Modified Stochastic Cell Transmission Model 1,a) 1,b) 1,c) Cell Transmission Model CTM Stochastic Cell Transmission Model SCTM CTM SCTM Modified Stochastic Cell Transmission Model MSCTM MSCTM CTM 1. Cell Transmission Model CTM Stochastic Cell Transmission Model SCTM CTM SCTM CTM SCTM SCTM 1 Nagoya Instatute of Technology a) tokuda.sho@itolab.nitech.ac.jp b) kanamori.ryo@nitech.ac.jp c) ito.takayuki@nitech.ac.jp Modified Stochastic Cell Transmission Model MSCTMMSCTM SCTM SCTM MSCTM SCTM CTM MSCTM 10 2. 2.1 Cell Transmission Model CTM Carlos F.Daganzo 1994 [1][2] CTM CTM 1 LWR LWR 1
LWR CTM LWR [3] LWR 1 1 LWR CTM 1 1 2.2 Stochastic Cell Transmission Model SCTM A. Sumalee 2011 [3][4] SCTM CTM CTM SCTM 2 1 2 2 SCTM 0 1 1 0 SCTM switching-mode [5][6] SCTM SCTM SCTM Zhong [7] SCTM Zhong 3 3 3 SCTM 1 [3] 3 Zhong [7] 2
3. Modified Stochastic Cell Transmission Model 3.1 Zhong [7] SCTM 3 3 3 SCTM 3 1 1 SCTM MSCTM 3 SCTM 3.2 (1) t = l v (1) (1) t l v & & [8] & (2) v = v f (1 k k j ) (2) (2) v v f k k j 0 0 (1) (2) [9] k (3) k = n l (3) 3
FF CC CF FC (4) (5) (6) (7) P F F = P r(ρ u < ρ c,1 ρ d < ρ c,2 ) (4) 4 5 (3) k n l (2) v k j v f (1) MSCTM 3.3 2 5 FF Free flow-free flowcc Congestion- CongestionCF Congestion-Free flow FC1 Free flow-congestion1 FC2 Free flow-congestion2 4 FF CC CF FC FC 2 FC1 FC2 2 P CC = P r(ρ u ρ c,1 ρ d ρ c,2 ) (5) P CF = P r(ρ u ρ c,1 ρ d < ρ c,2 ) (6) P F C = 1 (P F F + P CC + P CF ) (7) ρ u ρ d ρ c,1 ρ c,2 ρ c,1 ρ c,2 FF (ρ u < ρ c,1 ρ d < ρ c,2 ) ρ c,1 ρ c,2 FC1 FC2 FC1 (8) FC2 (9) P F C1 = P F C P r(v f,1 ρ u w c,2 (ρ J,2 ρ d )) (8) P F C2 = P F C P r(v f,1 ρ u > w c,2 (ρ J,2 ρ d )) (9) v f,1 w c,2 ρ J,2 FC1 FC2 v f,1 w c,2 ρ J,2 3.4 MSCTM SCTM S S 2 FF 4
CF S v f,1 ρ 1 CC FC S Q 1 v f,1 ρ 1 Q 1 S 4 ( 1 ) FF FC S Q 2 S ( 2 ) FF FC S Q 2 Q 2 ( 3 ) CC CF S w c,2 (ρ J,2 ρ 2 ) S ( 4 ) CC CF S w c,2 (ρ J,2 ρ 2 ) w c,2 (ρ J,2 ρ 2 ) Q 2 w c,2 ρ J,2 ρ 2 4 (10) (11) (12) (13) P 1 = (P F F + P F C )P r(s Q 2 ) (10) P 2 = (P F F + P F C )P r(s > Q 2 ) (11) P 3 = (P CC + P CF )P r(s w c,2 (ρ J,2 ρ 2 )) (12) P 4 = (P CC + P CF )P r(s > w c,2 (ρ J,2 ρ 2 )) (13) P 1 P 2 P 3 P 4 (14) S = P 1 S + P 2 Q 2 + P 3 S + P 4 w c,2 (ρ J,2 ρ 2 ) (14) S SCTM [10] Zhong [7] 4 Zhong 1 1 1 2 5 MSCTM SCTM MSCTM 4. 4.1 MSCTM Zhong [7] MSCTM SCTM Zhong MSCTM SCTM 4.1.1 Zhong [7] 3 1 2 2 1 5 5% 2 3.5 5 SCTM MSCTM 5
0 20 2000 20 40 7000 40 60 0 Zhong MSCTM Zhong 4.1.2 3 R 6 Zhong 3 R 7 6 7 6 7 MSCTM SCTM 4.2 [11] MSCTM CTM 4.2.1 MSCTM 8 130 18000 10% 100 MSCTM CTM 2 10 MSCTM CTM 10 4.2.2 MSCTM CTM MSCTM CTM 9 9 MSCTM CTM 45 MSCTM MSCTM CTM 6 7 Zhong [7] 8 6
5. 9 MSCTM 3.8 CTM 4.6 MSCTM 10 MSCTM CTM 10 10 MSCTM CTM 10 10 MSCTM CTM 10 CTM MSCTM MSCTM CTM MSCTM 19.8 CTM 32.3 MSCTM 10 MSCTM 10 10 CTM SCTM MSCTM SCTM SCTM MSCTM 10 CTM MSCTM [1] Carlos F. Daganzo: The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research Part B: Methodological Volume 28, 1994, Pages 269-287. [2] Carlos F. Daganzo: The cell transmission model, Part II: Network traffic, Transportation Research Part B: Methodological Volume 29, 1995, Pages 79-93. [3] A. Sumalee, R.X. Zhong, T.L. Pan and W.Y. Szeto: Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment, Transportation Research Part B: Methodological Volume 45, Issue 3, 2011, Pages 507533 [4] Agachai Sumalee, Tianlu Pan, Renxin Zhong, Nobuhiro Uno and Nakorn Indra-Payoong: Dynamic stochastic journey time estimation and reliability analysis using stochastic cell transmission model: Algorithm and case studies, Transportation Research Part C: Emerging Technologies Vol. 35, October 2013, P263-285. [5] Laura Munoz, Xiaotian Sun, Roberto Horowitz, Luis Alvarez: Trafic Density Estimation with the cell transmission model, Proceedings of the American Control Conference. Denver, Colorado, USA, pp. 3750-3755. [6] Xiaotian Sun, Laura Munoz and Roberto Horowitz: Highway Traffic State Estimation Using Improved Mixture Kalman Filters for Effective Ramp Metering Control, 42th IEEE Conference on Decision and Control, Vol.6, pp. 6333-6338, 2003. [7] R. X. Zhong, A. Sumalee, T. L. Pan and W. H.K. Lam: Stochastic cell transmission model for traffic network with demand and supply uncertainties, Transportmetrica A: Transport Science, P567-602, 2013. [8], :, (1992). [9] : - -, (1998). [10] S. Fruhwirth-Schnatter: Finite Mixture and Markov Switching Models, Springer 2006. [11] :, http://www.i-transportlab.jp/bmdata/ KichijojiBM/ave-dataset/ave-index.html. 7