Solution Of Such Models Research Articles

Interactions between Weather Stochasticity and the Locations of Pollution Sources and Receptors in Air Quality Planning: A Chance‐Constrained Approach

Optimization models for the design of regional air quality control strategies have been developed under the assumption that the annual frequencies of the different meteorological conditions remain constant from year to year. This paper demonstrates empirically that this assumption is not correct, and that the solutions of such models lead either to violation of the annual air quality standard or to unnecessarily high costs for pollution abatement. A chance‐constrained, geographically based approach is formulated to account for the interannual randomness of the meteorological conditions and for the locations of pollution sources and receptors and is applied with different approximation methods. The policy implications of the results in terms of optimal standard selection and implementation of the optimal chance‐constrained pollution abatement plan through decentralized decision‐making by individual pollution sources are assessed.

Efficient approximation for models of multiprogramming with shared domains

Queueing network models of multiprogramming systems with memory constraints and multiple classes of jobs are important in representing large commercial computer systems. Typically, an exact analytical solution of such models is unavailable, and, given the size of their state space, the solution of models of this type is approached through simulation and/or approximation techniques. Recently, a computationally efficient iterative technique has been proposed by Brandwajn, Lazowska and Zahorjan for models of systems in which each job is subject to a separate memory constraint, i.e., has its own memory domain. In some important applications, it is not unusual, however, to have several jobs of different classes share a single memory “domain” (e.g., IBM's Information Management System). We present a simple approximate solution to the shared domain problem. The approach is inspired by the recently proposed technique which is complemented by a few approximations to preserve the conceptual simplicity and computational efficiency of this technique. The accuracy of the results is generally in fair agreement with simulation.

The Fermion Approach to the Commensurate-Incommensurate System

The Schultz-Halperin-Henley model for an assembly of adsorbed atoms on an anisotropic rectangular lattice is considered. The Kosterlitz-Thouless dislocations are neglected. A rigorous solution of such model is presented by revising the free Fermion approach into an exact formalism. A complete phase diagram of this model is given. A new phase is found. The critical exponents are obtained. It is found that the particle-hole symmetry does not hold in the exact prediction. Finally an approach to a more extensive model including the KT dislocations is briefly presented.

UIMP: User Interface for Mathematical Programming

UIMP is a matrix-generator report-writer system designed to aid the reahzation (generation) of mathematical programming models and also the analysis-reporting of the solutions of such models The data-structure facility of the system allows the underlying structure of a user model to be captured and helps to define such models This data-structure feature is not only a powerful modeling aid, it also finds use in the analysis of solutions and report generation The experience of using the system, its shortcomings, and possible extensions are also discussed.

Rational Expectations in Stationary Linear Models

Linear time series models have come to dominate the macroeconomic literature on rational expectations and equilibrium business cycle theory. But the explicit solution of such models has generally required strong restrictions upon the exogenous process of stochastic shocks (e.g., temporal independence) as well as upon the values of various demand and supply elasticities. This paper exhibits a solution technique, the method of z-transforms, which does not require one to impose such restrictions. The value of this method is illustrated by applying it to completely characterize the symmetric, stationary, rational expectations equilibria of a naive linear model of land speculation. This approach also permits systematic study of the informationally asymmetric equilibria of the model. THIS PAPER develops a method for analyzing rational expectations (RE) equilibria in linear economic models. The methods I shall discuss usually enable one to determine whether or not a given model has a RE equilibrium and, if one exists, to exhibit an explicit expression for the stochastic process of equilibrium prices. The techniques apply to linear models driven by stationary processes of exogenous random shocks.

Periodic solutions of some ecological models

A result is given on the existence of an asymptotically stable periodic solution of a class of systems of periodic ordinary differential equations. The result is applied to a lake eutrophication model with seasonal effects, and some suggestions are made for the solution of such models.