O.V. Loginovskiy - Dr. Sc. (Eng.), Professor, Head of Department, South Ural State University (Chelyabinsk). E-mail: iaou@susu.ac.ru A.A. Shinkarev - Post-graduate Student, South Ural State University (Chelyabinsk). E-mail: sania.kill@mail.ru

Nowadays a necessity to create a qualitative and acceptable by cost process of traffic network topologies modeling is especially acute. On the contrary making infrastructure changes to the traffic network is not always acceptably and frequently just exacerbates problems of transport connection quality. Modeling of the traffic flow as an instrument allows to make the most of the existing city traffic network topology and also to verify design decisions that are based on peer reviews. This verification decreases the risk of wrong infrastructure changes to the city traffic network which are easier to prevent then to fix. The main families of the traffic flow models are microscopic, macroscopic, mesoscopic and higher-order models. Besides these families and their subgroups hybrid models are actively evolving nowadays. The hybrid models combine the best parts of the different traffic modeling schools. To solve problems of the cities which level of motorization hasn-t reached to the saturation the traffic flow models based on the cellular automata theory seems to be the most perspective choice. These models advantageously stand out from the other ones by their comparative simplicity and naturalness of the operating rules. Cellular automata models also often do not cede to the other models of the microscopic family by the modeling quality.

 

1. Banister D. The sustainable mobility paradigm // Transport Policy. 2008. V. 15. P. 73−80.
2. Stanley J., Hensher D.A., Stanley J., Currie G., Greene W.H., Vella-Brodrick D. Social Exclusion and the Value of Mobility // Journal of Transport Economics and Policy. 2011. V. 45(2). P. 197−222.
3. Semenov V.V. Matematicheskoe modelirovanie dinamiki transportnykh potokov megapolisa. M.: IPM im. M.V. Keldysha RAN. 2004. 44 s.
4. Yang H., Yagar S. Traffic assignment and signal control in saturated road networks // Transportation Research Part A. 1995. V. 29. P. 125−139.
5. Carey M., Ge Y.E. Comparing whole-link travel-time models // Transportation Research. 2003. V. 37 B. P. 905−926.
6. Pandian S., Gokhale S., Ghoshal A.K. Evaluating effects of traffic and vehicle characteristics on vehicular emissions near traffic intersections // Transportation Research Part D. 2009. V. 14. P. 180−196.
7. Hunt P.B., Robertson D.L., Bretherton R.D. The SCOOT on-line traffic signal optimization technique // Traffic Engineering and Control. 1982. V. 23. P. 190−192.
8. Hallmark S.L., Fomunung I., Guensler R., Bachman W. Assessing impacts of improved signal timing and transportation control measure using an activity-specific modeling approach // Transportation Research Record. 2000. V. 1738. P. 49−55.
9. Unal A., Rouphail N.M., Frey H.C. Effect of arterial signalization and level of service on measured vehicle emissions // Transportation Research Record. 2003. V. 1842. P. 47−56.
10. Li X., Li G., Pang S., Yang X., Tian J. Signal timing of intersections using integrated optimization of traffic quality, emissions and fuel consumption: a note // Transportation Research Part D. 2004. V. 9. P. 401−407.
11. Gasnikov A.V., Klenov S.L., Nurminskijj E.A., KHolodov JA.A., SHamrajj N.B. Vvedenie v matematicheskoe modelirovanie transportnykh potokov: Ucheb. posobie / Prilozhenija: Blank M.L., Gasnikova E.V., Zamjatin A.A. i Malyshev V.A., Kolesnikov A.V., Rajjgorodskijj A.M. / Pod red. A.V. Gasnikova. M.: MFTI. 2010. 362 s.
12. van Wageningen-Kessels F., van Lint H., Vuik K., Hoogendoorn S. Genealogy of traffic flow models // Springer Berlin Heidelberg. 2015. V. 4. P. 445−473.
13. Pipes L.A. An operational analysis of traffic dynamics // J. Appl. Phys. 1953 V. 24(3). P. 274−281.
14. Kometani E., Sasaki T. Dynamic behavior of traffic with a nonlinear spacing: speed relationship // Amsterdam: Elsevier Publishing Co. 1961. V. 105. P. 105−119.
15. Gipps P.G. A behavioral car-following model for computer simulation // Transportation Research Part B Methodological. 1981. V. 15(2). P. 105−111.
16. Newell G.F. Nonlinear effects in the dynamics of car following // Operations Research. 1961. V. 9(2). P. 209−229.
17. Leclercq L. Hybrid approaches to the solutions of the «Lighthill-Whitham-Richards» models // Transportation Research Part B Methodological. 2007. V. 41(7). P. 701−709.
18. Bourrel E., Lesort J.B. Mixing microscopic and macroscopic representations of traffic flow hybrid model based on Lighthill-Whitham-Richards theory // Transp. Res. Rec. J. Transp. Res. Board. 2003. V. 1852. P. 193−200.
19. Laval J.A., Leclercq L. A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic // Philos Trans R Soc A Math Phys Eng Sci. 2010. V. 368. P. 4519−4541.
20. Chandler R., Herman R., Montroll E. Traffic dynamics: studies in car following // Operations Research. 1958. V. 6(2). P. 165−184.
21. Herman R., Montroll E.W., Potts R.B., Rothery R.W. Traffic dynamics: analysis of stability in car following // Operations Research. 1959. V. 7(1). P. 86−106.
22. Helly W. Simulation of bottlenecks in single lane traffic flow // Herman R. (ed). Theory of traffic flow. Proceedings. Amsterdam: Elsevier Publishing Co. 1961. P. 207−238.
23. Gazis D.C., Herman R., Rothery R.W. Nonlinear follow-the-leader models of traffic flow // Operations Research. 1961. V. 9(4). P. 545−567.
24. Bando M., Hasebe K., Nakayama A., Shibata A., Sugiyama Y. Dynamical model of traffic congestion and numerical simulation // Phys Rev E Stat Nonlinear Soft Matter Phys. 1995. V. 51. P. 1035−1042.
25. Bando M., Hasebe K., Nakanishi K., Nakayama A. Analysis of optimal velocity model with explicit delay // Phys Rev E Stat Nonlinear Soft Matter Phys. 1998. V. 58(5). P. 5429−5435.
26. Treiber M., Hennecke A., Helbing D. Congested traffic states in empirical observations and microscopic simulations // Phys Rev E Stat Nonlinear Soft Matter Phys. 2000. V. 62(2). P. 1805−1824.
27. Treiber M., Kesting A. Verkehrsdynamik und -simulationen: Daten, Modelle und Anwendungen der Verkehrsflussdynamik // Springer - Lehrbuch. 2010. P. 380. (German).
28. Wilson R.E. Mechanisms for spatio-temporal pattern formation in highway traffic models // Philos Trans R Soc A Math Phys Eng Sci. 2008. V. 366(1872). P. 2017−2032.
29. Wilson R.E., Ward J.A. Car-following models: fifty years of linear stability analysis: a mathematical perspective // Transp Plan Technol. 2011. V. 34(1). P. 3−18.
30. Kerner B.S., Rehborn H. Experimental features and characteristics of traffic jams // Phys Rev E Stat Nonlinear Soft Matter Phys. 1996. V. 53. P. 1297−1300.
31. Kerner B.S. Introduction to modern traffic flow theory and control: the long road to three-phase traffic theory // New York: Springer. 2009.
32. Wiedemann R. Simulation des Strassenverkehrsflusses // Institute for Traffic Engineering, University of Karlsruhe, Tech. Rep. 1974.
33. Brackstone M., McDonald M. Car-following: a historical review // Transp Res Part F Traffic Psychol Behav. 1999. V. 2(4). P. 181−196.
34. Bexelius S. An extended model for car-following // Transp Res. 1968. V. 2(1). P. 13−21.
35. Lenz H., Wagner C.K., Sollacher R. Multi-anticipative car-following model // Eur Phys J B Condens Matter Complex Syst. 1999. V. 7. P. 331−335.
36. Treiber M., Kesting A., Helbing D. Delays, inaccuracies and anticipation in microscopic traffic models // Phys A Stat Mech Appl. 2006. V. 360(1). P. 71−88.
37. Ossen S., Hoogendoorn S.P. Multi-anticipation and heterogeneity in car-following empirics and a first exploration of their implications // In: Intelligent Transportation Systems Conference (ITSC-06). 2006. IEEE. P. 1615−1620.
38. Knospe W., Santen L., Schadschneider A., Schreckenberg M. Empirical test for cellular automaton models of traffic flow // Phys. Rev. 2004. V. 70.
39. Buckley D.J. A semi-Poisson model of traffic flow // Transp Sci. 1968. V. 2(2). P. 107−133.
40. Branston D. Models of single lane time headway distributions // Transp Sci. 1976. V. 10(2). P. 125−148.
41. Mahnke R., Kühne R. Probabilistic description of traffic breakdown // In: Schadschneider A., Poschel T., Kuhne R., Schreckenberg M., Wolf D.E. (eds). Trafficandgranularflow-05. NewYork: Springer. 2007. P. 527−536.
42. Prigogine I., Andrews F.C. A Boltzmann-like approach for traffic flow // Operations Research. 1960. V. 8(6). P. 789−797.
43. Prigogine I. A Boltzmann-like approach to the statistical theory of traffic flow // Herman R. (ed). Theory of traffic flow. Proceedings. Amsterdam: Elsevier Publishing Co. 1961. P. 158−164.
44. Hoogendoorn S.P., Bovy P.H.L. Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow // Transportation Research Part B Methodological. 2001. V. 35(4). P. 317−336.
45. Tampere C.M.J., van Arem B., Hoogendoorn S.P. Gas-kinetic traffic flow modeling including continuous driver behavior models // Transp Res Rec J Transp Res Board. 2003. V. 1852 P. 231−238.
46. Lighthill M.J., Whitham G.B. On kinematic waves II: a theory of traffic flow on long crowded roads // Proc R Soc Lond Ser A Math Phys Sci. 1955. V. 229(1178). P. 317−345.
47. Richards P.I. Shock waves on the highway // Operations Research. 1956. V. 4(1). P. 42−51.
48. Lebacque J.P. A two phase extension of the LWR model based on the boundedness of traffic acceleration // In: Taylor M. (ed). Transportation and traffic theory in the 21st century. Proceedings of the 15th international symposium on transportation and traffic theory. 2002. P. 697−718.
49. Leclercq L. A new numerical scheme for bounding acceleration in the LWR model // In: Heydecker B.G. (ed). Mathematics in transport. Selected. Proceedings of the 4th IMA international conference on mathematics in transport. Amsterdam.Elsevier. 2007. P. 279−292.
50. Treiterer J., Myers J.A. The hysteresis phenomenon in traffic flow // In Buckley D.J. (editor). Proc. 6thISTT, Artarmon, NewSouthWales. 1974. P. 13.
51. Daganzo C.F. The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory // Transp. Res. B. 1994. V. 28(4). P. 269−287.
52. Daganzo C.F., Lin W.H., delCastillo J. A simple physical principle for the simulation of freeways with special lanes and priority vehicles // Transportation Research Part B Methodological. 1997. V. 31(2) P. 103−125.
53. Laval J.A., Daganzo C.F. Lane-changing in traffic streams // Transportation Research Part B Methodological. 2006. V. 40(3). P. 251−264.
54. Jin W.L. A kinematic wave theory of lane-changing traffic flow // Transportation Research Part B Methodological. 2010. V. 44. P. 1001−1021.
55. Hoogendoorn S.P., vanLint J.W.C., Knoop V.L. Dynamic first-order modeling of phase-transition probabilities // In: Appert-Rolland C., Chevoir F., Gondret P., Lassarre S., Lebacque J.P., Schreckenberg M. (eds). TrafficGranulFlow 07. Berlin: Springer. 2009. P. 85−92.
56. Jabari S.E., Liu H.X. A stochastic model of traffic flow: theoretical foundations // Transportation Research Part B Methodological. 2012. V. 46(1). P. 156−174.
57. Jabari S.E., Liu H.X. A stochastic model of traffic flow: Gaussian approximation and estimation // Transportation Research Part B Methodological. 2013. V. 47. P. 15−41.
58. Daganzo C.F. A behavioral theory of multi-lane traffic flow. Part I: long homogeneous freeway sections // Transportation Research Part B Methodological. 2002. V. 36(2). P. 131−158.
59. Wong G.C.K., Wong S.C. A multi-class traffic flow model: an extension of LWR model with heterogeneous drivers // Transp Res Part A Policy Pract. 2002. V. 36(9). P. 827−841.
60. Treiber M., Helbing D. Macroscopic simulation of widely scattered synchronized traffic states // J Phys A Math Gen. 1999. V. 32(1).
61. Ngoduy D. Multiclass first-order traffic model using stochastic fundamental diagrams // Transportmetrica. 2011. V. 7(2). P. 111−125.
62. Bellomo N., Dogbe C. On the modeling of traffic and crowds: a survey of models, speculations and perspectives // SIAM. 2011. V. 53 P. 409−463.
63. Benzoni-Gavage S., Colombo R.M. An n-populations model for traffic flow // Eur J Appl Math. 2003. V. 14(05). P. 587−612.
64. Chanut S., Buisson C. Macroscopic model and its numerical solution for two-flow mixed traffic with different speeds and lengths // Transp Res Rec J Transp Res Board. 2003. V. 1852. P. 209−219.
65. Ngoduy D., Liu R. Multiclass first-order simulation model to explain non-linear traffic phenomena // Phys A Stat Mech Appl. 2007. V. 385(2). P. 667−682.
66. Ngoduy D. Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships // Transportmetrica. 2010. V. 6(2). P. 121−141.
67. van Lint J.W.C., Hoogendoorn S.P., Schreuder M. Fastlane: a new multi-class first order traffic flow model // Transp Res Rec J Transp Res Board. 2008. V. 2088. P. 177−187.
68. van Wageningen-Kessels F.L.M, van Lint J.W.C., Vuik C., Hoogendoorn S.P. Generic multi-class kinematic wave traffic flow modelling: model development and analysis of its properties // In: Transportation research board 92th annual meeting, under review for transportation research records. 2014.
69. Nair R., Mahmassani H.S., Miller-Hooks E. A porous flow model for disordered heterogeneous traffic streams // In: Transportation research board 89th annual meeting compendium of papers (DVD). Washington D.C. 2012.
70. Payne H.J. Models of freeway traffic and control // In: Mathematical models of public systems. Simulationcouncilproceedings. 1971. P. 51−61.
71. Daganzo C.F. Requiem for second-order fluid approximations of traffic flow // Transportation Research Part B Methodological. 1995. V. 29(4). P. 277−286.
72. Aw A., Rascle M. Resurrection of «second order models» of traffic flow - // SIAM J Appl Math. 2000. V. 60(3). P. 916−938.
73. Lebacque J.P., Mammar S. Generic second order traffic flow modeling // In: Allsop R.E., Bell M.G.H., Heydecker B.G. (eds). Transportationandtraffictheory. Oxford: Elsevier. 2007. P. 755−776.
74. SHinkarev A.A. Analiz i refaktoring predstavlenija modelejj transportnykh potokov na osnove kletochnogo avtomata // V mire nauchnykh otkrytijj. 2015. № 4.1(64). S. 585−595.
75. SHinkarev A.A. Trekhstupenchatoe unificirovannoe predstavlenie modelejj transportnykh potokov na osnove kletochnogo avtomata // Mezhdunar. nauchno-issledovatelskijj zhurnal. 2015. № 3(34). S. 126−128.
76. Shinkarev A.A. Traffic lane changing motivations for traffic flow mathematical models based on cellular automata theory // Control Systems and Information Technologies. 2015. V. 61. P. 48−51.