Moshe A. Pollatschek

A DECISION MODEL FOR GAP ACCEPTANCE AND CAPACITY AT INTERSECTIONS

The purpose of this paper is to present a microscopic decision model for driver gap-acceptance behavior when waiting at an unsignalized intersection on the secondary road and also to estimate the resulting intersection capacity. The model is based on evaluation of the risk associated with not accepting small gaps against the potential benefit of their acceptance, which is the time saved as a result of shorter waits at the entry line. The model takes into account individual preferences by defining individual critical gap, which is different from the traditional macroscopic critical-gap approach. The latter estimates the critical gap for the entire population of drivers. The paper presents the difference between different driver populations (risk-loving vs. cautious) and shows how this difference actually results in different capacities on the minor road.

Duality theorems for certain programs involving minimum or maximum operations

The relation of two mathematical programs—the so-called primal, (P) and dual, (D)—Are studied when (P) is a maximization of the minimum of two functions and (D) is the minimization of the maximum of two functions, and the function-pair of (D) are derived by certain, conjugate-like operators from that of (P). It is demonstrated that the weak duality holds when at least one of the pair is continuous. When further premises are met the strong duality is proved. From these results the usual Fenchel-duality may be deducted as well as few other primal-dual pairs.

Impact of Infrastructure Characteristics on Road Crashes on Two-Lane Highways

Objective. The main purpose of this study is to estimate and quantify the contribution of the infrastructure to highway crashes and to develop an infrastructure coefficient, that represents the overall characteristics of the highway and could be used as an independent variable in a crash-prediction model. Methods. The infrastructure is defined in this study as the highway and its geometric features, including alignment, road-side elements, sight-distances, presence of guardrails, access-points, roadway consistency, and additional variables that measure the overall quality of the highway alignment and elements. The analysis and developments are conducted for two-lane rural highways. The approach taken is to identify the high crash-rate roads, those with crash rates above 0.25 crashes per million vehicle-km, by Smallest Space Analysis. This type of analysis allows the aggregation of higher crash-rate roads versus lower-crash-rate roads only by their infrastructure coefficients, without consideration of their crash records. Results. Crash rates that are attached by Smallest Space Analysis to the group of roads that had less desirable infrastructure features show a high correlation between the same roads and high crash rates vs. identified better infrastructures and low crash rates. Further analysis shows that low crash-rate infrastructure, as defined in this study for two-lane rural highways, can reduce the crash rate by 44% versus high crash-rate infrastructure, at the 99% confidence level, which is almost a certainty. A model for the prediction of crash rates based on a proposed infrastructure coefficient is calibrated and presented. Conclusions. It is suggested that this model be used in evaluating alternatives for new highways or in improving the alignment and road features of existing highways.

Further results on fuzzy-mathematical programming

Theorems concerning fuzzy mathematical programs, formulated by Bellman and Zadeh, are derived. Existence of solutions, properties of solution-sets and relations between different programs, studied also by Tanaka et al., are discussed without any assumptions.

Layout simulation for keyboards

Abstract The oldest element on any personal computer is the keyboard: its design lthe spatial position of the keys in relation to each otherr and its layout lthe assignment of letters, numerals, and other signs to keysr. The are exactly the same as on the first typewriters of over 100 years ago or are theyq The layout has been the topic of improvement for more than 70 years but no real change has materialized. We contribute to the efforts of layout reformers in Pollatschek et al. l1986r. In this paper, we introduce a simple simulation tool for evaluating layout, while in an accompanying communication we advise on a cheap and effective way to convert any given layout to any desired one.

The customizable keyboard

Abstract The need for deviations from the widely accepted QWERTY keyboard layout of usual office typewriters or workstations has been discussed in our twin paper lGilad et al. 1986r. In this paper we examine a related issue: How to customize any keyboard to a given application, cheaply and effectively. We here discuss this issue and establish why such customization is necessary and how modern technology and keyboard design solve half the problem.

Option values, stipends and the returns to educational investment☆

Abstract In this paper we use a dynamic model of the returns to educational investment to analyze the flow of students moving through the various stages of an educational system. Dropout and graduation rate are linked to the profitability of an educational stage and thus may be influenced by an appropriate choice of stipend level. To determine the effects of changes in stipends on the output of the educational system we hypothesize a probability distribution of abilities in the population. The parameters of this distribution permit the estimation of the effects of stipends on the graduation rate of each educational stage.

AN OPTIMAL SCREENING POLICY FOR R & D PROJECTS

Publisher Summary This chapter presents a method suitable for the purpose of screening a large volume of research and development (R&D) projects. To accomplish this objective, a method is developed that uses stage approach for project screening. The proposed procedure is applicable to a company, or a government agency, which faces the problem of screening a large number of projects. In principle, this method is also suitable for other screening problems, such as screening load applications, candidates for a job, etc. Usually, the screening process involves two types of policy decision: selection policy and budget policy. The focus is on the selection problem. A systematic screening formula is developed that is based on sequential analysis. In the model, the R&D process is viewed as consisting of a number of stages. After each stage, the projects are examined and a decision is made on whether to continue or discontinue their development.

On stochastic integer programming

SummaryThe probability distribution of the optimum (Z) of an integer linear program is discussed in which the elements of the right-hand-side (RHS) are distributed independently. The assumptions of the asymptotic algorithm ofGomory are supposed to hold for each realization of the RHS. This algorithm serves also as the theoretic framework of the present communication. Bounds and approximations for the probability function of Z are derived demanding different levels of numerical efforts. The normal distribution is a satisfactory approximation which is asymptotically correct if the elements of the RHS are uniformly distributed within bounds satisfying some requirements and the number of inequalities approaches infinity.ZusammenfassungIm vorliegenden Aufsatz wird die Verteilung des optimalen Wertes Z der Zielfunktion von ganzzahligen linearen Programmen diskutiert, bei denen die Elemente der rechten Seite voneinander unabhängig verteilt sind. Hierbei wird unterstellt, daß die Annahmen, die beim asymptotischen Algorithmus vonGomory gemacht werden, für jede Realisation der rechten Seite Gültigkeit besitzen. Der soeben erwähnte asymptotische Algorithmus dient weiterhin als Rahmen für die weiteren Darstellungen.Im folgenden werden für die Verteilungsfunktion von Z Schranken und Approximationen vorgeschlagen, deren Ermittlung unterschiedlich rechenaufwendig ist. Es wird gezeigt, daß die Normalverteilung dann eine annehmbare Approximation darstellt, wenn die Elemente der rechten Seite in bestimmten Grenzen gleichverteilt sind, und wenn die Zahl der Nebenbedingungen nach Unendlich strebt.