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Table 1 Review of Fundamental diagrams of pedestrian flow characteristics
From: Fundamental diagrams of pedestrian flow characteristics: A review
Author | Purpose | Element | Type of Flow | Country | Design values | Remarks | ||||
|---|---|---|---|---|---|---|---|---|---|---|
Field Studies | ||||||||||
Lam et al. [5] | Speed-flow Relationship | Indoor walkways | B | Hong Kong, SAR, China | Description | Indoor walkways in | Proposed a generalized walking time function with bi-directional Pedestrian flow ratio (GBPR) | |||
Flow Ratio | shopping area | commercial area | ||||||||
Effective capacity (ped/m/min) | 1.0 | 68.0 | 75.0 | |||||||
0.1 | 56.1 | 66.7 | ||||||||
At-capacity walking speed (m/min) | 43.00 | 51.01 | ||||||||
Lee [11] | FD | Stairways, Escalators | U | Netherlands | Description | Stairs | Escalators | Pedestrians personal characteristics, infrastructure type and directions of movement influences free speeds | ||
d | a | d | a | |||||||
Vf (m/s) | 0.77 | 0.68 | 0.88 | 0.82 | ||||||
qmax (ms)−1 | 0.86 | 0.18 | 0.93 | 0.67 | ||||||
Seer et al. [38] | FD | Meanders, stairs | U | Austria | Description | Meanders | Stairs | Maximum and effective capacities for meanders and stairs were estimated from the developed FD’s. | ||
Maximum flow rate (Ped/min) | 48.25 | – | ||||||||
Median flow rate (Ped/min) | 47.6 | 111.11 | ||||||||
Median headway (sec) | 1.26 | – | ||||||||
Alhajyaseen et al. [39] | Speed-flow relationship | Crosswalk | B | Japan | Different capacity values for different directional split ratios with different age group of pedestrians | Reduction in capacity is maximum at approximately equal directional split. Capacity may reduce up to 30% because of presence of elderly pedestrians. | ||||
Burghardt et al. [9] | Effect of stair gradient on FD | Stairs | U | Germany | qsmax = 1.1 (ms)−1 Kmax = 3.4 m−2 | Flow decreases with increase in stair gradient. Flow values for a given density in experiments are slightly higher than field observations | ||||
Shah et al. [40] | FD | Stairs | – | India | Vavg (during afternoon) - 29.70 m/min Vavg (during evening) - 23.73 m/min Different design values on different staircases | Pedestrians walk faster during the afternoon or day time compared to evening. Presence of the pedestrians with luggage has significant effect on reduction in the average walking speed of pedestrian. | ||||
Kawsar et al. [41] | FD | walkways and stairs inside a hall room | U | Malaysia | Vf (m/s) | Flow rate (ped.(ms)−1) | Pedestrian flow characteristics are different for indoor and outdoor facilities | |||
min | max | |||||||||
Level walkways | 1.41 | 0.27 | 1.87 | |||||||
Stairs (a) | 0.51 | 0.06 | 0.73 | |||||||
Stairs (d) | 0.54 | 0.08 | 0.88 | |||||||
Corbetta et al. [42] | FD | Corridor between stairs | B | Netherlands | – | FDs shows that co-flow speed are higher for descending pedestrians than for ascending ones. Speeds in counter-flows appear to be higher than in corresponding co-flows | ||||
Qu et al. [19] | FD | Stairs | U | China | – | Pedestrians walked downstairs faster than upstairs. Sub-group behaviour and lane formation were observed | ||||
Experimental Studies | ||||||||||
Daamen and Hoogendoorn [43] | FD | Narrow bottleneck | U | Netherlands | Vfmin = 0.86 m/s Vfmax = 2.18 m/s Vavg = 1.58 m/s Capacity = 1.5 (ms)−1 | Usage of bottleneck is different during near-capacity and capacity flow conditions compared to free flow situations | ||||
Seyfried et al. [44] | FD for single-file motion of pedestrians | Corridor | U | Germany | – | Observed linear relation between Speed and the inverse of density | ||||
Seyfried et al. [8] | Capacity estimation from FD | Bottleneck | U | Germany | Different flow parameter values for different bottleneck widths | Observed linear growth of flow with width | ||||
Seer et al. [38] | FD | Meanders and stairs | U | Austria | Meanders | Stairs | Maximum and effective capacities for meanders and stairs were estimated from the developed FD’s. | |||
Group | 1 | 2 | 1 | 2 | ||||||
Median Flow rate (Ped/min) | 55.6 | 53.6 | 96.46 | 120.45 | ||||||
Headway (sec) | 1.08 | 1.12 | – | – | ||||||
Flow rate (Ped/min) | – | – | 89.82 | 113.65 | ||||||
Seyfried et al. [26] | Influence of measurement method on FD | Corridor | U | Germany | – | Application of different measurement methods leads to large deviations in the results | ||||
Chattaraj et al. [45] | Effect of culture, length of corridor on FD | Corridor | U | India and Germany | Vf (India) = 1.27 (±0.16) m/s Vf (Germany) = 1.24 (±0.15) m/s | Indian subjects speeds are higher than those of German subjects, Corridor length has no impact on the distance headway-speed relation | ||||
Zhang et al. [21] | Influence of ordering in bidirectional flows on FD | Corridor | B | Germany | Vfavg = 1.55 ± 0.18 m/s qsmax = 1.5 (ms)−1 at K = 2.0 m−2 qmax 2.0 (ms)−1 (U) qmax = 1.5 (ms)−1 (B) | Up to densities of 2 m−2 there is no significant difference observed in the FDs for various degrees of ordering (DML, SSL, BFR and UFR) | ||||
Zhang et al. [28] | Influence of measurement method on FD comparison of FD for T-Junction and corridor | T-Junction and Corridor | U | Germany | – | Different methods produces agreeable results with some differences. FDs of various elements cannot be compared | ||||
Zhang et al. [29] | FD | Corridor | U | Germany | – | FDs developed by various methods show equal tendency however with different accuracy. FDs for the same type of facility can be combined into single diagram for specific flow. | ||||
Tian et al. [30] | FD | Corridor acting as bottleneck | U | China | – | Observed a linear relationship between Flow rate and bottleneck width. Pedestrians behaviour in the corridor has a significant effect on time headways and their distribution when they form lanes | ||||
Yang et al. [46] | Speed-flow-density relationship | Stairs | U | China | Different values of parameters for different stairs and also for different situations | Flow rate and density exhibited different tendency for staircases with different dimensions. In emergency situation, the effect of velocity on density was more significant compared to normal situation | ||||
Lv et al. [4] | Pedestrian movement behaviour | Different environments | U | China | Vmax = 1.56 m/s | Incorporating local direction-changing mechanism, self- slowing and visual hindrance information, a 2-D continuous model has been proposed | ||||
Burghardt et al. [9] | Effect of stair gradient on FD | Stairs | U | Germany | qsmax = 1.1 (ms)−1 Kmax = 2.6 m−2 | Flow decreases with increase in stair gradient. Flow values for a given density in experiments are slightly higher than field observations | ||||
Zhang and Seyfried [22] | FD | Corridor | U&B | Germany | qmax = 2.0 (ms)−1(U) qmax = 1.5 (ms)−1(B) | Observed a clear difference between the FD’s of unidirectional and bidirectional flows | ||||
Bandini et al. [47] | FD | Corridor | U&B | Italy | – | High density conditions are simulated by extending the floor-field CA | ||||
Zhang and Seyfried [25] | Influence of intersection of pedestrian flows on FD | Corridor and other scenarios | B&C | Germany | Different flow parameters for different flow situation scenarios | Intersecting angles of 90° and 180° has no influence on the FD’s of various flow types. | ||||
Flötteröd and Lämmel [13] | FD | Straight corridor and round corridor | B | Germany | – | Proposed a one-on-one mapping between FD parameters of uni and bidirectional flows | ||||
Simulation Studies | ||||||||||
Seyfried et al. [14] | Effect of remote action and required space on FD | Corridor | U | Germany | Intended speed values are normally distributed with μ = 1.24 m/s σ = 0.05 m/s | Modified the Social force model. The replication of classical FD is achievable by increasing the required space and prevailing velocity of a person | ||||
Bruno [15] | Speed-Density Relation | Footbridge | – | Italy | Vfavg = 1.34 m/s | Proposed a model that considers the influence of travel purpose, geographic area and effect of lateral vibrations of platform on Speed-Density relation | ||||
Hao et al. [16] | FD | Unknown | U | China | – | A lattice gas model with parallel update rules is used to study unidirectional pedestrian flow | ||||
Chattaraj et al. [6] | Single file pedestrian movement | Corridor | U | India & Germany | – | Dissimilarities exist in FD due to cultural differences | ||||
Lv et al. [4] | Pedestrian movement behaviour | Different environments | U | China | For Evacuation simulation, Vmax = 0.75 m/s For Bottleneck simulation, qs obtained is 2.25(ms)−1 | Simulation of passage and bottleneck were carried out using 2-D continuous model | ||||
Bandini et al. [47] | FD | Corridor | U&B | Italy | Pedestrian Speed = 1.2 m/s | High density conditions are simulated by extending the floor-field CA | ||||
Qu et al. [19] | FD | Stairs | U | China | Different simulation results for different staircases | Estimated the evacuation time and capacity of stairs using simulations | ||||
Flötteröd and Lämmel [13] | FD | Straight corridor and round corridor | B | Germany | – | Proposed a one-on-one mapping between FD parameters of uni and bidirectional flows | ||||
Fu et al. [48] | Lock-step effect and Random slowdown process influence on FD | Unknown | U | China | Pedestrian desired Speed = 1.6 m/s | Influence of lock-step was analysed by Estimating-Correction Cellular Automaton (ECCA) model | ||||