Comparison of Tolling Strategies for Highway 407 in the Greater Toronto Area

1997 ◽  
Vol 1576 (1) ◽  
pp. 28-36 ◽  
Author(s):  
Ali Mekky
Keyword(s):  
Mathematical Model ◽  
North America ◽  
Urban Areas ◽  
Evaluation Process ◽  
Greater Toronto Area ◽  
Points Of View ◽  
Entrance Ramps ◽  
The Mathematical Model

Tolling strategies recently tested for Highway 407 in the Greater Toronto Area (GTA) are described and analyzed. The GTA is one of the fastest-growing urban areas in North America, with a population of about 5 million. Highway 407, a six-/four-lane freeway in the GTA, has been considered for many years as a relief for Highway 401. It is the busiest highway in North America and is used by more than 1 million vehicles per day. Highway 407 is being planned and constructed as a toll highway. Four strategies are compared. In the base strategy, the toll rate per kilometer is fixed and the value of the toll paid depends on the distance traveled on the highway. In Strategy 2, vehicles on Highway 407 are tolled on the entrance ramps as well as at some points on the highway (main “virtual” plazas). In Strategies 3 and 4, each driver has two choices. The first is to pay a toll depending on the distance traveled. The second is to pay a certain fixed toll once the driver crosses certain points on the highway (mainline plazas) and on the exit ramps. The strategies are compared from the points of view of the number of users, the vehicle-kilometers on the highway, the revenues, and the average toll paid. The GTA mathematical model, within the EMME/2 environment, is used. The mathematical model and the evaluation process are described.

Evaluation of Two Tolling Strategies for Highway 407 in Toronto

1998 ◽  
Vol 1649 (1) ◽  
pp. 17-25 ◽  
Author(s):  
Ali Mekky
Keyword(s):  
Mathematical Model ◽  
North America ◽  
Urban Areas ◽  
Evaluation Process ◽  
Long Distance ◽  
Greater Toronto Area ◽  
The Cost ◽  
Generalized Cost ◽  
Near Highway

Two tolling strategies were recently suggested for Highway 407 in the Greater Toronto Area (GTA). The GTA is one of the fastest growing urban areas in North America with a population of about 5 million. Highway 407, a six-/four-lane freeway, has been considered for many years as a relief for Highway 401—the busiest highway in North America, used by more than a million vehicles per day. Highway 407 is being planned and constructed as a toll highway. The first strategy investigated is to encourage long distance travelers to use Highway 407 by reducing the toll rate from CD$0.075/km to $0.06/km after the first 10 km. This is modeled by using multiclass trip assignment with generalized cost. Aside from the class of drivers who are not going to use the highway for various personal reasons, there are two main classes of drivers—namely, drivers who travel 10 km or more, and those who travel less than 10 km. The second strategy investigated is to put extra tolls on Highway 407 ramps connecting the highway with widened Highways 427, 400, and 404. The purpose of the second strategy is to recover the cost of widening these highways near Highway 407 through ramp toll revenues. The GTA mathematical model, within the EMME/2 environment, and the evaluation process used are described. Evaluation results are discussed.

Modeling Toll Pricing Strategies in Greater Toronto Area

1996 ◽  
Vol 1558 (1) ◽  
pp. 46-54 ◽  
Author(s):  
Ali Mekky
Keyword(s):  
Mathematical Model ◽  
North America ◽  
Evaluation Process ◽  
Feedback Loops ◽  
Pricing Strategies ◽  
Greater Toronto Area ◽  
Toll Pricing ◽  
Net Revenue ◽  
Generalized Cost ◽  
The Mathematical Model

Highway 407 (a four- to six-lane freeway), in the Greater Toronto Area (GTA) (with a population of 5 million) has been considered for many years as a relief for Highway 401, the busiest highway in North America. Highway 407 is being planned as a toll highway. Ideally, the driver of each car should have a transponder in the car to identify the vehicle for electronic toll billing purposes. The value of the toll (variable toll) would depend on the number of kilometers traveled on the highway. However, to attract some of the drivers who do not want their origins and destinations to be tracked, a fixed-toll option might be available. A study was developed to estimate the changes in the travel and the revenue of Highway 407 if a fixed-toll option were allowed simultaneously with a variable one. The GTA mathematical model, within the EMME/2 environment, was used. Although the available transportation planning packages were not originally designed for evaluating these kinds of toll strategies, it is possible to do the evaluation using several multiclass generalized cost assignment runs with feedback loops. The mathematical model and the evaluation process used are described. One of the results of the evaluation is the finding that allowing fixed-toll operation does not increase the number of users of Highway 407 (operating under a variable toll scheme) but will increase the revenues in a marginal way. Therefore, it is concluded that using only a variable toll rate would maximize the net revenue for the year under consideration.

scholarly journals MODELLING AND SIMULATION OF DISPERSIONS OF POWDER EMISSIONS FROM MULTIPLE SOURCES WITH THE MATHEMATICAL MODEL POL 15SM

2014 ◽  
Vol 22 (2) ◽  
pp. 151-160
Author(s):  
Mihaela Budianu ◽  
Valeriu Nagacevschi ◽  
Matei Macoveanu
Keyword(s):  
Mathematical Model ◽  
Air Pollution ◽  
Urban Areas ◽  
Point Sources ◽  
Multiple Point ◽  
Multiple Sources ◽  
Economic Agents ◽  
Sources Of Pollution ◽  
Simulation Based ◽  
The Mathematical Model

Over the last decades, air pollution has become one of the greatest challenges negatively affecting human health and the entire environment, including air, water, soil, vegetation, and urban areas. Lately, special attention has been given to mathematical modelling for diffusion of pollutants in the atmosphere as a particularly effective and efficient method that can be used to study, control and reduce air pollution. The diversity of models developed by different research groups imposed a rigorous understanding of model types in order to apply them correctly according to local or regional problems of air pollution phenomenon. Tus the authors have developed and improved two mathematical models for dispersion of air pollutants. Tis paper presents a case study of dispersion of powders in suspension originating from 14 point sources that correspond to 5 economic agents in the agroindustrial area of Vaslui city using a computer simulation based on the mathematical model Pol 15sm, for multiple point sources of pollution, designed by the authors.

scholarly journals ABOUT METHODS OF THE SUBSTANTIATION OF AN ALLOWABLE RISK LEVEL

2000 ◽  
Vol 6 (1) ◽  
pp. 60-65
Author(s):  
Anatoly V. Perelmuter
Keyword(s):  
Mathematical Model ◽  
Linear Dependence ◽  
Risk Estimation ◽  
Risk Level ◽  
The Public ◽  
Actual Risk ◽  
Life Saving ◽  
Points Of View ◽  
Public Reaction ◽  
The Mathematical Model

The problem of admissible risk optimisation is described in detail, especially for the case of possible human victims. Different points of view on the problem of «human being cost» are compared, and the approach based on comparing the numbers of saved lives and the risk for the persons, providing the life saving are considered. An information on actual risk level for different kinds of human activities is presented. The mathematical model of creating the public opinion in case of accidents and analysis of changing the function of society discomposibility function in time are presented. Effects commonly ignored during risk estimation are analysed—like departure from the principle of equal providing the risks for objects of equal responsibility, but different quantity and presence of non-linear dependence between the severity of accidents and public reaction.

scholarly journals Passage of a vehicle over a standard obstacle

2020 ◽  
Vol 313 ◽  
pp. 00012
Author(s):  
Darina Stachová
Keyword(s):  
Mathematical Model ◽  
Traffic Safety ◽  
Critical Condition ◽  
Point Contact ◽  
Hazardous Materials ◽  
Traffic Density ◽  
The Road ◽  
Road Profile ◽  
Points Of View ◽  
The Mathematical Model

Traffic safety depends on vehicle quality, traffic density and road conditions. Motion of a vehicle on a road or bridge body is therefore interesting from many points of view for various experts. We draw our attention to the unevenness of the road, specifically to the road profile with the so-called standard obstacle. In the article we present several alternatives for the mathematical model of such a road and also the mathematical model of the trajectory of the vehicle while traversing this standard obstacle. The shape of the obstacle meets the requirement of continuous one-point contact of the tire with the road; it does not contain singular points, and thus provides conditions for safer driving, especially when transporting persons in critical condition, or shocks-sensitive or hazardous materials.

The geometrical representation of fault-plane solutions of earthquakes

1957 ◽  
Vol 47 (2) ◽  
pp. 89-110 ◽  
Author(s):  
Adrian E. Scheidegger
Keyword(s):  
Mathematical Model ◽  
North America ◽  
Infinite Number ◽  
Fault Plane ◽  
Stereographic Projection ◽  
Fault Plane Solutions ◽  
Plausible Assumption ◽  
Long Time ◽  
First Motion ◽  
The Mathematical Model

Abstract Investigations into the mechanism at the focus of an earthquake have been in progress for a long time. In the course of these investigations it has been demonstrated that the mathematical model of a simple fault is a plausible assumption, at least so far as the explanation of the direction of first motion at distant seismic observatories is concerned. Various methods have been devised for representing and determining the elements of the focal fault of an earthquake, by investigators in Japan, Holland, North America, Italy, and Russia. It is often very difficult to see the connection between the various representations, and the present paper has been undertaken to demonstrate the relationships between them and to devise corresponding “translation schemes.” It is shown that there exists an infinite number of representations of fault-plane solutions all of which satisfy certain basic requirements. However, only four thereof have reached any popularity. It is shown that three of these four representations are entirely equivalent. In each, one uses a sphere; in each, one uses some stereographic projection of this sphere; and in each, one substitutes the tangent to the seismic ray at the focus for the ray itself. Whether one tabulates the angle i which that tangent makes with the vertical and plots tan i/2, as Ritsema and most Russians do, or whether one tabulates and plots tan i, as some of the Russians do, or tabulates and plots cot i, as Hodgson and his various co-workers do, one obtains identical results with equivalent amounts of work. What particular representation anyone will choose for studying an earthquake will therefore depend largely on his taste and previous custom.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

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