A theoretical analysis of congestion in a two-lane freeway

1970 ◽  
Vol 7 (02) ◽  
pp. 304-315
Author(s):  
Donald R. Mcneil
Keyword(s):  
Theoretical Analysis ◽  
Statistical Mechanics ◽  
Mathematical Theory ◽  
Road Traffic ◽  
Unified Theory ◽  
Conservation Of Mass ◽  
Limited Class

To current workers in the mathematical theory of road traffic, one of the most challenging and important problems is to describe and analyze the congestion suffered by motorists on freeways. While there is, as yet, no satisfactory unified theory, several different models have been suggested, each of which is reasonable for a limited class of situations. These approaches fall largely into two categories. The first may be described as looking at traffic “in the large” and its principal exponents were Lighthill and Whitham (1955) and Prigogine (1961). The theory of Lighthill and Whitham involves treating the system of vehicles as a fluid subject to a rule of conservation of mass (that is, vehicles) and an assumed relation between the flow and concentration at each point. This theory is completely deterministic. Prigogine's approach is to regard the system of vehicles as behaving like the particles in a gas and subject to the laws of statistical mechanics.

A theoretical analysis of congestion in a two-lane freeway

1970 ◽  
Vol 7 (2) ◽  
pp. 304-315
Author(s):  
Donald R. Mcneil
Keyword(s):  
Theoretical Analysis ◽  
Statistical Mechanics ◽  
Mathematical Theory ◽  
Road Traffic ◽  
Unified Theory ◽  
Conservation Of Mass ◽  
Limited Class

To current workers in the mathematical theory of road traffic, one of the most challenging and important problems is to describe and analyze the congestion suffered by motorists on freeways. While there is, as yet, no satisfactory unified theory, several different models have been suggested, each of which is reasonable for a limited class of situations. These approaches fall largely into two categories. The first may be described as looking at traffic “in the large” and its principal exponents were Lighthill and Whitham (1955) and Prigogine (1961). The theory of Lighthill and Whitham involves treating the system of vehicles as a fluid subject to a rule of conservation of mass (that is, vehicles) and an assumed relation between the flow and concentration at each point. This theory is completely deterministic. Prigogine's approach is to regard the system of vehicles as behaving like the particles in a gas and subject to the laws of statistical mechanics.

Diffusion approximations and models for certain congestion problems

1968 ◽  
Vol 5 (03) ◽  
pp. 607-623 ◽  
Author(s):  
D. P. Gaver
Keyword(s):  
Mathematical Theory ◽  
Review Paper ◽  
Diffusion Processes ◽  
Road Traffic ◽  
Diffusion Theory ◽  
Heavy Traffic ◽  
Integral Transforms ◽  
Diffusion Approximations ◽  
Discrete State ◽  
Traffic Theory

In a variety of the congestion or queueing problems that arise in practice, for example, in studies of the crossing and entry problems of road traffic, (see Evans, Herman, and Weiss [2]), and recently of the service afforded by large centralized and shared computer facilities, (see Scherr [12]), the understanding of system performance furnished by the present mathematical theory is inadequate. The reason is that while the consideration of simple problems typically yields elegant mathematical results, the form of these results—often expressed in terms of integral transforms—is not immediately comprehensible nor useful for simple comparisons. This fact has been remarked upon by Newell, who in [9] has suggested certain more comprehensible but approximate approaches based on diffusion theory; further promising developments and elaborations will be found in [10]. The latter approach is related to the “heavy traffic theory” of J. F. C. Kingman [8], and to some recent work of Iglehart [6]. Of course, the idea of approximating complex discrete-state processes by diffusion processes with continuous paths is not new. It has long been used in genetics, see Feller [3], and the review paper by Kimura [7]. Nonetheless, applications to congestion theory are apparently still rather rare.

scholarly journals The quest for a unified theory on biomechanical palm risk assessment through theoretical analysis and observation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Peter Sterken
Keyword(s):  
Mathematical Model ◽  
Risk Assessment ◽  
Wind Speed ◽  
Theoretical Analysis ◽  
Mechanical Behaviour ◽  
Beam Theory ◽  
Wind Loading ◽  
Unified Theory ◽  
Simple Mathematical Model ◽  
Wide Range

AbstractSeveral methodologies related to the biomechanical risk assessment and the uprooting and breaking potential of palms are reviewed and evaluated in this study. Also a simple mathematical model was designed, to simulate the results of critical wind speed predictions for a tall coconut palm by using classic beam theory and Brazier buckling. First, the review presents arguments that assess the applicability of some influential claims and tree and palm risk assessment methods that have been amply marketed in the last 20 years. Then, the analysis goes beyond the classical procedures and theories that have influenced the arboricultural industry and related press so far. And afterwards, rationale behind several postulated ideas are presented, that are hoped to be fruitful in the path towards a new biomechanical theory for the biomechanical risk assessment of palms. The postulated model envisages the palm stem as a viscoelastic and hollow cylinder that is not only prone to buckling, ovalization and kinking, but also fatigue, shear, splitting and crack propagation. This envisaging was also the main reason why simple Brazier buckling formulation was experimentally applied to simulate the breaking risk of a cocostem. This study also enables a better understanding of the wide range of factors that may influence the mechanical behaviour of trees and palms under (wind) loading.

Turnover and Tenure in the Canadian House of Commons, 1867–1968

1970 ◽  
Vol 3 (4) ◽  
pp. 655-661 ◽  
Author(s):  
Thomas W. Casstevens ◽  
William A. Denham
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Mathematical Theory ◽  
Predictive Power ◽  
Present Model ◽  
General Election ◽  
House Of Commons ◽  
Quantitative Studies ◽  
Continuous Service ◽  
The Mean

This article presents a theoretical analysis of the turnover and tenure of the members of the Canadian House of Commons from 1867 through 1968. Previous studies of such turnover and tenure have been quantitative, but not theoretical, yielding precise measurements but no pattern. A statistical résumé is no substitute for a mathematical model. Both may be accurate, parsimonious, and elegant; but a mathematical theory is distinguished by its generality and its explanatory or predictive power. With the present model, for example, the members’ median and mean continuous service can be logically derived from the mathematical theory; but the converse is not true, that is, the mathematical theory cannot be deduced from the median and/or mean continuous service. Specifically, the theory implies that the median continuous service is approximately 0.693 times the mean continuous service. Despite a plethora of quantitative studies of legislative turnover and tenure, this equation (so far as we know) has not previously been discovered.The process to be modeled can be abstractly characterized as follows: Consider the members of the House of Commons after some particular (zero) general election. These legislators are called theoriginal members, for expository convenience. With the occurrence of deaths, resignations, political defeats, etc., only some of the original members will continue to be members of the House of Commons after the next (first) general election. These survivors are called there-elected members.

Diffusion approximations and models for certain congestion problems

1968 ◽  
Vol 5 (3) ◽  
pp. 607-623 ◽  
Author(s):  
D. P. Gaver
Keyword(s):  
Mathematical Theory ◽  
Review Paper ◽  
Diffusion Processes ◽  
Road Traffic ◽  
Diffusion Theory ◽  
Heavy Traffic ◽  
Integral Transforms ◽  
Diffusion Approximations ◽  
Discrete State ◽  
Traffic Theory

In a variety of the congestion or queueing problems that arise in practice, for example, in studies of the crossing and entry problems of road traffic, (see Evans, Herman, and Weiss [2]), and recently of the service afforded by large centralized and shared computer facilities, (see Scherr [12]), the understanding of system performance furnished by the present mathematical theory is inadequate. The reason is that while the consideration of simple problems typically yields elegant mathematical results, the form of these results—often expressed in terms of integral transforms—is not immediately comprehensible nor useful for simple comparisons. This fact has been remarked upon by Newell, who in [9] has suggested certain more comprehensible but approximate approaches based on diffusion theory; further promising developments and elaborations will be found in [10]. The latter approach is related to the “heavy traffic theory” of J. F. C. Kingman [8], and to some recent work of Iglehart [6]. Of course, the idea of approximating complex discrete-state processes by diffusion processes with continuous paths is not new. It has long been used in genetics, see Feller [3], and the review paper by Kimura [7]. Nonetheless, applications to congestion theory are apparently still rather rare.

scholarly journals The essence of road safety in Poland. Recognition of theoretical and empirical

Securitologia ◽  
2016 ◽  
Vol 23 (1) ◽  
pp. 15-31
Author(s):  
Jarosław W. Przybytniowski ◽  
Wioletta M. Pacholarz
Keyword(s):  
Theoretical Analysis ◽  
21St Century ◽  
Road Safety ◽  
Road Traffic ◽  
Road Accidents ◽  
Prevention Measures ◽  
Financial Instrument ◽  
Eu Countries ◽  
Ongoing Development

This article consists of two parts. The first part is based on the theoretical analysis of the concept of safety and prevention measures in road traffic, described in the existing literature and statistics. Whereas the second part focuses on the analysis of vehicle insurance as a financial instrument of economic safety of road traffic participants. In the 21st century, one of very important problems, not only socially but also economically, referring to Poland and other EU countries is the ongoing development of motorisation and, consequently, the progress in transportation. Unfortunately, this development sometimes leads to the growing number of road accidents and their effects.

scholarly journals THEORETICAL ANALYSIS OF DYNAMIC RESPONSE OF A BRIDGE SECTION LOADING BY THE IMPULSIVE FORCE

2017 ◽  
Vol 18 (2) ◽  
Author(s):  
ADRIAN LEOPA
Keyword(s):  
Dynamic Response ◽  
Seismic Design ◽  
Mathematical Theory ◽  
Structural Integrity ◽  
Road Traffic ◽  
Physical Models ◽  
General Nature ◽  
Impulsive Force ◽  
Dynamic Insulation ◽  
Bridge Structures

<p>The work in seismic design of bridges is needed to develop physical models and mathematical theory, based on which will be assessed and quantified the dynamic response of bridge structures subjected to stress arising from road traffic or seismic activity.</p><p>The need for this modeling is imposed three requirements: to ensure the structural integrity of the bridge elements for subjected impulsive, proper choice of dynamic insulation elements placed as a interface between the superstructure and infrastructure, as well as analysis of effects on joints in these situations demand. This paper proposes a physical model of a general nature, enabling customization depending on the specific constructive bridge, or the way it is solicited. Customize this model was developed for this study based on the existing viaduct Transylvania highway located between km 29 +602.75 and km 29 +801.25.</p>

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