Objective versus subjective measures of Paris Metro map usability: Investigating traditional octolinear versus all-curves schematics

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Abstract

Schematic maps are an important component of assistance for navigating transport networks worldwide. By showing routes as simple straight lines, they reduce the cognitive load of journey planning, and by revealing the underlying structure of networks, they make their key features easier to identify and learn. However, although there are many suggestions for optimizing schematic maps so as to maximize these benefits, to date these have not been directly supported by published usability studies or psychological theory. In this paper, we suggest that there are circumstances in which conventional schematic maps fail to yield benefits, and we compare journey planning using the current official RATP Paris Metro map with an all-curves design which replaces straight lines and corners with gentle curves. Three separate usability studies with slightly different methodologies showed that the journey planning time for the all-curves map was better than the RATP version, with effect sizes ranging from 0.48 to 1.12. Subjective usability ratings were derived from questionnaires, and user preferences, but neither were correlated with objective usability measures. We conclude that (1) in terms of designing schematics, there is no evidence to suggest that any rule-set can be claimed to be a gold-standard, and it is important to match the design rules to the properties of the network, (2) in some circumstances, radical departures from traditional ideas can yield usability benefits, and (3) map usability appears to be distinct from map engagement, although the latter is undoubtedly important in encouraging people fully to make use of navigation aides.

Highlights

► Two Paris Metro maps are compared, official octolinear design and all-curves design. ► All curves design better than octolinear design for objective usability measures. ► No relationships between objective usability measures and subjective ratings. ► For complex networks, breaking traditional design rules can improve usability.

Introduction

Throughout the world, schematic network maps have become particularly associated with self-contained urban rapid transit (or metro) systems, and are an important means of showing routes and interchanges for the purpose of journey planning. For such networks, the simplicity and frequency of services, and the importance of station sequences and inter-connections (topological information) as opposed to exact route trajectories (topographical information) makes them particularly well-suited to being depicted in this way. Maps in this style originated at least as early as the 1920s, and became widespread from the 1970s onwards. They can be seen all round the world (Ovenden, 2005) although there are notable exceptions, such as the official map of the New York Subway network.1

Like many concepts, defining whether or not a network map can strictly be categorized as being schematic is not easy (Dow, 2005, Roberts, 2008a). The key criteria are that street details are absent (although major landmarks such as parks, rivers, and seas may be shown), and that lines or routes are shown as straight lines with sharply radiused corners. The aim is broadly to simplify the information presented so that the user can identify the key elements for journey planning (routes and interchanges) and follow the line trajectories easily. Usually, a restricted number of angles is permitted, typically just four, with horizontal, vertical, and 45° diagonals. This is also known as octolinearity (Nöllenburg and Wolff, 2011, Wolff, 2007): In other words, at any point on a line, only eight different trajectories are possible.2 Applying these design rules almost always results in topographical distortion, especially if the map is organized so that station names do not interrupt lines. This usually requires an expanded centre at the expense of more sparsely-served outer areas, which also balances the design in terms of data density.

In many parts of the world, cities are investing substantially in metro construction. If we define a complex Metro system as exceeding a route mileage of 200 km, with ten major trunk routes or more, the historically complex networks, such as the London Underground, Moscow Metro, New York Subway, Paris Metro, and Tokyo Subway have been joined by the networks of Madrid, Mexico City and Seoul, with others set to follow. With complementary light rail and suburban rail also added to network maps, this high quantity of information comes at a potential usability cost. For example, with a printed size of just 20 cm by 20 cm, the current Paris Metro map includes fourteen metro lines, two metro shuttles, five RER lines, three peripheral tram routes, four suburban rail termini and their routes out of Paris, a river bus service, airport shuttle, a short funicular, and around 380 stations. Producing a clear usable map under such circumstances is a major design challenge, and identifying the underlying principles and cognitive theory of schematic usability in order to assist the designer is a task for which psychologists can potentially assist. The scale of the problem for a complex network can be appreciated when we consider an early usability study (Bronzaft and Dobrow, 1976) in which every single one of 20 novice participants made at least one error when using the then-current New York Subway schematic map to plan a series of journeys.

Most research into the cognitive psychology of map design has focused on topographical maps and perceptual/psychophysical issues, for example symbol discriminability and interpretation (e.g., Montello, 2002, Phillips and Noyes, 1982, Phillips et al., 1990). Another topographical theme concerns how, for example, journeys by car or on foot are planned and sketched (e.g., Tversky and Lee, 1999). The task demands of planning a metro journey from station to station, or communicating one, differs from this in many important ways: Precise spatial directions (e.g., go straight ahead, take the second left, then turn right at the third set of traffic lights) are irrelevant, and instead a sequence of operations more akin to a computer program or a recipe must be devised (e.g., take Line 1 towards La Défense, change to Line 2 at Nation, change to Line 11 at Belleville heading towards Mairie des Lilas). Spatial descriptions become mere flags, necessary to indicate only the broad direction of travel, and even when overtly spatial terms are used (e.g., Northbound Victoria Line) these are effectively only keywords to be identified on signage: After negotiating a maze of passages, the platforms for different directions of travel will be otherwise indiscriminable. As such, the task of creating good network schematics presents its own unique problems compared with topographical maps, and the literature on the latter offers little assistance other than very general suggestions. For example, Tversky and Morrison (2002) highlight the apprehension principle: “the structure and content of the external representation should be readily and accurately perceived and comprehended” (pp. 255–256) but without specific proposals for how to apply this principle to static graphics.

Specific to schematic map design for transport networks, there have been numerous suggestions for good practice (e.g., see Ovenden, 2008, p. 151 for many possibilities, and also Avelar, 2007, Nöllenburg and Wolff, 2011, Stott et al., 2011, Roberts, 2008a, ch. 9; Wolff, 2007). Examples include: always use octolinearity; preserve spatial relationships between stations wherever possible; make the x-height of the lettering the same as the point-width of the lines; do not interrupt lines with station names; etc. However, to date there are no published usability studies with the underlying intention of demonstrating these directly, or identifying the psychological reasons why some designs might be more usable than others.3 Often, where usability between designs is compared, this simply comprises a schematic map versus a topographically accurate one. One of the more well-known investigations into map design, reported by Bronzaft and Dobrow (1984), led to the demise of the New York Subway schematic map, and the adoption of a design that is a forerunner of today’s broadly topographical version. But even this investigation dispensed with objective usability studies after initially failing to find any clear improvements for new designs, switching to user ratings instead.4 In contrast, Bartram (1980) found faster planning for a schematic bus map, but the topographically accurate version had considerably more detail, i.e., streets as well as bus routes. The disadvantage for the topographical map might have been owing to the considerable quantity of potentially distracting supplementary information, irrelevant to the set tasks, rather than complex route trajectories. This is in line with Everett et al. (1977), who showed that a greater level of detail on pamphlets was associated with more planning errors.

Another important issue concerns the effects of topographical distortion. Where this is excessive, users express dissatisfaction with designs, such as when the 2007 Madrid Metro map was introduced, but to date no studies have investigated whether a high degree of distortion interferes with journey planning amongst city experts versus novices to any substantial degree. However, Berendt et al. (1998) have shown that users can and do make spatial inferences about station locations from schematic network maps, and Guo (2011) suggests that map configuration can mislead people into planning inefficient journeys under certain circumstances. Hence, designers generally distort topography only where this yields clear benefits, such as a balanced design or simplified line trajectories.

The most fundamental detail of a transport schematic, what angles should be used in order to simplify the network, has received as little direct empirical or theoretical attention as the other suggested principles of good practice. This lack of scrutiny may partly be due to the widespread belief amongst graphic designers, researchers, commentators and users, particularly in Europe (as opposed to the Americas), that octolinearity, as first used in London in 1933, constitutes some sort of design gold standard. In other words, applying this will result in the best design possible no matter what the structure of the network (e.g., Ovenden, 2005, p. 39).5 In recent research to develop computer routines to automate the generation of schematic maps, and optimize these according to usability criteria, initial attempts did not achieve octolinear designs (e.g., Hong et al., 2006) but this rapidly became a key objective (e.g., Nöllenburg and Wolff, 2011, Wolff, 2007). Hence, Nöllenburg and Wolff (2011) describe octolinearity as a Hard Constraint (i.e., it should never be broken) and suggest that “the main benefit of octilinear layouts is that they potentially consume less space and use fewer bends while still having a tidy and schematic appearance” (p. 626) and that “we believe that octilinearity, which is strictly followed by most real metro maps, is an essential ingredient for tidy and easy-to-read metro map layouts” (p. 627). Empirical evidence in support of this view is very difficult to identify. In some circumstances, there is a memory bias such that diagonal lines tend to be remembered as closer to 45° than reality (Schiano and Tversky, 1992, Tversky and Schiano, 1989) but in these studies mean error never exceeded a few degrees. There is some evidence that people have an octolinear bias (but not necessarily a regular one) in organizing space, but this does not interfere with their perception of this (Klippel and Montello, 2007). Overall, these sorts of findings might explain the tendency towards octolinearity amongst designers, but do not suggest that a non-octolinear map will inevitably cause any difficulties for the user, especially as such maps will be in view while planning takes place, and remembering precise trajectories will not be necessary in order to recall a plan. In any case, in circumstances where octolinearity breaks down (see later), any supposed advantages implied will be lost.

The octolinearity as a gold standard belief has two consequences, first it discourages attempts to determine whether alternatives might result in better designs. For example, Mijksenaar and Vroman (1983) proposed a hybrid map. This had a topographical centre, where there are many tourist attractions and stations within easy walking distance of each other, and octolinear schematic suburbs, where there are fewer tourist attractions and nearby stations. This concept was rejected by London Transport despite the research underlying it (Roberts, 2008a). Furthermore, there may even be circumstances in which the particular properties of a network are poorly suited to octolinearity and result in a map with more complexity in terms of numbers of kinks than might have been created had different design rules been used (see later). Second, the assumption that adopting a gold-standard will result in the best possible map deflects from the issue of whether different implementations that obey the same design rules might be differently usable (Roberts, 2009, Newton and Roberts, 2009). Despite the lack of usability studies to guide us, we can nonetheless identify circumstances in which map usability is likely to be poor, and support these predictions theoretically by turning to cognitive psychology.

Why do schematic maps assist users in navigating transport networks compared with topographical maps (assuming that they do)? From this, how can we capitalize on these aspects in order to improve schematic design? A transport schematic is effectively a pre-prepared representation of the underlying structure of the network, meaning that the user does not need to identify this for him or herself (see also Freska, 1999, pp. 8–9). This reduces task demands and therefore the cognitive load for the user, along with the associated risk of making errors during the planning process. The benefits of this can be identified from the literature on reasoning and intelligence. For example, theories of deductive reasoning (e.g., Mental Models theory, Johnson-Laird and Byrne, 1991, and Deduction Rules theory, Braine and O’Brien, 1998) have, as an initial step, the need to identify key elements of the problem and represent them. Pre-represented information can improve performance (Roberts and Sykes, 2005). One aspect of optimizing a schematic map, therefore, is to heighten the salience of the underlying network structure. How should this be achieved?

The effects of item appearance and logical structure on task difficulty have been particularly investigated in the domain of intelligence testing. For example, analyses of non-verbal items, such as Raven’s Progressive Matrices (e.g., Raven et al., 1993) show that the hardest items, for which correct solutions indicate the highest intelligence, are those which are most demanding on working memory capacity: They have many rules and elements to identify, and rules which require more processing steps to execute (e.g., Carpenter et al., 1990). In other words, information quantity affects performance. Overall, the cognitive load of a reasoning task, specifically, its working memory demands, and the cognitive capacity of the individual, determine the likelihood of success (e.g., Stanovich and West, 1998a, Stanovich and West, 1998b, Stanovich and West, 2000).

In terms of schematic maps, quantity of lines and stations is clearly related to cognitive load, but it should also be noted that a line trajectory with many corners contains more information than a straight line. The consequence of this additional information is more than simply making a line harder to follow. In the domain of intelligence testing, Roberts et al. (2000) and Meo et al. (2007) have shown that element salience is an important component of item difficulty: Problems can have the same underlying logic, but if this is concealed via complex, difficult to identify (or name) shapes and patterns, then items will be harder to solve (see Fig. 1). Crucially, therefore, complexity of problem elements directly relates to people’s ability to identify them, and from this to identify item structure and underlying logic. In other words, it is hard to reason if it is hard to identify what is to be reasoned about.

Roberts, 2008a, Roberts, 2009, Roberts, 2012, Newton and Roberts (2009) argues that the simplification of line trajectories is a crucial aspect of optimizing a schematic map. Taking meandering complex trajectories in real life, and converting them to simple straight lines will minimize the cognitive load associated with journey planning, and reveal the underlying structure of the network. Reduced cognitive load alongside increased structural salience increases the opportunity for learning, setting up a virtuous circle and reducing the cognitive load still further in the future. For a well-optimized map, we would therefore expect fast journey planning, few errors, better remembered plans, and more easily reconstructed plans in the event of a failure to remember. In comparison, a poorly designed schematic, with many unnecessary changes of direction, will not have these benefits, and may even have little to offer compared with a topographic map, other than the simplification entailed in removing street details and most other landmarks. Hence, converting a network representation from topographical to schematic is only beneficial if the meandering curves really have been straightened. If curvature is merely converted into short segments of straight lines linked by many corners, then the original trajectories have not been simplified, instead the shape of the complexity has merely been changed. Any supposed benefits for an octolinear layout, as discussed earlier, such as trackability, memorability and reproducibility, will be considerably reduced if the configuration comprises complex sequences of zigzags.

From the analyses above, it is proposed that to maximize the benefits of a schematic map, this should be optimized by simplifying line trajectories in order to minimize changes of direction, but without distorting the topographical relationships between lines and stations excessively. In the absence of evidence to suggest that octolinearity has a special status in relation to map usability, then depending on the structure of the network, breaking the octolinearity rule may permit better optimization. However, for most simple networks, a perfectly adequate schematic is likely to result if octolinearity is used. There are also the expectations of the user to consider: A map that breaks with tradition may be met with resistance. For particularly familiar designs, where the image itself has become the mental model of the city (complete with all the distortions induced by the map, see Vertesi, 2008), user-resistance to new designs may be heightened, at least initially, no matter what the potential usability benefits. Even so, at the time of writing, the octolinear official London Underground map may not be well-optimized. The current design, squeezed into dimensions of 21.5 cm by 14.5 cm approx. has no fewer than 12 kinks inside the Circle Line. Findings suggest a clear ordinal relationship between the number of kinks on a design and its usability (Newton and Roberts, 2009).

If departures from octolinearity are permissible, the task of the designer becomes somewhat more complex. Alternative approaches include higher linearity maps (e.g., dodecalinear: horizontal, vertical, 30°, and 60° lines) which almost always offer the possibility of fewer changes of direction, especially for complex networks, but at the expense of the greater number of angles increasing the complexity and reducing the coherence of the design (Roberts, 2012). Alternatively, linearity need not be regular, in other words, angles need not be evenly spaced. For a particular network, the actual trajectories taken by its lines may mean that its structure is better suited to a certain level of linearity and particular angles than others. A hexalinear map has just three angles at 60° intervals. Roberts, 2009, Roberts, 2012 has shown that the central area of the London Underground map (inside the Circle Line) is better suited to this than an octolinear design, because fewer changes of direction are necessary in order to show the lines in this key area (six, versus a minimum of nine for an octolinear map).

In some cases there may be no adequate compromise available for a linear map, no matter what angles are adopted. Paris is an excellent example, with a dense network of highly interconnected lines, few of which follow anything like a straight-line trajectory in reality. A conventional octolinear design with any longevity was not produced by the RATP, the Paris transport authority, until 2001 (Ovenden, 2008). However, the requirement for a compact design which minimized distortions in spatial relationships between stations has led to one of extreme complexity. For example, Line 4, the busiest metro line in Paris, has no fewer than 16 changes of direction from end to end, and there is a mean of ten changes of direction per metro line. It is far from clear that this offers any degree of simplification, and therefore reduction in cognitive load and assistance to the user, compared with a topographically accurate map: The many changes in direction make line trajectories difficult to follow, and mask what little structure the network has. Other official straight-line maps of Paris have also been attempted using higher levels of linearity (see Ovenden, 2008) but even these have failed to simplify the network adequately: The use of additional angles adds a new source of complexity and reduces visual coherence, diluting the supposed advantages of using straight lines. The limitations of the designs, both octolinear and higher-order linear, and the complexities of this network, suggest that it is unlikely that a linear design is possible without a high level of cognitive load for the user. This led to the current study, in which an alternative Paris Metro map, a departure from traditional linear rules, was investigated.

For the experiments reported here, an all-curves design was created manually by the first author using a vector graphics package (see Fig. 2). The principles underlying this are that if an effective conventional schematic cannot be created, then a non-linear design may be preferable. Hence, instead of numerous short zigzagging straight-line segments, smooth curves should be used. Rather than changes in direction being minimized, as on a conventional schematic, changes in curvature are minimized instead (see Roberts, 2009, Roberts, 2012). This translates into using Bézier curves with the following optimization criteria: S-bends and other points of inflexion must be avoided where possible and, for an individual metro line, the aim should be to have the smallest number of control points necessary in order to maintain interchanges and to ensure sufficient space for station names. Also, all control points should be tangents, with no cusps permitted. Specific to the Paris metro design here, it was intended to be as topographically accurate as the official RATP version (which is by no means perfect in this respect) but with the trajectories of all lines smoothed, and attention paid to the orbital lines (2 and 6) which together form a loop within Paris. These criteria served to simplify the design and to emphasize the underlying structure of the network in an attempt to reduce the cognitive load associated with using it. In terms of information complexity and cognitive load, the suggestion is that a Bézier curve, with a minimum number of control points (and hence changes in curvature) comprises less information than short straight-line segments, interrupted by frequent changes of direction. For example, the 16 changes of direction of Line 4 on the RATP map compared with eight intermediate control points on the all curves design.

Section snippets

General methodology and experiment one

For all experiments, participants were asked to plan various complicated (i.e., minimum two interchanges required) cross-Paris journeys using one single Paris Metro map. For a dense network such as this, many journeys will have multiple options, and the two-interchange criterion maximizes competing potential alternative routes, thus increasing the complexity of the planning task in an attempt to maximize effect size. The Paris Metro network is very dense but compact (for example, compared with

Experiment two

For Experiment 2, only the RATP and all-curves maps were tested with the same journeys and materials as before, but using a methodology where a person plans a journey without drawing on a map during the process. Instead, participants planned journeys mentally and, when each was completed, this was announced to the experimenter, who then supplied a paper map on which the plan could be transcribed. Such a methodology might be expected to raise the cognitive load of the task, and also separates

Experiment three

For Experiments 1 and 2, participants were timed for planning their journeys, but other than this there was no particular requirement for rapid planning. For the final experiment, we sought to include an element of time pressure, attempting to mimic a situation in which a person knows from a platform indicator than a train is due soon, and must determine the journey before deciding whether or not to get on the train. Based on previous results, a deadline of 40 s per trial was decided upon. This

General discussion

Across the three experiments, the all-curves map outperformed the RATP map in terms of mean planning time, with effect sizes ranging from moderate to strong. For two of the three experiments, the all-curves map was superior taking into account all three measures of performance using MANOVA. Even for Experiment 3, with no significant MANOVA, means for all three objective measures of performance favoured the all-curves map. There was some evidence for a slight overall ability effect: faster

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