Alexander P. Buslaev

Traffic and Granular Flow '13

The Intelligent Driver Model (IDM) is studied and several dr awbacks with respect to driving simulators are defined. We present two mod ifications of the IDM. The first one gives any predefined distance to the leading vehi cle in a steady state. The second modification is a combination of the first one and th e optimal velocity model. It takes into account driver’s reaction time expl icitly and is described by delay differential equation. This model always results in r ealistic vehicles accelerations what allows simulating real traffic collisions. Necessary and sufficient conditions are obtained, that guar antee a non-oscillating solution near the equilibrium for the vehicle platoon. We su ggest the calibrating framework based on a numerical solution of the constrained o ptimization problem. Nonlinear constraints are generated by the numerical integ ra ion scheme. The suggested procedure incorporates the local stability conditi ons obtained and takes into account vehicle dynamics, drivers’ behavior and weather co nditions.Part I: Pedestrian Dynamics and Evacuation Dynamics.- Part II: Highway and Urban Vehicular Traffic.- Part III: Biological Systems and Granular Flow.

A dynamical communication system on a network

A dynamical system is introduced and investigated. The system contains N vertices. The vertices send messages at discrete time instants according to a given rule. A conflict of two vertices takes place if the vertices try to send messages to each other at the same instant. Each vertex sends a message to another vertex at every step if no conflict takes place. In case of a conflict, only one of the two competing vertices sends a message. Deterministic and stochastic conflict resolution rules are considered. We investigate the average number of messages sent by a vertex per a time unit, called the productivity of this vertex, the total productivity of the system and other characteristics. The productivity of vertices depends on the initial state of the system, and the criterion of efficiency is the expected average productivity of vertices provided all possible initial states of the system are equiprobable. An ergodic version of the system is also considered in which any particle moves with approximately equal to 1 probability provided there is no conflict.

Monotonic walks on a necklace and a coloured dynamic vector

Stochastic and deterministic versions of a discrete dynamical system on a necklace are investigated. This network consists of a sequence of contours NSWE with nodes, i.e. the nodes are common points at W and E. There are two cells and a particle on each contour. Each time instance, the particle occupies a cell and, at every time unit, comes to the next cell in the same direction. The particles of the neighbouring contours move in accordance with rules of stochastic or deterministic type. The behaviour of the model with the rule of the first type is stochastic only at the beginning and after a time interval becomes a pure deterministic system. The system with the second rule comes to a steady mode, which depends on the initial state. The average velocity of particles and characteristics of the system are studied.

On real-valued oscillations of a bipendulum

Abstract Theoretical and computational aspects of special case of logistical-routing problem are considered. Fluctuation of two particles on a grid connected by a channel also is considered. Velocity rate and sufficient conditions of system self-regulation are obtained.

Stability of Flows on Networks

The problems of traffic flow forecasting on complex traffic networks are still almost not explored. However these problems are very actual for scientists as well as for traffic engineers. In this paper we consider problems of stability of particle (car) flows on networks. The definitions of critical, stable and unstable flow states on networks are obtained as properties of solutions of nonlinear differential equations on graphs. For networks with different geometry the necessary and sufficient conditions of flow stability on networks are found. The perspective problems of exploration of qualitative properties of flows on networks are formulated.

On Irrational Oscillations of a Bipendulum

In this paper there are discussed the problems associated with yearly introduced by authors the class of dynamical systems, which have occurred from traffic. But now these dynamical systems become one of indicators of rational and irrational numbers connected with computer sciences basics.

About Synergy of Flows on Flower

Classical traffic flow theory was broadly separated into two branches: fluid-dynamical approach and and car-following micromodelling, and most important and difficult problems are network modelling of traffic flow. There exist many works of experimental and computer simulation types, but exact results fot saturated traffic flow on networks are appeared not often. We consider a movement of particles on network of special type as a set of contours with a common node. In 2009 we introduced a flower as network type for transport model, where the dynamical system defined by a system of differential equations on flower was developed. In this paper we study, for the system of connected contours, problem of search the conditions, such that the system becomes synergy mode independence on initial particles configuration at finite time, i.e. all particles move without delay for next time. It is proved, besides all the other results, that the search of synergy conditions is reduced to the investigation of the existence of solutions of linear Diophantine equations with two variables.

Algorithmic and Software Aspects of Information System Implementation for Road Maintenance Management

A distributed information system for business processes of road maintenance is presented in the paper. The architecture of developed system is the type of client-server system with terminal devices such as smart phones with the Android and IOS Operating Systems. The system has been called “Server – Smartphone – Student – Receiver (SSSR) – Road”, and it gives possibility to fulfill the optimal scheduling, local routing for services movements and maintenance organization on the road traffic network by communications technology. Problems of dependability and system reliability are essentially developing on the accuracy of objects positioning. So methods of accuracy improving are provided in the paper.

Dynamical Systems on Honeycombs

Stochastic and deterministic versions of a discrete dynamical system on a necklace network are investigated. This network contains several contours. There are three cells and a particle on each contour. The particle occupies one of the cells and, at each step, it makes an attempt to move to the next cell in the direction of movement. As well as on neighboring contours the particles move in accordance with rules of stochastic or deterministic type. We prove that the behavior of the model with a rule of the first type is stochastic only at the beginning, and after a time interval the behavior becomes purely deterministic. The system with a rule of the first type reaches a stationary mode which depends on the initial state. The average velocity of particles and other characteristics of the dynamical systems are studied.

Stability of Flow on a Ring with Three Links

The qualitative properties of solutions of nonlinear differential equation system that describe traffic flow on a ring are developed. The ring consists of three links. The stationary points of the system have been found. The flow behavior in the neighborhood of this point has been considered. The stability of the stationary points is studied. The behavior of the solution near the boundary is considered.