journal article
LitStream Collection
Home
Johnson, Mary A.; Luhman, Jennifer A.
1994 Applied Stochastic Models and Data Analysis
We investigate moment–based queueing approximations in the presence of sampling error. Let L be the steady–state mean number in the system for a GI/M/1 queue. We focus on the estimation of L under the assumption that only sample moments of the interarrival–time distribution are known. A simulation experiment is carried out for several interarrival–time distributions. For each case, sample moments from the interarrival–time distribution are matched to an approximating phase–type distribution and the corresponding estimate L is obtained. We show that the sampling error in the moments induces bias as well as variability in L. Based on our simulation experiment, we suggest matching only two moments when the sample coefficient of variation is low or when sample size is low; otherwise, matching three moments is preferable.
1994 Applied Stochastic Models and Data Analysis
A sub–class of phase–type distributions is defined in terms of a Markov process with sequential transitions between transient states and transitions from these states to absorption. Such distributions form a very rich class; they can be fitted to data, and any structure revealed by the parameter estimates used to develop more parsimonious re–parametrizations. Several example data sets are used as illustrations.
Dohi, Tadashi; Kitaoka, Eiichi; Osaki, Shunji
1994 Applied Stochastic Models and Data Analysis
This paper proposes two types of alternative criteria of optimality for the continuous time portfolio selection problem. The optimality criteria, the so–called Laplace–Stieltjes transform (LST) criteria, are based on the assumption that the financial agent has a target level for the wealth accumulation process. These criteria are closely related to the so–called threshold stopping investment rule. We analytically derive the LST criteria and numerically compare them with the well–known Kelly criterion. It is shown that the portfolio strategies suggested may overcome the problem that the growth portfolio is often overestimated in several investment situations.
1994 Applied Stochastic Models and Data Analysis
The problem of periodicity for a non–homogeneous Markov model in a stochastic environment is studied. The stochastic concept is established through the notion of optional scenarios applied on the transition process. It is proved that the sequence of so–called aggregate structures follows a certain periodic pattern that can split into converging subsequences according to alternative policies. These limits are highly influenced by the different scenarios utilized in the model, but always lie on a convex region that also depends on the pool of alternatives.
1994 Applied Stochastic Models and Data Analysis
Consider a repairable system at the time instants t and t + x, where t, x ≥0. The joint availability of the system at these time instants is defined as the probability of the system being functional in both t and t + x. A set of integral equations is derived for the joint availability of a system modelled by a finite semi–Markov process. The result is applied to the semi–Markov model of a two–unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two–point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results obtained by this method are shown to be in good agreement with those from simulation.
Showing 1 to 10 of 14 Articles