Evacuation Design Focused on Quality of Flow

Evacuation Design Focused on Quality of Flow - Utilizing Multi-Agent Pedestrian Simulator, SimTread - Yoshikazu Minegishi 1 ; Yoshiyuki Yoshida 1 ; Naohiro Takeichi 1 ; Akihide Jo 2 ; Tomonori Sano 3 ; Takeshi Kimura 4 1 Firesafety Section, Design Management Department, Takenaka Corporation, 1-1-1 Shinsuna, Koto-ku, Tokyo 136-0075, Japan. 2 M&E Engineering Section, Building Design Department, Takenaka Corporation, 1-1-1 Shinsuna, Koto-ku, Tokyo 136-0075, Japan. 3 Associate Prof., Faculty of Human Sciences, Waseda University, 2-579-15 Mikajima, Tokorozawa-shi, Saitama 359-1192, Japan. 4 Development Department, A&A Coporation, 2-3-15 Kanda-Surugadai, Chiyoda-ku, Tokyo 101-0062, Japan. ABSTRACT In this paper, a method for the evaluation of evacuation flow is presented. An index of quality of flow (QOF) is defined as a normalized sample moment of the mean velocity during an evacuation of evacuee agents in a multi-agent simulation. The effectiveness of the index is evaluated for three types of scenarios: crowd flow in a straight infinite-loop pathway, evacuation for typical office plans, and total building evacuation of highly densely used buildings. The results for these scenarios confirmed that QOF performs well as a relative measure of evacuation quality for similar evacuation plans, allowing a quantitative way of measuring improvements. The multi-agent pedestrian simulator used, SimTread, was previously developed by the authors. 1. INTRODUCTION In many cases, evacuation plans are evaluated based only on evacuation time. Evacuation characteristics of each evacuee, for example, velocity, and degree of congestion, are rarely considered. However, by using a multi-agent pedestrian simulator, each agent's quantitative data during the evacuation can be acquired, not just holistic data such as evacuation time. Therefore, to use multi-agent pedestrian simulators more effectively for evacuation planning, statistics to understand the data of each agent s status during an evacuation should be considered and evaluated. Specifically, the velocity of evacuees is strongly related to the density of and distance between evacuees, which are important because they are thought to strongly affect the psychological state, specifically, the degree of comfort, of evacuees. The present study focuses on each agent's status to evaluate quality of evacuation as an approach for developing a new method of evacuation safety planning. To this purpose, an evaluation method using the velocities of all evacuees, acquired from a multi-agent pedestrian simulator, is proposed. 2. CONCEPT OF QUALITY OF FLOW (QOF) To evaluate the quality of evacuation flow quantitatively, quality of flow (QOF) is defined. If walking at the free walking velocity (maximum velocity) is assumed to be preferred, then QOF can be regarded as an indicator of evacuees degree of comfort, an aspect of their psychological status. It can also be considered an indicator of the capacity of the pathway, building, or space in which walking takes place. QOF is defined as follows. The mean velocities all evacuees over an evacuation are calculated from simulator data and used to compute a k-dimensional moment of mean velocity.

QOF 1 N N n V V n 1 max mean k (1) QOF : quality of flow [-] N : number of evacuees [persons] n : evacuee number [-] V(n) mean : mean velocity during an evacuation of evacuee n [m/s] V max : maximum velocity of evacuees [m/s] k : dimension (in the present study, taken as ) [-] From this definition, when all people can walk at their maximum velocity, QOF is. When people are crowded and therefore reduce their velocities, QOF decreases. Figure 1 shows velocity distributions of two office plans. As shown, Plan 1-B tends to produce higher velocities. In this research, it is hypothesized that evacuation under Plan 1-B flows smoother than that under Plan 1-A. Evacuee Frequency distribution [%] 0 0.35 0.30 5 0 0.15 0.10 0.05 0.00 0.0 1.2 Plan 1-A Plan 1-B Interval of mean velocity [m/s] Figure 1. Comparison of mean velocity distribution. 1.2 1.4 3. Multi-Agent Pedestrian Simulator SimTread In this research, as a multi-agent pedestrian simulator, SimTread 1),2),3) is adopted. Each agent s status, such as position and velocity, are calculated in intervals of sec. In this research, to ignore minute differences in agent s ability, due to differences in, for example, free walking velocity, body size, and decision behavior, agents are assumed to be identical. In this case, the aggregation of agents is thought to be an "ideal crowd". 4. QOF OF STRAIGHT INFINITE-LOOP PATHWAYS 4.1. Objective and Concept of the Model In this section, the fundamental relationship between the density of a steady liner flow and QOF is clarified. For this purpose, a straight infinite-loop pathway is simulated. As shown in Figure 2, agents are randomly allocated within a 20 m long, 2 m wide straight

pathway. By changing the number of agents, the density on the pathway can be controlled. Agents start the simulation walking in the positive x direction, and when they reach the warp area at the end of the pathway (right, in the figure), they are warped to the warp area at the beginning (left). During this warp, the y coordinate is left unchanged. In this way, an infinite straight pathway is simulated. The agents are allowed to walk and, over several minutes, gradually reach an almost steady flow, at which time velocities and flow rates are measured. In this scenario, V max is taken to be 1.2 m/s. warp (retaining the y coordinate value) y 2 m x warp area 20 m warp area Figure 2. Model of straight infinite-loop pathway. 4.2. Results 4.2.1. Relation between density and QOF Figure 3 illustrates agent velocities among steady flows with different agent densities. Figure 4 shows a plot of the relation between density and QOF. Also shown in Figure 4 are flow rate (N [(persons/m)/s]) and Vx mean /V max (where Vx mean is the mean x-direction velocity of the crowd [m/s]). In the case of densities lower than 1.2 persons/m 2, QOF is, meaning that every agent can walk at their maximum velocity without being disturbed by other agents. For densities higher than 1.2 persons/m 2, QOF decreases as density increases. From the definition of QOF, QOF is essentially equal to Vx mean /V max (since k = 1). But because of the way the model is constructed, there are some differences in some dense sections. Overall, QOF tends to be slightly larger than Vx mean /V max. The reason for this is as follows. In SimTread, when agents avoid running into other agents, they preferentially change direction while maintaining their current velocity rather than slowing. Because Vx mean is the mean velocity in the x-direction, agent velocities are usually higher than Vx mean. ρ = persons/m 2 ρ = 1.6 persons/m 2 ρ = 2.4 persons/m 2 Maximum Velocity (1.2 m/s) Slowed Stopped (0.0 m/s) ρ = 3.2 persons/m 2 Figure 3. Steady flow of different densities.

QOF, Vxmean/Vmax QOF [-] 0.9 0.7 0.5 0.3 0.1 0.0 Fruin s level of service (A F) A B C D E F QOF Vx mean /V max N 0.0 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 Density density [persons/m2] 2 ] Figure 4. QOF vs. density for an infinite-loop pathway. 2.0 1.8 1.6 1.4 1.2 0.0 N: Flow flow rate Rate [(persons/m)/s] [persons/ms 4.2.2. Comparison with Fruin s level of service The level of service proposed by Fruin 4) is precisely defined for low densities (0.0 persons/m 2 ). However, QOF in this density interval is almost constant. One recommendation that can be made on the basis of this result is that minute level of service in high density might be necessary for evacuation evaluation. Also, the areas and widths of paths and bottlenecks in architectural and transportation plans should be chosen to keep the crowd density less than 1.2 persons/m 2. 5. QOF OF TYPICAL OFFICE PLANS To analyze the application QOF to evaluating floor evacuations, QOF was calculated for typical office plans. Next, modifications typically recommended for improving evacuation flow were made to the plans and QOF was recalculated. A comparison of these two sets of QOF data was conducted to examine the suitability of using QOF to evaluate plan safety with respect to floor evacuations. 5.1. Model Plans and Settings In this scenario, three model office plans 1, 2, and 3, illustrated respectively in Figures 5, 6, and 7, where the -A plans are the original typical office plans and the -B plans are the modified versions are used. In each plan, there are two staircases and a central corridor connecting them. Several doorways connect offices and the central corridor, but one doorway in each office plan cannot be used for evacuation because of a nearly fire. V max of evacuees is taken to be 1.2 m/s.

Setting 56 m Plan 1-A 20 m 10 m staircase office (258 persons) fire corridor vestibule vestibule Evacuation start time 1:07 staircase Feature A doorway to the corridor is near each doorway to a staircase Width Corridor: 1.6 m Doorway to vestibule: 1.6 m Doorway to staircase: 0.9 m Value QOF = 0.533 Evacuation time = 3:12 Plan 1-B Feature Doorways to staircases are located at far ends of the corridor Width Corridor: 2.7 m Doorway to vestibule: 1.6 m Doorway to staircase: 0.9 m Value QOF = 0.595 Evacuation time = 3:02 Result Plan 1-A merging point d a1 d a2 Time 2:00 Plan 1-B merging point d b1 d b2 Time 2:00 d a1 <d b1, d a2 <d b2 Maximum velocity (1.2 m/s) Slowed Stopped (0.0 m/s) Figure 5. Plans 1-A and 1-B: floor plan, settings, and calculation results for time 2:00.

13 m Setting 6.5 m vestibule fire ( ) : number of evacuee [persons] 64 m office 1 (210) corridor staircase staircase office 2 (20) Evacuation start time: office 1, 0:58; office 2, 1:56 Plan 2-A Feature Right-hand side staircase connects directly to the corridor. Width Corridor: 1.9 m Doorway to vestibule: 0.9 m Doorway to staircase: 0.9 m Value QOF = 0.556 Evacuation time = 2:42 Plan 2-B vestibule Feature Both staircases have a vestibule. Width Corridor: 1.9 m Doorway to vestibule: 1.2 m Doorway to staircase: 0.9 m Value QOF = 20 Evacuation time = 2:44 Result Plan 2-A q a1 Time 1:30 Plan 2-B q b1 q b2 Time 1:30 q a1 q b2 < q b1 q: flow rate [persons/s] Maximum velocity (1.2 m/s) Slowed Stopped (0.0 m/s) Figure 6. Plans 2-A and 2-B: floor plan, settings, and calculation results for time 1:30.

Setting 48 m ( ) : number of evacuee [persons] Plan 3-A 22.5 m vestibule staircase office 4 corridor (34) fire office 1 office 2 office 3 (98) (19) (58) Evacuation start time: office 1, 0:38; offices 2 4, 0:76 Feature Doorways to corridor and doorways to staircases are relatively close. Width Corridor: 1.6 m Doorway to vestibule: 1.2 m Doorway to staircase: 0.9 m Value QOF = 0.529 Evacuation time = 2:22 Plan 3-B Feature Doorways to staircases are located at the far ends of the corridor Width Corridor: 1.9 m Doorway to vestibule: 1.6 m Doorway to staircase: 0.9 m Value QOF = 04 Evacuation time = 2:31 Result Plan 3-A Time 1:30 Plan 3-B curved route moderate density Time 1:30 Maximum velocity (1.2 m/s) Slowed Stopped (0.0 m/s) Figure 7. Plans 3-A and 3-B: floor plans, settings, and calculation results for time 1:30.

5.2. Result Figures 8, 9, and 10 show the mean velocity distributions for the different pairs of plans, and Figure 11 shows a comparison of QOF across plans. Evacuee Frequency distribution [%] 0 0.35 0.30 5 0 0.15 0.10 0.05 Plan 1-A Plan 1-B 0.00 0.0 Interval of mean velocity [m/s] 1.2 1.2 1.4 Figure 8. Plans 1-A and 1-B: velocity distributions. Evacuee Frequency distribution [%] 0 0.35 0.30 5 0 0.15 0.10 0.05 Plan-2-A Plan-2-B 0.00 0.0 1.2 Interval of mean velocity [m/s] 1.2 1.4 Figure 9. Plans 2-A and 2-B: velocity distributions. Evacuee Frequency distribution [%] 0 0.35 0.30 5 0 0.15 0.10 0.05 0.00 0.0 1.2 Interval Velocity of mean Interval velocity [m/s] [m/s] Plan 3-A Plan 3-B 1.2 1.4 Figure 10 Plans 3-A and 3-B: velocity distributions

QOF [-] 0.9 0.7 0.5 0.3 0.1 0.0 50 0 Plan 1 1 Plan 2 2 Plan 3 3 A B A B A B 250 200 150 100 Figure 11. QOFs and evacuation times for floor evacuations. Evacuation Time [s] QOF Evacuation time 5.3. DISCUSSION Plans 1-A and 1-B Figure 8 shows an increase in the distribution of velocities in the interval from to m/s in Plan 1-B (modified plan) relative to Plan 1-A. This increase leads to an increase in QOF. In these plans, doorways to a vestibule and an adjacent staircase are bottlenecks to the downstream flow from a merge point in the corridor. Thus, these points strongly affect the evacuation flow. The distance between the right-hand side office room corridor doorway and the nearest corridor vestibule doorway, and that between the corridor vestibule doorway and the corresponding vestibule staircase doorway in Plan 1-B are greater than those in Plan 1-A. In Plan 1-B, evacuees pass through the corridor vestibule doorway and go straight for approximately 5 m to a vestibule staircase doorway. In contrast, in Plan 1-A, evacuees have to turn to pass through the vestibule staircase doorway immediately after passing through the corridor vestibule doorway, which leads to the flow rate at the vestibule staircase doorway being much smaller for Plan 1-A than for Plan 2-B. The evacuation time of Plan 1-B is shorter than that of Plan 1-A, and its QOF is higher. Thus, from the viewpoint of both evacuation time and QOF, Plan 1-B is preferable to Plan 1-A. Plans 2-A and 2-B Similar to the case of Plans 1-A and 1-B, Figure 9 shows an increase in the distribution of velocities from to m/s for Plan 2-B (modified) relative to Plan 2-A, which leads to an increase in QOF. But in the case of Plans 2-A and 2-B, evacuation times are almost identical, whereas QOF is higher for Plan 2-B than Plan 2-A. Flow rate at the right-hand side corridor staircase doorway in Plan 2-A is almost identical to that of at vestibule staircase doorway in Plan 2-B, leading to the nearly identical evacuation times. In the case of Plan 2-B, the flow rate at the corridor vestibule doorway is a little longer that at the vestibule staircase doorway; therefore, in the case of Plan 2-B, evacuees can continue walking relatively for long time, rather than just being kept waiting in front of staircase, as in the case of Plan 2-A. Thus Plan 2-B flows smoother than Plan 2-A, and the degree of congestion on Plan 2-B is smaller than that of Plan 2-A. This difference of flow quality is illustrated quantitatively through QOF. Evacuation times for Plans 2-A and 2-B are almost identical; however, the QOF of Plan 2-B is higher than that of Plan 2-A. And thus, overall, Plan 2-B is preferable to Plan 2-A. Plans 3-A and 3-B Similar to the previous two cases, Figure 10 shows an increase in the distribution of velocities from to 1.4 m/s, which leads to an increase in QOF. However, unlike in the previous two cases, evacuation time of the modified plan, Plan 3-B, is longer than that of the original, Plan

3-A. The reason is as follows. In Plan 3-B, the route just before the vestibule staircase doorway turns and this acts as a bottleneck, evacuation time becomes long. But before this bottleneck, evacuees can walk at a moderate velocity amid a crowd of moderate density. Thus, there is much safe retention area like vestibule in Plan 3-B, Plan 3-B indicates high QOF score. Shortening the distance from office room exit to staircase doorway leads shortening of evacuation time. But this shortening causes decrease of safe retention area such as corridor and vestibule, and this also leads to high densely situation in case of evacuation. Especially this design inclination is often seen on office buildings. The evacuation time of Plan 3-A is shorter than that of Plan 3-B, but the QOF of Plan 3-A is higher than that of Plan 3-B. Thus QOF can illustrate the effect of retention area for improvement on quality of flow. 6. QOF OF TOTAL BUILDING EVACUATION* In this chapter, QOF of total building evacuations is examined. As a model building containing many occupants, a night club is used. When an unspecified number of occupants are in narrow rooms, excessive congestion will occur on routes with bottlenecks during an evacuation. In this section, adopting the proposed index, QOF, quality of evacuation flow is examined. 6.1 Model Building The model building is a night club having four floors, one underground floor and three aboveground floors. Floors 0, 1, and 2 contain bars and dance floors, and most of the occupants are on these floors. Floor 3 is dominated by a balcony overlooking Floor 2 (See Figures 12 and 13). 6.2 Variation of plan Case 0 This is the original plan. Evacuees use all stairs and the following evacuee groups pass through the dance floor on Floor 1: Evacuees from the bar on Floor 1 Evacuees from Floor 0 by way of stairs 3 Evacuees from Floor 2 by way of stairs 4 Case 1 Evacuees from Floor 2 do not pass through the dance floor room on Floor 1. That is, rather than using stairs 4, evacuees on Floor 2 evacuate to Floor 1 using only stairs 1 and 2. Case 2 In addition to the condition imposed in Case 1, additional exits connected directly to the outside are added to the floor plan. These exits are added on Floor 1: one is from the barroom and the other is from the dance floor room. In this plan, evacuees in the bar of Floor 1 evacuate outside through the additional exit from the bar and evacuees using stairs 3 evacuate through the additional exit from the dance floor room. Evacuees starting on the dance floor of Floor 1 evacuate through exit 2. * This section is an expansive deliberation of the case study Fire Safety Design of Night Club, Japanese Case Study, 8th International Conference on Performance-Based Codes and Fire Safety Design Methods, 16 18 June 2010, Lund. from the viewpoint of QOF.

bar dance floor bar Floor 0 Floor 1 Floor 2 Floor 3 corridor bar dance floor balcony Figure 12. Plans of Night Club. stairs 3 stairs 3 stairs 1 stairs 1 stairs 2 stairs 2 stairs 1 stairs 2 stairs 4 stairs 1 stairs 4 exit 1 exit 2 exit 3 Figure 13. Floor plans for total building evacuation simulations. DANCEFLOORBARKITCHENSTORAGESHOPGARBAGESTORAGESTAGEBARWARDROBEDJ(OTHERTENANT)1FL±0 STAIRS1 STAIRS2 STAIRS3 STAIRS4 Use stairs4 DANCEFLOORBARKITCHENSTORAGESHOPGARBAGESTORAGESTAGEBARWARDROBEENTRANCEFl2DJ(OTHERTENANT)1FL±0 STAIRS1 STAIRS2 STAIRS3 STAIRS4SMOKETOWERnal exit Not use stairs4 Case 0 Case 1 Case 2 DANCEFLOORBARKITCHENSTORAGESHOPGARBAGESTORAGESTAGEBARWARDROBEDJ(OTHERTENANT)1FL±0 STAIRS1 STAIRS2 STAIRS3 STAIRS4 Not use stairs4 stairs 4, not useable stairs 4, useable additional exits stairs 4, not useable

6.3 Settings The distribution of occupants is shown in Table 1. Maximum walking velocity varied by situation, such as walking on level ground versus walking on stairs, as shown in Table 2. All occupants in the night club began to evacuate simultaneously. In this section on total building evacuation, stairs are included along the evacuation routes, and on these stairs, the maximum walking velocity is defined to be lower than that for level walking. Therefore, when evacuees have to use stairs, the QOF does not reach even under ideal evacuation conditions. 6.4 Results Table 1. Evacuee distribution. Room Area (m 2 ) Occupant density (persons/m 2 ) Evacuee (persons) Floor 0-bar 87.5 2.5 219 Floor 0-corridor 36.0 36 Floor 1-bar 73.7 74 Floor 1-dance floor 7 2.5 178 Floor 2-bar 38.4 0.5 20 Floor 2-dance floor 66.8 2.5 164 Floor 2-stage 34.9 0.7 24 Floor 3-balcony 37.6 38 Total - - 753 Table 2. Maximum walking velocity. situation velocity (m/s) Level walking 0 Stairs up 5 Stairs down 0 Figure 14 shows the initial agent distribution. Figures 15, 16, and 17 show the results after 60 seconds for the three cases. The results of these simulations are as follows. Case 0 Evacuees came from Floor 0 using stairs 3 and from Floor 2 using stairs 4 and gathered on the dance floor of Floor 1. A crowd formed at the exit from the dance floor room of Floor 1 to the outside (exit 2), and the area of accumulation extended to stairs 3 and 4. After completion of evacuation from Floors 0 and 2, many evacuees still remained on the dance floor of Floor 1. Case 1 Because stairs 4 were not useable, the evacuation time of Floor 2 was longer than in Case 0; however, the total building evacuation time was shorter. Not using stairs 4 led to evacuees dispersing equally to exits 1, 2, and 3. The efficient use of these three exits led to the shorter total building evacuation time by reducing the accumulation of evacuees next to exit 2 on the dance floor of Floor 1 Case 2 The number of people accumulating on the dance floor of Floor 1 is smaller in this case than in Cases 0 and 1, and the total building evacuation time was also shorter.

Figure 14. Initial agent distribution. Total building evacuation time 3:52 Figure 15. Case 0 (after 60 s). Total building evacuation time 3:16 Figure 16. Case 1 (after 60 s). Total building evacuation time 2:31 Figure 17. Case 2 (after 60 s). Maximum velocity ( m/s) Slowed Stopped (0.0 m/s)

6.5 Discussion 6.5.1 Velocity distribution Figure 18 shows the distribution of mean velocities during the total building evacuation. Comparing Cases 1 and 0, the frequencies for 0.0 m/s were larger for Case 0, whereas those of m/s were larger for Case 1. This indicates that the velocities of evacuees were improved by simply changing the evacuation route inside of the building, even with the same exits. Comparing Case 2 to Cases 0 and 1, Case 2 had the superior velocity distribution. Adding additional exits to the outside led to a shorter total building evacuation time, as well as shorter waiting times before passing through an exit. Therefore, distribution of the lower velocities decreased and distribution of higher velocities increased, relative to Cases 0 and 1. 0.70 Evacuee distribution [%] 0 0.50 0 0.30 0 0.10 Case 0 Case 1 Case 2 0.00 0.0- - - - - - 1.2 Interval of mean velocity [m/s] Figure 18. Total building evacuation velocity distributions. 6.5.2 QOF of three cases Figure 19 shows the QOF of the three cases. Compared to Case 0, the QOF of Case 1 increased about 6% and that of Case 2 increased about 18%. These increases indicate that evacuation flows in Cases 1 and 2 were improved over that of Case 0. However, the differences in QOF were modest. In these simulated evacuations, there were too many people in the building, and so most evacuees had to wait in front of bottlenecks for a long time. Compared with these long waiting times, the walking time was relatively short because of the short distance to an exit. Thus, the influence of the plan changes made for Cases 1 and Case 2 on QOF in terms of absolute change was relatively small. This suggests that, when using QOF, a comparison of QOF between cases with similar plans and crowd conditions is preferable to a simple evaluation of QOF for the case of interest.

QOF 0.50 0 0.30 0 0.10 250 200 150 100 50 Evacuation Time [s] QOF Evacuation time 0.00 Case 1 0 Case 2 1 Case 3 2 0 Figure 19. QOFs and evacuation times for total building evacuations. 7. CONCLUSION In the present paper, QOF is presented as an evaluation method for measuring the quality of evacuation flow. QOF is defined as the moment of mean velocity calculated from pedestrian simulator data of mean velocities all evacuees over an evacuation. If the evacuation flow is smooth, the value of QOF is high (maximum ) and if congestion occurs, the value of QOF is small. In many of the scenarios considered herein, the QOF of the plans which are thought to be preferable were higher. In this way, QOF is demonstrated as suitable for making relative evaluations of evacuation quality of similar plans in order to indicate the improvement effect of plan changes in a quantitative way. For more sensitive application to cases with many evacuees, evacuation time was strongly governed by bottlenecks, and so improvements in the proposed method will be considered in future research. REFERENCES 1. Kimura, T., Sano, T., Hayashida, K., Takeichi, N., Minegishi, Y., Yoshida, Y. and Watanabe, H., Representation of crowds in a multi-agent model: Development of the pedestrian simulation system SimTread [in Japanese], Journal of Architecture and Planning, Architectural Institute of Japan, 74 (636), 2009, pp. 371 377. 2. Sano, T., Yoshida, Y., Takeichi, N., Kimura, T. and Minegishi, Y., Experimental study of crowd flow passing through simpleshaped room and validation for an evacuation simulator, Proceedings of the 5th International Conference on Pedestrian and Evacuation Dynamics, 8 10 March 2010, Gaithersburg, in print. 3. Takeichi, N., Jo, A. et al., Fire safety design of night club, Japanese case study, Chapter 4 Evacuation plan by using evacuation simulator, Proceedings of 8th International Conference on Performance-Based Codes and Fire Safety Design Methods, 16 18 June 2010, Lund, in print. 4. Fruin, J. J., PEDESTRIAN Planning and Design, 1971, Metropolitan Association of Urban Designers and Environmental Planners, New York.