1 Introduction
2 Fundamental diagrams of pedestrian flow characteristics
3 Fundamental diagrams of various flow types
4 Fundamental diagrams for various infrastructural elements
4.1 Corridors
4.2 Bottlenecks
4.3 T - Junction
4.4 Stairs and escalators
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 |
5 Walking speeds at various facilities
6 Conclusions and future directions
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Even though a considerable amount of literature on development of FDs based on theoretical and experimental concepts is available, literature based on empirical findings are limited. From the previous studies it is observed that mostly the research is focused on experiments. As the emotional status of the participants is relaxed during the experiments, they cannot at times reflect the actual behaviour of pedestrians which exists in real life situations. Hence there is a great need to focus on development of FDs by conducting field studies for various pedestrian infrastructure elements with different flow situations.
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Because of the favourable controlled conditions, researchers [3, 4, 6‐9, 22, 24‐26, 28‐31, 43‐46] are interested in conducting experimental studies. The results obtained in experiments can be comparable only if the field studies are conducted on the same element [9]. Otherwise the accuracy of the experimental results cannot be justified. Moreover, differences between filed, experimental and simulation data across different cultures and environments needs to be established and suitable adjustment factors between these studies should be proposed.
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Zhang et al. [29] shows that the FDs of same element with different widths can be combined into a single diagram whereas for different elements it cannot be combined. For instance, the FDs of T-junctions and corridors cannot be combined as the inflow and outflow are different [28]. This shows that FDs are different for different elements as well as different flow conditions. So further deep examination is needed in this area.
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Cultural differences do influence the pedestrian flow characteristics as well as capacities of the pedestrian infrastructural facilities [10, 12, 36, 45, 58]. In order to understand the cultural differences, it is suggested to conduct the research in various regions and compare the design values of flow parameters across various cultures. In addition, it is observed that individual pedestrian characteristics and external conditions are influencing the pedestrian speeds. Some of the factors are age, culture, gender, shy away distance, temperature, travel purpose, type of infrastructure, walking direction. Moreover, the extent to which these factors influence the fundamental diagrams is unknown. [3] Future studies need to focus in this direction.
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Fundamental relationships of pedestrian flow characteristics for various classes of pedestrians are different [3, 56]. This infers that pedestrians walking speed differs with respect to the facility and trip purpose. Hence the application of walking speeds of one facility for the design of other facility may not lead to fruitful results. As walking speeds decides capacity of the facility, it needs to be examined with respect to the context.
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Even for a simple element like a corridor, the application of various measurement methods leads to a large variation in the observations of FD [26]. This reveals that measurement method does influence the results and hence it should be examined further.