Analysis of the exits locations impact on the evacuation efficiency in enclosures: a study case using a rectangular room with two exits of equal sizes

I wrote this manuscript a few years ago (probably over 15 years and thought to save/publish it here for the records).

The topic is related with travel distances and population density and brings a reflection on the correlation between these two (design) parameters. Building (fire safety) regulations/standards/codes do not appear to take into account the ratio between pop density and travel distance. I have published papers on this matter highlighting this aspect already. In this manuscript, I bring the geometry of the enclosure as well into the equation.

ABSTRACT

In this manuscript, an evacuation simulation model was used to determine the optimal positioning of exits around the perimeter of a rectangular room in order to minimize evacuation times. The solution was found through trial-and-error exploration of the possible significant exit locations. The evacuation simulations were conducted assuming idealized conditions of zero response times and population behavior such that occupants elect to move towards their nearest exit. The analysis revealed that strategic positioning of exits on the perimeter of the room can result in reduced evacuation times.? In fact, the author has already shown in previous studies that the positioning of exits does impact the evacuation efficiency. In these previous cases, the room was based on a square shape and the “corner effect” was observed. Now in this paper, the exits’ locations have shown to impact as well the evacuation efficiency in rectangular rooms. Nevertheless, differently from the square rooms, a different phenomenon was observed for the particular case of rectangular rooms: “the bifurcation effect”. This difference seems to be consequence of the room geometry’s shape. The results obtained for this study using rectangular room with two exits are presented; and the bifurcation effect is discussed in this paper.?

Key-words: evacuation simulation; evacuation time; optimal positioning of exits; evacuation efficiency; “corner effect”; “bifurcation effect”.

1.0 INTRODUCTION

A common problem faced by fire safety engineers in evacuation analysis concerns the optimal positioning of exits within an arbitrarily complex structure in order to minimize the evacuation times [1]. To a certain extent, fire safety codes provide some guidance for the positioning of exits; however, these requirements are more concerned with the avoidance of exposing the occupants to smoke rather than minimizing evacuation times. For an arbitrarily complex room, ignoring constraints imposed by regulations such as minimizing travel distances and avoiding dead-end corridors, where should exits be placed in order to minimize evacuation times?? Indeed, based on our previous study, for an arbitrarily shaped room with a given number of exits, the distribution of exits around the perimeter has shown to influence the evacuation efficiency. This was clearly observed through the results’ analyses performed for the square room, in where the evacuation times’ values were impacted by the locations of the exits [1-6]. In fact, in these previous cases, the “corner effect” was observed, which was a consequence of the exits’ locations.

Despite this finding, it is correct to say that the relation between the evacuation efficiency and the positions of the exits is still a challenging issue to understand. In reality, it becomes more difficult as the available options and hence complexity of the evacuation scenario increases. For instance, it can reasonably be expected that for a given population size, the solution of the problem will be dependent on the shape and size of the compartment and the relative distance between the available exits.

For this reason, this manuscript investigates the influence of the exits’ locations on the evacuation efficiency in rectangular rooms. Similarly to what has observed for the square rooms, the analysis of the results for the rectangular rooms has revealed that strategic positioning of exits on the perimeter of the room can reduce evacuation times. Nevertheless, differently from the square rooms, a different phenomenon was observed for the particular case of rectangular rooms: “the bifurcation effect”. This difference seems to be consequence of the room geometry’s shape.

In summary, in this manuscript, we attempt to determine the relative location of two exits of equal size in a rectangular room which minimizes the evacuation time for an arbitrary number of occupants.? The solution is found through trial-and-error exploration of the possible significant exit locations. The evacuation times for each exit configuration are determined through evacuation simulation.

The results obtained for this study using rectangular room with two exits are presented as well as the bifurcation effect is discussed in section 4 of this manuscript.

In the next section, the problem specification is presented.?

?

2.0 PROBLEM SPECIFICATION

The problem to be investigated can be stated very simply as follows: for a room of given size, containing an arbitrarily large population, is there an optimal location for two exits that will minimize the evacuation times?

In our previous investigation, the study was based on square rooms. In this study, rectangular rooms with two exits of the same width, 1.0m, are investigated. The rectangular rooms analysed here had the dimensions of 10m x 40m (i.e., 400m2) and were populated by 1280 occupants (i.e., which gives a population density of 3.2p/m2), see Figure 1.

?

In addition, a parameter of separation “f” is defined. As the name suggests, this parameter defines the separation between the two exits. (It is important to observe that for the rectangular room, the two exits are located in the same wall: the shortest wall L; while that for the square room, this issue is not relevant, since the walls had the same dimensions). For instance, when f is equal to 0 (f=0), this means that the two exits will be located side by side in the middle of the wall. As long as the value of f increases, the two exits start to become apart from each other until the maximum value of f (f=8) is reached. Therefore, when this value is reached, this means that the two exits will be located in the opposite corners from each other in the same wall. The values which the parameter f assumes represent the distance in meters between the two exits as shown in Figure 2. Furthermore, for f = 8 the two exits are separated 8m from each other. These values are also the same for the square room; i.e., f = 0 is the minimum value for f and f = 16 is the maximum value for f.

Unlike the square room results, it was observed that for enclosed environments where the relation between the perpendicular walls L and B is asymmetrical (i.e., for instance rectangular rooms where L is different from B, as shown in Figure 1), for f =0 and f = 16 the evacuation times do not have the lowest values. Surprisingly, they actually have the highest values.

In the next section, the solution methodology is presented.

3.0 SOLUTION METHODOLOGY

The approach adopted involves the use of computer simulation software to simulate the evacuation for each relevant exit configuration.

3.1 Simulation software

To determine the evacuation times for the various configurations, the EXODUS evacuation software was used (more particularly the buildingEXODUS version). The basis of the model has frequently been described in other publications [8-12] and so it will be briefly described here.

?The EXODUS model was developed by the Fire Safety Engineering Group (FSEG) of the University of Greenwich in the UK (https://fseg.gre.ac.uk/exodus/exodus_products.html). This model is used to represent occupants' movement under both normal and emergency situations. For this reason, EXODUS is considered a “hybrid” model, since it can function as an evacuation model as well as a pedestrian model.

The EXODUS model has been widely used for large-scale and complex scenarios, such as metro stations, airports, shopping malls. In fact, it has been applied for several applications: from transportation to crowd management. This model uses nodes (i.e., cells) to represent the space. The simulation can be seen in 3D via its Virtual Reality (VR) function which allows to identify important issues which happen during evacuation processes, such as: bottlenecks; congestion; preferred exits; queuing etc.

In EXODUS, each occupant uses one cell at any given time and moves in the desired direction if the next cell is empty. Each occupant has its own characteristics, such as patience and familiarity behavior factors.

The mechanism in which EXODUS simulates the occupants' movement within enclosures is very similar to the manner how SIMULEX [13-16] and STEPS [22] represent.

EXODUS is a robust model as it also enables the user to address a set of important issues in order to simulate in a realistic way evacuation processes. For instance, in EXODUS, it is possible to insert the response times for each occupant; it also allows the occupants to make their own decision based on the occupants-occupants and also on the occupants-structure interactions. The occupants can decide their own walking speeds and these walking speeds are reduced as the occupants get closer together.

Another useful feature of EXODUS is that it can be used in conjunction, in real-time 3D simulation, with fire modelling outputs obtained from a CFD (Computational Fluid Dynamics) fire model as well as a zone fire model.

Table 1 presents a summary of the EXODUS model.

Table 1: EXODUS model's summary

3.2 Model Parameters

All the other relevant parameters, such as walking speed, response times (RT = 0), patience etc. are described in Table 2. And regarding the simulations, all the scenarios were performed 50 times and the occupants' locations were randomized for each run. With this procedure, it was intended to reduce any bias during the evacuation simulations; and therefore, to obtain more realistic results.

?Table 2: Parameters used for the evacuation simulation modelling analysis

Clearly, evacuation times will depend on the response time of the participants which typically take a log-normal distribution [26].? This means that some occupants may have quite long response times which could impact the overall evacuation times. In these cases, the overall evacuation time will be strongly influenced by the nature of the response time distribution rather than simply the exit location.? In these simulations, we remove the influence of response time by assuming that the entire population reacts instantly. This means that all the simulated occupants react immediately at the start of the simulation.? The population was randomly generated. The combination of instant response times, travel speeds and relatively short travel distances combine to produce large areas of congestion around the exits almost immediately.?

Behavior exhibited by people during egress and evacuation situations can be quite complex [27-28], even in relatively simple situations involving a rectangular room. For example, room occupants may; move in groups and at the speed of the slowest member of the group, attempt to re-unite separated groups prior to egress, select an exit for which they are most familiar, follow the movement of other unrelated room occupants, recommit to different exits during the egress and so on.? In order to simplify the analysis and isolate issues associated with room configuration and exit location these complex behaviors are greatly simplified.? The behavioral response imposed on the population is such that occupants will elect to move towards their nearest exit and furthermore, that the occupants know the location of their nearest exit. While this behavior may be considered simple it is nevertheless reasonable for our purpose.? Indeed, this type of assumption is not very dissimilar to the type of assumptions implicit in most building regulations and used in many performance-based evacuation analyses.

The simulations were repeated a total of 50 times for each scenario.? Furthermore, all the results presented in this paper represent an average over 50 simulations.? At the start of each simulation, the starting location of the population was also randomized.? This ensured that the population was distributed throughout the confines of the geometry with little bias resulting from population starting position contributing significantly to the overall results.

Before, presenting the results, it is important to mention that a similar study in where the optimal positioning of exits to minimize evacuation times for a rectangular room with one or two exits of equal size was performed [29]. Nevertheless, it seems that the study did not use adequate parameters in their model. As consequence of it, the results do not capture realistic behavior in terms of how the occupants move during their simulation. Indeed, this particular study presents several limitations and some of these issues are listed in the next lines.

a) The average walking speed of 0.8m/s was used, which was assumed to be a typical value in a dense crowd. It is also important to mention that it was assumed that everyone had the same walking speed, and this is unrealistic; since this means that there will not be any overtaking;

b) In the model, the exits were not represented properly, since the flow rate and the unit flow rate which have been considered were too small: 4.5p/s and 1.13p/m/s respectively;

c) The “von Newman neighborhood” approach was used for simulating the occupant's movement, which implied that: “if the occupants cannot go forward, they will not go to the sides”. This is not realistic, because in real situations people during an escape movement, especially during emergency situations, which are associated with competitive behavior, would try to overtake people. This is why the behavior observed during the simulation is unrealistic (see Figure 3 on page 276 and Figure 6 page 278 of the refereed paper), because the way the occupants were simulated, it was assumed that there would not be overtaking. In other words, the von Newman approach is not enough for simulating the occupants’ movements; it just provides 4 possible directions for the occupants’ movement. And in order to model more realistically, the occupants should have at least 8 directions. This may explain why the agents (i.e., the occupants) appear to avoid the side walls;

d) And finally, on page 271 of the mentioned paper, it was mentioned that the paper focuses on human behavior, and this is not true, since no details were given on how the occupants in terms of their psychological attributes were set up into the model.

In summary, with no overtaking abilities as well as the use of von Newman approach, the occupants can only queue up. This has caused the unusual building upon crowds. In the next section, the results are presented and discussed.

4.0 RESULTS AND DISCUSSION

In total, 450 simulations were run for the rectangular room cases. The detailed results for these scenarios are presented and discussed in this section.

?The Table 3 presents the evacuation times obtained for this case and Figure 3 shows the graph Evacuation Times (ET) x Values for f.

?Table 3: Values for the rectangular room 10mx40m with 1280 occupants

Figure 3 shows that the trends in behavior for these cases were very similar. When the exits are located in configurations such as for f = 0 and for f = 8 the evacuation times have the highest values.

The travel distances for all the scenarios for this case, do not seem to influence the evacuation efficiency, since the results for the cases are all very similar. For instance, the values of the travel distances vary from 27.5m (minimum value) to 29.5m (maximum value).

For the situation where f = 0, despite the exits being side by side, the location seems to be not ideal for this type of enclosure's geometry (i.e., geometries where the perpendicular walls L and B do not have the same dimensions), since the occupants will be travelling to the same point. This generates congestion during the movement escape which impacts the evacuation performance in a negative way, hence reducing the evacuation times, see Figure 4.

The red dashed arrows represent the escape movements of the occupants. As it is possible to see, all the arrows are pointing to the same location (the exit) and during the evacuation process; some of these “arrows” will be crossing each other’s paths. This is explained by the fact that the occupants have the capability of overtaking each other during the escape movement and/or change the decision of which path they should follow and so on. This will negatively impact the evacuation performance, since this generates more congestion during the escape movement and consequently the flow rate decreases and hence, the evacuation times increase.

Conversely, once the value of f starts to increase, it is clear that the evacuation time decreases substantially. This can be observed by the values of the evacuation times for the intermediary values of f between 0 and 8, as shown in table 1 and figure 3. This can be explained by the fact that, as soon as the exits separate from each other, there will be an improvement on the flow rates of occupants' movement. In fact, it seems that the escape movement becomes “less chaotic”, since the occupants separate into two main groups according to their exit preference. In other words, there will be less congestion during the escape movement, and this improves the evacuation efficiency.?

This phenomenon can be called a “bifurcation effect” and it can be seen for enclosure's geometries where the perpendicular walls L and B are asymmetrical (i.e., these walls do not have the same dimensions, just like the rectangular room in this study). In summary, the occupants, for these situations, will not need to rush into the same point; therefore, there is less competitive behavior and the movement becomes more coordinated and less chaotic. It seems that for a rectangular room, the parameter f plays a similar function that the barriers played in the square room scenarios.

Nevertheless, it is relevant to mention that this phenomenon is not observed when f assumes the maximum value (i.e., f = 8). In fact, when the exits are located in the opposite corner to each other in the same wall, the evacuation time increases substantially, just like when f = 0. This might be explained by the phenomenon that “faster is slower” [30-34]. The evacuation movement, through the room, is now very fast because there is less congestion due to the separation of the population between the two target exits; however, this introduces greater queuing (and hence increases congestion) close to the exits, which adversely affects the evacuation efficiency.

These conclusions are supported by the values obtained for the waiting times, WT, which are shown in Table 4.

Table 4: Values for the Waiting Times for the rectangular room 10mx40m with 1280 occupants

In summary, it seems that, for asymmetrical enclosure's geometry like the rectangular room (i.e., where the perpendicular walls L and B do not have the same dimensions), unlike the square room cases, the time spent towards the exits area – T2) (i.e.,? the queuing time at the doors) does not represent such an important factor (for the relationship between the exits locations and the evacuation efficiency) compared to the time spent during the escape movement (T1), see equation 2 shown previously.?

?In fact, it is the opposite, the time spent during the movement (T1) now becomes a more important factor on the relationship between the exits locations and the evacuation efficiency than the time spent towards the exits (T2); apart from the case where f = 8, where the occupants seem to spend more time in the congestion areas towards the exits.

In order to better understand these results, additional square room scenarios were constructed and analysed. These new scenarios were based on our previous studies. The dimensions were 10m x 10m, but the population now was defined as 320 occupants to create the same population density used for the rectangular room (i.e., 3.2p/m2).

?The new cases used the same parameter for the separation f.

It was observed previously that for enclosed environments, where the relation between the perpendicular walls L and B is symmetrical (i.e., square room where L= B), to have exit(s) located in the corner will produce shorter evacuation times. This was well discussed and validated. This effect can be called as the “corner effect”. And as mentioned, this effect seems to be valid for symmetrical geometries as it will be discussed further later in this paper.

It is important to observe that this effect was found for the square room (10m x 10m) with one single exit (and also with two exits located side by side in the corner) and populated by 200 occupants, which had a population density of 2p/m2. However, this same effect was also found to be true when the population density is increased to 3.2p/m2 (the value adopted for this new study) for both square and rectangular rooms. It might be also relevant to mention that for f = 0, both situations were performed considering the exits located side by side and also using a single big exit. The results have also shown that for f = 0 when the exits are located side by side, there is a small advantage in relation with the other scenario, a single big exit, since the evacuation times were shorter for the previous case. This was also well discussed and understood in the previous studies which looked at the advantage of using barriers in the middle of exits. Therefore, this issue will not be discussed here in this section. Furthermore, every time that f = 0 is mentioned in this study, it means the two exits are side by side).

A total of 450 simulations were performed for the analysis of these square room cases. The results of these evacuation modelling simulations are presented in the next paragraphs. Table 5 and Figure 5 present the results for the square room with 200 occupants and Table 6 and Figure 6 present the results for the square room with 320 occupants.

Table 5: Values for the Evacuation Times for the square room 10mx10m with 200 occupants

Table 6: Values for the Evacuation Times for the square room 10mx10m with 320 occupants

The figures show that the trends of behavior for these cases were very similar. When the exits are located in configurations such as for f = 0 and for f = 8 the evacuation times are at their lowest values.

?For the situation where f = 0, it is common knowledge that the wider the exit is, so the higher the flow rate will become and consequently the evacuation time will be reduced, as equation 1 shows:

??????????? where:

??????????? ET – Evacuation Time;

??????????? EW – Exit Width.

?

Also, for f = 0, the travel distance is at its shortest value (i.e., 5.42m). Therefore, these two factors combine to make the evacuation time decrease to the lowest value.

And when f = 8, the evacuation times are also reduced. This can be explained by the “corner effect” as previously discussed in our previous studies for the square room with one exit cases as well as the two exits cases.

A scenario where the two exits are located in the opposite corner of each other in the same wall reduces the evacuation times, because there is less conflict between the occupants and therefore, the congestion is reduced, the flow rate is improved and consequently the evacuation time decreases.

Nevertheless, for the intermediary values of f, a different behavior is seen for the evacuation times curve.

When the values of f start to increase, it is possible to see that for f = 2, f = 3 and f =4, the values of the evacuation time are proportional to this increase. (For f = 1, the evacuation times also increase, but show only a small difference. And in fact, for f = 1, it can said that it is still an advantage to have the exits located in this configuration, because the “barrier effect” is still occurring). The evacuation times start to increase gradually showing that for these values of f , the evacuation times will not be as good as for f = 0. This can be explained by the fact that, as the exits are separated further apart, the congestion between the occupants is now divided between two areas. And since the exits are still close to each other for these cases, these “congestion areas” will impact each other. In other words, the conflict between the occupants is more chaotic, because the congestion area for one exit will be impacted by the congestion area of the other exit and vice-versa, see Figure 7.

The dashed red lines represent the congestion areas for each exit. It is possible to see that, given the short distance between the two exits defined by the value of f, there is a partial overlapping of the two congestion areas. As consequence, there will be conflict between some of the occupants attempting to escape using exit 1 and some of the occupants attempting to escape using exit 2. And in fact, because of the proximity of these exits, some occupants who are in the congestion area of exit 1 might change his decision to use the exit 2 instead and vice-versa. This interaction between the two areas causes more conflict between the occupants and consequently, the flow rate is reduced and as a result, the evacuation time increases.

On the other hand, once the value of f continues to increase, there is an improvement on the evacuation performance. This can be seen from f = 5, when the evacuation time starts to decrease. In fact, for f = 5, f = 6, f = 7 and until f reaches the value of 8, a decrease is observed for the values of the evacuation times.

This can be explained by the fact that, since the values of f increase, the two exits start to become more distant from each other; and with this, the congestion areas are also more distant from each other. Furthermore, the conflict between the occupants is reduced since there will be much less interaction between them. As a consequence of this, the flow rates are improved, and the evacuation times are reduced.

In summary, the tables 7 and 8 present the values of the average cumulative waiting time, CWT.

It is clear to see that the CWT is growing with increasing values of f, from f = 0 to f =8 until it then starts decreasing as the values of f, increase from f = 5 to f = 8. The CWT represents the time that the occupant spends waiting during the evacuation process and this time is clearly influenced by the time spent near to the exits areas.

Table 7: Values for the Waiting Times for the square room 10mx10m with 200 occupants

Table 8: Values for the Waiting Times for the square room 10mx10m with 320 occupants

These logical relations support the idea that the closer the exits are to each other, the closer the congestion areas will be to each other, and so more interaction will take place between the occupants. With increased interaction, there will be more conflicts between the occupants, which generate more congestion, hence reducing the flow rate, increasing the cumulative waiting time and increasing the evacuation time.

Conversely, when the exits become more distant from each other, the opposite behavior is observed with the result that the evacuation times decrease.

In summary, it seems that for symmetrical enclosure, like the square room (i.e., where the perpendicular walls L and B have the same dimensions), the time spent moving towards the exit areas (T2), represents a more important factor for the relationship between the exits locations and the evacuation efficiency, than the time spent during the escape movement (T1), see equation below:

????????? where:

??????????? ET – Evacuation Time;

??????????? T1 – Time spent during the escape movement;

??????????? T2 – Time spent towards the exits.

Comparing the results obtained from the rectangular room and the square room, it is possible to see that even having the same population density, different behavior was observed for similar scenarios (i.e., same value for f). In the next paragraphs, this issue is discussed with more details.

?4.1 Comparison between the results obtained for the square room with two exits and the rectangular room with two exits

?For the rectangular room, the results have shown that for f = 0 and f = 8, the worst evacuation times are obtained. Nevertheless, when f assumes values between 0 and 8, the evacuation times are lower than these previously mentioned cases. In fact, for the intermediate values between 0 and 8, very similar evacuation times are produced. This trend of behavior can be summarized in a general graph as Figure 8 presents.

When these results are compared with previous results, such as those produced for the square room (with two exits with the same dimensions, i.e., 1.0m width, and same population density, i.e. 3.2p/m2, as used for the rectangular room), it is clear to observe that the results are different, see Figure 9. This might indicate that, associated with the exits locations, the shape of the room is playing an important rule on the evacuation efficiency.?

?

In fact, as Figure 9 shows, for the square room cases, the trend of same graph assumes very different behavior, as Figure 10 shows.

?

In reality, it seems that the relation between the perpendicular walls L and B within the enclosure's geometry's boundaries does have an impact on the relationship between the exits locations and the evacuation times. For instance, as shown previously, considering the case where the relation between the perpendicular walls is asymmetrical (i.e., rectangular room where L is different from B), for the same values of f, the evacuation times are different for the case where the relationship between the perpendicular walls is symmetrical (i.e., square room where L is equal to B).

Therefore, it seems that the shape of the room (i.e., the enclosure's geometry) does have an impact on the evacuation efficiency. This might be explained by the fact that the enclosure's geometry is also associated with key factors which have direct impact on the evacuation efficiency, such as travel distance and population density. Furthermore, it can be said that the enclosure's geometry has an indirect impact on the evacuation efficiency, because it is related, for instance, with the travel distance and the population density.

For this reason, the locations of the exits, along the wall perimeter of any room, do impact the evacuation performance and this impact varies according to the enclosure's geometry. As an example, if an exit, that is located in the corner of a room with a specific shape, generates the lowest evacuation times, this will not necessarily be true for another room with a different shape.

As mentioned previously, both the geometries (square and rectangular rooms) had the same population density, i.e., 3.2p/m2. For instance, the square room had 10m x 10m as dimensions (i.e., 100m2) and 320 occupants. And the rectangular room had 15m x 12m as dimensions (i.e., 180m2) and 576 occupants. These settings allowed a fair comparison to be made between the results in order to check if the geometry of the enclosure had an impact on the relationship between the exits locations and the evacuation efficiency.

In theory, for similar scenarios in which the population density is the same and the lay-out configuration of the exits along the walls is the same (just like the square and rectangular rooms here discussed), the evacuation performance expressed by the evacuation time would be the same or at least similar. Nevertheless, according to what was shown in the previous section, it is clear that the enclosure's geometry does have an impact on this relationship between the exits’ locations along the wall perimeter and the evacuation efficiency.

The question which now arises is: why does this difference exist?

Therefore, in this section, the possible answers for this question are presented and discussed.

From the results, it was observed that what is an advantage in terms of exits locations for a specific enclosure's geometry is not necessarily true for another different enclosure's geometry. For instance, for the rectangular room when f = 0, the evacuation time assumes the highest value. This starts to change when the value for f increases, making the values of the evacuation times decrease until f = 8, when the evacuation time starts increasing again. While, for the square room, the opposite trend is observed, as the evacuation time assumes the lowest value. When f = 0, the evacuation time assumes the lowest value. And this starts to change when the value of f increases, making the values of the evacuation times, increase until f = 8, when the evacuation time starts decreasing again.

Possible explanations for this might be found in the relationship between the exits’ locations and the travel distance and also other physical phenomena (i.e., created by the relation occupants-structure) which happen during the evacuation process, such as the ‘faster is slower’ effect [30-34] and the congestions during the escape movement towards the exits and the congestions near to the exits’ areas.?

With these two case studies, namely the square room and the rectangular room, it becomes clear to conclude that the relationship between exits locations and evacuation efficiency is influenced by the shape of the room (i.e., the enclosure's geometry).

In the next section, the concluding comments for this study are presented.

?

5.0 CONCLUDING COMMENTS

In this manuscript, the optimal positioning of exits around the perimeter of a rectangular room was explored, in order to minimize the evacuation times. The evacuation simulations were conducted assuming ideal conditions of zero response times and population behavior such that occupants would move to their nearest exits.? Both assumptions are made to simplify the analysis and to isolate issues associated with exit location.?

For this purpose, a case study was based on a rectangular room with two exits.

The results revealed that the relationship between exit locations and evacuation efficiency is influenced by the shape of the room (i.e., the enclosure's geometry). This conclusion is based on the fact that, for the same exit locations, the trends of evacuation efficiency were completely different for the square room when compared with the rectangular room. For instance, instead of having the “corner effect” observed in the square room cases; the “bifurcation” effect was observed for the rectangular room cases.

The author is currently exploring this issue based on several other evacuation cases, involving different shapes (such as circular, triangular, pentagonal, hexagonal and heptagonal). The results have been showing that the enclosure's geometry does also seem to have a significant influence on the evacuation performance for this other shapes. This type of investigation is particularly relevant for crowd management, where the importance of the exits’ locations can be crucial in terms of the occupants′ safety.

It is expected that the present case studies will help to explain some of these issues. The significance of the findings is such that more research should be directed towards gaining a better understanding of these issues.

?

6.0 ACKNOWLEDGEMENTS:

I would like to thank the Fire Safety team of ARCADIS for the motivation in working in the Fire Safety industry. I would like also to thank the Fire Safety Engineering Group (FSEG) of the University of Greenwich, where I have done my PhD and where I started using EXODUS, particularly to Professor Ed. Galea for his support when starting to use this type of technology. And finally, I would like to to express my gratitude to Philip, Samuel, Jessica and Valerie-Margaret for their continuous inspiration in my life (four special souls in my life).

?

?

7.0 REFERENCES:

1.???? Tavares, R.M., Design for horizontal escape in buildings: the use of the relative distance between exits as an alternative approach to the maximum travel distance, Safety Science, Volume 50, Issue 7, August 2012, Pages 1485-1489, Elsevier, 2010 (10.1016/j.ssci.2010.03.009);

1. Tavares, R.M., A New Methodology for Evacuation Modelling Analysis Using Numerical Optimisation Techniques, Derivative-Free Optimization Session, 2008 SIAM Conference on Optimization, Boston, Massachusetts, USA;
2. Tavares, R.M. and Galea, E. R., Numerical Optimisation Applied to Evacuation Analysis, PED 2008, 4th International Conference on Pedestrian and Evacuation Dynamics. Wuppertal, Germany;
3. Tavares, R.M., Evacuation modelling analysis within the operational research context: A combined approach for improving enclosure designs, Building and Environment, Volume 44, Issue 5, May 2009, Pages 1005-1016;
4. J. M. Wall and N. P. Watterson, Predicting evacuation times – a comparison of the STEPS simulation approach with NFPA 130, Fire Command Studies, Vol. 1, No. 1, 2002.;
5. N.P. Watterson, Predicting people movement, Panstadia International Quarterly Report, Volume 8, No 1, July 2001;
6. N. Rhodes and N. A. Hoffmann, Modelling Newcastle’s International Centre for Life for Fire Safety, Building Performance, Issue 3, Winter 2000/1, BEPAC, 2000;
7. N Rhodes and N. A. Hoffmann, Fire safety engineering for the International Centre for Life, N.ewcastle-upon-Tyne, Interflam 99, Edinburgh, UK, June 1999;
8. N. A. Hoffmann, D. A. Henson and C. W. Pope, Analysis of the evacuation of a crush loaded train in a tunnel, 3rd International Conference on Safety in Road and Rail Tunnels, Nice, France, March 1998;
9. D. G. Newman, N. Rhodes and H. A. Locke, Simulation versus code methods for predicting airport evacuation, 1st International Symposium on Human Behaviour in Fire, Ulster, 1998;
10. N. A. Hoffmann and D. A. Henson, Simulating Emergency Evacuations in Stations, American Public Transit Association (APTA) Rapid Transit Conference, Washington DC, USA, June 1997;
11. N. A. Hoffmann and D. A. Henson, Simulating transient evacuation and pedestrian movements in stations, International Conference On Mass Transit Management, Kuala Lumpur, Malaysia, May 1997;

13.? Thompson, P.A. and Marchant, E.W., Computer and Fluid Modelling of Evacuation, Journal of Safety Science, 18 (1995), pp 277-289;

14.? Thompson, P.A. and Marchant, E.W., A Computer Model for the Evacuation of Large Building Populations, Fire Safety Journal 24 (1995), pp 131-148;

15.? Thompson, P.A., Wu, J., and Marchant, E.W. Modelling Evacuation in Multi-storey Buildings with Simulex, Fire Engineers Journal (vol. 56, no. 185), November 1996, pp 6-11;

1. Thompson, P.A. and Marchant, E.W. Testing and Application of the Computer Model ‘Simulex’, Fire Safety Journal 24 (1995), pp 149-166;

17.? Galea ER, Perez Galparsoro JM. A computer based simulation model for the prediction of evacuation from mass transport vehicle. Fire Safety J 1994;22:341–66;

18.? Gwynne, S., Galea, E., R.,Lawrence, L.and Filippidis, L., “Modelling Occupant interaction with fire conditions using the buildingEXODUS evacuation model”, Fire Safety Journal, 36, pp 327-357, 2001;

19.? Park J., Gwynne S., Galea E.R., and Lawrence P., Validating the buildingEXODUS evacuation model using data from an unannounced trial evacuation. Proc 2nd Int Pedestrian and Evacuation Dynamics Conference, Ed: E.R.Galea, CMS Press, Greenwich, UK, ISBN 1904521088, pp295-306, 2003;

20.? Gwynne S., Galea E.R., and Lawrence? P., The Introduction of social adaptation within evacuation modelling.”,? Fire and Materials, Vol 30, No4, pp 285-309, 2006. DOI:10.1002/fam.913;

21.? Filippidis L, Galea E, Gwynne S, Lawrence P., Representing the Influence of Signage on Evacuation Behaviour within an Evacuation Model, Journal of Fire Protection Engineering, Vol 16, No1, pages 37-73, 2006. DOI: 10.1177/1042391506054298;

1. https://www.mottmac.com/skillsandservices/software/stepssoftware
2. https://www.fire.nist.gov/fds
3. Purser, D.A. Quantification of behaviour of engineering design standards and escape time calculations. Proc First Int. Symposium. Human Behaviour in Fire. University of Ulster, Belfast, 497-508, 1998;
4. Gwynne S., Galea E.R., Owen M. and Lawrence P.J., Escape As A Social Response, Report Published by the Society of Fire Protection Engineers, USA, 1999;
5. Tavares, R.M., Gwynne S., Galea E.R. Journal of Applied Fire Science, Baywood Publishing Company, Inc., Volume 15, Issue 1, p.23-40 (2006);

27.? D. L. Zhao, L. Z. Yang, J. Li, Y. Zhu, and L. Zou, Relationship between Performance-based Design of Building Exits and State Transition of Pedestrian Flow during Occupant Evacuation, Journal of Fire Protection Engineering, Nov 2006; vol. 16: pp. 269 – 281;

28.? Helbing, D. et al. Simulating Dynamical Features of Escape Panic. NATURE 407, 487- 490, 2000; (https://angel.elte.hu/~panic);

1. D. Helbing, I. Farkas, and T. Vicsek (2000), Simulating dynamical features of escape panic, Nature 407, 487-490;
2. A. Johansson, D. Helbing and P.S. Shukla (2007), Specification of the social force pedestrian model by evolutionary adjustment to video tracking data, Advances in Complex Systems;
3. D.R.Parisi and C.O.Dorso, Why faster is slower?, Pedestrian and Evacuation Dynamics 2005, ISBN 978-3-540-47062-5, pages 341-346 , Springer Berlin Heidelberg, 2007;
4. Song Wei-Guo, Yu Yan-Fei, Wang Bing-Hong and Fan Wei-Cheng, Evacuation behaviors at exit in CA model with force essentials: A comparison with social force model, Physica A: Statistical and Theoretical Physics, Vol. 371, Issue 2, 15 November 2006, Pages 658-666.

?

?

?