Empirical Research on the Occurrence Mechanism of Congested Regime in a Macroscopic Fundamental Diagram

Empirical Research on the Occurrence Mechanism of Congested Regime in a Macroscopic Fundamental Diagram 20 th Hongkong Society for Transportation Studies Dec.12 th ~ 14 th, 201, Hongkong 1) P. Wang, 1) T. Akamatsu, 2) K. Wada 1) Tohoku Univ., 2) Univ. of Tokyo 1

Background (1) Limitations of current traffic forecasting models Require too many inputs (e.g., dynamic OD matrices) Driver navigation is an unpredictable gaming activity Congested networks behave chaotically It is difficult to put these forecasting models into practice Daganzo (2007) [Theoretical study] Proposed a macroscopic observation-based model called Macroscopic Fundamental Diagram (MFD) The MFD relates the number of vehicles (accumulation) in an area to the area s traffic production 2

Background (2) Geroliminis and Daganzo (2008) [Empirical study] Demonstrated that the well-defined MFD exists with a field experiment in downtown Yokohama, Japan It is reproducible and invariant when the traffic demand changes both within-day and day-to-day Average occupancy Area of Analysis Average flow Uncongested Regime Critical density Congested Regime Average density [Geroliminis and Daganzo (2008)] 3

Background (3) Analysis on MFD features (e.g., hysteresis loops) Analyzed the relationship between the MFD features and the spatial distribution of link density MFDs Spatial distribution of link density Average flow Average occupancy [Geroliminis and Sun (2011b)] It is still difficult to understand the mechanism of the MFD features, especially the occurrence of the congested regime in an MFD 4

Previous empirical studies on MFD Urban road networks Geroliminis and Daganzo (2008): Yokohama Tsubota et al. (2014): Brisbane He et al. (2014): Beijing Saeedmanesh and Geroliminis (201): Sydney Wang et al. (201): Sendai Expressway networks Buisson and Ladier (2009): Toulouse Geroliminis and Sun (2011a, b): Minnesota Saberi and Mahmassani (2012), (2013): Portland, Chicago Knoop and Hoogendoom (2013): Amsterdam It is much less than the number of theoretical and simulation studies

Purpose of this study Limitations of previous empirical studies on MFD Use data for only several days at most, which may be insufficient to investigate the robust features of the MFD Do not explore the mechanism of the MFD features (e.g., relationship between MFD features and congestion pattern) This study Use a long-term detector data to analyze the robust features of the MFD for an urban road networks Explore the mechanism by investigating the relationship between the MFD features and the congestion pattern 6

Contents Basic information of the detector data Data record MFD definition Characterization of MFDs Different demand condition (weekday/weekend) Different supply condition (sunny/rainy) Mechanism analysis MFD features v.s congestion pattern Evolution process of congestion pattern 7

Basic information of detector data (1) Analysis area CBD road networks in Naha (Okinawa Pref., Japan) Number of detectors: 122 Analysis area Spatial distribution of detectors in analysis area [Origin:Google Earth] Road network structure in analysis area 9

Basic information of detector data (2) Analysis period /1/2012 ~ 4/30/2013 (One year) -min period during each 24-h day (T=288) Data records of detector i during t (-min period) Traffic flow: Vehicle speed: i q t i v t Traffic density: k q i t i t v i t 10

MFD definition The calculation of coordinates for each plot Accumulation: Traffic production: N P t t I i 1 I i 1 k q i t i t l l i i i l I i 1 q i t v i t l :length of link i i Production (veh km/ :0:00~6:00 :6:00~13:00 +:13:00~20:00 :20:00~24:00 Accumulation (veh) 11

MFDs for the entire year Maximum production Production (veh km/ Uncongested Regime Critical accumulation Congested Regime Weekdays Saturdays Sundays/Holidays Accumulation (veh) The congested regime occurs in an MFD for Naha CBD road networks on some weekdays and only several Saturdays 13

MFDs for different demand condition MFDs on sunny weekdays and weekends 12/21/2012 (Fri) 11/3/2012 (Sat) Production (veh km/ Maximum production Critical accumulation Congested Regime Accumulation (veh) Production (veh km/ Accumulation (veh) The congested regime occurs on 12.0% of sunny weekdays and do not occur on sunny weekends (including Saturdays, Sundays, and holidays) 14

Production (veh km/ MFDs for different supply condition MFDs on rainy weekday and weekend 10/17/2012 (Wed) Production (veh km/ Accumulation (veh) Accumulation (veh) 12/1/2012 (Sat) The congested regime occurs on 31.1% of rainy weekdays and 4.2% of rainy weekends 1

MFDs with congested regime (Example 1) On sunny weekdays Production (veh km/ 6/26/2012 (Tue) Accumulation (veh) Production (veh km/ 12/6/2012 (Thu) Accumulation (veh) Production (veh km/ 12/2/2012 (Tue) Accumulation (veh) 16

MFDs with congested regime (Example 2) On rainy weekdays Production (veh km/ 8/8/2012 (Wed) The evening peak hours Accumulation (veh) Production (veh km/ 12//2012 (Wed) Accumulation (veh) Production (veh km/ 2/12/2013 (Tue) Accumulation (veh) Summary Congested regime occurs in an MFD is not a rare phenomenon The occurrence times are always during the evening peak hours on sunny or rainy weekdays (16:30~19:30) 17

Analysis on the congested regime (1) Clustering classification based on the MFD shapes Demand Supply Height Demand (sunny) (Demand + Supply) Supply (rainy) Date The MFDs with congested regime which is due to the demand increase or supply decrease can be clearly classified into two groups 18

Analysis on the congested regime (2) Comparison of MFD shapes Production (veh km/ Maximum production Critical accumulation Demand increase group Supply decrease group Accumulation (veh) The MFDs with congested regime which is due to the demand increase exhibits higher critical accumulation and maximum traffic production 19

Aggregated analysis on congested pattern Hypothesis If the number of queue-spillbacks become large to a high value, the congested regime may occur in an MFD Definition of queue-spillbacks during time period t Case-1 Case-2 Case-3 S 0 S 1 3 t : Congested link ( v i t 20[ km / h] ) : Uncongested link t S t 21

Comparison of queue-spillbacks Time series of the number of queue-spillbacks Evening peak hours Evening peak hours Number of queue-spillbacks Number of queue-spillbacks Time (h) Time (h) Congested days for one year Uncongested days for one year Congested regime occurs in an MFD when the number of queuespillbacks become large to a high value during the evening peak hours 22

Congestion pattern during the entire year Congested days Uncongested days No. No.1 No.1 Latitude No.2 No.3 Latitude No.2 No.3 No.6 No.4 No.4 Longitude Longitude No.1-No.4: congested frequencies for each link and the spatial distribution of congested links are extremely different between the two kinds of days For the Naha CBD road networks, if the congestion spreads in Nos.1-4, the congested regime occurs in an MFD 23

MFD v.s Congestion pattern (Example 1) 6/26/2012 (Congested day, sunny) Congestion pattern MFD Latitude Congested link Longitude Production (veh km/ 16:40 Accumulation (veh) Uncongested regime 24

MFD v.s Congestion pattern (Example 1) 6/26/2012 (Congested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 17:3 Accumulation (veh) Maximum production 2

MFD v.s Congestion pattern (Example 1) 6/26/2012 (Congested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 17: Accumulation (veh) Congested regime 26

MFD v.s Congestion pattern (Example 1) 6/26/2012 (Congested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 18:3 Accumulation (veh) Maximum accumulation 27

MFD v.s Congestion pattern (Example 1) 6/26/2012 (Congested day, sunny) No.1 Latitude Production (veh km/ The congested regime occurs gradually as the congestion spreads in cluster Nos.1-4 No.2 Longitude Longitude Longitude Longitude 16:40 Uncongested regime Maximum production No.4 17:3 17: 18:3 Congested regime Maximum accumulation Accumulation (veh) Accumulation (veh) Accumulation (veh) Accumulation (veh) No.3 28

MFD v.s Congestion pattern (Example 2) /8/2012 (Uncongested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 16:30 Accumulation (veh) Uncongested regime 29

MFD v.s Congestion pattern (Example 2) /8/2012 (Uncongested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 17:0 Accumulation (veh) Uncongested regime 30

MFD v.s Congestion pattern (Example 2) /8/2012 (Uncongested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 18:20 Accumulation (veh) Maximum production 31

MFD v.s Congestion pattern (Example 2) /8/2012 (Uncongested day, sunny) Congestion pattern MFD Latitude Longitude Production (veh km/ 18:3 Accumulation (veh) Maximum accumulation 32

MFD v.s Congestion pattern (Example 2) /8/2012 (Uncongested day, sunny) Latitude Production (veh km/ No.1 No.2 Longitude Longitude Longitude Longitude Maximum production No.4 16:30 17:0 18:20 18:3 Uncongested regime Uncongested regime Maximum accumulation Accumulation (veh) Accumulation (veh) Accumulation (veh) Accumulation (veh) We do not observe the congestion spreading in cluster Nos.1-4 during the entire traffic evolution, even if at the maximum accumulation! No.3 33

Summary and future plans Throughout the observation during the entire year, Congested regime occurs in an MFD (Sunny & Rainy) weekdays:20.3% (Rainy) weekends:4.2% The MFDs with congested regime on sunny weekdays exhibits higher critical accumulation and higher production Relationship between MFD and congestion pattern The number of queue-spillbacks is large Congestion spreading in cluster Nos.1-4 of the network Future plans Establish a model to explore the occurrence mechanism of the congested regime in an MFD 34

Thank you very much for your attention! 3

Reference (1) Buisson, C. and Ladier, C. (2009): Exploring the impact of homogeneity of traffic measurements on the existence of macroscopic fundamental diagrams. Transportation Research Record: Journal of the Transportation Research Board 2124(12), pp.127-136. Daganzo, C.F. (2007): Urban gridlock: Macroscopic modeling and mitigation approaches. Transportation Research Part B 41(1), pp.49-62. Geroliminis, N. and Daganzo, C. (2008): Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings. Transportation Research Part B 42(9), pp.79-770. Geroliminis, N. and Sun, J. (2011a): Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transportation Research Part B 4(3), pp.60-617. Geroliminis, N. and Sun, J.(2011b): Hysteresis phenomena of a macroscopic fundamental diagram in freeway networks. Transportation Research Part A 4(9), pp.966-979. 36

Reference (2) Geroliminis, N. and Skabardonis, A. (2011): Identification and analysis of queue spillovers in city street networks. IEEE Transactions on Intelligent Transportation System 12(4), pp.1107-111. He, Z., Guan, W., Fan, L. and Guan, J. (2014): Characteristics of macroscopic fundamental diagram for Beijing urban ring freeways. Journal of Transportation Systems Engineering and Information Technology 14(2), pp.199-20. Ji, Y.X.. Geroliminisn, N. and Luo, J. (2014): Empirical observation of congestion propagation and dynamic partitioning with probe data for large scale systems. Transportation Research Record: Journal of the Transportation Research Board 2422(14), pp.1-11. Knoop, V.L. and Hoogendoorn, S.P. (2013): Empirics of a generalized macroscopic fundamental diagram for urban freeways. Transportation Research Record: Journal of the Transportation Research Board 2391(13), pp.133-141. 37

Reference (3) Lu, S., Wang, J., Liu, G. and Shao, W. (2014): Macroscopic fundamental diagram of urban road network based on traffic volume and taxi GPS data. Journal of Highway and transportation Research and Development 31(9), pp.138-144. Sabri, M. and Mahmassani, H.S. (2012): Exploring properties of network wide flow-density relations in a freeway network. Transportation Research Record: Journal of the Transportation Research Board 231(16), pp.13-163. Sabri, M. and Mahmassani, H.S. (2013): Hysteresis and capacity drop phenomena freeway networks: Empirical characterization and interpretation. Transportation Research Record: Journal of the Transportation Research Board 2391(), pp.44-. Saeedmanesh, M. and Geroliminis, N. (201): Empirical observation of MFDs and hysteresis loops for multi-region urban networks with stop-line detectors. Transportation Research Record: Journal of the Transportation Research Board, In press. 38

Reference (4) Wang, P., Wada, K., Akamatsu, T. and Hara, Y. (201): An empirical analysis of macroscopic fundamental diagrams for Sendai road networks. Interdisciplinary Information Sciences 21(1), pp.49-61. Wang, P., Wada, K., Akamatsu, T., Sugita, M., Nagoya, T. and Sumi, H.: Characterization of macroscopic fundamental diagrams based on longterm detectors data: Case studies of Sendai and Kyoto cities. JSTE Journal of Traffic Engineering, Submitted. Zhu, L., Yu, L. and Song, G. (2012): MFD-Based investigation into macroscopic traffic status of urban networks and its influencing factors. Journal of South China University of Technology (Natural Science Edition) 40(11), pp.138-146. 39

Appendix (1) The condition of the existence of well-defined MFD The statistical distribution of link density is the same for two different time intervals with the same average density { sd( t1) ~ sd( t2) and O( t1) O( t2)} Q( t1) Q( t2) Average occupancy 1% Average occupancy 2% Probability 7:00 21:4 Probability 12:00 7:0 Occupancy group [Geroliminis and Sun (2011a)] Occupancy group 40

Appendix (2) Geroliminis and Skabardonis (2011) Sanfrancisco CBD road networks Investigated the relationship between the number of vehicles in spillovers and the output using simulation Mean speed Output Number of vehicles in spillovers Number of vehicles in spillovers If the number of vehicles in spillovers become larger than the critical value, the output of an area decrease 41

Production (veh km/ Appendix (3) MFDs on rainy weekdays (evening peak hours) 10/17/2012 (Wed) Time series of Rainfall Accumulation (veh) Rainfall (mm) Morning Morning Afternoon Time (h) The variation of MFD (the range of traffic production observed for each accumulation) is larger than that on sunny weekdays 42

Appendix (4) MFDs on rainy weekdays (morning peak hours) Production (veh km/ 7/9/2012 (Mon) Time series of Rainfall Accumulation (veh) Because of the large rainfall (27mm/h), the congested regime occurs during the morning peak hours Rainfall (mm) Time (h) Morning 43

Appendix () Occurrence frequency and time of congested reimage Sunny weekday Rainy weekday Sunny weekend Rainy weekend Total Days 16 32 0 2 0 Total days 133 103 69 48 33 Rate 12.0% 31.1% 0% 4.2% 14.2% Congested regime occurs in an MFD is not a rare phenomenon A.M/Sunny P.M/Sunny A.M/Rainy P.M/Rainy Total Days 0 16 1 31 48 Total days 133 133 103 103 236 Rate 0% 12.0% 0.97% 30.1% 20.3% The occurrence times are always during the evening peak hours (16:30~19:30) 44

Upstream Appendix (6) Example of demand increase Flow (veh/ Downstream Flow (veh/ Time (h) Flow (veh/ Time (h) 4 Flow (veh/ Time (h) Flow for each link 3 Time (h) 2 1 Inflow is 1.3 times larger than that of uncongested days 4

Upstream Appendix (7) Example of supply decrease Flow (veh/ Flow (veh/ Downstream Flow (veh/ Time (h) Flow (veh/ Time (h) Time (h) Flow (veh/ Time (h) Flow for each link 4 3 Time (h) 2 1 Outflow is 0% lower than that of uncongested days The flow decrease by about a factor of 0% 46

Appendix (8) Analysis on the rainfall during evening peak hours The number of congested days: 47 days The number of rainy days in congested days: 16 days Rainfall [mm/3h] Date Rate (*/47) 0-10 ****** (13) 27.7% 11-20 2012/10/17 (1) 2.1% 21-30 2012/12/ (1) 2.1% 31-40 2013/2/22 (1) 2.1% Summary The rainfall (during the evening peak hours) is not an essential reason for the occurrence of the congested regime in an MFD, but the congested regime occurs more easily when the rain falls 47

Appendix (9) Bus transit lane/link during 17:30-19:00 Summary Bus transit lane is not an essential reason for the occurrence of the congested regime in an MFD :Bus transit lane :bus transit link 48

Appendix (10) Distribution of the intersections with accidents Summary Traffic accidents may be an important reason for the occurrence of the congested regime, but it is not an essential reason :worst-1, Tomari :worst-2, Matsushima :worst-3, Uenoya 49

Appendix (11) Congested days No.1 No. Red:0%~ Purple:40%~0% Blue:30%~40% Uncongested days No.1 Latitude No.2 No.3 Latitude No.2 No.3 No.6 No.4 No.4 Longitude Longitude No.1-No.4: congested frequencies for each link and the spatial distribution of congested links are extremely different between the two kinds of days For the Naha CBD road networks, if the congestion spreads in Nos.1-4, the congested regime occurs in an MFD 0

Appendix (12) The basic information of Naha road networks (1) Famous tourist/largest city in Okinawa prefecture, Japan The public transport system is not developed Population: 316 thousand Links: have 1-3 lanes in each direction Average length of links: 30[m] Speed limit: 60[km/h] Summary The number of visitors is larger than the number of local commuters Most visitors rent cars to travel, due to the undeveloped public transport 1

Appendix (13) The basic information of Naha road networks (2) Tokyo Analysis area Naha Summary The spatial distribution of the sight-seeing spots (the destinations of the most users) is dispersed. This is a very important reason for the users do not center in Naha CBD area during the morning peak hours 2

Appendix (14) The basic information of Naha road networks (3) Latitude Longitude Summary The users can not select a new route to avoid the congested links, especially in Route 8 and Route 330. For this reason, if the congestion occurs in any link, it can spread to the upstream quickly 3

Appendix (1) Clustering classification method (1) Represent the MFD shape of each day by a 0-1 matrix M P ij : the number of plots in the mesh Example of meshed MFD Production (veh km/ Accumulation (veh) Production (veh km/ Accumulation (veh) 4

Appendix (16) Clustering classification method (2) The effective mesh number of day a, b and the common effective mesh: Calculate the distance between day a and day b