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Assessing sign occlusion in buildings using discrete event simulation
Automation in Construction 17 (2008) 799 – 808 www.elsevier.com/locate/autcon
Assessing sign occlusion in buildings using discrete event simulation Khaled Nassar a,b,⁎, Ahmed Al-Kaisy c a
c
Department of Architectural Engineering, University of Sharjah, PO Box 27272 Sharjah, United Arab Emirates b Department of Architectural Engineering, Cairo University, Egypt Department of Civil Engineering, Montana State University, P.O. Box 172220, Bozeman, MT 59717-2220, United States Accepted 15 October 2007
Abstract Correct sign placement in large buildings such as airports, railway stations or large academic buildings will have a significant impact on the usability of the building as well as having a beneficial impact on the way-finding characteristics of the pedestrian in these environments. This paper presents a discrete event simulation model that evaluates the effect of placement on the sign occlusion in architectural spaces. The simulation model allows the designers to identify optimum location for signs in a space to maximize visibility and minimize occlusion. The model takes into account the geometric configuration of the space, the occupant/pedestrian travel flow patterns, and the location of obstructions as well as the legibility distance. An analytical tool was developed where the movement and location of occupants'/pedestrians' legibility zones and obstructions are simulated at any point in time. The model also accounts for variables like the location of obstructions, sign design, and the primary and secondary travel paths of occupants/pedestrians. The occlusion of wall and ceiling-mounted signs by obstructions is estimated using two measures. The first measure is the probability of a sign being occluded under certain space design and geometric conditions. The second measure estimates the likelihood of an occupant/pedestrian missing the sign based on the minimum time required for that occupant/pedestrian to detect, recognize and read the sign. © 2007 Elsevier B.V. All rights reserved. Keywords: Sign visibility; Sign occlusion; Signage; Discrete event simulation; Sign placement and location; Way finding
1. Introduction The placement of signs in large buildings and urban spaces is an important part of the successful design of these places. Correct sign placement in large buildings such as airports, railway stations or large academic buildings will have a significant impact on the usability of the building or urban setting as well as having a beneficial impact on the way-finding characteristics of the pedestrian in these environments. Signing provides pedestrians/ occupants with clear instructions for easy progress to their destinations. Moreover, sign installations should be an integral part of the space design and therefore are best planned in tandem with the design of the space itself. With the advent of more ⁎ Corresponding author. Department of Architectural Engineering, University of Sharjah, PO Box 27272 Sharjah, United Arab Emirates. E-mail addresses: [email protected] (K. Nassar), [email protected] (A. Al-Kaisy). 0926-5805/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2007.10.006
sophisticated and costly signage and announcement boards (such as Liquid Crystal Displays, LCD), the optimum placement of these signs to maximize visibility by occupants/pedestrians and minimize occlusion has gained an increased importance. For optimal location, plans for sign placements should be investigated during the earliest stage of preliminary design, and then the details should be developed as final design progresses [6]. Currently however, the factors to be considered for the installation of overhead sign displays have not been defined in specific numerical terms [6] and this leaves much of this decision to engineering judgment. There is a lack of systematic and methodical models or techniques for optimized sign placement in spaces. Albeit, a few very basic guidelines on sign design such as font, text and lighting tools that aid in the sign placement are virtually inexistent. The most detailed sign placement guidelines are for the placement of exit signs which outline the exact size and location of sign placement in basic corridor-type layouts. On the other hand, the placements of
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other wall-mounted or ceiling-mounted directional signs and announcement boards have not been studied. In the absence of such design tools, the location of the signs is often left to professional judgment or experience. The ultimate objective of this research is to explore and assess the effect of the different space configurations and geometry, and sign placement on the occlusion of ground-mounted and ceilingmounted signs. This paper is mainly concerned with developing a simulation model to assess this effect. While the model was developed primarily to investigate the effect of fixed obstacles and building space geometry on sign visibility, it is part of a larger research effort aimed at modeling situations where pedestrian sightline is obstructed by a moving obstacle such as in urban contexts. The remainder of this paper is organized as follows; first a literature review is presented that cites the major research efforts addressing sign placement and occlusion. This is followed by identifying the main requirements and variables of the model for sign occlusion and optimum placement. The developed model is presented next along with a description of its various sub models. An example application of the model in a real building is provided along with results and analysis. Finally, conclusions are drawn and recommendations for future research are presented. 2. Previous research Review of previous research suggests that there is little information in the literature that addresses the issue of sign visibility and optimum placement of signs based on scientific models. The majority of studies in the literature can be broken into 2 main directions; firstly basic guidelines on sign design, especially for emergency egress applications and secondly studies in the field of traffic engineering that deal with models for road related variables. Basic guidelines on the placement of signs and especially way-finding and emergency egress signs have been presented in the literature [7,2,3,4,5] (Romedi 1984). These deal primarily with size of the signs, font and text size to use (Table 1 and Table 1 Viewing distance and character size (Adapted from Treasury Board of Canada 1992) View distance (m)
Character size (mm)
1 2 4 5 7 9 12 15 18 24 30 36 48 60 72 90 120
5 6 8 10 12 15 20 25 30 40 50 60 80 100 120 150 200
Fig. 1. Acceptable legibility (adapted from [10]).
Fig. 1), location of emergency exist signs (Fig. 2), as well as lighting and materials used. In the field of traffic engineering, a study by [9] investigated the obstruction of ground-mounted and overhead signs by heavy vehicles using two different approaches. First, field data were used to develop empirical relationships to estimate sign obstruction using variables such as traffic volume, percentage of heavy vehicles, average speed, etc. A video camera mounted at the roadside at the location of the sign was used to recognize the obstruction of the driver's sight line to the sign by heavy vehicles. Regression analyses were carried out and equations were developed from the collected data. In the second approach, a simulation model was used to assess sign obstruction by heavy vehicles. The study concluded that the simulation failed to provide results that are reasonably close to those from empirical equations. Another study by [12] provided an analytical approach to assess the potential impacts of vertical curves, horizontal curves, and heavy vehicles on Variable Message Sign (VMS) readability. The analyses were mainly based on the premise that each of these factors can significantly limit the distance at which a VMS can be read. This in turn translates into shorter available reading times and the need to display a shorter message with fewer units of information. In addition, Al Kaisy et al. (Al Kasiy et al 2003) developed a simulation model for assessing the occlusion of signs from passenger cars by large vehicles. Some of the concepts presented in that research are utilized in the model presented here. In addition to the above two directions, some governmental guidelines exist for sign placement with the aim of aiding the public to clearly recognize activities in public buildings and spaces [11]. These guidelines provide means of consistent sign identification to improve the service to the public by facilitating access and wayfinding. However, these guidelines also are focused on the physical properties of the sign itself (size, illumination, etc…) and provide very little in terms of placement location within a facility. 3. Occlusion of signs: important variables When planning sign placement one should consider the physical characteristics of the building or site, the direction and
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Fig. 2. EXIT sign placement guidelines (adapted from [8]).
type of traffic flow, the means of access, the type of sign used, as well the placement and design of the sign. In general, correct sign placement involves two main aspects; firstly, placing them in a manner to minimize occlusion and maximize visibility. This involves choosing the best location in the space to increase the number of occupants/pedestrians that can see the sign during their regular traveling routes and minimize sign occlusion by the obstacles in the space. Secondly, correct sign placement involves sign-specific variables such as using appropriate material, legible font and the type of sign used. The model presented in
this paper is concerned with the first of these two aspects and mainly placing the sign to minimize occlusion. The sign design itself is an underlying input variable of the model as will be explained below. Many variables are believed to affect the occlusion of groundmounted and ceiling signs by obstacles in architectural and urban spaces, such as building elements (columns, stairs, street furniture, cars, other pedestrians, etc…) and therefore should be accounted for in modeling this effect. These variables are either related to conditions in the particular space e.g. occupant traffic flow
Fig. 3. Legibility distance and legibility zone.
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Fig. 4. Occupant/pedestrian travel flow directions and the divergence angle.
direction (and vehicular traffic in case of urban spaces) or variables relate to the geometry of the space. These variables include: 1. Legibility distance: this is the maximum distance along the occupant/pedestrian sightline from the subject sign where the occupant/pedestrian is able to read the sign (Fig. 3). It is mainly a function of sign design (e.g. letter size, font, color contrast, etc) and human vision characteristics particularly vision acuity. Displacement on the other hand is the distance between the centre of a sign and an observer's central line of vision (measured at a right angle to the central line of vision). The angle of displacement should fall between 5 and 15 degrees in order to optimize legibility, e.g., 0.25 m of displacement per 1.00 m of viewing distance provides an angle of approximately 15 degrees at the eye of an observer [11]. The sign's legibility and ultimate size are determined form the viewing distance and character size. 2. Divergence angle θ: this is the angle between the occupant/ pedestrian's sightline and the centerline of the direction of travel (Fig. 3). 3. Legibility zone: this is an imaginary zone upstream of the sign where the occupant/pedestrian is able to read the sign. This zone is delineated by the legibility distance along the driver's sightline (upstream) and the line that represents the maximum divergence angle θ (downstream). This zone is represented by the shaded area in Fig. 3. 4. Expected walking speed of occupant/pedestrian: this variable determines the time spent by the occupant/pedestrian within the legibility zone described earlier. The viewing distances referred to in Table 1 are for the normal occupant/ pedestrian who is standing or walking towards a sign. Signs intended for vehicular traffic, are additionally affected by the normal speed of traffic passing the sign. 5. Location of the obstruction relative to the occupant/pedestrian when the latter arrives at the legibility zone: this variable also
affects the time during which occupant/pedestrian sightline is hindered by the obstruction. 6. Size of the obstruction: for example in building spaces, the size of columns, walls, stairs, or any other architectural element that may hinder the visibility of the sign. 7. Occupant/pedestrian traffic volumes and directions of travel. This is determined in terms of the arrival rate in occupants/ hour. 4. Model development 4.1. Model requirements and assumptions In order to assess the occlusion of ground-mounted and ceiling-mounted signs by the obstructions, any model should include a number of initial requirements. The model should have the ability to dynamically model the movement and location of the occupant/pedestrian as well as the obstruction in the building/urban space upstream of the sign and the continuity of sightline between the occupant/pedestrian and the sign. The model should also have the ability to model variables that are relevant to the occlusion of signs by obstacles such as building features (columns, stairs, etc…). Furthermore, the model should incorporate the occupant/pedestrian traffic flow patterns in the space under consideration and include provisions for primary and secondary flow directions as well as nonlinear travel directions (Fig. 4). Finally, the model should have the ability to model variables that define the geometry of the problem such as lateral distance of sign placement, legibility distance, relative location of obstruction, etc. A number of assumptions are made to simplify the development of the model. The main assumptions of the proposed occlusion model include the assumption that the occupant/ pedestrian is fully attentive, i.e. no distraction of any kind within the legibility zone. The model assumes also that the occupant/
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Fig. 5. Flowchart of the simulation model.
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Fig. 6. Static layout for the occlusion problem and the main geometric variables.
pedestrian travels at a constant walking speed, i.e. no acceleration or deceleration within the legibility zone. Furthermore, it is assumed that the sign and font size are determined a priori and the legibility distance and legibility zone are determined accordingly. In addition the sign text, font, uniformity and all the other signrelated variables have been correctly planned. The model is applicable to architectural and urban spaces and can be used to optimize the location of fixed signs of various kinds e.g. LCDs. 4.2. Model description The proposed discrete event simulation model assesses the occlusion of ground-mounted and ceiling-mounted signs by obstructions from static architectural/urban elements (columns, stairs, trees, street furniture, etc…). Specifically, the model estimates two measures in assessing the amount of occlusion under certain occupant/pedestrian traffic flow, geometric configuration, and sign design variables. The first is the absolute probability of the sign being occluded while the second is the probability of an occupant/pedestrian missing the sign. The simulation utilizes discrete time steps to simulate occupant/pedestrian movement in the space. At each time step a number of calculations are performed based on the inputs to the model. The calculations performed at each time step can be divided into three main parts. Firstly, the model calculates the amount of occlusion caused by one or more obstruction that happens to be in the legibility zone upstream of the subject sign. Secondly, having calculated the amount of occlusion, the model determines the probability of having one or more obstructions within the legibility zone of the sign. Finally, the model developed estimates for the two measures of occlusion mentioned above. In the next sections the three parts of the model are explained.
4.2.1. Determining the amount of occlusion caused by one or more obstruction The first step is determining the probability of a sign being occluded and the probability of an occupant/pedestrian missing the subject sign during the time when there are one or more obstructions within the legibility zone. The flow chart shown in Fig. 5 explains the main processes performed in the model. As shown in this flow chart the location of the occupant/ pedestrian and the obstruction(s) in the flow direction within the legibility zone is updated. Also, the continuity of the sightline between the occupant/pedestrian and the sign is evaluated every tenth of a second. This is done by determining the points of intersection of the occupant/pedestrian's sightline with the two planes that represent the left and right sides of the obstruction (s), and comparing these points with points that represent the area occupied by obstruction(s) at any time t. The model utilizes a binary variable that represents the status of the continuity of sightline at any time t. The model then calculates the amount of time when occlusion is in effect during the total duration when the occupant/pedestrian traverses the legibility zone. Finally, by estimating the minimum time required to read the sign, this submodel determines the probability of an occupant/pedestrian missing the sign. Fig. 6 shows the geometry of the sign occlusion problem at any time t when an obstruction occupies the legibility zone. The model assumes that the occupants/pedestrians travel along predefined paths that represent the main travel directions in the architectural or urban spaces. The model further assumes that the occupants/pedestrians travel at a certain distance from the center of the predefined paths. This distance is randomly generated and is bound by the space dimensions. The model also assumes that the center of the text or symbol message is at
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the center of the sign. While the latter assumption may add an approximation to model results, this approximation is expected to be very small due to the small dimension of message width with respect to the legibility distance. Therefore, this approximation was deemed an appropriate trade-off for the sake of model simplicity. Analyzing the problem detailed in Fig. 6, it therefore follows that the legibility distance is (the derivation is shown in the Appendix), ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Dleg ðY Þ2 Y Cot h Tlz ¼ ð1Þ Spc To find the coordinates X1(t) and X11(t), the distance traveled by occupant/pedestrian at time t upon entering the legibility zone (Dpc(t)) one can write (derivations are shown in the Appendix),
X1ðtÞ
Y Y1 Y Y1 ¼ X DJC ¼ X X Spc t Y Y
X11ðtÞ ¼ X Xf ðtÞ ¼ D5 þ
Y Y11 X Spc t Y
n D4 þ Shv t 100
XbðtÞ ¼ Xf ðtÞ Lhv ¼ D5 þ
n D4 þ Shv t Lhv 100
ð2Þ ð3Þ ð4Þ ð5Þ
If X1(t) b Xf (t) and Xb(t) b X11(t), then occlusion is in effect, i.e. occupant/pedestrian's sightline is obstructed. Otherwise, the sightline is clear. The continuity of the sightline is checked every tenth of a second until the occupant/pedestrian leaves the legibility zone. The time during which occlusion was in effect (Tocc) is then determined by adding the time during which the sightline is obstructed. Time available to read the sign Ta is Ta ¼ Tlz Tocc
ð6Þ
The percentage of time when occlusion is in effect (one form of probability) for a specific position of an obstruction (i) is, PoccðiÞ ¼
ToccðiÞ 100 Tlz
ð7Þ
The average walking speed of the occupant/pedestrian, the relative speed of the dynamic obstruction(s) with respect to the occupant/pedestrian, and the legibility distance (mainly a function of legend size) are user-specified. These variables can reasonably be estimated for the situation at hand. The amount of occlusion for that particular situation is then estimated by determining the mean value of occlusion from all these different scenarios. n P
Pocc ¼
1
PoccðiÞ n
ð8Þ
The increment used in this model is equivalent to one hundredth of the distance mentioned earlier (n = 100). This means that for a particular situation at hand, the simulation runs 100 different scenarios and finds the average occlusion.
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Also, the probability of an occupant/pedestrian missing the sign Pm is found by estimating the minimum time required to read the sign (Tmin). Tmin is mainly a function of the number of words and symbols in a particular sign and can be estimated using several theoretical models. For each relative position of the dynamic obstruction, the model determines whether the occupant/pedestrian is able to read the sign by comparing Ta to Tmin. If Ta is less than Tmin, then the occupant/pedestrian will miss the sign (Pm(i) = 1), otherwise, he will be able to read the sign (Pm(i) = 0). The model used a binary variable (Pm(i)) to represent the two possibilities. The model then estimates the probability of an occupant/pedestrian missing the sign by dividing the number of scenarios when Pm(i) = 1 by the total number of scenarios (n). n P
Pm ¼
1
PmðiÞ n
ð9Þ
Similar logic is used to check the continuity of sightline when multiple dynamic obstructions happen to occupy the legibility zone. The model updates the location of the obstruction every tenth of a second and compares the coordinates of the points of intersection (X1(t) and X11(t)) with the coordinates that represent the location of each dynamic obstruction within the legibility zone. 4.2.2. Determining the probability of obstructions within the legibility zone At this stage, the amount of occlusion when one or more obstructions occupy the legibility zone has been estimated. The next step in the model development is to know the likelihood of this event taking place for a particular sign under certain occupant/pedestrian traffic patterns and space geometric conditions. In other words, we seek to answer the following question: what are the chances of a sign being occluded? Referring back to Fig. 6, we seek to find the chances of an occupant (say at point G) missing the sign at M. This likelihood is mainly a function of occupant/pedestrian travel paths, the arrival rate of the occupants/pedestrians, the size, paths and arrival rates of dynamic obstructions. The probability of the legibility zone being occupied by one or more dynamic obstruction can be determined from the amount of time this zone is occupied by one or more obstructions and the total amount of time elapsed in the simulation. The probability of a sign being occluded has to be calculated while the occupant is walking. The model developed here utilizes discrete event simulation to detect the individual events where an obstruction occupies the zone at a time, while the occupant/pedestrian is moving. In this case there are two scenarios. The first happens when the sign is positioned at a high enough location such that it would not be occluded by other occupants or any other dynamic obstruction. This case is simple and can be handled in a way similar to what is described in the previous section. The second case happens when there is a chance that the sign can get occluded by the presence of other occupants. In that case special consideration is needed to account for the movement of the
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Fig. 7. The example building.
obstructing occupant. Each obstructing occupant will occupy the legibility zone for an amount of time determined by its speed, and its body width (or the length for other dynamic obstructions). The calculation would be straight forward if each obstruction would occupy the zone individually. In that case, the total time the legibility zone is occupied can be estimated from the number of obstructions and the time it takes for that obstruction to traverse and completely clear the legibility zone. Practically however, the legibility zone may be occupied by more than one obstruction at a time. This adds another dimension to the analysis in that two specific events have to be accounted for: individual events and overlapped events. Individual events occur when only one obstruction occupies the zone at a time. Overlapped events occur when two or more obstructions occupy the zone at the same time. The model estimates the percentage of time the legibility zone is occupied by individual events and overlapped events individually similar to the method described in (Al-Kaisy et al. 2004). In that model, individual events occur when the headway
between two successive obstructions is equal to or greater than the time required to traverse a distance within the legibility zone plus the length of an obstruction (tD4). Therefore in individual events, the leading obstruction clears the legibility zone before the following one enters the zone, while overlapped events
Table 2 Results of the analysis Legibility distance Dlz (m) 6 9 12 15 18 21 24 27
P1 (%)
P2 (%)
A
B
C
D
A
B
C
D
32 29 28 21 21 21 20 20
31 29 27 24 16 15 12 8
30 27 24 18 14 15 12 8
28 25 25 22 18 14 7 4.2
44 41 41 41 41 40 40 40
43 42 41 36 31 30 28 26
43 42 39 31 30 30 26 21
42 39 38 27 18 12 9.2 6.2
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occur when the headway between two successive obstructions is smaller than tD4 and the following obstruction enters the legibility zone before the leading one clears the zone. The time overlap between two successive obstructions is equivalent to tD4 − h, and hence the time duration of that overlapped event (two-obstruction scenario) is tD4 + h. Similarly, for multiple successive obstructions with short headways, the time duration for the overlapped event becomes tD4 + ∑ h. However unlike the model developed in [1] we are mainly interested here in the percentage of time the legibility zone is occupied by obstructions for individual events. This can be given by, TperðiÞ ¼
TocðiÞ 3600
ð10Þ
Where Toc(i) is the amount of time during the simulation when the sign is occluded. The simulation is run and Toc(i) is calculated based on the specific configuration of the plan specified, taking into account the location of obstructions and the placement of the sign. 4.2.3. Estimating the occlusion measures Estimate of the two occlusion measures can now be calculated given the results above: the first is the absolute probability of a sign being occluded by obstructions while the second is the likelihood of an occupant/pedestrian missing the sign. To find the first measure, the percentage of time for individual events (Tper(i)) are multiplied by the amount of occlusion found earlier. This probability is expressed as P1 ¼ TperðiÞ PoccðiÞ
ð11Þ
Also, the absolute probability of an occupant/pedestrian missing the sign is estimated as P2 ¼ TperðiÞ PmðiÞ
ð12Þ
5. An example using the model In order to verify the model, an actual building was used to run the simulation model. The building used for the application of the model is a large academic building located on the campus of a typical university. The building consists of a big atrium as well as lecture halls and passageways to other buildings on the campus. The problem that the model was applied to is finding the best location for a large LCD that displays student related information and announcements about upcoming activities. The design of the spaces where the major occupant traffic is expected is represented in Fig. 7. Input to the model includes the possible locations of signs, space and obstruction boundaries and dimensions as well as occupant/ pedestrian traffic flow directions. The traffic flow directions are inputted to the model in the form of centerline for the main pathways. Each traffic flow direction is assigned an arrival rate based on the expected number of occupants traveling. Their rates assume a Poisson distribution as explained earlier.
807
Four different alternate locations were investigated as shown in Fig. 7. Although it may seem clear that the location of the sign should be placed so that is perpendicular to the line of sight of the main flow direction, the presence of the columns in the space along with the varying occupant traffic patterns and flow directions complicate the problem. The simulation was therefore run by means of generating occupants traveling along the flow directions. At each time step the model checks the line of site of the occupants and sign occlusion using the procedure described in the above section and the two occlusion measures, P1 and P2 are calculated accordingly. By analyzing the results of the simulation, one would be able to identify which of the four locations provide the best placement location to maximize visibility and minimize occlusion. Table 2 shows the results of the analysis. It is clear from the results that as the legibility distance increases, i.e. by using a large sign with larger text size, the two measures of occlusion will generally decrease. However, this is not always true because of the location of the sign in relation to other occluding objects in space. If a sign is occluded by a column for most of the occupant traffic flow for example, the high legibility distance becomes irrelevant to the occlusion measures used. This is true for placement location A, where the visibility of the sign will not significantly increase beyond the 15 meter legibility distance. Therefore if location A becomes the final location of the sign, it does not make any sense to increase the sign any larger than would provide a 15 m legibility distance. One can also see from the results that alternate position D is the best performer in terms of the two occlusion measures used. Although this conclusion seems logical, it may not have appeared to be obvious initially. 6. Conclusions and recommendations for future research Correct sign placement is a very important aspect of urban and architectural design. However, the location of signs in architectural spaces is often left to engineering judgment. Not withstanding a few basic guidelines on the placement of signs, there is currently no developed models for the placement of signs to maximize visibility and minimize occlusion, even though the correct placement will have a great impact on the usability and functionality of the building or urban context being designed. This paper presented a discrete event simulation model that evaluates the effect of placement on the sign occlusion in architectural spaces. The model utilized two measures: the first measure is the probability of a sign being occluded under certain space design and geometric conditions. The second measure estimates the likelihood of an occupant/pedestrian missing the sign based on the minimum time required for that occupant/ pedestrian to detect, recognize and read the sign. Suggestions for future research include expanding the model to more accurately model urban spaces and modeling the effect of occlusion by dynamic obstructions in the urban environment such as vehicles or other pedestrians. Also, another direction for future research is developing an optimization routine that searches for the best location in the space for the sign.
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From the similarity of △BCM and △FEM shown in Fig. 6, X2 can be expressed as
Appendix A A.1. Determining the legibility distance Tlz Looking at Fig. 6 one can write, Ws þ Wlo Y ¼ 2 Ws Wo þ Wl þ Y1 ¼ Y 2 2 Ws Wo þ Wl Y11 ¼ Y 2 2
X2 ¼ D2
ð13Þ ð14Þ ð15Þ
Where, Ws = sign width, Wlo = lateral offset, Wl = lateral offset of obstruction and, Wo = width of obstruction. Assuming Spc as the average walking speed of the occupant/pedestrian, Tlz as the time required for the occupant/pedestrian to traverse the legibility zone, and Dleg as the legibility distance, then D1 ¼ Tlz Spc
ð16Þ
D2 ¼ Y Cot h
ð17Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 X ¼ D1 þ D2 ¼ Dleg ðY Þ2
ð18Þ
Substituting Eqs. (16) and (17) into (18) and solving for Tlz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Dleg ðY Þ2 Y Cot h Tlz ¼ Spc A.2. Determining the coordinates X1(t) and X11(t) To find the coordinates X1(t) and X11(t), the distance traveled by occupant/pedestrian at time t upon entering the legibility zone (Dpc(t)) can be expressed as DpcðtÞ ¼ Spc t
ð19Þ
Distance between points J and C (DJC) at any time t can be expressed as DJC ¼ X Spc t
ð20Þ
From the similar triangles △JCM and △KDM Y Y1 Y Y1 ¼ X X Spc t X1ðtÞ ¼ X DJC Y Y
Also, from the similar triangles △JCM and △LEM Y Y11 X11ðtÞ ¼ X X Spc t Y
Y Y11 Y
ð21Þ
Also, from the similarity of △ACM and △GDM, D3 can be expressed as Y Y1 D3 ¼ ðD1 þ D2 Þ ð22Þ X2 Y Substituting X2 from Eq. (21) into Eq. (22), Y Y1 Y Y11 D3 ¼ ðD1 þ D2 Þ D2 Y Y The distance traveled by the dynamic obstruction at time t after entering the legibility zone (Dhv(t)) is DhvðtÞ ¼ Shv t
ð23Þ
If the position of the dynamic obstruction at the moment the occupant/pedestrian arrives at the legibility zone is at a distance equivalent to n% of D4, Xf (t) and Xb(t) at time t can be expressed as: n D4 þ Shv t 100 n D4 þ Shv t Lhv ¼ Xf ðtÞ Lhv ¼ D5 þ 100
Xf ðtÞ ¼ D5 þ XbðtÞ
References [1] Ahmed Al-Kaisy, Jigar Bhatt, Rakha Hesham, Modeling the effect of heavy vehicles on sign occlusion at multilane highways, J. Transp. Eng. 131 (3) (2005) 219–228. [2] Paul Arthur, Passini Romedi, Wayfinding: People, Signs, and Architecture, McGraw Hill, Inc., New York, 1992. [3] Cherry Colin, On Human Communication, The MIT Press, Cambridge, Massachusetts, 1978. [4] J. Follis, D. Hammer, Architectural Signing and Graphics, Whitney Library of Design, New York, 1979. [5] Charles B. McLendon, M. Blackistone, Signage: Graphic Communications in the Built World, McGraw Hill, Inc., New York, 1982. [6] Federal Highway Administration, “Manual on Uniform Traffic Control Devices” FHWA, U.S. Department of Transportation, Washington, D.C., 2000. [7] International Code Council, Uniform Building Code, 2006 Washington DC. [8] James Patterson, Simplified Design for Building Fire Safety, Wiley Interscience, New York, 1993. [9] M. McDonald, O. Starkey, K.S. Rutley, Obstruction of traffic signs and signals, Transport and Road Research Laboratory, Contractor Report 100, Department of Transport, United Kingdom, 1988. [10] Nicholas Dines, Kyle Brown, Landscape Architect's Portable Handbook, McGraw-Hill, New York, 2001. [11] Treasury Board of Canada, Signage: System Overview and Implementation, Government of Canada, Toronto, Canada, 1992. [12] G. Ullman, C. Dudek, Effect of roadway geometrics and large trucks on variable message sign readability, Proceedings of the Transportation Research Board 80th Annual Meeting, Washington, D.C. (on CD-ROM), 2001.
Assessing sign occlusion in buildings using discrete event simulation Khaled Nassar a,b,⁎, Ahmed Al-Kaisy c a
c
Department of Architectural Engineering, University of Sharjah, PO Box 27272 Sharjah, United Arab Emirates b Department of Architectural Engineering, Cairo University, Egypt Department of Civil Engineering, Montana State University, P.O. Box 172220, Bozeman, MT 59717-2220, United States Accepted 15 October 2007
Abstract Correct sign placement in large buildings such as airports, railway stations or large academic buildings will have a significant impact on the usability of the building as well as having a beneficial impact on the way-finding characteristics of the pedestrian in these environments. This paper presents a discrete event simulation model that evaluates the effect of placement on the sign occlusion in architectural spaces. The simulation model allows the designers to identify optimum location for signs in a space to maximize visibility and minimize occlusion. The model takes into account the geometric configuration of the space, the occupant/pedestrian travel flow patterns, and the location of obstructions as well as the legibility distance. An analytical tool was developed where the movement and location of occupants'/pedestrians' legibility zones and obstructions are simulated at any point in time. The model also accounts for variables like the location of obstructions, sign design, and the primary and secondary travel paths of occupants/pedestrians. The occlusion of wall and ceiling-mounted signs by obstructions is estimated using two measures. The first measure is the probability of a sign being occluded under certain space design and geometric conditions. The second measure estimates the likelihood of an occupant/pedestrian missing the sign based on the minimum time required for that occupant/pedestrian to detect, recognize and read the sign. © 2007 Elsevier B.V. All rights reserved. Keywords: Sign visibility; Sign occlusion; Signage; Discrete event simulation; Sign placement and location; Way finding
1. Introduction The placement of signs in large buildings and urban spaces is an important part of the successful design of these places. Correct sign placement in large buildings such as airports, railway stations or large academic buildings will have a significant impact on the usability of the building or urban setting as well as having a beneficial impact on the way-finding characteristics of the pedestrian in these environments. Signing provides pedestrians/ occupants with clear instructions for easy progress to their destinations. Moreover, sign installations should be an integral part of the space design and therefore are best planned in tandem with the design of the space itself. With the advent of more ⁎ Corresponding author. Department of Architectural Engineering, University of Sharjah, PO Box 27272 Sharjah, United Arab Emirates. E-mail addresses: [email protected] (K. Nassar), [email protected] (A. Al-Kaisy). 0926-5805/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2007.10.006
sophisticated and costly signage and announcement boards (such as Liquid Crystal Displays, LCD), the optimum placement of these signs to maximize visibility by occupants/pedestrians and minimize occlusion has gained an increased importance. For optimal location, plans for sign placements should be investigated during the earliest stage of preliminary design, and then the details should be developed as final design progresses [6]. Currently however, the factors to be considered for the installation of overhead sign displays have not been defined in specific numerical terms [6] and this leaves much of this decision to engineering judgment. There is a lack of systematic and methodical models or techniques for optimized sign placement in spaces. Albeit, a few very basic guidelines on sign design such as font, text and lighting tools that aid in the sign placement are virtually inexistent. The most detailed sign placement guidelines are for the placement of exit signs which outline the exact size and location of sign placement in basic corridor-type layouts. On the other hand, the placements of
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other wall-mounted or ceiling-mounted directional signs and announcement boards have not been studied. In the absence of such design tools, the location of the signs is often left to professional judgment or experience. The ultimate objective of this research is to explore and assess the effect of the different space configurations and geometry, and sign placement on the occlusion of ground-mounted and ceilingmounted signs. This paper is mainly concerned with developing a simulation model to assess this effect. While the model was developed primarily to investigate the effect of fixed obstacles and building space geometry on sign visibility, it is part of a larger research effort aimed at modeling situations where pedestrian sightline is obstructed by a moving obstacle such as in urban contexts. The remainder of this paper is organized as follows; first a literature review is presented that cites the major research efforts addressing sign placement and occlusion. This is followed by identifying the main requirements and variables of the model for sign occlusion and optimum placement. The developed model is presented next along with a description of its various sub models. An example application of the model in a real building is provided along with results and analysis. Finally, conclusions are drawn and recommendations for future research are presented. 2. Previous research Review of previous research suggests that there is little information in the literature that addresses the issue of sign visibility and optimum placement of signs based on scientific models. The majority of studies in the literature can be broken into 2 main directions; firstly basic guidelines on sign design, especially for emergency egress applications and secondly studies in the field of traffic engineering that deal with models for road related variables. Basic guidelines on the placement of signs and especially way-finding and emergency egress signs have been presented in the literature [7,2,3,4,5] (Romedi 1984). These deal primarily with size of the signs, font and text size to use (Table 1 and Table 1 Viewing distance and character size (Adapted from Treasury Board of Canada 1992) View distance (m)
Character size (mm)
1 2 4 5 7 9 12 15 18 24 30 36 48 60 72 90 120
5 6 8 10 12 15 20 25 30 40 50 60 80 100 120 150 200
Fig. 1. Acceptable legibility (adapted from [10]).
Fig. 1), location of emergency exist signs (Fig. 2), as well as lighting and materials used. In the field of traffic engineering, a study by [9] investigated the obstruction of ground-mounted and overhead signs by heavy vehicles using two different approaches. First, field data were used to develop empirical relationships to estimate sign obstruction using variables such as traffic volume, percentage of heavy vehicles, average speed, etc. A video camera mounted at the roadside at the location of the sign was used to recognize the obstruction of the driver's sight line to the sign by heavy vehicles. Regression analyses were carried out and equations were developed from the collected data. In the second approach, a simulation model was used to assess sign obstruction by heavy vehicles. The study concluded that the simulation failed to provide results that are reasonably close to those from empirical equations. Another study by [12] provided an analytical approach to assess the potential impacts of vertical curves, horizontal curves, and heavy vehicles on Variable Message Sign (VMS) readability. The analyses were mainly based on the premise that each of these factors can significantly limit the distance at which a VMS can be read. This in turn translates into shorter available reading times and the need to display a shorter message with fewer units of information. In addition, Al Kaisy et al. (Al Kasiy et al 2003) developed a simulation model for assessing the occlusion of signs from passenger cars by large vehicles. Some of the concepts presented in that research are utilized in the model presented here. In addition to the above two directions, some governmental guidelines exist for sign placement with the aim of aiding the public to clearly recognize activities in public buildings and spaces [11]. These guidelines provide means of consistent sign identification to improve the service to the public by facilitating access and wayfinding. However, these guidelines also are focused on the physical properties of the sign itself (size, illumination, etc…) and provide very little in terms of placement location within a facility. 3. Occlusion of signs: important variables When planning sign placement one should consider the physical characteristics of the building or site, the direction and
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Fig. 2. EXIT sign placement guidelines (adapted from [8]).
type of traffic flow, the means of access, the type of sign used, as well the placement and design of the sign. In general, correct sign placement involves two main aspects; firstly, placing them in a manner to minimize occlusion and maximize visibility. This involves choosing the best location in the space to increase the number of occupants/pedestrians that can see the sign during their regular traveling routes and minimize sign occlusion by the obstacles in the space. Secondly, correct sign placement involves sign-specific variables such as using appropriate material, legible font and the type of sign used. The model presented in
this paper is concerned with the first of these two aspects and mainly placing the sign to minimize occlusion. The sign design itself is an underlying input variable of the model as will be explained below. Many variables are believed to affect the occlusion of groundmounted and ceiling signs by obstacles in architectural and urban spaces, such as building elements (columns, stairs, street furniture, cars, other pedestrians, etc…) and therefore should be accounted for in modeling this effect. These variables are either related to conditions in the particular space e.g. occupant traffic flow
Fig. 3. Legibility distance and legibility zone.
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Fig. 4. Occupant/pedestrian travel flow directions and the divergence angle.
direction (and vehicular traffic in case of urban spaces) or variables relate to the geometry of the space. These variables include: 1. Legibility distance: this is the maximum distance along the occupant/pedestrian sightline from the subject sign where the occupant/pedestrian is able to read the sign (Fig. 3). It is mainly a function of sign design (e.g. letter size, font, color contrast, etc) and human vision characteristics particularly vision acuity. Displacement on the other hand is the distance between the centre of a sign and an observer's central line of vision (measured at a right angle to the central line of vision). The angle of displacement should fall between 5 and 15 degrees in order to optimize legibility, e.g., 0.25 m of displacement per 1.00 m of viewing distance provides an angle of approximately 15 degrees at the eye of an observer [11]. The sign's legibility and ultimate size are determined form the viewing distance and character size. 2. Divergence angle θ: this is the angle between the occupant/ pedestrian's sightline and the centerline of the direction of travel (Fig. 3). 3. Legibility zone: this is an imaginary zone upstream of the sign where the occupant/pedestrian is able to read the sign. This zone is delineated by the legibility distance along the driver's sightline (upstream) and the line that represents the maximum divergence angle θ (downstream). This zone is represented by the shaded area in Fig. 3. 4. Expected walking speed of occupant/pedestrian: this variable determines the time spent by the occupant/pedestrian within the legibility zone described earlier. The viewing distances referred to in Table 1 are for the normal occupant/ pedestrian who is standing or walking towards a sign. Signs intended for vehicular traffic, are additionally affected by the normal speed of traffic passing the sign. 5. Location of the obstruction relative to the occupant/pedestrian when the latter arrives at the legibility zone: this variable also
affects the time during which occupant/pedestrian sightline is hindered by the obstruction. 6. Size of the obstruction: for example in building spaces, the size of columns, walls, stairs, or any other architectural element that may hinder the visibility of the sign. 7. Occupant/pedestrian traffic volumes and directions of travel. This is determined in terms of the arrival rate in occupants/ hour. 4. Model development 4.1. Model requirements and assumptions In order to assess the occlusion of ground-mounted and ceiling-mounted signs by the obstructions, any model should include a number of initial requirements. The model should have the ability to dynamically model the movement and location of the occupant/pedestrian as well as the obstruction in the building/urban space upstream of the sign and the continuity of sightline between the occupant/pedestrian and the sign. The model should also have the ability to model variables that are relevant to the occlusion of signs by obstacles such as building features (columns, stairs, etc…). Furthermore, the model should incorporate the occupant/pedestrian traffic flow patterns in the space under consideration and include provisions for primary and secondary flow directions as well as nonlinear travel directions (Fig. 4). Finally, the model should have the ability to model variables that define the geometry of the problem such as lateral distance of sign placement, legibility distance, relative location of obstruction, etc. A number of assumptions are made to simplify the development of the model. The main assumptions of the proposed occlusion model include the assumption that the occupant/ pedestrian is fully attentive, i.e. no distraction of any kind within the legibility zone. The model assumes also that the occupant/
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Fig. 5. Flowchart of the simulation model.
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Fig. 6. Static layout for the occlusion problem and the main geometric variables.
pedestrian travels at a constant walking speed, i.e. no acceleration or deceleration within the legibility zone. Furthermore, it is assumed that the sign and font size are determined a priori and the legibility distance and legibility zone are determined accordingly. In addition the sign text, font, uniformity and all the other signrelated variables have been correctly planned. The model is applicable to architectural and urban spaces and can be used to optimize the location of fixed signs of various kinds e.g. LCDs. 4.2. Model description The proposed discrete event simulation model assesses the occlusion of ground-mounted and ceiling-mounted signs by obstructions from static architectural/urban elements (columns, stairs, trees, street furniture, etc…). Specifically, the model estimates two measures in assessing the amount of occlusion under certain occupant/pedestrian traffic flow, geometric configuration, and sign design variables. The first is the absolute probability of the sign being occluded while the second is the probability of an occupant/pedestrian missing the sign. The simulation utilizes discrete time steps to simulate occupant/pedestrian movement in the space. At each time step a number of calculations are performed based on the inputs to the model. The calculations performed at each time step can be divided into three main parts. Firstly, the model calculates the amount of occlusion caused by one or more obstruction that happens to be in the legibility zone upstream of the subject sign. Secondly, having calculated the amount of occlusion, the model determines the probability of having one or more obstructions within the legibility zone of the sign. Finally, the model developed estimates for the two measures of occlusion mentioned above. In the next sections the three parts of the model are explained.
4.2.1. Determining the amount of occlusion caused by one or more obstruction The first step is determining the probability of a sign being occluded and the probability of an occupant/pedestrian missing the subject sign during the time when there are one or more obstructions within the legibility zone. The flow chart shown in Fig. 5 explains the main processes performed in the model. As shown in this flow chart the location of the occupant/ pedestrian and the obstruction(s) in the flow direction within the legibility zone is updated. Also, the continuity of the sightline between the occupant/pedestrian and the sign is evaluated every tenth of a second. This is done by determining the points of intersection of the occupant/pedestrian's sightline with the two planes that represent the left and right sides of the obstruction (s), and comparing these points with points that represent the area occupied by obstruction(s) at any time t. The model utilizes a binary variable that represents the status of the continuity of sightline at any time t. The model then calculates the amount of time when occlusion is in effect during the total duration when the occupant/pedestrian traverses the legibility zone. Finally, by estimating the minimum time required to read the sign, this submodel determines the probability of an occupant/pedestrian missing the sign. Fig. 6 shows the geometry of the sign occlusion problem at any time t when an obstruction occupies the legibility zone. The model assumes that the occupants/pedestrians travel along predefined paths that represent the main travel directions in the architectural or urban spaces. The model further assumes that the occupants/pedestrians travel at a certain distance from the center of the predefined paths. This distance is randomly generated and is bound by the space dimensions. The model also assumes that the center of the text or symbol message is at
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the center of the sign. While the latter assumption may add an approximation to model results, this approximation is expected to be very small due to the small dimension of message width with respect to the legibility distance. Therefore, this approximation was deemed an appropriate trade-off for the sake of model simplicity. Analyzing the problem detailed in Fig. 6, it therefore follows that the legibility distance is (the derivation is shown in the Appendix), ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Dleg ðY Þ2 Y Cot h Tlz ¼ ð1Þ Spc To find the coordinates X1(t) and X11(t), the distance traveled by occupant/pedestrian at time t upon entering the legibility zone (Dpc(t)) one can write (derivations are shown in the Appendix),
X1ðtÞ
Y Y1 Y Y1 ¼ X DJC ¼ X X Spc t Y Y
X11ðtÞ ¼ X Xf ðtÞ ¼ D5 þ
Y Y11 X Spc t Y
n D4 þ Shv t 100
XbðtÞ ¼ Xf ðtÞ Lhv ¼ D5 þ
n D4 þ Shv t Lhv 100
ð2Þ ð3Þ ð4Þ ð5Þ
If X1(t) b Xf (t) and Xb(t) b X11(t), then occlusion is in effect, i.e. occupant/pedestrian's sightline is obstructed. Otherwise, the sightline is clear. The continuity of the sightline is checked every tenth of a second until the occupant/pedestrian leaves the legibility zone. The time during which occlusion was in effect (Tocc) is then determined by adding the time during which the sightline is obstructed. Time available to read the sign Ta is Ta ¼ Tlz Tocc
ð6Þ
The percentage of time when occlusion is in effect (one form of probability) for a specific position of an obstruction (i) is, PoccðiÞ ¼
ToccðiÞ 100 Tlz
ð7Þ
The average walking speed of the occupant/pedestrian, the relative speed of the dynamic obstruction(s) with respect to the occupant/pedestrian, and the legibility distance (mainly a function of legend size) are user-specified. These variables can reasonably be estimated for the situation at hand. The amount of occlusion for that particular situation is then estimated by determining the mean value of occlusion from all these different scenarios. n P
Pocc ¼
1
PoccðiÞ n
ð8Þ
The increment used in this model is equivalent to one hundredth of the distance mentioned earlier (n = 100). This means that for a particular situation at hand, the simulation runs 100 different scenarios and finds the average occlusion.
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Also, the probability of an occupant/pedestrian missing the sign Pm is found by estimating the minimum time required to read the sign (Tmin). Tmin is mainly a function of the number of words and symbols in a particular sign and can be estimated using several theoretical models. For each relative position of the dynamic obstruction, the model determines whether the occupant/pedestrian is able to read the sign by comparing Ta to Tmin. If Ta is less than Tmin, then the occupant/pedestrian will miss the sign (Pm(i) = 1), otherwise, he will be able to read the sign (Pm(i) = 0). The model used a binary variable (Pm(i)) to represent the two possibilities. The model then estimates the probability of an occupant/pedestrian missing the sign by dividing the number of scenarios when Pm(i) = 1 by the total number of scenarios (n). n P
Pm ¼
1
PmðiÞ n
ð9Þ
Similar logic is used to check the continuity of sightline when multiple dynamic obstructions happen to occupy the legibility zone. The model updates the location of the obstruction every tenth of a second and compares the coordinates of the points of intersection (X1(t) and X11(t)) with the coordinates that represent the location of each dynamic obstruction within the legibility zone. 4.2.2. Determining the probability of obstructions within the legibility zone At this stage, the amount of occlusion when one or more obstructions occupy the legibility zone has been estimated. The next step in the model development is to know the likelihood of this event taking place for a particular sign under certain occupant/pedestrian traffic patterns and space geometric conditions. In other words, we seek to answer the following question: what are the chances of a sign being occluded? Referring back to Fig. 6, we seek to find the chances of an occupant (say at point G) missing the sign at M. This likelihood is mainly a function of occupant/pedestrian travel paths, the arrival rate of the occupants/pedestrians, the size, paths and arrival rates of dynamic obstructions. The probability of the legibility zone being occupied by one or more dynamic obstruction can be determined from the amount of time this zone is occupied by one or more obstructions and the total amount of time elapsed in the simulation. The probability of a sign being occluded has to be calculated while the occupant is walking. The model developed here utilizes discrete event simulation to detect the individual events where an obstruction occupies the zone at a time, while the occupant/pedestrian is moving. In this case there are two scenarios. The first happens when the sign is positioned at a high enough location such that it would not be occluded by other occupants or any other dynamic obstruction. This case is simple and can be handled in a way similar to what is described in the previous section. The second case happens when there is a chance that the sign can get occluded by the presence of other occupants. In that case special consideration is needed to account for the movement of the
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Fig. 7. The example building.
obstructing occupant. Each obstructing occupant will occupy the legibility zone for an amount of time determined by its speed, and its body width (or the length for other dynamic obstructions). The calculation would be straight forward if each obstruction would occupy the zone individually. In that case, the total time the legibility zone is occupied can be estimated from the number of obstructions and the time it takes for that obstruction to traverse and completely clear the legibility zone. Practically however, the legibility zone may be occupied by more than one obstruction at a time. This adds another dimension to the analysis in that two specific events have to be accounted for: individual events and overlapped events. Individual events occur when only one obstruction occupies the zone at a time. Overlapped events occur when two or more obstructions occupy the zone at the same time. The model estimates the percentage of time the legibility zone is occupied by individual events and overlapped events individually similar to the method described in (Al-Kaisy et al. 2004). In that model, individual events occur when the headway
between two successive obstructions is equal to or greater than the time required to traverse a distance within the legibility zone plus the length of an obstruction (tD4). Therefore in individual events, the leading obstruction clears the legibility zone before the following one enters the zone, while overlapped events
Table 2 Results of the analysis Legibility distance Dlz (m) 6 9 12 15 18 21 24 27
P1 (%)
P2 (%)
A
B
C
D
A
B
C
D
32 29 28 21 21 21 20 20
31 29 27 24 16 15 12 8
30 27 24 18 14 15 12 8
28 25 25 22 18 14 7 4.2
44 41 41 41 41 40 40 40
43 42 41 36 31 30 28 26
43 42 39 31 30 30 26 21
42 39 38 27 18 12 9.2 6.2
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occur when the headway between two successive obstructions is smaller than tD4 and the following obstruction enters the legibility zone before the leading one clears the zone. The time overlap between two successive obstructions is equivalent to tD4 − h, and hence the time duration of that overlapped event (two-obstruction scenario) is tD4 + h. Similarly, for multiple successive obstructions with short headways, the time duration for the overlapped event becomes tD4 + ∑ h. However unlike the model developed in [1] we are mainly interested here in the percentage of time the legibility zone is occupied by obstructions for individual events. This can be given by, TperðiÞ ¼
TocðiÞ 3600
ð10Þ
Where Toc(i) is the amount of time during the simulation when the sign is occluded. The simulation is run and Toc(i) is calculated based on the specific configuration of the plan specified, taking into account the location of obstructions and the placement of the sign. 4.2.3. Estimating the occlusion measures Estimate of the two occlusion measures can now be calculated given the results above: the first is the absolute probability of a sign being occluded by obstructions while the second is the likelihood of an occupant/pedestrian missing the sign. To find the first measure, the percentage of time for individual events (Tper(i)) are multiplied by the amount of occlusion found earlier. This probability is expressed as P1 ¼ TperðiÞ PoccðiÞ
ð11Þ
Also, the absolute probability of an occupant/pedestrian missing the sign is estimated as P2 ¼ TperðiÞ PmðiÞ
ð12Þ
5. An example using the model In order to verify the model, an actual building was used to run the simulation model. The building used for the application of the model is a large academic building located on the campus of a typical university. The building consists of a big atrium as well as lecture halls and passageways to other buildings on the campus. The problem that the model was applied to is finding the best location for a large LCD that displays student related information and announcements about upcoming activities. The design of the spaces where the major occupant traffic is expected is represented in Fig. 7. Input to the model includes the possible locations of signs, space and obstruction boundaries and dimensions as well as occupant/ pedestrian traffic flow directions. The traffic flow directions are inputted to the model in the form of centerline for the main pathways. Each traffic flow direction is assigned an arrival rate based on the expected number of occupants traveling. Their rates assume a Poisson distribution as explained earlier.
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Four different alternate locations were investigated as shown in Fig. 7. Although it may seem clear that the location of the sign should be placed so that is perpendicular to the line of sight of the main flow direction, the presence of the columns in the space along with the varying occupant traffic patterns and flow directions complicate the problem. The simulation was therefore run by means of generating occupants traveling along the flow directions. At each time step the model checks the line of site of the occupants and sign occlusion using the procedure described in the above section and the two occlusion measures, P1 and P2 are calculated accordingly. By analyzing the results of the simulation, one would be able to identify which of the four locations provide the best placement location to maximize visibility and minimize occlusion. Table 2 shows the results of the analysis. It is clear from the results that as the legibility distance increases, i.e. by using a large sign with larger text size, the two measures of occlusion will generally decrease. However, this is not always true because of the location of the sign in relation to other occluding objects in space. If a sign is occluded by a column for most of the occupant traffic flow for example, the high legibility distance becomes irrelevant to the occlusion measures used. This is true for placement location A, where the visibility of the sign will not significantly increase beyond the 15 meter legibility distance. Therefore if location A becomes the final location of the sign, it does not make any sense to increase the sign any larger than would provide a 15 m legibility distance. One can also see from the results that alternate position D is the best performer in terms of the two occlusion measures used. Although this conclusion seems logical, it may not have appeared to be obvious initially. 6. Conclusions and recommendations for future research Correct sign placement is a very important aspect of urban and architectural design. However, the location of signs in architectural spaces is often left to engineering judgment. Not withstanding a few basic guidelines on the placement of signs, there is currently no developed models for the placement of signs to maximize visibility and minimize occlusion, even though the correct placement will have a great impact on the usability and functionality of the building or urban context being designed. This paper presented a discrete event simulation model that evaluates the effect of placement on the sign occlusion in architectural spaces. The model utilized two measures: the first measure is the probability of a sign being occluded under certain space design and geometric conditions. The second measure estimates the likelihood of an occupant/pedestrian missing the sign based on the minimum time required for that occupant/ pedestrian to detect, recognize and read the sign. Suggestions for future research include expanding the model to more accurately model urban spaces and modeling the effect of occlusion by dynamic obstructions in the urban environment such as vehicles or other pedestrians. Also, another direction for future research is developing an optimization routine that searches for the best location in the space for the sign.
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From the similarity of △BCM and △FEM shown in Fig. 6, X2 can be expressed as
Appendix A A.1. Determining the legibility distance Tlz Looking at Fig. 6 one can write, Ws þ Wlo Y ¼ 2 Ws Wo þ Wl þ Y1 ¼ Y 2 2 Ws Wo þ Wl Y11 ¼ Y 2 2
X2 ¼ D2
ð13Þ ð14Þ ð15Þ
Where, Ws = sign width, Wlo = lateral offset, Wl = lateral offset of obstruction and, Wo = width of obstruction. Assuming Spc as the average walking speed of the occupant/pedestrian, Tlz as the time required for the occupant/pedestrian to traverse the legibility zone, and Dleg as the legibility distance, then D1 ¼ Tlz Spc
ð16Þ
D2 ¼ Y Cot h
ð17Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 X ¼ D1 þ D2 ¼ Dleg ðY Þ2
ð18Þ
Substituting Eqs. (16) and (17) into (18) and solving for Tlz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Dleg ðY Þ2 Y Cot h Tlz ¼ Spc A.2. Determining the coordinates X1(t) and X11(t) To find the coordinates X1(t) and X11(t), the distance traveled by occupant/pedestrian at time t upon entering the legibility zone (Dpc(t)) can be expressed as DpcðtÞ ¼ Spc t
ð19Þ
Distance between points J and C (DJC) at any time t can be expressed as DJC ¼ X Spc t
ð20Þ
From the similar triangles △JCM and △KDM Y Y1 Y Y1 ¼ X X Spc t X1ðtÞ ¼ X DJC Y Y
Also, from the similar triangles △JCM and △LEM Y Y11 X11ðtÞ ¼ X X Spc t Y
Y Y11 Y
ð21Þ
Also, from the similarity of △ACM and △GDM, D3 can be expressed as Y Y1 D3 ¼ ðD1 þ D2 Þ ð22Þ X2 Y Substituting X2 from Eq. (21) into Eq. (22), Y Y1 Y Y11 D3 ¼ ðD1 þ D2 Þ D2 Y Y The distance traveled by the dynamic obstruction at time t after entering the legibility zone (Dhv(t)) is DhvðtÞ ¼ Shv t
ð23Þ
If the position of the dynamic obstruction at the moment the occupant/pedestrian arrives at the legibility zone is at a distance equivalent to n% of D4, Xf (t) and Xb(t) at time t can be expressed as: n D4 þ Shv t 100 n D4 þ Shv t Lhv ¼ Xf ðtÞ Lhv ¼ D5 þ 100
Xf ðtÞ ¼ D5 þ XbðtÞ
References [1] Ahmed Al-Kaisy, Jigar Bhatt, Rakha Hesham, Modeling the effect of heavy vehicles on sign occlusion at multilane highways, J. Transp. Eng. 131 (3) (2005) 219–228. [2] Paul Arthur, Passini Romedi, Wayfinding: People, Signs, and Architecture, McGraw Hill, Inc., New York, 1992. [3] Cherry Colin, On Human Communication, The MIT Press, Cambridge, Massachusetts, 1978. [4] J. Follis, D. Hammer, Architectural Signing and Graphics, Whitney Library of Design, New York, 1979. [5] Charles B. McLendon, M. Blackistone, Signage: Graphic Communications in the Built World, McGraw Hill, Inc., New York, 1982. [6] Federal Highway Administration, “Manual on Uniform Traffic Control Devices” FHWA, U.S. Department of Transportation, Washington, D.C., 2000. [7] International Code Council, Uniform Building Code, 2006 Washington DC. [8] James Patterson, Simplified Design for Building Fire Safety, Wiley Interscience, New York, 1993. [9] M. McDonald, O. Starkey, K.S. Rutley, Obstruction of traffic signs and signals, Transport and Road Research Laboratory, Contractor Report 100, Department of Transport, United Kingdom, 1988. [10] Nicholas Dines, Kyle Brown, Landscape Architect's Portable Handbook, McGraw-Hill, New York, 2001. [11] Treasury Board of Canada, Signage: System Overview and Implementation, Government of Canada, Toronto, Canada, 1992. [12] G. Ullman, C. Dudek, Effect of roadway geometrics and large trucks on variable message sign readability, Proceedings of the Transportation Research Board 80th Annual Meeting, Washington, D.C. (on CD-ROM), 2001.