What is done

Research of transportation streams

Mathematical model of transportation streams. Establishment of conformities to the law between different descriptions of transportation streams can be carried out by the method of mathematical design and subsequent computer simulation. Designing of transportation streams by distinguishing between two basic approaches: Macro and Micro.

For construction of MATLAB -program; a model, that will be based on a microscopic approach, was used. It gave possibility more in detail to present cooperation of cars in a transportation stream.

The entry parameters of the model are:

● configuration of the working field- The file is saved in a .bmp format, with a resolution of 32X32 pixels;

● matrix of distributing powers of initial streams- is saved in the .txt format;

● quantity of times of design (it is accepted even 1000);

● presence of parameters (the value of variable switch_on=1 answers a presence, switch_on=0-absence) and mode of operations (time of switch period) of traffic lights. The job performance of the program is:

● to optimize routes of motion from access points to the points of output;

● the graph distributing density probability and place of the car at any given point within the working field;

● value of middle density of transportation streams;

● time it takes for the computer to perform the operation in seconds

After middle density of the transportation stream is in accordance with the task a user can choose the optimum location an modes of operation of traffic-lights, parking places and estimate the consequences of road construction that result in crossing or narrowing transportation on the highways. What is necessary to conduct trials of the modified working fields.

Structure of the working field and configuration of the file. (A user on the basis of a unit within the computer in within the city (for example, crossing from the street Lichacivscoi and I. Mechnicova) forms the file of the working field.



Fig 2. Crossroads: Lichacivscoi & I. Mechnicova



Background regions are filled by a white color, regions, roads- by a black. The points of entrances are reflected as 1 pixel red color, points of outputs- 1 dark blue colored pixel, traffic lights- by the rectangles of different colors (magenta or yellow), that crossing is fully occupied (fig.2).







Fig 2 Example of the working field



There may be a necessity for a user to modify the working field in such a case the user may use a standard graphics editor such as Microsoft paint. The name of the file must be saved as mapxx. bmp, for example, map01. bmp.

Structure of the file: The given file contains a matrix p, by a size m*n, where the quantity of lines is m- number of access points, quantity of columns n-number of points of output of transportation stream. Integers are the elements of the matrix in a range of 0-10, that are divided by back spice. The numbers present the indicated probabilities







A user forms the indicated file (fig. 3) and if necessary modifies it by means of a standard word processor such as notepad and Microsoft Word. The name of the file must be set as pxx. txt, for example, po1. txt.







Fig.3. The Matrix And Distribution Of Initial Streams



Job performances of the program. 01.avi. Below, on figures 4,5 the results of computer design for transportation streams are presented by graphics for the set working field and matrix of distributing efficiency of initial streams. The results are presented on fig. 5, a user can see the presence of congestion in a stream and make a decision about quantity, locations and modes of operations of traffic lights. It is possible to go through the program cycle multiple times to compare the average time a car might have to stay in the same place in the computer working field. For a working variant this value must be minimum.







Fig 4. Computation of optimum routes of motion from access points to the points of output







Fig.5. Example graphics displaying the probability of certain wait times in the working field