Solving the linear inhomogeneous differential equation in the simulation model of passenger car tire

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 233-234
Author(s):  
Pavel Sarkisov ◽  
Günther Prokop ◽  
Jörg Wensch
Keyword(s):  
Differential Equation ◽  
Simulation Model ◽  
Passenger Car ◽  
Inhomogeneous Differential Equation ◽  
Linear Inhomogeneous Differential Equation

scholarly journals Passenger Car Unit Estimation at Signalized Intersection for Non-lane Based Mixed Traffic Using Microscopic Simulation Model

2017 ◽  
Vol 45 (1) ◽  
pp. 12 ◽  
Author(s):  
Gowri Asaithambi ◽  
Hayjy Sekar Mourie ◽  
Ramaswamy Sivanandan
Keyword(s):  
Simulation Model ◽  
Signalized Intersection ◽  
Accurate Estimation ◽  
Mixed Traffic ◽  
Passenger Car ◽  
Traffic Conditions ◽  
Passenger Car Unit ◽  
Road Width ◽  
On The Road ◽  
Chennai City

In India, traffic on roads is mixed in nature with widely varying static and dynamic characteristics of vehicles. At intersections, vehicles do not follow ordered queue and lane discipline. Different vehicle types occupy different spaces on the road, move at different speeds, and start at different accelerations. The problem of measuring volume of such mixed traffic has been addressed by converting different vehicles categories into equivalent passenger cars and expressing the volume in terms of Passenger Car Unit (PCU) per hour. The accurate estimation of PCU values for different roadway and traffic conditions is essential for better operation and management of roadway facilities. Hence, the objective of the present study is to estimate the PCU values at signalized intersection in mixed traffic and to study the influence of traffic volume, traffic composition and road width on PCU values.For this purpose, a mixed traffic simulation model developed specifically for a signalized intersection was used. The model was calibrated and validated with the traffic data collected from a signalized intersection in Chennai city. Simulation runs were carried out for various combinations of vehicular composition, volume levels and road width. It was observed that presence of heavy vehicles and increase in road width affects the PCU values. The obtained PCU values were statistically checked for accuracy and proven to be satisfied. The PCU values obtained in this study can be used as a guideline for the traffic engineers and practitioners in the design and analysis of signalized intersections where mixed traffic conditions exist.

A method for determining the parametric sensitivity of the dynamical systems phase coordinates

2020 ◽  
Author(s):  
O.N. Tushev ◽  
A.V. Belyaev
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Fundamental Matrix ◽  
Initial Point ◽  
External Effects ◽  
Parametric Sensitivity ◽  
System Parameters ◽  
Sensitivity Functions ◽  
Phase Coordinates ◽  
Linear Inhomogeneous Differential Equation

The article presents a rational method for determining sensitivity functions of the first and second orders of phase coordinates to changes in system parameters and external effects. With this approach it is not necessary to integrate intricate chain- coupled differential equations with respect to sensitivity functions of various orders. A vector of additional variables (invariants) of the same dimension is introduced as the vector of phase coordinates. To find it, a conjugate linear inhomogeneous differential equation is obtained, which must be integrated in the inverse time. The sensitivity functions of any order can be calculated independently from each other using this vector. No assumptions reducing the accuracy of the result or restricting the capabilities of the method are made. The linearity of the equation with respect to invariants allows solving the problem in the more convenient form. Using the recurrence relation, the sensitivity functions are calculated sequentially in time from the initial point. The solution of the equation is expressed through a fundamental matrix which is computationally treated as a multiplicative integral. The results are illustrated by the example.

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