Optimal Flow Pattern Research Articles

OPTIMIZATION OF SOLVENT FLOW PATTERN FOR EXTRACTIVE REACTORS IN SERIES

The optimal solvent flow pattern for multistage reactors with extraction is investigated. The general structure is considered by introducing structure variables and is optimized by use of the method of Goldfarb et al. Numerical calculations are carried out for parameter values tentatively chosen. The results indicate some basic features of the optimal solvent flow pattern. Some qualitative considerations suggest that these features will probably be the general properties of the optimal pattern.

Flow Dependent Traffic Assignment on a Circular City

Consider a circular central business district of a city with n evenly spaced radial streets and m circular streets. We assume that during the evening rush hour driver origins are all inside the city and exits at the circumference with a joint distribution that depends only upon the relative angle between original and final radii, and the radial coordinate of the origin. Travel time on any directed link is assumed to be a function of the flow along that directed link and the radial coordinate of the link. For a flow of Q vehicles per hour leaving the city, our problem is to find an assignment of drivers to paths such that every driver follows a path of minimum travel time between his origin and exit. This extends some work of Smeed who considers a similar model with no flow dependence of the travel time and a uniform distribution of origins. It is first shown that this circularly symmetric system gives rise to a circularly symmetric optimal flow pattern. This flow pattern can be generated by assigning each driver to a path that uses at most one of the circular streets. Eventually the assignment is expressed explicitly as a function of 2(m − 1) unknown parameters that satisfy a system of equations and/or inequalities. The general solution of these equations were not found, but solutions were obtained for a number of special cases that showed the effect of congestion at the center and the effect of a belt expressway. Differential equations were also obtained for n → ∞ and m → ∞.

Analytical Methods in Transportation: Systems Analysis for Arterial Street Operation

An application is presented of a linear-programming model, the multicopy mixing model developed by Charnes and Cooper, to the problem of arterial street system analysis, and an example demonstrates how the use of the model provides a simulation of traffic flow over a street network containing branches or links with capacity constraints. The example presents a specific use of the technique, that of holding the freeway volume at or below a fixed amount and developing the resulting optimum flow pattern in the system. It is shown how the results of the simulation can be used as a guide for determining what control measures, such as one way street routings, or freeway ramp closures, should be used to get optimum use of the street system. The paper also illustrates how the nonlinear travel time-volume curve (delay curve) can be piece-wise, linearly approximated and included in the traffic assignment procedure in order to closely simulate actual traffic behavior in a street network.