the approach based upon renewal-process theory yields more information about the system's behavior than does the PE solution.

A branching process with disasters

Abstract: A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.

Simulating Stable Stochastic Systems, IV: Approximation Techniques

Abstract: The previous papers in this series developed a methodology for obtaining from certain simulations confidence intervals for parameters associated with the steady-state distribution. This methodology required the simulations to contain an embedded renewal process at whose epochs the simulation started from scratch. The present paper contains four approximation techniques for obtaining confidence intervals when the simulation does not contain the required renewal process.

An interaction model of a poisson and a renewal process related to neuron firing

Abstract: This paper discusses a neuronal model based on a model of Coleman and Gastwirth (1969). It is assumed that the excitatory input forms a Poisson process while the inhibitory input forms a stationary renewal process. The proposed interaction scheme is as follows: an inhibitor deletes at most N consecutive excitatory inputs and a response only occurs after the cummalative storage of M excitatory inputs. The Laplace transform of the probability density function (p.d.f.) of the inter-response intervals is derived together with results of the numerical inversions.

Recurrence times of draft-patterns from reservoirs

Abstract: Expressions for the mean and variance of the recurrence time of nonoverlapping draft-patterns of draft from a Moran Reservoir Model (discretestate and discrete-time Markov chain) are derived using Feller's Renewal argument. In addition an expression for the mean recurrence time for selfoverlapping patterns of draft is derived using run-theory. RENEWAL THEORY; RUNS; MARKOV CHAIN; MORAN RESERVOIR

Basic analysis of a head-of-the-line priority queue with renewal type input

Abstract: A single server is fed by a renewal stream of individual customers. These are of type k with probability πk, k = 1, …, N, and are all served individually. Upon completion of a service the server proceeds immediately with a customer of the lowest type (= highest priority) present, if any. Service times for type k are drawn from a general distribution function Bk (t) concentrated on (0, ∞). We lay the foundations for a broad analysis of the model.

On a Terminating Renewal Process with Reliability Applications

Abstract: An alternating renewal process is considered which has four random variables; the process terminates when a specified event happens. It is shown with several examples that the results are of great use in reliability theory.