A multilane traffic flow model accounting for lane width, lane-changing and the number of lanes. (English) Zbl 1338.90116
Summary: Multilane widely exists in the urban traffic system and its traffic flow is more complex than the single-lane traffic flow since it may be affected by each lane’s width, the number of lanes and lane-changing. In this paper, we first use empirical data to study the impacts of lane width and the number of lanes on multilane traffic flow, then propose a new multilane traffic flow model and finally use numerical tests to explore the influences of the variation of lane width, closing lane and changing the number of lanes on each lane’s traffic flow. The numerical results show that the new model can qualitatively reproduce the complex traffic phenomena resulted by the variation of lane width, closing lane and changing the number of lanes and that changing each lane’s width, closing lane and changing the number of lanes may reduce the reliability of the multilane traffic system. In addition, some numerical results are qualitatively consistent with the phenomena that are resulted by the heavy rain in
Beijing on July 21, 2012, which shows that our model can perfectly reproduce some complex traffic phenomena in multilane system from the qualitative perspective.
MSC:
| 90B20 | Traffic problems in operations research |
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
References:
| [1] | Aw A, Rascle M (2000) Resurrection of “second order” models of traffic flow. SIAM J Appl Math 60:916-938 · Zbl 0957.35086 · doi:10.1137/S0036139997332099 |
| [2] | Carey M, Balijepalli C, Watling D (2013) Extending the cell transmission model to multiple lanes and lane-changing. Netw Spat Econ. doi:10.1007/s11067-013-9193-7 · Zbl 1338.90101 · doi:10.1007/s11067-013-9193-7 |
| [3] | Castillo JM (2012) Three new models for the flow-density relationship: derivation and testing for freeway and urban data. Transportametrica 8:443-465 · doi:10.1080/18128602.2011.556680 |
| [4] | Chowdhury D, Santen L, Schreckenberg A (2000) Statistics physics of vehicular traffic and some related systems. Phys Rep 329:199-329 · doi:10.1016/S0370-1573(99)00117-9 |
| [5] | Daganzo CF (1997) A continuum theory of traffic dynamics for freeways with special lanes. Transp Res B 31:83-102 · doi:10.1016/S0191-2615(96)00017-3 |
| [6] | Feng SW (1997) Mathematical modeling, field calibration and numerical simulation of low-speed mixed traffic flow in cities. Ph.D. Dissertation of Shanghai University (in Chinese) · Zbl 1181.90069 |
| [7] | Flötteröd G, Chen Y, Nagel K (2012) Behavioral calibration and analysis of a large-scale travel microsimulation. Netw Spat Econ 12:481-502 · Zbl 1332.90148 · doi:10.1007/s11067-011-9164-9 |
| [8] | Gupta AK, Katiyar VK (2007) A new multi-class continuum model for traffic flow. Transportmetrica 3:73-85 · doi:10.1080/18128600708685665 |
| [9] | Helbing D (2001) Traffic and related self-driven many-particle systems. Rev Mod Phys 73:1067-1141 · doi:10.1103/RevModPhys.73.1067 |
| [10] | Hoogendoorn SP, Bovy PHL (2001) Platoon-based multiclass modeling of multilane traffic flow. Netw Spat Econ 1:137-166, http://www.jishinet.com/html/FocusNet/2012/0725/780.html (in Chinese) · doi:10.1023/A:1011533228599 |
| [11] | Jiang R, Wu QS, Zhu ZJ (2002) A new continuum model for traffic flow and numerical tests. Transp Res B 36:405-419 · doi:10.1016/S0191-2615(01)00010-8 |
| [12] | Jin WL (2010) A kinematic wave theory of lane-changing traffic flow. Transp Res B 44:1001-1021 · doi:10.1016/j.trb.2009.12.014 |
| [13] | Jin S, Wang DH, Tao PF, Li PF (2010) Non-lane-based full velocity difference car-following model. Physica A 389:4654-4662 · doi:10.1016/j.physa.2010.06.014 |
| [14] | Kerner BS (2001) Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories. Netw Spat Econ 1:35-76 · doi:10.1023/A:1011577010852 |
| [15] | Kerner BS, Konhäuster P (1993) Cluster effect in initially homogeneous traffic flow. Phys Rev E 48:R2335-R2338 · doi:10.1103/PhysRevE.48.R2335 |
| [16] | Laval JA, Daganzo CF (2006) Lane-changing in traffic streams. Transp Res B 40:251-264 · doi:10.1016/j.trb.2005.04.003 |
| [17] | Lighthill MJ, Whitham GB (1955) On kinematic waves: II. A theory of traffic flow on long crowed roads. Proc R Soc London 229:317-345 · Zbl 0064.20906 · doi:10.1098/rspa.1955.0089 |
| [18] | Liu GQ, Lyrintzis AS, Michalopoulos PG (1996) Modelling of freeway merging and diverging flow dynamics. Appl Math Model 20:459-469 · Zbl 0869.90024 · doi:10.1016/0307-904X(95)00165-G |
| [19] | Long JC, Gao Z, Zhao X, Lian A, Orenstein P (2011) Urban traffic jam simulation based on the cell transmission model. Netw Spat Econ 11:43-64 · doi:10.1007/s11067-008-9080-9 |
| [20] | Mathew TV, Radhakrishnan P (2010) Calibration of micro simulation models for non-lane-based heterogeneous traffic at signalized intersections. J Urban Plan Dev ASCE 136:59-66 · doi:10.1061/(ASCE)0733-9488(2010)136:1(59) |
| [21] | Michalopoulos PG, Yi P, Lyrintzis AS (1993) Development of an improved high order continuum traffic flow model. Transp Res B 27:125-132 · doi:10.1016/0191-2615(93)90041-8 |
| [22] | Moridpour S, Rose G, Sarvi M (2012) The effect of surrounding traffic characteristics on lane changing behavior. J Transp Eng 136:1-12 |
| [23] | Ngoduy D (2010) Multiclass first order modelling of traffic networks using discontinuous flow-density relationships. Transportmetrica 6:121-141 · doi:10.1080/18128600902857925 |
| [24] | Ngoduy D (2011) Multiclass first-order traffic model using stochastic fundamental diagrams. Transportmetrica 7:111-125 · doi:10.1080/18128600903251334 |
| [25] | Payne HJ (1971) Models of freeway traffic and control. Math Models Publ Syst Simul Counc Proc Ser 1:51-61 |
| [26] | Qi HS, Wang DH, Chen P, Bie YM (2013) Location-dependent lane-changing behavior for arterial road traffic. Netw Spat Econ. doi:10.1007/s11067-013-9202-x · Zbl 1339.90093 · doi:10.1007/s11067-013-9202-x |
| [27] | Richards PI (1956) Shock waves on the highway. Oper Res 4:42-51 · Zbl 1414.90094 · doi:10.1287/opre.4.1.42 |
| [28] | Tang CF, Jiang R, Wu QS (2007) Extended speed gradient model for traffic flow on two-lane freeways. Chin Phys B 16:1570-1575 · doi:10.1088/1009-1963/16/6/013 |
| [29] | Tang TQ, Huang HJ, Xu G (2008) A new macro model with consideration of the traffic interruption probability. Physica A 387:6845-6856 · doi:10.1016/j.physa.2008.08.036 |
| [30] | Tang TQ, Huang HJ, Shang HY (2009a) A new dynamic model for heterogeneous traffic flow. Phys Lett A 373:2461-2466 · Zbl 1231.60106 · doi:10.1016/j.physleta.2009.05.006 |
| [31] | Tang TQ, Huang HJ, Wong SC, Gao ZY, Zhang Y (2009b) A new macro model for traffic flow on a highway with ramps and numerical tests. Commun Theor Phys 51:71-78 · Zbl 1170.90355 · doi:10.1088/0253-6102/51/1/15 |
| [32] | Tang TQ, Li CY, Huang HJ, Shang HY (2011) Macro modeling and analysis of traffic flow with road width. J Cent S Univ Technol 18:1757-1764 · doi:10.1007/s11771-011-0899-8 |
| [33] | Tian C, Sun DH (2010) Continuum modeling for two-lane traffic flow with consideration of the traffic interruption probability. Chin Phys B 19:120501 · doi:10.1088/1674-1056/19/12/120501 |
| [34] | Wong GCK, Wong SC (2002) A multi-class traffic flow model-an extension of LWR model with heterogeneous drivers. Transp Res A 36:827-841 |
| [35] | Wu Z (1994) A fluid dynamics model for low speed traffic system. Acta Mech Sinica 26:149-157 (in Chinese) |
| [36] | Yang XB, Zhang N, Gao ZY (2008) Changes in traffic characteristics affected by number of lanes on freeways. Proceedings of The Transportation Research Board (TRB) 87th Annual Meeting, Washington, D.C. January 13-17 |
| [37] | Yu L, Shi ZK (2009) Density wave in a new anisotropic continuum model for traffic flow. Int J Mod Phys C 20:1849-1859 · Zbl 1181.90069 · doi:10.1142/S0129183109014771 |
| [38] | Zhang HM (1998) A theory of nonequilibrium traffic flow. Transp Res B 32:485-498 · doi:10.1016/S0191-2615(98)00014-9 |
| [39] | Zhang HM (2001) New perspectives on continuum traffic flow models. Netw Spat Econ 1:9-23 · doi:10.1023/A:1011539112438 |
| [40] | Zhang HM (2002) A non-equilibrium traffic model devoid of gas-like behavior. Transp Res B 36:275-290 · doi:10.1016/S0191-2615(00)00050-3 |
| [41] | Zhang HM, Shen W (2009) Numerical investigation of stop-and-go traffic patterns upstream of freeway lane drop. Transp Res Rec 2124:3-17 · doi:10.3141/2124-01 |
| [42] | Zhang P, Wong SC (2006) Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models. Phys Rev E 74:026109 · doi:10.1103/PhysRevE.74.026109 |
| [43] | Zhang P, Liu RX, Wong SC (2005a) High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities. Phys Rev E 71:056704 · doi:10.1103/PhysRevE.71.056704 |
| [44] | Zhang P, Wong SC, Shu CW (2005b) A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway. J Comput Phys 212:739-756 · Zbl 1149.65319 · doi:10.1016/j.jcp.2005.07.019 |
| [45] | Zhang P, Wong SC, Dai SQ (2006) Characteristic parameters of a wide cluster in a higher-order traffic flow model. Chin Phys Lett 23:516-519 · doi:10.1088/0256-307X/23/2/067 |
| [46] | Zhang J, Lam William HK, Chen BY (2013) A stochastic vehicle routing problem with travel time uncertainty: trade-off between cost and customer service. Netw Spat Econ. doi:10.1007/s11067-013-9190-x · Zbl 1332.90186 · doi:10.1007/s11067-013-9190-x |
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