International Interdisciplinary Seminar MMCP2017 Dubna, Russia July, 2017 SIMULATION OF MULTILANE VEHICULAR TRAFFIC ON THE BASIS OF CELLULAR AUTOMATA THEORY Antonina Chechina, Natalia Churbanova, Marina Trapeznikova, Mikhail German and Alexey Ermakov Keldysh Institute of Applied Mathematics RAS The work is supported by the Russian Foundation for Basic Research

Goals of investigation Depiction of homogeneous and heterogeneous traffic flows dynamic on the elements of the road network, taking into consideration its real geometry; Modeling of traffic flows interaction on the crossroads, intersections, enters/exits, road junctions; Traffic flow modeling on the city/district road network; Traffic lights regime optimization; Road infrastructure planning, development and optimization.

2D Microscopic Model The algorithm of the cell state update: V = 3 The algorithm of the cell state update: Lane change (if necessary and possible) Movement along the road by the rules of one-lane traffic Vehicle properties: Unique ID Current speed Maximal speed Final destination Базовое описание модели, рисунок с клеточками и машинками, характеристики моделей 1 time step = 1 sec 1 cell ≈ 7.5 m 3

Conditions for changing lanes A vehicle is located in a domain where lane change is allowed; Lane change leads to the speed increase (density decrease) or is necessary to reach the destination; There is an obstacle not far away on the current lane; Target cell is empty; The safety condition is satisfied - on the target lane the distance behind is greater or equal to the maximal/current velocity of the previous car (cautious/aggressive drivers), the distance in front is greater or equal to the concerned vehicle velocity; Lane change takes place with a given probability.

Movement along the road by the rules of Nagel-Schreckenberg Model 1. Acceleration vn  min(vn+1, vmax) 2. Deceleration vn  min(vn, dn-1) 3. Randomization vn  max(vn-1, 0) with probability p 4. Vehicle movement xn  xn +vn

The algorithm of crossroad overcoming Within 100 meters before traffic lights the vehicle changes lane under its purpose according to the road laws. A vehicle accelerates or decelerates according to the Nagel- Schreckenberg model. Additional speed decreasing takes place under the following conditions: If a vehicle is located near the turning point (at the turning point it stops); If a traffic light is red; If there is the collision threat on the crossroad. A vehicle moves under the foregoing rules with randomization. A vehicle turns if it is located in the turning point and has got the corresponding target. 6

Driving strategies Cautious drivers change lanes only if the gap between the target cell and the first occupied cell upstream is greater than maximal speed. Aggressive drivers change lanes if the gap between the target cell and the first occupied cell upstream is greater than actual speed of the vehicle, situated in the first occupied cell. Cooperative drivers can be either cautious or aggressive. The % of cooperative drivers in the system can vary. These drivers: slow down (v=v-1, v≥1), if they see a traffic jam before the obstacle or road bottleneck on the neighboring lane; if there is a jam before the obstacle on the neighboring lane, and there are drivers that want to change their lane, cooperative drivers stop and let them pass; wait for several time steps if the cars from the other lane can’t move right away, because the target cell is occupied by other car. 7

Possible fragments of the road configuration Module size: 31x31 cell 232,5x232,5 m

Road fragment example Crossroad 1 Crossroad 2

Modeling of different road elements T-Cross X-Cross Straight road Widening

Road Accident and different driving strategies Cautious drivers Aggressive drivers

User Interface and visualization

Traffic flow modeling on small road networks Traffic lights

Conclusions The model and algorithms developed showed results comparable with the simulation by the standard program software. Created program package “Cam-2D” can be used for traffic modeling on city road networks. Due to inner parallelism and simplicity of numerical algorithms of the model the calculations can be carried out using high performance supercomputers on large-scale road networks. The capacity and performance of modern multicore hybrid computer systems allows real time predictions.