ɆȺɌȿɆȺɌɂɑȿɋɄɈȿ ɆɈȾȿɅɂɊɈȼȺɇɂȿ ɄȺɄ ɂɇɋɌɊɍɆȿɇɌ ɌɊȺɇɋɉɈɊɌɇɈ-ɉɅȺɇɂɊɈȼɈɑɇɈɃ ɈɊȽȺɇɂɁȺɐɂɂ ȽɈɊɈȾȺ
THE MATHEMATICAL MODELING AS AN INSTRUMENT OF
ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɞɨɪɨɠɧɨɝɨ ɞɜɢɠɟɧɢɹ ɛɵɥɢ ɡɚɥɨɠɟɧɵ ɜ 1912 ɝɨɞɭ ɪɭɫɫɤɢɦ ɭɱɟɧɵɦ, ɩɪɨɮɟɫɫɨɪɨɦ Ƚ.Ⱦ.Ⱦɭɛɟɥɢɪɨɦ.
ɉɟɪɜɨɫɬɟɩɟɧɧɨɣ ɡɚɞɚɱɟɣ, ɩɨɫɥɭɠɢɜɲɟɣ ɪɚɡɜɢɬɢɸ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɧɫɩɨɪɬɧɵɯ ɩɨɬɨɤɨɜ, ɫɬɚɥ ɚɧɚɥɢɡ ɩɪɨɩɭɫɤɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɦɚɝɢɫɬɪɚɥɟɣ ɢ ɩɟɪɟɫɟɱɟɧɢɣ – ɦɚɤɫɢ-ɦɚɥɶɧɨ ɜɨɡɦɨɠɧɨɟ ɱɢɫɥɨ ɚɜɬɨɦɨɛɢɥɟɣ,ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɩɪɨɣɬɢ ɱɟɪɟɡ ɫɟɱɟɧɢɟ ɞɨɪɨɝɢ ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ.ɗɬɨɬ ɩɚɪɚɦɟɬɪ ɹɜɥɹɟɬɫɹ ɫɟɝɨɞɧɹ ɜɚɠɧɟɣɲɢɦ ɤɪɢɬɟɪɢɟɦ ɨɰɟɧɤɢ ɤɚ-ɱɟɫɬɜɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɬɪɚɧɫɩɨɪɬɧɨɣ ɫɟɬɢ.
ɉɟɪɜɚɹ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɚɹ ɦɨɞɟɥɶ,ɜ ɤɨɬɨɪɨɣ ɞɜɢɠɟɧɢɟ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨɬɨɤɚ ɪɚɫ-ɫɦɚɬɪɢɜɚɥɨɫɶ ɫ ɩɨɡɢɰɢɣ ɦɟɯɚɧɢɤɢ ɫɩɥɨɲɧɨɣ ɫɪɟɞɵ, ɛɵɥɚ ɩɪɟɞɥɨɠɟɧɚ ɜ 1955 ɝɨɞɭ Ʌɚɣɬɯɢɥɥɨɦ (Ligthill) ɢ ɍɢɡɟɦɨɦ (Whitham) [12] [3]. Ɉɧɢ ɩɨɤɚɡɚɥɢ,ɱɬɨ ɦɟɬɨɞɵ ɨɩɢɫɚ-ɧɢɹ ɩɪɨɰɟɫɫɨɜ ɩɟɪɟɧɨɫɚ ɜ ɫɩɥɨɲɧɵɯ ɫɪɟɞɚɯ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɦɨɞɟɥɢɪɨ-ɜɚɧɢɹ ɡɚɬɨɪɨɜ.
ȼ 60 - 70-ɟ ɝɨɞɵ ɩɪɨɲɥɨɝɨ ɜɟɤɚ ɚɤɬɢɜɧɵɟ ɪɚɡɪɚɛɨɬɤɢ ɜ ɨɛɥɚɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜɟɥɢɫɶ ɜɟɞɭɳɢɦɢ ɭɱɟɧɵɦ - ɫɩɟɰɢɚɥɢɫɬɚɦ ɜ ɨɛɥɚɫɬɢ ɦɚɬɟɦɚɬɢɤɢ, ɮɢɡɢ-ɤɢ,ɩɪɨɰɟɫɫɨɜ ɭɩɪɚɜɥɟɧɢɹ,ɬɚɤɢɦ ɤɚɤ ɇɨɛɟɥɟɜɫɤɢɣ ɥɚɭɪɟɚɬ ɂ.ɉɪɢɝɨɠɢɧ,ɫɩɟɰɢɚɥɢɫɬ ɩɨ ɚɜɬɨɦɚɬɢɱɟɫɤɨɦɭ ɭɩɪɚɜɥɟɧɢɸ Ɇ.Ⱥɬɚɧɫ,ɚɜɬɨɪ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ ɪɚɛɨɬ ɩɨ ɫɬɚɬɢɫɬɢɤɟ Ʌ.Ȼɪɟɣɦɚɧ,ɆȽɍ ɢ ɞɪ. [2]. ȼ 1990 ɝɨɞɚɯ ɜ ɋɒȺ ɩɪɨɛɥɟɦɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɬɪɚɧɫɩɨɪɬɧɵɯ ɫɢɫɬɟɦ ɛɵɥɢ ɜɨɡɜɟɞɟɧɵ ɜ ɪɚɧɝ ɩɪɨɛɥɟɦ ɧɚɰɢɨɧɚɥɶɧɨɣ ɛɟɡɨɩɚɫɧɨɫɬɢ.
ɂɧɜɟɫɬɢɰɢɢ ɜ ɬɪɚɧɫɩɨɪɬɧɭɸ ɢɧɮɪɚɫɬɪɭɤɬɭɪɭ ɞɨ ɫɢɯ ɩɨɪ ɨɫɧɨɜɵɜɚɥɢɫɶ,ɤɚɤ ɩɪɚ-ɜɢɥɨ,ɧɚ ɦɨɞɟɥɢ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɪɨɝɧɨɡɚ ɜ ɪɚɫɫɪɟɞɨɬɨɱɟɧɧɨɦ ɢ ɭɩɪɨɳɟɧɧɨɦ ɜɢɞɟ,ɯɨɬɹ ɫɢɬɭɚɰɢɹ ɜ ɪɟɝɢɨɧɚɯ ɪɚɡɥɢɱɧɚɹ.Ʉ ɩɪɢɦɟɪɭ,ɜ Ɋɨɫɫɢɢ ɧɟɞɨɫɬɚɬɨɤ ɢɥɢ ɩɨɥɧɨɟ ɨɬɫɭɬɫɬ-ɜɢɟ ɞɨɥɝɨɫɪɨɱɧɵɯ ɬɪɚɧɫɩɨɪɬɧɵɯ ɢ ɨɛɳɟɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɪɨɝɧɨɡɨɜ,ɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢ-ɦɵ ɞɥɹ ɩɪɢɧɹɬɢɹ ɪɟɲɟɧɢɣ,ɨɛɭɫɥɨɜɥɟɧɵ,ɜ ɱɚɫɬɧɨɫɬɢ,ɩɨɥɢɬɢɱɟɫɤɨɣ ɢ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɧɟɫɬɚɛɢɥɶɧɨɫɬɶɸ,ɜɨɡɧɢɤɲɟɣ ɩɪɢ ɪɚɫɩɚɞɟ ɋɋɋɊ.
ȼ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɞɨɪɨɠɧɨɝɨ ɞɜɢɠɟɧɢɹ ɢɫɬɨɪɢɱɟɫɤɢ ɫɥɨɠɢɥɨɫɶ ɞɜɚ ɨɫɧɨɜɧɵɯ ɩɨɞɯɨɞɚ - ɞɟɬɟɪɦɢɧɢɫɬɢɱɟɫɤɢɣ ɢ ɜɟɪɨɹɬɧɨɫɬɧɵɣ (ɫɬɨɯɚɫɬɢɱɟɫɤɢɣ).
ȼ ɨɫɧɨɜɟ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɯ ɦɨɞɟɥɟɣ ɥɟɠɢɬ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ,ɧɚɩɪɢɦɟɪ,ɫɤɨɪɨɫɬɶɸ ɢ ɞɢɫɬɚɧɰɢɟɣ ɦɟɠɞɭ ɚɜɬɨɦɨɛɢɥɹɦɢ ɜ ɩɨɬɨɤɟ.ȼ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ ɦɨɞɟɥɹɯ ɬɪɚɧɫɩɨɪɬɧɵɣ ɩɨɬɨɤ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɜɟɪɨɹɬɧɨ-ɫɬɧɵɣ ɩɪɨɰɟɫɫ.
ȼ ɧɚɫɬɨɹɳɟɟ ɠɟ ɜɪɟɦɹ ɜɫɟ ɦɨɞɟɥɢ ɬɪɚɧɫɩɨɪɬɧɵɯ ɩɨɬɨɤɨɜ ɦɨɠɧɨ ɪɚɡɛɢɬɶ ɧɚ ɬɪɢ ɤɥɚɫɫɚ [1]: ɦɨɞɟɥɢ-ɚɧɚɥɨɝɢ,ɦɨɞɟɥɢ ɫɥɟɞɨɜɚɧɢɹ ɡɚ ɥɢɞɟɪɨɦ ɢ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɦɨɞɟɥɢ.
ȼ ɦɨɞɟɥɹɯ-ɚɧɚɥɨɝɚɯ ɞɜɢɠɟɧɢɟ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɫɪɟɞɫɬɜɚ ɭɩɨɞɨɛɥɹɟɬɫɹ ɤɚɤɨɦɭ-ɥɢɛɨ ɮɢɡɢɱɟɫɤɨɦɭ ɩɨɬɨɤɭ (ɝɢɞɪɨ-ɢ ɝɚɡɨɞɢɧɚɦɢɱɟɫɤɢɟ ɦɨɞɟɥɢ) [9] [10] [13]. ɗɬɨɬ ɤɥɚɫɫ ɦɨ-ɞɟɥɟɣ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɦɢ.
ȼ ɦɨɞɟɥɹɯ ɫɥɟɞɨɜɚɧɢɹ ɡɚ ɥɢɞɟɪɨɦ ɫɭɳɟɫɬɜɟɧɧɨ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɨ ɧɚɥɢɱɢɢ ɫɜɹɡɢ ɦɟɠɞɭ ɩɟɪɟɦɟɳɟɧɢɟɦ ɜɟɞɨɦɨɝɨ ɢ ɝɨɥɨɜɧɨɝɨ ɚɜɬɨɦɨɛɢɥɹ [4]. ɉɨ ɦɟɪɟ ɪɚɡɜɢɬɢɹ ɬɟɨɪɢɢ ɜ ɦɨɞɟɥɹɯ ɷɬɨɣ ɝɪɭɩɩɵ ɭɱɢɬɵɜɚɥɨɫɶ ɜɪɟɦɹ ɪɟɚɤɰɢɢ ɜɨɞɢɬɟɥɟɣ,ɢɫɫɥɟɞɨɜɚɥɨɫɶ ɞɜɢɠɟ-ɧɢɟ ɧɚ ɦɧɨɝɨɩɨɥɨɫɧɵɯ ɞɨɪɨɝɚɯ,ɢɡɭɱɚɥɚɫɶ ɭɫɬɨɣɱɢɜɨɫɬɶ ɞɜɢɠɟɧɢɹ [7]. ɗɬɨɬ ɤɥɚɫɫ ɦɨ-ɞɟɥɟɣ ɧɚɡɵɜɚɸɬ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɦɢ.
ȼ ɜɟɪɨɹɬɧɨɫɬɧɵɯ ɦɨɞɟɥɹɯ ɬɪɚɧɫɩɨɪɬɧɵɣ ɩɨɬɨɤ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɪɟɡɭɥɶɬɚɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɚɧɫɩɨɪɬɧɵɯ ɫɪɟɞɫɬɜ ɧɚ ɷɥɟɦɟɧɬɚɯ ɬɪɚɧɫɩɨɪɬɧɨɣ ɫɟɬɢ.ȼ ɫɜɹɡɢ ɫ ɠɟ-ɫɬɤɢɦ ɯɚɪɚɤɬɟɪɨɦ ɨɝɪɚɧɢɱɟɧɢɣ ɫɟɬɢ ɢ ɦɚɫɫɨɜɵɦ ɯɚɪɚɤɬɟɪɨɦ ɞɜɢɠɟɧɢɹ ɜ ɬɪɚɧɫɩɨɪɬɧɨɦ ɩɨɬɨɤɟ ɫɤɥɚɞɵɜɚɸɬɫɹ ɨɬɱɟɬɥɢɜɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɱɟɪɟɞɟɣ, ɢɧɬɟɪɜɚ-ɥɨɜ,ɡɚɝɪɭɡɨɤ ɩɨ ɩɨɥɨɫɚɦ ɞɨɪɨɝɢ ɢ ɬ.ɩ.ɗɬɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɧɨɫɹɬ ɫɬɨɯɚɫɬɢɱɟɫɤɢɣ ɯɚ-ɪɚɤɬɟɪ.
ȼ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ ɜ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɬɪɚɧɫɩɨɪɬɧɵɯ ɩɨɬɨɤɨɜ ɫɬɚɥɢ ɩɪɢɦɟɧɹɬɶ ɦɟɠ-ɞɢɫɰɢɩɥɢɧɚɪɧɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɢɞɟɢ, ɦɟɬɨɞɵ ɢ ɚɥɝɨɪɢɬɦɵ ɧɟɥɢɧɟɣɧɨɣ ɞɢɧɚɦɢɤɢ.
ɂɯ ɰɟɥɟɫɨɨɛɪɚɡɧɨɫɬɶ ɨɛɨɫɧɨɜɚɧɚ ɧɚɥɢɱɢɟɦ ɜ ɬɪɚɧɫɩɨɪɬɧɨɦ ɩɨɬɨɤɟ ɭɫɬɨɣɱɢɜɵɯ ɢ ɧɟ-ɭɫɬɨɣɱɢɜɵɯ ɪɟɠɢɦɨɜ ɞɜɢɠɟɧɢɹ,ɩɨɬɟɪɶ ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɭɫɥɨɜɢɣ ɞɜɢɠɟ-ɧɢɹ,ɧɟɥɢɧɟɣɧɵɯ ɨɛɪɚɬɧɵɯ ɫɜɹɡɟɣ,ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜ ɛɨɥɶɲɨɦ ɱɢɫɥɟ ɩɟɪɟɦɟɧɧɵɯ ɞɥɹ ɚɞɟɤɜɚɬɧɨɝɨ ɨɩɢɫɚɧɢɹ ɫɢɫɬɟɦɵ.
ɋɨɜɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ,ɥɟɠɚɳɢɟ ɜ ɨɫɧɨɜɟ ɦɚɤɪɨɦɨɞɟɥɟɣ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨ-ɬɨɤɚ, ɧɚɱɚɥɢ ɮɨɪɦɢɪɨɜɚɬɶɫɹ ɫ 80-ɯ ɝɨɞɨɜ XX ɜɟɤɚ. ɉɟɪɜɨɧɚɱɚɥɶɧɨ ɫɱɢɬɚɥɨɫɶ, ɱɬɨ ɬɪɚɧɫɩɨɪɬɧɵ ɤɨɦɛɢɧɚɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɚɜɬɨɦɨɛɢɥɟɣ ɧɚ ɦɚɝɢɫɬɪɚɥɹɯ, ɩɪɨɹɜɥɹɸɬ ɜɨɫɩɪɨɢɡɜɨɞɢɦɵɟ ɫɜɨɣɫɬɜɚ, ɡɚɜɢɫɹɳɢɟ ɨɬ ɬɟɯɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɚɜɬɨɦɨɛɢɥɟɣ, ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɧɢɦɢ ɢ ɪɟɚɤɰɢɢ ɜɨɞɢɬɟɥɟɣ. Ʉɨɝɞɚ ɞɢɫɬɚɧɰɢɹ ɦɟɠɞɭ ɜɨɞɢɬɟɥɹɦɢ ɫɬɚɧɨɜɢɬɫɹ ɧɢɠɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɡɧɚɱɟɧɢɹ, ɡɚɞɟɪɠɤɚ ɜ ɪɟɚɤɰɢɢ ɜɨɞɢɬɟɥɟɣ ɩɪɢɜɨɞɢɬ ɤ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɞɜɢɠɟɧɢɹ:ɫɬɚɪɬ-ɫɬɨɩ ɜɨɥɧɚɦ.ɉɨɡɞɧɟɟ Ʉɟɪɧɟɪ ɢ Ɋɟɛɨɪɧ [11] ɜɵɹɜɢɥɢ ɟɳɟ ɧɟɫɤɨɥɶɤɨ ɮɚɡ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɬɪɚɧɫɩɨɪɬɧɵɣ ɩɨɬɨɤ. ȼ ɢɬɨɝɟ, ɫɨɜɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɫɬɚɞɢɹɯ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨɬɨɤɚ, ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɫ ɩɨɡɢɰɢɣ ɮɚɡɨɜɵɯ ɩɟɪɟɯɨɞɨɜ ɫɨɫɬɨɹɧɢɹ ɠɢɞɤɨɫɬɢ:ɝɚɡ - ɠɢɞɤɨɫɬɶ - ɡɚɦɟɪɡɚɸɳɚɹ ɠɢɞɤɨɫɬɶ – ɥɟɞ [6]. Ɍɚ-ɤɚɹ ɦɨɞɟɥɶ ɩɨɡɜɨɥɹɟɬ ɜɵɩɨɥɧɢɬɶ ɚɧɚɥɢɡ ɩɨɜɟɞɟɧɢɹ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨɬɨɤɚ ɜ ɪɚɡɥɢɱɧɵɯ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɫ ɭɱɟɬɨɦ ɢɡɦɟɧɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɚɜɬɨɦɚɝɢɫɬɪɚɥɟɣ, ɚɜɬɨɦɨɛɢ-ɥɟɣ,ɩɨɜɟɞɟɧɱɟɫɤɢɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɜɨɞɢɬɟɥɹ.Ɋɟɡɭɥɶɬɚɬɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ,ɜɵɩɨɥɧɟɧɧɵɟ ɧɚ ɨɫɧɨɜɟ ɷɬɨɣ ɦɨɞɟɥɢ ɩɨɡɜɨɥɢɥɢ ɨɬɤɪɵɬɶ ɢ ɨɛɨɫɧɨɜɚɬɶ ɷɮɮɟɤɬ ɤɥɚɫɬɟɪɨɜ, ɩɪɨɹɜ-ɥɹɸɳɟɣɫɹ ɧɚ ɚɜɬɨɫɬɪɚɞɚɯ (Ʉɟɪɧɟɪ-Ʉɨɧɯɨɣɡɟɪ), ɚ ɬɚɤɠɟ ɭɫɬɚɧɨɜɢɬɶ,ɱɬɨ ɜɧɟɲɧɢɟ ɜɨɡ-ɞɟɣɫɬɜɢɹ ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ ɨɩɪɟɞɟɥɹɸɳɢɯ ɮɚɤɬɨɪɨɜ ɩɨɜɟɞɟɧɢɹ ɩɨɬɨɤɚ.
ȼ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ ɡɚɪɨɠɞɚɸɬɫɹ ɧɨɜɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ [8]: ɩɨɜɟɞɟɧɢɟ ɬɪɚɧɫɩɨɪɬ-ɧɨɝɨ ɩɨɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɭɠɟɧɢɹɦɢ ɢ ɪɚɫɲɢɪɟɧɢɹɦɢ ɞɨɪɨɝɢ; ɨɫɧɨɜɧɵɦ ɨɛɴɟɤɬɨɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɵɫɬɭɩɚɸɬ ɨɱɟɪɟɞɢ (ɢɯ ɫɜɨɣɫɬɜɚ,ɫɬɪɭɤɬɭɪɵ,ɩɨɜɟɞɟɧɢɟ ɢ ɩɪɨɱ.), ɜɨɡɧɢ-ɤɚɸɳɢɟ ɨɤɨɥɨ ɫɭɠɟɧɢɣ;ɞɥɹ ɩɪɢɟɦɥɟɦɵɯ ɩɪɟɞɫɤɚɡɚɧɢɣ ɩɨɜɟɞɟɧɢɹ ɩɨɬɨɤɚ ɞɨɫɬɚɬɨɱɧɨ ɩɨɫɬɪɨɢɬɶ ɝɪɭɩɩɭ ɩɪɨɫɬɵɯ ɦɨɞɟɥɟɣ ɫɭɠɟɧɢɣ ɞɨɪɨɝɢ.
ȼ Ⱦɶɸɢɫɛɟɪɝɟ (Ƚɟɪɦɚɧɢɹ)ɮɢɡɢɤ Ɇɚɣɤɥ ɒɪɟɤɟɧɛɟɪɝ (Michael Schreckenberg) ɩɨ-ɥɭɱɢɜɲɢɣ ɩɪɨɡɜɢɳɟ «ɉɪɨɮɟɫɫɨɪ ɉɪɨɛɨɤ»ɢ 15 ɟɝɨ ɤɨɥɥɟɝ ɩɪɨɜɨɞɢɥɢ ɷɤɫɩɟɪɢɦɟɧɬɵ, ɩɪɟɞɧɚɦɟɪɟɧɧɨ ɫɨɡɞɚɜɚɹ ɡɚɬɨɪɵ.ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɧɢ ɩɪɢɲɥɢ ɤ ɜɵɜɨɞɭ - ɩɟɪɟɯɨɞ ɨɬ ɫɜɨ-ɛɨɞɧɨɝɨ ɩɨɬɨɤɚ ɤ ɫɢɧɯɪɨɧɢɡɢɪɨɜɚɧɧɨɦɭ ɦɨɠɟɬ ɫɥɭɱɚɬɶɫɹ ɫɩɨɧɬɚɧɧɨ - ɧɚɦɧɨɝɨ ɛɵɫɬ-ɪɟɟ,ɱɟɦ ɷɬɨ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ ɪɚɧɶɲɟ.ɑɚɫɬɨ,ɷɬɨ ɫɥɭɱɚɟɬɫɹ ɨɤɨɥɨ ɧɚɤɥɨɧɧɵɯ ɜɴɟɡɞɨɜ ɧɚ ɚɜɬɨɦɚɝɢɫɬɪɚɥɶ,ɤɨɝɞɚ ɩɪɨɢɫɯɨɞɢɬ ɜɧɟɡɚɩɧɨɟ ɜɡɪɵɜɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɱɢɫɥɚ ɚɜɬɨɦɨɛɢɥɟɣ ɧɚ ɞɨɪɨɝɟ,ɱɬɨ ɦɨɠɟɬ ɩɪɟɜɪɚɳɚɬɶ ɩɨɬɨɤ ɜ «ɞɜɢɠɭɳɟɟɫɹ ɠɟɥɟ».Ɍɚɤɨɟ ɢɧɟɪɬɧɨɟ ɫɨɫɬɨɹ-ɧɢɟ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɜɜɟɪɯ ɢ ɜɧɢɡ ɩɨ ɞɨɪɨɝɟ,ɫɨɯɪɚɧɹɹɫɶ,ɜɨɡɦɨɠɧɨ ɧɟɫɤɨɥɶɤɨ ɱɚɫɨɜ, ɞɚɠɟ ɩɨɫɥɟ ɬɨɝɨ ɤɚɤ ɧɚɤɥɨɧɧɵɣ ɜɴɟɡɞ ɨɩɭɫɬɟɟɬ [15].
ɉɟɪɫɩɟɤɬɢɜɧɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɹɜɥɹɟɬɫɹ ɩɪɢɦɟɧɟɧɢɟ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ.ɇɚɩɪɢɦɟɪ, ɜ ɪɚɛɨɬɟ [14] ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɞɢɫɤɪɟɬɧɚɹ ɦɨɞɟɥɶ ɡɚɝɪɭɡɤɢ ɫɟɬɢ ɝɨɪɨɞɫɤɢɯ ɞɨɪɨɝ, ɩɨ-ɫɬɪɨɟɧɧɚɹ ɧɚ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɰɟɩɨɱɤɚɯ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ. Ⱥɜɬɨɪɵ ɦɨɞɟɥɢɪɭɸɬ ɹɜɥɟɧɢɟ ɡɚɬɨɪɚ ɤɚɤ ɡɚɜɢɫɢɦɨɫɬɶ,ɫɜɹɡɵɜɚɸɳɭɸ ɨɝɪɚɧɢɱɟɧɢɹ ɧɚ ɜɯɨɞɹɳɢɟ ɢ ɜɵɯɨɞɹɳɢɟ ɬɪɚɧɫɩɨɪɬɧɵɟ ɩɨɬɨɤɢ,ɤɨɬɨɪɵɟ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɡɚɬɪɚɬɚɦɢ ɜɪɟɦɟɧɢ ɧɚ ɩɟɪɟɦɟɳɟɧɢɹ ɜ ɫɟɬɢ.Ɉɝɪɚɧɢɱɟɧɢɹ ɧɚ ɜɯɨɞ ɜ ɫɟɬɶ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɢɬɶ ɷɮɮɟɤɬɵ ɨɛɪɚɬɧɨɝɨ ɪɚɫɩɪɨɫɬɪɚ-ɧɟɧɢɹ ɡɚɬɨɪɨɜ.
ɋɜɨɟɨɛɪɚɡɧɭɸ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɭɸ ɩɪɨɝɪɚɦɦɭ ɩɪɟɞɥɚɝɚɟɬ ɜ ɫɜɨɟɣ ɪɚɛɨɬɟ [8] Ⱦɚ-ɝɚɧɡɨ: «ə ɜɟɪɸ,ɱɬɨ ɦɵ ɧɚɱɧɟɦ ɢɡɜɥɟɤɚɬɶ ɧɚɢɛɨɥɶɲɭɸ ɩɨɥɶɡɭ ɢɡ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɧɢɦɚ-ɧɢɹ ɧɚ ɞɜɭɯ ɨɫɧɨɜɧɵɯ ɜɨɩɪɨɫɚɯ. ɉɟɪɜɵɣ - ɩɨɜɟɞɟɧɢɟ ɡɚɬɨɪɧɵɯ ɭɱɚɫɬɤɨɜ. ȼɬɨɪɨɣ – ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɪɨɫɬ ɨɱɟɪɟɞɟɣ. ə ɛɵ ɩɪɟɞɩɨɱɟɥ ɢɡɦɟɪɹɬɶ ɩɚɪɚɦɟɬɪɵ, ɤɨɬɨɪɵɟ ɪɟ-ɚɥɶɧɨ ɞɨɥɠɧɵ ɩɪɟɞɫɤɚɡɵɜɚɬɶ ɦɨɞɟɥɢ - ɞɥɢɧɚ ɨɱɟɪɟɞɢ, ɜɪɟɦɹ ɩɪɨɟɡɞɚ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɫɪɟɞɫɬɜɚ ɦɟɠɞɭ ɞɚɬɱɢɤɚɦɢ,ɢ ɞɚɥɟɟ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɯ ɞɥɹ ɜɵɛɨɪɚ ɦɨɞɟɥɢ».Ɍɚɤɢɦ
ɨɛɪɚ-ɡɨɦ,ɞɚɧɧɵɣ ɩɨɞɯɨɞ ɨɫɧɨɜɚɧ ɧɚ ɷɦɩɢɪɢɱɟɫɤɢɯ ɦɨɞɟɥɹɯ,ɩɚɪɚɦɟɬɪɵ ɤɨɬɨɪɵɯ ɭɫɬɚɧɚɜ-ɥɢɜɚɸɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ.
Ɉɞɧɨɣ ɢɡ ɫɥɨɠɧɟɣɲɢɯ ɡɚɞɚɱ ɹɜɥɹɟɬɫɹ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɛɪɚɡɨɜɚɧɢɹ ɩɪɟɞɡɚɬɨɪɧɵɯ ɢ ɡɚɬɨɪɧɵɯ ɫɢɬɭɚɰɢɣ.ɗɬɚ ɩɪɨɛɥɟɦɚ ɧɚɯɨɞɢɬɫɹ ɜ ɫɬɚɞɢɢ ɢɡɭɱɟɧɢɹ: «ɋɨɫɬɨɹɧɢɟ ɞɟɥɚ ɜ ɷɬɨɣ ɨɛɥɚɫɬɢ ɧɚ ɫɟɝɨɞɧɹ ɬɚɤɨɜɨ,ɱɬɨ,ɧɟ ɫɦɨɬɪɹ ɧɚ ɡɧɚɱɢɬɟɥɶɧɵɣ ɩɪɨɝɪɟɫɫ,ɩɨɥɧɨɟ ɩɨ-ɧɢɦɚɧɢɟ ɩɪɢɪɨɞɵ ɚɜɬɨɦɨɛɢɥɶɧɵɯ ɩɪɨɛɨɤ ɟɳɟ ɧɟ ɞɨɫɬɢɝɧɭɬɨ» [15]. Ⱥ ɦɧɟɧɢɟ ɨɞɧɨɝɨ ɢɡ ɜɟɞɭɳɢɯ ɚɦɟɪɢɤɚɧɫɤɢɯ ɷɤɫɩɟɪɬɨɜ ɜ ɬɟɨɪɢɢ ɞɜɢɠɟɧɢɹ ɚɜɬɨɦɨɛɢɥɶɧɵɯ ɩɨɬɨɤɨɜ ɩɪɨ-ɮɟɫɫɨɪ ɭɧɢɜɟɪɫɢɬɟɬɚ ɒɬɚɬɚ Ɍɟɯɚɫ ɏɚɧɢ Ɇɚɯɦɚɫɚɧɢ (Hani S. Mahmassani) ɫɜɨɞɢɬɫɹ ɤ ɫɥɟɞɭɸɳɟɦɭ: «ɉɪɢɱɢɧɚ ɜɧɟɡɚɩɧɨɝɨ ɩɟɪɟɯɨɞɚ ɨɬ ɪɟɠɢɦɚ ɫɜɨɛɨɞɧɨɝɨ ɞɜɢɠɟɧɢɹ ɤ ɫɬɚɪɬ-ɫɬɨɩ ɪɟɠɢɦɭ ɨɫɬɚɟɬɫɹ ɨɞɧɨɣ ɢɡ ɬɚɣɧ ɧɚɲɟɝɨ ɜɪɟɦɟɧɢ».
ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɩɪɢɦɟɧɹɟɦɵɟ ɡɚ ɪɭɛɟɠɨɦ ɢɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɢ ɬɪɚɧɫ-ɩɨɪɬɧɨɟ ɩɥɚɧɢɪɨɜɚɧɢɟ,ɤɨɬɨɪɵɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɬɪɚɧɫɩɨɪɬɧɭɸ ɫɟɬɶ ɤɚɤ ɟɞɢɧɭɸ ɫɢɫɬɟ-ɦɭ, ɩɨɡɜɨɥɹɸɬ ɷɮɮɟɤɬɢɜɧɨ ɩɪɢɧɢɦɚɬɶ ɪɟɲɟɧɢɹ ɩɨ ɪɚɡɝɪɭɡɤɟ ɫɭɳɟɫɬɜɭɸɳɢɯ ɞɨɪɨɝ, ɨɩɬɢɦɢɡɚɰɢɢ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɧɨɜɵɯ ɞɨɪɨɝ ɢ ɨɛɴɟɤɬɨɜ ɬɪɚɧɫɩɨɪɬɧɨɣ ɢɧɮɪɚɫɬɪɭɤɬɭɪɵ, ɫɧɢɠɟɧɢɸ ɚɜɚɪɢɣɧɨɫɬɢ ɧɚ ɞɨɪɨɝɚɯ. ɋɨɜɪɟɦɟɧɧɵɣ ɭɪɨɜɟɧɶ ɪɚɡɜɢɬɢɹ ɧɚɭɤɢ ɢ ɬɟɯɧɢɤɢ ɩɨɡɜɨɥɹɟɬ ɫɨɡɞɚɜɚɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ, ɤɨɬɨɪɵɟ ɞɚɸɬ ɧɚɝɥɹɞɧɨɟ ɢ ɫɢɫɬɟɦɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɪɚɛɨɬɟ ɬɪɚɧɫɩɨɪɬɚ ɜ ɝɨɪɨɞɟ,ɨɬɨɛɪɚɠɚɸɬ ɛɥɢɡɤɢɟ ɤ ɪɟɚɥɶɧɵɦ ɡɚɤɨɧɨ-ɦɟɪɧɨɫɬɢ ɬɪɚɧɫɩɨɪɬɧɵɯ ɩɪɨɰɟɫɫɨɜ [5]. Ɍɚɤɚɹ ɬɟɯɧɨɥɨɝɢɹ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɧɚ ɷɬɚɩɟ ɩɥɚɧɢɪɨɜɚɧɢɹ ɪɟɚɥɢɡɨɜɚɬɶ ɜɚɪɢɚɧɬɧɭɸ ɩɪɨɪɚɛɨɬɤɭ ɢ ɨɰɟɧɢɜɚɬɶ ɩɨɫɥɟɞɫɬɜɢɹ ɩɪɢɧɹ-ɬɵɯ ɪɟɲɟɧɢɣ.
Ɉɫɧɨɜɧɵɟ ɜɵɜɨɞɵ:
1.ɇɚ ɨɫɧɨɜɟ ɜɵɩɨɥɧɟɧɧɨɝɨ ɚɧɚɥɢɡɚ ɦɟɬɨɞɨɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɧɫ-ɩɨɪɬɧɵɯ ɩɨɬɨɤɨɜ ɜɵɹɜɥɟɧɵ ɨɫɧɨɜɧɵɟ ɬɟɧɞɟɧɰɢɢ ɢ ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɧɚɢɛɨɥɟɟ ɩɟɪ-ɫɩɟɤɬɢɜɧɵɦ ɹɜɥɹɟɬɫɹ ɢɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɧɫɩɨɪɬɧɨɣ ɫɢɫɬɟɦɵ.
2.ɋɚɦɨ ɩɨ ɫɟɛɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɧɟ ɪɟɲɚɟɬ ɬɪɚɧɫɩɨɪɬɧɵɟ ɩɪɨɛɥɟɦɵ,ɧɨ ɜɤɭɩɟ ɫ ɝɪɚɦɨɬɧɵɦɢ ɫɩɟɰɢɚɥɢɫɬɚɦɢ ɨɧɨ ɫɬɚɧɨɜɢɬɫɹ ɧɚɢɛɨɥɟɟ ɬɨɱɧɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɥɚɧɢɪɨɜɚɧɢɹ,ɪɟɲɚɹ ɝɥɚɜɧɭɸ ɡɚɞɚɱɭ – ɫɨɤɪɚɳɚɬɶ ɡɚɬɪɚɬɵ ɧɚ ɩɟɪɟɦɟ-ɳɟɧɢɹ.
3.Ɉɩɪɟɞɟɥɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɟɣ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɧɚ ɨɫɧɨɜɟ ɧɚɬɭɪɧɵɯ ɧɚɛɥɸ-ɞɟɧɢɣ,ɢɥɢ ɨɛɴɟɤɬɚɯ-ɚɧɚɥɨɝɚɯ,ɤɨɬɨɪɵɟ ɞɨɥɠɧɵ ɛɵɬɶ ɩɪɟɞɫɬɚɜɢɬɟɥɶɧɵɦɢ ɢ ɞɨɫɬɚɬɨɱ-ɧɵɦɢ ɞɥɹ ɨɛɨɛɳɟɧɢɹ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɢ ɞɨɤɚɡɚɬɟɥɶɫɬɜɚ ɢɯ ɞɨɫɬɨɜɟɪɧɨɫɬɢ.
Ʌɢɬɟɪɚɬɭɪɚ
1.Ȼɪɚɣɥɨɜɫɤɢɣ ɇ.Ɉ.,Ƚɪɚɧɨɜɫɤɢɣ Ȼ.ɂ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɧɫɩɨɪɬɧɵɯ ɫɢɫɬɟɦ / Ɇ.: Ɍɪɚɧɫɩɨɪɬ, 1978 - 125 ɫ.
2.ɋɦɢɪɧɨɜ ɇ.ɇ.,Ʉɢɫɟɥɟɜ Ⱥ.Ȼ.,ɇɢɤɢɬɢɧ ȼ.Ɏ., ɘɦɚɲɟɜ Ɇ.ȼ. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɚɜɬɨɬɪɚɧɫɩɨɪɬɧɵɯ ɩɨɬɨɤɨɜ // ɦɟɯ-ɦɚɬ ɆȽɍ, 1999.
3.ɍɢɡɟɦ Ⱦɠ.Ʌɢɧɟɣɧɵɟ ɢ ɧɟɥɢɧɟɣɧɵɟ ɜɨɥɧɵ // Ɇ.: Ɇɢɪ, 1977.
4.ɒɜɟɰɨɜ ȼ.Ʌ.Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɧɫɩɨɪɬɧɵɯ ɩɨɬɨɤɨɜ // Ⱥɜɬɨɦɚɬɢɤɚ ɢ ɬɟɥɟɦɟ-ɯɚɧɢɤɚ. 11, 2003.
5.ɒɜɟɰɨɜ ȼ.Ʌ., Ⱥɧɞɪɟɟɜɚ ȿ.Ⱥ.,ɍɩɪɚɜɥɟɧɢɟ ɬɪɚɧɫɩɨɪɬɧɨɣ ɫɢɫɬɟɦɨɣ ɧɚ ɨɫɧɨɜɟ ɤɨɦɩɪɶɸɬɪɧɨɣ ɦɨɞɟɥɢ PTV VISION® VISUM,ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝ
The literature
1. Brailovsky N.O., Granovsky B.I. Modeling transport systems / M.: Trans port 1978 – p. 125.
2. Smirnov N.N., Kiselev A.B., Nikitin V.F., Yumashev M.V. Mathematical simulation of transport streams / / Mechanics and Mathematics Moscow State University, 1999.
3. Whitham G.B., Linear and Nonlinear Waves, Moscow: Mir, 1977.
4. Shvetsov V.L. Mathematical modeling of transport streams. November, 2003.
5. Swetsov V.L., Andreeva E.A., Management of transport system on the basis of computer model PTV VISION® VISUM, St. Petersburg
6. 3rd Swiss Transport Research Conference, Monte Verita / Ascona, March 19-21, 2003, Traffic Jam Dynamics in Traffic Flow Models, STRC 03 Conference paper.
7. Chandler R.E. at al. Traffic dynamics: Studies in car following // Opreations Research. 1958, Vol. 6, p. 165-185.
8. Daganzo C.F. Remarks on Traffic Flow Modeling and its Applications // Dept. of Civil and Envi-ronmental Engeneering University of California, Berkeley.
9. Greenberg H. An analysis of traffic flow // Operations Research. 1959, Vol. 7, p. 79-85.
10. Greenshields B.D. A study of traffic capacity // Proc. (US) highway research. Board, 1934, Vol. 14, p. 448-494.
11. Kerner B.S., Rehborn H. // Phys. Rev. E., 1996, Vol. 53, p. 42-45.
12. Ligthill M.J., Whitham F.R.S. On kinetic waves II. A theory of traffic flow on crowded roads //
Proc. of the Royal Society Ser. A. 1995, Vol. 229, No. 1178, p. 317-345.
13. Nagel K., Wagner R., Woesler R. Still flowing: Approaches to traffic flow and traffic jam model-ing, January 2, 2003.
14. Static and Dynamic Traffic Assignment with Recurrent Neural Networks, Paul Mathias, Siemens AG, ATD SV PSM, Department of Computer Sciense 4, Aachen University of Technology
15. Studying the ebb and flow of stop-and-go; Los Alamos Lab using cold war tools to scrutinize traffic patterns. Alan Sipress washington post staff writer, Thursday, August 5, 1999, www.science.com Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɦɨɞɟɥɢɪɨɜɚɧɢɟ, ɢɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ, ɬɪɚɧɫɩɨɪɬ, ɬɪɚɧɫɩɨɪɬɧɚɹ ɢɧ-ɮɪɚɫɬɪɭɤɬɭɪɚ,ɭɥɢɱɧɨ-ɞɨɪɨɠɧɚɹ ɫɟɬɶ,ɝɨɪɨɞɫɤɚɹ ɬɟɪɪɢɬɨɪɢɹ,
Keywords: modeling, simulation, transport, transport system, network of street, urban area
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