Knowledge that Transforms

The manner in which vehicles follow each other on a highway (without passing) and the propagation disturbances down a line of vehicles has been investigated. Experimental data is presented which indicates that the acceleration at time t of a car which is attempting to follow a leader is proportional to the difference in velocity of the two cars at a time (t − Δ), Δ being about 1.5 sec and the proportionality constant being about 0.37 sec−1. It is shown theoretically that the motion of a long line of vehicles becomes unstable when the product of the lag time and the proportionality constant exceeds one-half. The experimental data implies that driving is done on the verge of instability. A variety of other laws of following is analyzed theoretically.

A network, in which two integers tıj (the traversal time) and cıj (the capacity) are associated with each arc PıPj, is considered with respect to the following question. What is the maximal amount of goods that can be transported from one node to another in a given number T of time periods, and how does one ship in order to achieve this maximum? A computationally efficient algorithm for solving this dynamic linear-programming problem is presented. The algorithm has the following features (a) The only arithmetic operations required are addition and subtraction (b) In solving for a given time period T, optimal solutions for all lesser time periods are a by-product (c) The constructed optimal solution for a given T is presented as a relatively small number of activities (chain-flows) which are repeated over and over until the end of the T periods. Hence, in particular, hold-overs at intermediate nodes are not required (d) Arcs which serve as bottlenecks for the flow are singled out, as well as the time periods in which they act as such (e) In solving the problem for successive values of T, stabilization on a set of chain-flows (see (c) above) eventually occurs, and an a priori bound on when stabilization occurs can be established. The fact that there exist solutions to this problem which have the simple form described in (c) is remarkable, since other dynamic linear-programming problems that have been studied do not enjoy this property.

The traveling-salesman problem is a generalized form of the simple problem to find the smallest closed loop that connects a number of points in a plane. Efforts in the past to find an efficient method for solving it have met with only partial success. The present paper describes a method of solution that has the following properties (a) It is applicable to both symmetric and asymmetric problems with random elements (b) It does not use subjective decisions, so that it can be completely mechanized (c) It is appreciably faster than any other method proposed (d) It can be terminated at any point where the solution obtained so far is deemed sufficiently accurate.

This paper is concerned with a target assignment model of a probabilistic and nonlinear nature, but nevertheless one which is closely related to the “personnel-assignment” problem. It is shown here that, despite the apparent nonlinearities, it is possible to devise a linear programming formulation that will ordinarily provide a close approximation to the original problem.