Quality Properties of Connected Flow Model and Application for Traffic

Abstract

Sequential moving of particles in one direction is considered. Model of totally-connected  flow is introduced in [1] -[4] and concerned to the type of follow-the-leader in traffic flow theory.Properties of traffic flow are significantly determinate by state-function. For describing of non connected  flow  we introduce new model when acceleration of particles takes into consideration the dynamics of neighborhoods particles.For a chain of particles the model is describing by differential equations of second degree. The function of communication for this model is defined. Inpartial  case the sufficient conditions for convergence of solution the model to totally-connected state are obtained.In the case of leader-follower pair of particles with linear state and communication functionsthe statements of belonging of solutions to some Sobolev classes of function are proved.

References

1. V.V. Kozlov, A.P. Buslaev. On a system of
2. nonlinear differential equations for the model of
3. totally connected traffic. Journal of Concrete and
4. Applicable Mathematics. Eudoxus Press, LLC. Vol. 12
5. Num’s 1-2, 2014, 86 – 93.
6. Rothery R.W. Car Following Models in Traffic Flow
7. Theory, Transportation research board, ed. Gartner
8. N, Special report, 165, 1992, p. 4.1 - 4.42

9. Pipes L.A. An Operational Analysis of Traffic
10. Dynamics, Journal of Applied Physics, 1953, v. 24, p.
11. -281.
12. Buslaev A.P. et al. Selected Mathematical Problems
13. of Traffic Flow Theory International Journal of
14. Computer Mathematics Vol. 89, 3, 2012, p.409-432
15. A.N. Kolmogorov, Selected works. In 6
16. volumes.Volume 1: Mathematics and mechanics. Nauka
17. Moscow, 1985, pp. 1469 (in Russian) (V.M.
18. Tikhomirov and G.G. Magaril – Ilyaev, Inequalities for
19. derivatives, pp. 387389).
20. Bugaev A.S., Buslaev A.P., Kozlov V.V., Yashina M.V.
21. Distributed Problems of Monitoring and Modern
22. Approaches to Traffic Modeling, p. 6, 14th International
23. IEEE Conference on Intelligent Transportation Systems
24. (ITSC 2011), Washington, USA, 5-7.10.2011
25. Buslaev A.P., Provorov A.V., Yashina M.V.
26. Infocommunication Systems of Saturated Traffic
27. Control in Megalopolises. Proceedings of the 2013
28. International Conference on Internet Computing and
29. Big Data (WORLDCOMP13), 2013, Las Vegas, USA.
30. pp. 622-625.
31. Yashina M.V., Provorov A.V. Verification of
32. Infocommunication System Components for Modeling
33. and Control of Saturated Traffic in Megalopolis.
34. Proceedings of the 8th International Conference on
35. Dependability and Complex Systems DepCoSRELCOMEX
36. Brunow, Poland. Springer, 2013. pp.
37. -542.
38. A.P. Buslaev, M.G. Gorodnichev, A.V. Provorov. Onedimensional
39. Models of Particles Flow and
40. Infocommunication Methods of Verification.
41. Proceeding of The 2014 International Conference on
42. Computational Science and Computational
43. Intelligence, 10-12 March 2014, Las Vegas, USA
44. V.V. Kozlov, A.P. Buslaev. On a system of
45. nonlinear differential equations for the model of
46. totally connected traffic. Journal of Concrete and
47. Applicable Mathematics. Eudoxus Press, LLC. Vol. 12
48. Num’s 1-2, 2014, 86 – 93.
49. Rothery R.W. Car Following Models in Traffic Flow
50. Theory, Transportation research board, ed. Gartner
51. N, Special report, 165, 1992, p. 4.1 - 4.42
52. Pipes L.A. An Operational Analysis of Traffic
53. Dynamics, Journal of Applied Physics, 1953, v. 24, p.
54. -281.
55. Buslaev A.P. et al. Selected Mathematical Problems
56. of Traffic Flow Theory International Journal of
57. Computer Mathematics Vol. 89, 3, 2012, p.409-432
58. A.N. Kolmogorov, Selected works. In 6
59. volumes.Volume 1: Mathematics and mechanics. Nauka
60. Moscow, 1985, pp. 1469 (in Russian) (V.M.
61. Tikhomirov and G.G. Magaril – Ilyaev, Inequalities for
62. derivatives, pp. 387389).
63. Bugaev A.S., Buslaev A.P., Kozlov V.V., Yashina M.V.
64. Distributed Problems of Monitoring and Modern
65. Approaches to Traffic Modeling, p. 6, 14th International
66. IEEE Conference on Intelligent Transportation Systems
67. (ITSC 2011), Washington, USA, 5-7.10.2011
68. Buslaev A.P., Provorov A.V., Yashina M.V.
69. Infocommunication Systems of Saturated Traffic
70. Control in Megalopolises. Proceedings of the 2013
71. International Conference on Internet Computing and
72. Big Data (WORLDCOMP13), 2013, Las Vegas, USA.
73. pp. 622-625.
74. Yashina M.V., Provorov A.V. Verification of
75. Infocommunication System Components for Modeling
76. and Control of Saturated Traffic in Megalopolis.
77. Proceedings of the 8th International Conference on
78. Dependability and Complex Systems DepCoSRELCOMEX
79. Brunow, Poland. Springer, 2013. pp.
80. -542.
81. A.P. Buslaev, M.G. Gorodnichev, A.V. Provorov. Onedimensional
82. Models of Particles Flow and
83. Infocommunication Methods of Verification.
84. Proceeding of The 2014 International Conference on
85. Computational Science and Computational
86. Intelligence, 10-12 March 2014, Las Vegas, USA