Navigation – Plan du site

AccueilRubriquesSystèmes, Modélisation, Géostatis...2011An Evaluation of Road Network Pat...

2011
542

An Evaluation of Road Network Patterns Based on the Criteria for Fire-Fighting

Une évaluation des schémas de réseaux de routes basée sur le critère de la prévention des incendies
Hiroyuki Usui et Yasushi Asami

Résumés

Une évaluation des schémas de réseaux de routes est importante non seulement pour comprendre la structure urbaine, mais aussi pour évaluer sa conformité au texte de loi du Building Standards Law (code de l’urbanisme au Japon), qui permet de préserver les petites voies (i.e. routes étroites de moins de quatre mètres de largeur). Ce texte, par ailleurs, n’est pas assorti d’une méthode pour évaluer la cohérence du schéma du réseau de routes. Un entretien dans un bureau administratif local a révélé que cette disposition est intimement liée au besoin d’assurer un accès aux dispositifs matériels et humains de lutte contre les incendies. Ainsi, en déterminant si dans une aire encerclée par de larges routes il existe des « aires d’impossible extinction d’incendie » (‘fire-inextinguishable area’ (FIA)) à plus de 140 mètres d’une large route (c'est-à-dire des aires dans lesquelles on ne peut pas enrayer efficacement un incendie), il est possible de déterminer si le réseau est convenablement structuré. De plus, un modèle mathématique est utilisé pour montrer que l’absence de FIA dans une aire encerclée est synonyme d’absence de positions inadéquates pour la lutte contre les incendies. Grace à ce critère de différenciation, ainsi que celui de la facilité à tourner à gauche ou à droite aux intersections dans les zones encerclées par de larges routes, il a été constaté que les schémas de réseaux routiers en grille sont adéquatement organisés. En utilisant également des indices basés sur la théorie des graphes comme outils complémentaires pour évaluer les schémas de réseaux de routes, il est ressorti qu’alors que la plupart des réseaux de voies étroites sont classifiés comme des réseaux en arbres, certains des réseaux de voies étroites sont presque considérés comme des réseaux en grille et sont directement connectés aux larges routes. Ceci indique que les réseaux de routes à Tokyo ont une faible connectivité, ce qui peut causer des difficultés pour assurer des doubles issues de secours.

Haut de page

Texte intégral

Introduction

1Road network patterns reflect the structure of a city. There are cities like Kyoto and New York whose road network patterns are primarily grid systems. Other cities, like greater London and Paris, have chiefly radial and ring systems. There are additional cities whose road network patterns are classified as neither grid systems nor radial or ring systems. The road networks of western districts in Tokyo 23 wards, for example, appear to be in obvious disorder. As Jinnai (1992) points out, however, there is a logic that focuses on the geographical features of a district, and this logic governs the road networks in these areas.

2Road network patterns need to be evaluated not only from the point of view of the structure of a city but also in a perspective of compliance with a key rule of the Building Standards Law, the basic law related to buildings and cities in Japan. In 2004, the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) proposed the rule that makes it possible to preserve lanes. Since then, lanes have been defined as roads with a width greater than or equal to 2.7 meters, and less than four meters. This rule can be applied when road network patterns are ‘appropriately laid out’ and if lanes have traditional and beautiful landscapes. No method has been provided, however, for evaluating road network patterns quantitatively, and for establishing the types of spatial units that would be in conformity with this rule.

3To date, many methods for evaluating road network patterns have been proposed. One such method is the index using graph theory, e.g., the alpha index or the gamma index (Kansky (1963), Okudaira (1976), Okuno (1977), Noda (1996), and Aderamo et al. (2010). In graph theory, road networks are considered to be a ‘set of nodes’ and a ‘set of links’. In road networks, an intersection and a road between two neighboring intersections correspond respectively to a node and a link. The Alpha index is based on the number of ‘faces’ there are in a road network. [A ‘face’ is defined as an area encircled by links (Jonathan & Jay, 2004). In the context of city planning, a face is equivalent to a block. See Figure 10, pp. 11-12]. The number of faces is equal to the number of areas encircled by links. Peponis et al. (2008) also define these areas as urban block ‘faces’. Given the number of nodes on road networks, the greater the number of faces the higher the value of the alpha index. Also, the gamma index focuses on the number of links in each road network. Given the number of nodes on road networks, the greater the increase in the number of links, the higher will be the value of the gamma index. The difference between these two indices is related to what is being measured: that is, on whether we focus on the number of blocks, or on the degree of connectivity of road networks. Two disadvantages of indices based on graph theory are 1) the difficulties involved in dealing with metric information, and 2) the challenge of how to set criteria for judging whether or not road network patterns are well laid out. Marshall (2005) proposes four indices, X ratio, T ratio, cell ratio and CdS ratio, for identifying the configuration of real road network patterns. X ratio and T ratio are defined respectively as the ratio of X-junctions to the total number of junctions, and the ratio of T-junctions to the total number of junctions. Clearly in networks comprising only T-junctions and X-junctions, the sum of the X ratio and the T ratio will equal one. In almost any real road network, there will be a mixture of T- and X-junctions, and corresponding ratios will lie somewhere between zero and one. Also, the cell ratio and the CdS ratio are defined respectively as the number of faces to the number of faces-plus-cul-de-sacs, and the number of cul-de-sacs to the number of ‘faces’ plus cul-de-sacs. The sum of the cell ratio and the CdS ratio will equal one. Comparing the T ratio-X ratio to the cell ratio-CdS ratio, we find that both are plotted to generate a two-dimensional space. This plotting helps to describe how ‘griddy’ or ‘tree-like’ the road network configurations are. Furthermore, the relationship between T-junctions, X-junctions and cul-de-sacs may be plotted in a triangular diagram--called the nodegram because it distinguishes between the proportions of different types of nodes. The left diagonal edge of the nodegram represents road networks with no four-way junctions (which is typical of modern suburban road networks), while the right diagonal edge of the nodegram represents road networks with no cul-de-sacs. The use of the nodegram makes it possible to trace the post-war shift to a preference for network patterns, from grid to tributary to grid. Gastner et al. (2006) state that road networks are drawn on a map in such a way that no links cross each other. This gives the roads a two-dimensional form, and helps us to understand why their links are so short: if links are not allowed to cross each other, then they cannot travel far before running into each other. These features are closely related to the small number of nodes in road networks. Hillier (1999) indicates that highly obtuse angles of intersection are associated with longer links, and the near right angles with shorter links. He also suggests that the two principle geometric variables—the length of links and the angle of intersection—appear to play a distinct role in the formation of road networks. Hillier et al. (2007) have observed from an examination of sections of metropolitan Tokyo and London that shorter links tend to form clusters, and that these localized groups tend to form more grid-like local patterns, with links either passing through each other, or ending in other links, at near-right angles. Peponis et al. (2008) define the metric reach Rv(Pi,μ) of a point Pi on road networks according to a metric threshold, μ , as the length of the road links and fractions of road links covered by the union of all paths for which an aggregate length, s, is less than or equal to μ. The authors explore the correlation between the metric reach and the number of blocks per area in a 2-mile by 2-mile square boundary. They indicate that as urban blocks become larger, road networks become more curvilinear and fragmented. Porta et al. (2006) evaluate the road network patterns in a one-mile by one-mile square boundary, and point out the so-called ‘boundary-effect’, in the sense that the higher graph-theoretical index scores are consistently grouped around the geometrical center of the study area. Although the boundary effect is overwhelming in areas with denser urban fabric, like parts of Venice, and dominates the spatial distribution of the value of indices, it is minimized by preventing road networks from being artificially fragmented, or broadening the study area in order to leave out of the picture the areas that are the most boundary-affected. Dalton et al. (2003) refer to the problem of relativization, which needs to be considered when dealing with highly segmented road networks in order to calculate Average Mean Depth, one of the indices in traditional syntactical analysis. Relativization allows us to compare road networks of different sizes. It is not required for dealing with the analysis of a single road network at radius infinity. In dealing with road networks in a district scale, however, we need to handle relativization. Batty (2004a) introduces the formulation that the measure of the deviation from planarity can be formed for any graph as Ψ=Σi li/2n, where li and n are the number of nodes associated with any given link i and the number of nodes, respectively. For the village of Gassin in France, Ψ = 1.065 which implies that there is an average of only 6.5 percent more nodes associated with street segments than in the planar case. Batty (2004b) states that, in urban morphology, graph-theoretical representations are firmly embedded within geographical space and provide useful and easily visualized map patterns of relative nearness or accessibility. Waters (2006) states that geographers have recently published a number of articles that revisit the topic of network topology, and have not only given new life to the old measures of network structure, but also introduced new indices of network complexity and nodal importance. Barrat et al. (2008) covers a large amount of theory and applications related to complex networks whose processes are not only static but also dynamic. In this paper, we deal with road networks whose processes are static.

4In order to apply the rule mentioned above, we clarify the conditions for establishing the criterion: whether or not road network patterns are well set up, and examine a local administrative office’s interpretation of this criterion. By considering this interpretation, we evaluate the road network patterns by focusing on whether there is a ‘fire-inextinguishable area’ (FIA) in a given network, and propose suitable conditions for well-established road networks based on fire-extinguishing criteria.

5This paper consists of 7 sections. We discuss the background and objectives of the paper in this first section. In Section 2, we summarize the history of ways of dealing with lanes under the basic law related to buildings or cities in Japan. In Section 3, we conduct an interview to determine how a local administrative office interprets the criteria related to road network patterns. In Section 4, we evaluate road network patterns according to whether or not there is a ‘fire-inextinguishable area’ (an area where a fire cannot be successfully extinguished), in a region encircled by wide roads with a width equal to or more than six meters. In Section 5, we clarify the conditions for suitably laid-out road networks based on fire-extinction criteria. In Section 6, we evaluate road network patterns by using an index based on graph theory, indicating problems and solutions. In the last section, we make our concluding remarks and propose future tasks.

The history of lane-planning under the basic law related to buildings and cities in Japan

6The rule mentioned in the previous section is called ‘the 3rd paragraph rule’, because it is provided in the third paragraph of the forty-second article in the Building Standards Law. The ‘3rd paragraph rule’ was passed in 1959. There is a history behind the passage of this bill. Previously there had been many buildings on lots adjacent to lanes, which were legally allowed to exist until 1950. That year, however, the Building Standards Law was passed, as a revision of the Urban Building Law, the earlier basic law relating to buildings and cities, passed in 1919. This revision stipulated that the lots which were adjacent to lanes were not ‘unadjacent’ lots and declared the buildings on ‘unadjacent lots’ to be ‘illegal’. While the law prior to this revision permitted the existence of buildings on lots adjacent to lanes, since the passage of the new law in 1950, it is no longer permissible for buildings to exist on lots that are adjacent to lanes. In order to avoid making the buildings on ‘unadjacent’ lots illegal, ‘the 2nd paragraph rule’, in paragraph 2 of the 42nd article in the Building Standards Law, was enacted in 1950. The ‘2nd paragraph rule’ was applied to lanes along which buildings had existed since before 1950. As illustrated in Figure 1, if a new building is erected on a lot adjacent to lanes where the 2nd paragraph rule is applied, the distance from the center line of lanes to the boundary line of the lot and the front road of the lot must be equal to or more than two meters wide. The ‘2nd paragraph rule’ differs from the ‘3rd paragraph rule’ in that while the former rule required a widening of the lanes, the latter rule does not. Therefore, any building erected after 1950 exists on a lot adjacent to a road with a width of four or more meters. On the other hand, a building erected before 1950 will be on a lot adjacent to the road with a width of four meters or more, but such a building can also be on a lot adjacent to lanes.

Figure 1: Widening lanes where the 2nd paragraph rule is applied in rebuilding

Figure 1: Widening lanes where the ‘2nd paragraph rule’ is applied in rebuilding

7The reason the provision for minimum road width was modified from 2.7 meters to 4 meters was to improve sanitation and cleanliness in the area, and to ensure sufficient room for fire engines to pass, as well as to impede the spreading of fires. In particular, for two cars to pass each other and for fire engines to pass through, the road needs to be at least four meters wide. Also, the greater the distance between two adjacent buildings, the less there is a risk of fire spreading. As Aoki (2006) explains, if the space between two adjacent buildings ranges from two to four meters, by slightly increasing this space, it will be possible to dramatically decrease the risk of fire spreading. Thus, from the perspective of the prevention of fire spreading, it is important to make the width of roads equal to or more than four meters.

8In the event of a serious earthquake occurring in a mega city—like the Great Kanto Earthquake of 1923 or the Great Hanshin Earthquake of 1995—it is difficult to prevent the spreading of fire for two reasons: the existence of flammable materials used in the construction of the buildings, and the high density of the buildings. In particular, a characteristic of buildings in urban areas of Japan is the use of flammable materials in their construction. In the case of the district in the Tokyo 23 wards, the average percentage of buildings made from wood is 56.2%. Furthermore, the average density of buildings per hectare is 32.4 and the average space between two adjacent buildings is 11 meters. Figure 2 shows the percentage of buildings made of wood and the average space between two adjacent buildings in each district of the Tokyo 23 wards. In Figure 2, it can be seen that there are adjacent flammable buildings that are quite close to each other, especially in districts with distances from the center of Tokyo 23 wards ranging from about from about 5 km to 10 km. Certainly when fires occur under usual conditions, it is possible to prevent their spreading by firefighting. If, however, fires occur simultaneously in disasters such as great earthquakes, it is not possible to extinguish them all, because of a shortage of firefighting equipment (fire engines), and because of the blocking off of narrow networks, especially in the districts mentioned above. To improve this situation, various policies have been implemented for over a century: e.g., making flammable buildings inflammable, widening narrow roads, and improving densely-built areas by increasing open spaces. These provisions, however, have not been developed further, and they do not contribute substantially to improving the situation. More time will be needed to do this. Therefore, the problem of vulnerability to fires in urban areas of Japan has not yet been solved.

Figure 2: The percentage of the remaining buildings made from wood, and the average space between two adjacent buildings (right) in the Tokyo 23 wards districts

Figure 2: The percentage of the remaining buildings made from wood, and the average space between two adjacent buildings (right) in the Tokyo 23 wards districts

9Of course not only the physical means of firefighting described above, but also non-physical, means, e.g., firefighting by self-help or with the assistance of other residents, may be effective. Whether the secondary ways can be useful during and after a great earthquake has, however, not been determined, and is questionable. In this paper, we suppose the worst scenario in which virtually all self-help activities, mutual aid and public firefighting are not effective enough. In such a situation, broader road width and wide road networks are considered important factors in preventing the spread of fires and facilitating rescue activities.

10While narrow road width is considered a distinct disadvantage for disaster prevention, it may on the contrary be considered an advantage from the perspective of townscape. Today the attractive features of lanes, called Roji in Japanese, are seen in a new light. In particular, narrower roads are considered an indispensable factor in creating attractive townscapes and contributing to an atmosphere that is on a more human scale. Increasingly, the ‘3rd paragraph rule’ is being applied in cases in which lanes have traditional and beautiful landscapes. To apply the ‘3rd paragraph rule’ appropriately, we need to implement a method for evaluating road network patterns quantitatively.

Interpretation by a local administrative office of the criteria related to road network patterns

11In this section, to clarify the appropriate spatial unit for evaluating road network patterns, we conduct an interview to gain a sense of how a local administrative office interprets the criteria related to road network patterns. The local office where we conducted our interview was the Chuo ward office in the 23 wards of Tokyo. In the Chuo ward, there are districts called Tsukishima districts where many lanes are less than four meters wide.

12Since the Chuo ward office considered that these lanes were set in traditional and beautiful landscapes¸ they applied the ‘3rd paragraph rule’ in Section 2 in order to preserve attractive townscapes. The Tsukishima districts, however, are the only areas where this rule is actually applied, as the rule was amended in 2004. It was for this reason that we chose the Chuo ward office for our interview.

13As the result of our interview with the Chuo ward office, we received the reply that in the case of Tsukishima districts, because the road networks forming blocks are well laid out, there is no obstacle for fire-extinguishing even if the ‘3rd paragraph rule’ is applied. Thus the purpose of establishing conditions for road network patterns is to judge whether or not in a given network it is possible to ensure the possibility of fire-extinguishing activity. Figure 3 shows road network patterns in the Tsukishima districts. From this Figure, it can be seen that one end point of each lane connects to the road that is equal to or more than four meters wide. Whenever this is the case, fire engines are able to enter the road, making it possible to extend fire hoses into the lanes.

Figure 3: Road networks in Tsukishima districts

Figure 3: Road networks in Tsukishima districts

Evaluating road network patterns by focusing on fire-inextinguishable areas in the 23 wards of Tokyo

14In the previous section, we explain that the purpose of establishing conditions for road network patterns is related to the need to make it possible to put out fires. In this section, to determine whether or not there is an obstacle to fire-extinguishing, we judge whether, in the 23 wards of Tokyo, there is an area that should be called ‘the fire-inextinguishable area’ (FIA).

15A ‘fire-inextinguishable area’ (FIA) is defined as an area in which the distance from the nearest road with a width of more than six meters is greater than 140 meters—in other words, greater than the complementary area of a fire-extinguishable area (FEA). This is because the maximum length of fire hoses can be extended to 200 meters. In figure 4, we consider road network patterns as grid patterns. ‘O’ is the location of a fire engine and ‘P’ is a randomly chosen location. Let R be the Euclid distance from a fire engine on wide roads and let u and v be the x component of vector OP and y component of vector OP, respectively. Therefore, u + v is the Rectilinear distance between O and P. In this case, the minimum R is the optimal value of the following optimization problem.

­

Figure 4: The Definition of FIA

Figure 4: The Definition of FIA

16By solving this problem, we arrive at the minimum R = 141 meters as the optimal value, and u = v = 100 meters as the optimal solutions. This means that it is possible to put out fires occurring in FEA (‘Fire Extinguishable Areas’) by extending 200-meter hoses along grid roads. This is why a fire-inextinguishable area is defined as complementary to a ‘Fire Extinguishable Area’. From now on, roads with a width equal to or more than six meters will be designated as wide roads. Figure 5 shows wide roads and FIA in the northeast area of the 23 wards of Tokyo. In Figure 5, we define the inner area encircled by wide roads as ‘an encircled area’, an area generated by partitioning a plane based on road networks.

17There are two advantages in considering encircled areas. First, it is possible to determine whether or not there is a fire-inextinguishable area in a randomly-selected encircled area. By using the encircled area as the spatial unit to judge whether or not wide road network patterns are well laid out, if there is no FIA in an encircled area, we can judge road network patterns in this encircled area to be well laid out from the perspective of the possibility of fire-extinguishing. Secondly, since the shape of an encircled area and road network patterns are closely related to each other, it is possible to evaluate road network patterns based on the shape of an encircled area. As Hillier (1999) points out, the partitioning model, in effect, does not work on the basis of road networks per se, but on the basis of geometric shapes represented as road networks. If the shape of an encircled area is well laid out, we can judge that road network patterns within this encircled area will also be well laid out.

Figure 5: Networks of wide roads and FIA

Figure 5: Networks of wide roads and ‘FIA’

18Figure 6 illustrates the distribution of fire-inextinguishable areas’ and of encircled areas with lanes and FIA. In figure 6, black-colored areas indicate FIA. There are 383 encircled areas with FIA. Dark gray-colored encircled areas with large FIAs indicate encircled areas that satisfy the following two conditions: 1). the encircled areas with FIA, 2). the encircled area with lanes that satisfy the following two conditions for applying the 3rd paragraph rule: a). not cul-de-sacs, b). the length of a narrow road is less than 60 meters. The conditions a) and b) are two of the three conditions mentioned in the 3rd paragraph rule. The remaining condition is whether or not road network patterns are well laid out. The dark gray-colored encircled areas covering a large space are distributed in the Nakano ward, the southeast area of Suginami ward and the northern part of the Setagaya ward. In the 23 wards of Tokyo, there are 371 dark gray-colored encircled areas. On the other hand, the light gray-colored and dotted encircled areas do not have FIA, and do have lanes satisfying the condition a) and b) mentioned above. In the 23 wards of Tokyo, there are 1646 of the light gray-colored encircled and dotted areas. Thus, from the perspective of the possibility of fire-extinction, the gray-colored and dotted encircled areas are judged to be well laid out. In this case, if there are lanes with attractive townscapes in the gray-colored and dotted encircled areas, ‘the 3rd paragraph rule’ can be applied for these lanes.

Figure 6: FIA and the encircled area with well laid-out road network patterns in the 23 wards of Tokyo

Figure 6: FIA and the encircled area with well laid-out road network patterns in the 23 wards of Tokyo

The condition of well laid-out road network patterns based on fire-extinction criteria

19In the previous section, we consider the encircled areas with well laid-out road network patterns to determine whether or not there is a ‘fire-inextinguishable area’ in a randomly chosen encircled area. As we see in Figure 6, whether or not FIA exists in a randomly selected encircled area depends on the road network patterns in that area. Knowing about road network patterns, for example that FIA exists in a randomly chosen encircled area, is indispensable for carrying out in a reasonable manner the broadening of roads whose width is less than 6 meters. In this section, we discuss road network patterns where there is no FIA in a randomly selected encircled area.

20First of all, we discuss the fact that there is no ‘fire-inextinguishable area’ in a rectangular encircled area where the length of the longer and shorter edges are a and b, respectively. In this case, the necessary and sufficient condition for preventing the existence of a ‘fire-inextinguishable area’ in a rectangular encircled area is as follows:

21This condition means that the rectangular encircled area with a large space does not always have FIA. Therefore it is not possible to judge on the basis of the size of a rectangular encircled area whether or not there is a ‘fire-inextinguishable area’ in that space.

22Well laid-out road networks depend not only on whether there is an FIA in a randomly selected encircled area, but also on the number of cul-de-sacs in the encircled area. As Maki et al. (1980) point out, the larger the space in an encircled area, the greater the likelihood of more cul-de-sacs in that area. To discuss this relation more quantitatively, let the number of cul-de-sacs and the area of an encircled area be edeg=1 and S[ha], respectively. By linear regression analysis, using S as the explanatory variable and edeg=1 as the explained variable, we arrive at the following regression equation:

where the coefficient of determination, R2, is 0.90. Also, let the summation of length of cul-de-sacs in an encircled area be L deg=1[m]. By linear regression analysis, using S as the explanatory variable and Ldeg=1 as the explained variable, we arrive at the following regression equation:

where the coefficient of determination, R2, is 0.92. From equation (3) and equation (4), if the space within an encircled area increases by one hectare, it is found that a cul-de-sac is created, and that the average length of such a cul-de-sac is about 32 meters. This relation is simple, and easy to understand.

23Figure 7 illustrates the scatter plot of logS and log(edeg=1+1). Figure 7 illustrates the cases of the encircled areas both with and without FIA . By comparing the left and right sides of Figure 7, we discover the following tendency. First, if there is no FIA in encircled areas, there is an upper limit for the possible number of cul-de-sacs. Secondly, there is no upper limit for the number of FIAs in encircled areas. If there is a ‘fire-inextinguishable area’ in an encircled area, the minimum dimension of the encircled area is 4.8 hectares. On the other hand, if there is no FIA in an encircled area, the maximum dimension within the encircled area is about 200 hectares.

Figure 7: The scatter plot of logS and log(edeg=1+1) (left: with FIA, right: without FIA)

Figure 7: The scatter plot of logS and log(edeg=1+1) (left: with FIA, right: without FIA)

24Thus, if an encircled area takes up more than 4.8 hectares and less than 200 hectares, it is impossible to judge by the dimensions whether or not there is an FIA in an encircled area according to the dimensions of that area. This indicates that in order to determine whether or not there is a ‘fire-inextinguishable area’ in an encircled space, we need to evaluate the shape of the encircled area.

25The necessary and sufficient condition for there to be no FIA in a rectangular encircled area is the equation given in (2). In general, however, since the shape of the encircled area is almost a multi polygon, it is impossible to consider it as easily as one could consider the case of a rectangular encircled area. In this case, what is the condition corresponding to equation (2)? As is shown in figure 8, we consider an encircled area as a convex polygon. Let one of vertices of a convex polygon with n vertices be Pi (i=1,…,n). In the case of figure 8, n equals 5. Let the interior angle at Pi be Pi-1PiPi+1 =θi, where, if i = n, then Pn-1PnP1 =θn and if i = 1, then PnP1P2 =θ1. Let the vertex of FIA corresponding to Pi of an encircled area be Qi. Drawing the perpendicular line from Qi to Pi-1Pi and PiPi+1, let the intersection of this perpendicular line and Pi-1Pi or that of this perpendicular line and PiPi+1 be Hi1 and Hi2, respectively. In this case, for a randomly chosen edge, PiPi+1, there is no FIA in an encircled area if the following condition is satisfied:

26Moreover, by drawing the line from Pi to Qi, we get two right triangles which are congruent to each other: ΔPiQiHi1ΔPiQiHi2. Therefore, PiQi is the bisector of θi. In this case, the length of PiHik (k = 1, 2) is as follows:

27Thus, for a randomly chosen edge, PiPi+1, there is no FIA in an encircled area if the following condition is satisfied:

­

Figure 8: The encircled area depicted as a convex polygon (n = 5)

Figure 8: The encircled area depicted as a convex polygon (n = 5)

28If θi =θi+1 =π/2 , then the condition (7) corresponds to the condition (2). By comparing the condition (2) with the condition (7), we find that if the shape of an encircled area is not rectangular, whether or not FIA exists in an encircled area depends on the degree of θi. This property agrees with Hillier’s suggestion that geometric variables, length of links and angle of intersection, appear as distinct pattern formers in the road networks (Hillier (1999)).

29The mean value of θi is (n–2)π/n. As n increases, the mean value of θi also increases and the value of the condition (7) on the right side decreases. This means that the higher n becomes, the greater the possibility that there is FIA in an encircled area, unless the length of PiPi+1 is shortened. Conversely, the lower n becomes, the more the condition is relaxed. Certainly, the minimum value of n is three. From the point of view of ease of turning right or left at intersections, however, a square region, n = 4, is superior to a triangular-shaped region. Thus, it is by considering the condition (7) that grid pattern road networks can best be laid out. As Hillier (1999) points out qualitatively, highly obtuse angles of incidence are associated with longer links, and near right angles with shorter links. Highly obtuse angles and near-right angles at intersection are achieved simultaneously if road network patterns are in a grid pattern. This feature enables fire engines to pass and turn right or left at intersections more easily. Also, as Hillier et al. (2007) point out, the shorter the links, the more likely they are to end in a right angle or near-right angle and in general to be embedded in an almost rectilinear local structure. This relation between shorter links and a grid road networks pattern supports our suggestion above.

30For all PiPi+1, the condition (7) does not have to be satisfied for there to be no FIA in an encircled area. In the case of the encircled area in Figure 8, if, for a randomly-chosen three out of five edges of an encircled area, the condition (7) is satisfied, FIA does not exist in this area. For example, if P1P2 and P3P4 satisfy the condition (7), then the area of triangle Q1Q2Qj (j=3, 4, 5) and that of Q3Q4Qj (j=1, 2, 5) should be 0, and only the pink-colored area remains susceptible for FIA. If at least one of three edges, P2P3, P4P5 or P5P1, satisfies the condition (7), then the whole area can be considered to be FEA and not FIA. In practice, if all three edges do not satisfy the condition (7), and therefore a ‘fire-inextinguishable area’ remains, then one of the narrow roads of this area that can be connected to a road that is six meters in width or wider, represented as P2P3, P4P5 or P5P1, should be widened to diminish the FIA .

Evaluating road networks on the basis of graph theory

31In the previous sections, we evaluate road network patterns by considering whether or not there is a ‘fire-inextinguishable area’ (FIA) in a randomly selected encircled area, and discuss road network patterns that do not lead to FIA in these areas. We of course evaluate wide road network patterns by focusing on FIA; however, we are unable to evaluate narrow road network patterns.

32In this section, we evaluate road network patterns using indices based on graph theory. From the perspective of graph theory, we can consider road networks as a plane graph. A plane graph is a planar graph together with a given imbedding in the plane (Jonathan & Jay (2004)). A planar graph is a graph of minimum genus 0, with no intersecting edges except on nodes. Figure 9 provides examples of both plane graph and non-plane graph. There are two main indices based on graph theory to evaluate road networks: the alpha index and the gamma index. These indices are presented for use in the discipline of quantitative geography. In addition, Noda (1996) proposes the grid-tree-proportion index (GTP index), which is the extension of these two indices. We begin by considering the features of these three indices.

Figure 9: Plane graph (left) and non-plane graph (right)

Figure 9: Plane graph (left) and non-plane graph (right)

The Alpha index and the gamma index

33The Alpha index is the ratio of the number of ‘faces’ to the maximum number of faces it is possible to make according to the number of nodes on a graph. A ‘face’ is defined as the region encircled by links (Jonathan & Jay (2004)). In the context of city planning, a face is equivalent to a block. Figure 10 illustrates faces in a network.

Figure 10: Faces in a network

Figure 10: Faces in a network

34We denote the number of nodes, the number of links and the number of disconnected graphs by v, e and p, respectively. Given the number of nodes, the maximum number of faces is 2v – 5. Also, in Eulers formula, the number of faces of graphs, f, is ev + p. Hence, the alpha index is defined as follows:

35Since the number of faces is equivalent to the number of blocks, it is possible to judge that regions where the value of the alpha index is high have many blocks. This indicates that if the area of a region is fixed, the number of blocks is higher, and the average area of a block is smaller. In the context of fire-extinguishing activity, the smaller the area of a block becomes, the less likely it is that the block will have a ‘fire-inextinguishable area’.

36The Gamma index is the ratio of the actual number of links to the maximum number of links that can be made according to the number of nodes on a graph. Given the number of nodes, the maximum number of links is 3(v – 2). Hence, the gamma index is defined as follows:

37The Gamma index focuses on the connectivity of road networks. In the context of city planning, the road networks with a high value of the gamma index are well laid out in terms of the abundance of roads to choose from. Also, from the point of view of the possibility of a two-way escape, we can say that road networks with high value of the gamma index are well laid out.

38The difference between these two indices is whether the focus is on the number of blocks or on the strength of connectivity of the road networks. As Okuno (1977) points out, while the alpha index does not accurately indicate the strength of connectivity of road networks, the gamma index overcomes this disadvantage.

GTP index

39The GTP index is derived by considering both typical types of road network patterns: the grid pattern and the tree pattern, and general road network patterns that are not classified as belonging in either the grid pattern or the tree pattern category. By calculating the value of both the alpha index and the gamma index of general road networks, Noda (1996) points out the two following properties:

(a). The value of both the alpha index and the gamma index of general road networks is usually less than that of square lattice pattern road networks with the same number of nodes as are in the general road network.

(b). The value of both the alpha index and the gamma index of general road networks is more than that of the tree road network patterns with the same number of nodes as are in the general road network.

40From these two properties, GTP index is defined as follows:

where xG is the value of each index of the square lattice road network patterns, xT is the value of each index of the tree road network patterns, and xS is the value of each index of actual road networks.

41The GTP index can be expressed as the function of xS : f(xS). If a network pattern is a complete tree pattern, then xS = xT. In this case, the value of the GTP index is equal to 0. Also, if a network pattern is a square lattice pattern, then xS = xG. In this case, the value of the GTP index is equal to 1. Since in the case of actual road networks, the formation of the networks is usually between the tree pattern and the square lattice pattern, the value of the GTP index is between 0 and 1.

42One of the features of the GTP index is that if we represent xS, xG and xT by only v, and substitute them for equation (10), we arrive at the following equation:

where the denominator of the right hand of equation (11) is the number of faces in a network with a square lattice pattern. Thus the GTP index is considered as a new index combining the alpha and the gamma index.

43If we apply the GTP index for evaluating road network patterns, we have to consider the validity of the fact that a square lattice pattern is considered to be an ideal pattern. As shown in figure 11, the value of the GTP index of a square lattice pattern differs from that of a grid pattern. In the context of city planning, however, is it possible to determine the difference between a square lattice pattern and a grid pattern? We should probably not consider that a road network with a grid pattern is inferior to a road network with a square lattice pattern, but that it is in fact just as well laid out as a road network with a square lattice pattern. This matter is discussed in subsection 6.5.

Figure 11: The validity of considering a square lattice pattern as an ideal pattern

Figure 11: The validity of considering a square lattice pattern as an ideal pattern

Criteria for well laid out road networks

44To evaluate road network patterns, we need not only indices but also criteria for judging whether or not road network patterns are well set out. Okuno (1977) considers as basic patterns of road networks the three types of network patterns shown in figure 12: a tree pattern, a grid pattern and a delta pattern. These basic patterns are frequently used in the field of traffic engineering. In the context of city planning, the delta pattern can hardly be considered to be well laid out, because it has many intersections with a degree equal to or more than 5.

Figure 12: The basic patterns of road networks

Figure 12: The basic patterns of road networks

45Table1 shows the relation of the basic patterns and the value of the alpha, gamma and GTP indexes. Assuming that a grid pattern is well laid out, road network patterns will be well laid out if more than one of the following three conditions are satisfied: the value of the alpha index is between 1/4 and 1/2, the value of the gamma index is between 1/2 and 2/3, and the value of GTP index is between 0 and 1. These values are the criteria for judging whether or not road network patterns are well laid out. Detailed calculations of these criteria are shown in Appendix 1.

Table1: Relation of the value of each index and the basic formation patterns

Table1: Relation of the value of each index and the basic formation patterns

Calculating the value of each index by using GIS in the case of the Bunkyo ward, Tokyo-

46In this subsection, we evaluate road network patterns in the Bunkyo ward, one of the central regions of the 23 wards of Tokyo, by using the alpha, gamma and GTP indices. Figure 13 shows the road networks of the Bunkyo ward. As shown in figure 13, the Bunkyo ward has various types of road network patterns. This is why we have selected the road networks of the Bunkyo ward for evaluating road network patterns.

Figure 13: Road networks of the Bunkyo ward

Figure 13: Road networks of the Bunkyo ward

47To calculate the value of each index, we have to determine a spatial unit of data aggregation. In other words, we need to count v, e and p in a region. Noda (1995) selects as a spatial unit of data aggregation a square region with an edge length of 500 meters. Also, Crucitti et al. (2006) and Porta et al. (2006) select one square mile as a spatial unit of data aggregation. Clearly because square regions are regular segmentations, it is easy to analyze the spatial distribution of data in these regions. When we consider whether or not road network patterns are well laid out, however, we need to acknowledge that a square region is not an appropriate spatial unit of data aggregation. Noda (1995) refers to the factor of ease of analysis in square regions mentioned above as an advantage of using a square region as a spatial unit. He also points out, however, that there is a disadvantage in using a square region as a spatial unit. If road networks are segmented according to the shape of square regions, many ‘cul-de-sacs’ will be created, because a road intersecting an edge in square regions cuts across it and becomes two sections of road. In fact, these ‘cul-de-sacs’ are not actual cul-de-sacs. Doubtless as Dalton et al. (2003) and Porta et al. (2006) point out, this problem tends to be minimized if the area of a square region is widened to leave the most boundary-affected parts out of the picture. If the area of a square region is enlarged, however, it becomes impossible to evaluate road network patterns on a smaller scale. In particular, when we consider whether or not the ‘3rd paragraph rule’ presented in Section 2 is applicable, we need to evaluate road network patterns in the scale of a district. In this case, it is not appropriate to make the area of a square region larger. We consider that there is a trade-off relationship between the accuracy of evaluation and the scale of the area of a square region. To resolve this problem, we try in this paper to use as a spatial unit of data aggregation a district with boundary lines that very nearly correspond to roads.

48Table 2 shows the result of counting v, e and p and of calculating the value of the alpha index, the gamma index and the GTP index in each district of the Bunkyo ward. While it is possible to count v and e by using the GIS application, it is difficult to count p by using this application. Instead of using the GIS application, we count p manually. Also, Figure 14 shows the choropleth map of the alpha and GTP indices, respectively, in the districts of the Bunkyo ward. Using this table and these figures, we found that the district with the highest alpha index, GTP index and gamma index values is the Hongo 2-chome district. The values of the alpha, GTP and gamma indices in the Hongo 2-chome district are 0.16, 0.38 and 0.44, respectively. According to Table 1, not only the road network patterns in the Hongo 2-chome district, but also road networks in all districts of the Bunkyo wards are considered to be tree patterns. This result is unexpected, because some of road networks had been considered to be almost grid patterns.

Figure 14: Choropleth map (left: alpha index, right: GTP index)

Figure 14: Choropleth map (left: alpha index, right: GTP index)

Table 2: The result of counting v, e and p and of calculating the value of alpha and GTP

Table 2: The result of counting v, e and p and of calculating the value of alpha and GTP

Problems with using indices based on graph theory

49The unexpected result mentioned in section 6.4 is attributed to boundary effects. As shown in figure 15, although road network patterns of the Hongo 2-chome district seem to be in what is almost a grid pattern, the values of the alpha and gamma indices are lower than what we would have intuitively attributed to them. This is because many ‘quasi-cul-de-sacs’ are formed when road links are segmented by the boundary lines of districts. This means that the number of ‘faces’ is underestimated. Also, according to Table 1, there is no district with a grid road network pattern in the Bunkyo ward because the value of the gamma index of all districts in the Bunkyo ward is below 0.5. This result is very different from the impression received when looking at Figure 15.

Figure 15: Road network patterns in the Hongo 2-chome district

Figure 15: Road network patterns in the Hongo 2-chome district

50Added to this is the fact that the existence of the boundary effect is an obstacle when comparing road network patterns in more than two districts. The boundary effect results in an evaluation of road network patterns that is in the wrong order. A road network that is better laid out than others is judged to be less well laid out than others, and vice-versa. Also, with the existence of the boundary effect, it is difficult to judge whether a valid square lattice pattern is considered to be an ideal pattern.

Methods of avoiding boundary effects

51Boundary effects occur because we use districts as a spatial unit to aggregate e, v and p. Certainly the boundary line around districts almost corresponds to roads. This boundary line between districts does not, however, always correspond to road links. A slight difference between the location of a district’s boundary lines and the position of road links creates boundary effects. In particular, if the data source of district boundaries is different from that of road links, this difference may occur. Therefore, as one of the solutions to avoid triggering boundary effects, we should use spatial unit data, e.g., districts data, which are consistent with the data of road links. Another solution is to create spatial unit data, e.g., the encircled areas mentioned in section 4, by partitioning a finite plane based on road links.

52In this subsection, we evaluate narrow road network patterns in encircled areas by using indices based on graph theory, to complement the evaluation of road network patterns on the basis of fire extinction criteria. Figure 16 shows a large encircled area and roads whose width is less than six meters. Aggregating e and v in the encircled area is thought to avoid triggering boundary effects. There is one problem, however: how to count the number of nodes connected with roads that are not in this encircled area. If the number of these nodes is added up to calculate indices, boundary effects occur. To avoid this problem, only the nodes on wide roads and those connected with roads in this encircled area are counted. From now on, we call these nodes ‘main nodes’ of an encircled area. Let the number of nodes and that of links in an encircled area denote vin and ein, respectively. Also, let the number of main nodes denote vm and the number of links between adjacent two main nodes denote em. Without loss of generality, em is equal to vm. In addition, it is possible to suppose that the number of disconnected graphs, p, in an encircled area equals one. This property is important because it is difficult to count p by using GIS. Therefore, the number of faces, f, is calculated by using the following equation:

Equation (12) indicates that it is enough to count only vin and ein for calculating f.

Figure 16: Road networks in an encircled area

Figure 16: Road networks in an encircled area

53Also, when we calculate the values of the alpha and the gamma indices, we need to count v and e in an encircled area including the perimeter of the encircled area. Let the number of nodes on the perimeter of an encircled area denote vperi and the number of links on the perimeter of an encircled area denote eperi. Without loss of generality, eperi is equal to vperi. This property is important, because it is difficult to count e. Compared with counting eperi, counting vperi is easy if we use the following equation:

54Therefore, e in an encircled area including the perimeter of the encircled area is calculated by using the following equation:

55We can calculate the values of the alpha and gamma indices using the following equations:

56Figure 17 shows the choropleth map of the alpha and gamma indices, respectively, in the Bunkyo ward, by using an encircled area as the spatial unit for aggregating v and e. As stated in subsection 6.3, if the value of alpha index is close to 0.5, then road network patterns in an encircled area are close to the grid pattern. Also, the higher the value of gamma index, the better the arrangement of road network patterns in an encircled area in terms an abundance of roads to choose from, and the possibility of two-way escape. From figure 17, since the value of gamma index is less than or equal to 0.5, we find that, based on the criteria shown in Table 1, almost all of the narrow road networks in encircled areas are classified as belonging in the tree pattern category. This means that it is difficult to ensure the possibility of two-way escape. On the other hand, although the value of the gamma index is less than 0.5, some narrow road networks are considered to be almost in the grid pattern, and connected directly to wide roads, e.g., road networks in the light gray encircled areas shown in figure 18. Furthermore, from the left side of Figure 17, a few narrow road networks in encircled areas located in the southeast are classified as belonging to the grid pattern. In these areas, in a comparison with the patterns of wide road networks, the pattern of narrow road networks is given the same classification as the pattern of wide road networks.

Figure 17: Choropleth map (left: alpha index, right: gamma index)

Figure 17: Choropleth map (left: alpha index, right: gamma index)

*Spatial unit for aggregating v and e: an encircled area.
**Green colored links and black colored links mean wide roads and roads in an encircled area, respectively.

57Figure 18 shows the connectivity of road networks in FEA without cul-de-sacs, in the 23 wards of Tokyo, by using the gamma index. In particular, three encircled areas, colored dark gray, in (a), (b) and (c), have the high value of the gamma index, which is above 0.5. From Figure 18, it can be seen that network patterns of both wide roads and narrow roads including lanes are nearly in the grid pattern. It is therefore possible in these three areas to apply the ‘3rd paragraph rule’ to conserve lanes if they have attractive townscapes, and to retain an atmosphere with a human scale.

Figure 18: Connectivity of road networks in FEA without cul-de-sacs by using the gamma index

Figure 18: Connectivity of road networks in FEA without cul-de-sacs by using the gamma index

Conclusions

58In this paper, we discuss how to evaluate road network patterns in order to apply the 3rd paragraph rule for lanes, as presented in Section 2. In Sections 3 and 4, we ask the local administrative office how to interpret the criteria related to road network patterns in the rule, and we discover that road network patterns are closely related to the possibility of fire-extinguishing. We therefore evaluate road network patterns on the basis of fire-extinction criteria to get a sense of the distribution of ‘fire-inextinguishable areas’ and of encircled areas with or without FIA. If a lane with attractive landscapes exists in the encircled area without FIA, it is possible to apply the ‘3rd paragraph rule’ for this lane, since we consider that road network patterns in this area are well laid out. In section 5, we discuss a situation in which there is no FIA in an encircled area, and we recognize the condition (7) as the sufficient condition. From the condition (7), we conclude that, in the context of city planning, in order to prevent FIA, it is necessary to shorten the distance between two neighboring intersections. In Section 6, we try to evaluate road network patterns by using the index based on graph theory, and point out some problems related to the use of indices based on graph theory for evaluating road network patterns. We find that the difference between the data sources for districts and the sources for road links triggers the difference between the location of a district’s boundaries and the location of road links, which causes the boundary effects. By making spatial unit data, e.g., encircled areas, to aggregate v and e, however, we avoid triggering boundary effects. We therefore conclude that we can use indices based on graph theory as a complementary method for evaluating narrow road network patterns in a randomly selected encircled area. By applying this method for real narrow road networks, we clarified that, while almost all narrow road networks are classified as belonging in the tree pattern category, some narrow road networks are considered to be almost in the grid pattern, and are connected directly to wide roads. We also suggested that the pattern of narrow road networks is classified in the same way as the pattern of wide road networks.

59There are some aspects to be resolved. In Section 5, we suppose that an encircled region is a convex multi polygon. There are, however, many encircled areas which do not satisfy this supposition. We must therefore confirm the condition that FIA does not exist in a non-convex encircled area. Furthermore, as stated in subsection 6.6, although almost all narrow road networks in encircled areas are classified in the tree pattern category, some narrow road network patterns are considered to be ‘almost’ grid patterns. In fact, there are many road networks with patterns that are ‘almost’ grid patterns. We must therefore determine the criteria for judging not only whether or not road network patterns are complete grid patterns, but also whether or not road network patterns are nearly in the ‘grid’ category. Furthermore, we want to propose the indices that confirm intuitive evaluations of road network patterns.

Haut de page

Bibliographie

1. Aderamo J. A. and Magaji A. S., 2010, “Rural transportation and the distribution of public facilities in Nigeria: A case of Edu local government area of Kwara state”, Journal of Human Ecology, Vol.29, No.3, 171-179.

2. Aoki Y., 2006, Mathematics for architecture planning and city planning, Tokyo, Suri Kogakusya.

3. Barrat A., Barthélemy M. and Vespignani A., 2008, Dynamical processes on Complex Networks, Cambridge, Cambridge University Press.

4. Batty M., 2004a, “A new theory of space syntax”, Working Paper, No.75, Centre for Advanced Spatial Analysis, University College London, 23/02/04, 34p. (http://www.casa.ucl.ac.uk/).

5. Batty M., 2004b, “Distance in space syntax”, Working Paper, No.80, Centre for Advanced Spatial Analysis, University College London, 12/04/04, 32p. (http://www.casa.ucl.ac.uk/).

6. Crucitti P., Latora V. and Porta S., 2006, “Centrality measures in spatial networks of urban streets”, Physical Review E, Vol.73, 036125.

7. Dalton S. N., Peponis J. and Dalton R., 2003, “To tame a TIGER one has to know its nature: Extending weighted angular integration analysis to the description of GIS toad-centerline data for large scale urban analysis”, Proceedings 4th International Space Syntax Symposium, London.

8. Gastner T. M and Newman J. E. M., 2006, “The spatial structure of networks”, The European Physical Journal B, Vol.49, No.2, 247-252.

9. Hillier B., 1999, “The hidden geometry of deformed grids: or, why space syntax works, when it looks as though it shouldn’t”, Environment and Planning B: Planning and Design, Vol.26, 169-191.

11. Hillier B., Turner A., Yang T. and Park H., 2007, “Metric and Topo-geometric properties of urban street networks: some convergences, divergences and new results”, Proceedings 6th International Space Syntax Symposium, Istanbul.

12. Jinnai H., 1992, Tokyo no Kuukan Jinrui Gaku, Tokyo, Chikuma Gakugei Bunko.

13. Jonathan L. G. and Jay Y., 2004, Handbook of Graph Theory, London, CRC Press.

14. Kansky K. J., 1963, “Structure of transportation networks”, Research Paper, No.84, Department of Geography, University of Chicago Press.

15. Maki F., 1980, Miegakuresuru Toshi, Tokyo, Kajima publishing.

16. Marshall S., 2005, Streets and Patterns, London, Spon Press.

17. Noda H., 1996, “A quantitative analysis on the patterns of street networks using mesh data system”, City Planning Review, Vol.202, 64-72 (in Japanese).

18. Okudaira K., 1976, Toshi Kougaku Dokuhon (Urban Engineering Guidebook), Tokyo, Shokokusya.

19. Okuno T., 1977, Keiryochirigaku no kiso, Tokyo, Taimeidou.

20. Porta S., Crucitti P. and Latora V., 2006, “The network analysis of urban streets: a primal approach”, Environment and Planning B: Planning and Design, Vol.33, No.5, 705-725.

21. Peponis J., Bafna S. and Zhang Z., 2008, “The connectivity of streets: reach and directional distance”, Environment and Planning B: Planning and Design, Vol.35, 881-901.

22. Waters N., 2006, “Network and nodal indices. Measures of complexity and redundancy: A review”, in Reggiani A. and Nijkamp P. (eds.), Spatial Dynamics, Networks and Modeling, Cheltenham, Edward Elgar Publishing.

Haut de page

Annexe

Appendix 1: calculation of the criteria for each index for judging whether or not road network patterns are classified in the grid pattern

The alpha index

The criteria of the alpha index for judging whether road network patterns are classified as belonging to the grid pattern or not are derived as the infimum of the value of the alpha index in the case of the grid pattern network, and the infimum of the value of the alpha index in the case of the delta pattern network. Let the alpha index in the case of the tree pattern and the alpha index in case of the delta pattern be αG and αD, respectively. The value of αG and αD is calculated by using the following equations:

Therefore, the infimum of the value of αG and that of αD are as follows:

Also, the infimum of the value of GTP index in case of the grid pattern network, GTPG and the infimum of the value of GTP index in case of the delta pattern network, GTPD are calculated by using the following equations:

Gamma index

The criteria of the gamma index for judging whether or not road network patterns are classified as belonging to the grid pattern are derived as the supremum of the value of gamma index in the case of the tree pattern network and the infimum of the value of the alpha index in the case of the delta pattern network. Let gamma index in the case of the tree pattern and the gamma index in the case of the delta pattern be γT and γD, respectively. The value of γT and γD is calculated by using the following equations:

Therefore, the supremum of the value of γT and the infimum of the value of γD are as follows:

Haut de page

Table des illustrations

Titre Figure 1: Widening lanes where the ‘2nd paragraph rule’ is applied in rebuilding
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-1.png
Fichier image/png, 22k
Titre Figure 2: The percentage of the remaining buildings made from wood, and the average space between two adjacent buildings (right) in the Tokyo 23 wards districts
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-2.png
Fichier image/png, 108k
Titre Figure 3: Road networks in Tsukishima districts
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-3.png
Fichier image/png, 144k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-4.png
Fichier image/png, 6,2k
Titre Figure 4: The Definition of FIA
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-5.png
Fichier image/png, 14k
Titre Figure 5: Networks of wide roads and ‘FIA’
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-6.png
Fichier image/png, 424k
Titre Figure 6: FIA and the encircled area with well laid-out road network patterns in the 23 wards of Tokyo
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-7.png
Fichier image/png, 397k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-8.png
Fichier image/png, 6,1k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-9.png
Fichier image/png, 4,3k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-10.png
Fichier image/png, 4,4k
Titre Figure 7: The scatter plot of logS and log(edeg=1+1) (left: with FIA, right: without FIA)
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-11.png
Fichier image/png, 26k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-12.png
Fichier image/png, 4,2k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-13.png
Fichier image/png, 6,5k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-14.png
Fichier image/png, 8,9k
Titre Figure 8: The encircled area depicted as a convex polygon (n = 5)
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-15.png
Fichier image/png, 26k
Titre Figure 9: Plane graph (left) and non-plane graph (right)
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-16.png
Fichier image/png, 4,4k
Titre Figure 10: Faces in a network
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-17.png
Fichier image/png, 5,1k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-18.png
Fichier image/png, 6,6k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-19.png
Fichier image/png, 6,4k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-20.png
Fichier image/png, 6,0k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-21.png
Fichier image/png, 6,6k
Titre Figure 11: The validity of considering a square lattice pattern as an ideal pattern
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-22.png
Fichier image/png, 8,0k
Titre Figure 12: The basic patterns of road networks
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-23.png
Fichier image/png, 14k
Titre Table1: Relation of the value of each index and the basic formation patterns
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-24.png
Fichier image/png, 19k
Titre Figure 13: Road networks of the Bunkyo ward
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-25.png
Fichier image/png, 199k
Titre Figure 14: Choropleth map (left: alpha index, right: GTP index)
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-26.png
Fichier image/png, 216k
Titre Table 2: The result of counting v, e and p and of calculating the value of alpha and GTP
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-27.jpg
Fichier image/jpeg, 352k
Titre Figure 15: Road network patterns in the Hongo 2-chome district
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-28.png
Fichier image/png, 174k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-29.png
Fichier image/png, 5,5k
Titre Figure 16: Road networks in an encircled area
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-30.png
Fichier image/png, 166k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-31.png
Fichier image/png, 4,0k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-32.png
Fichier image/png, 5,6k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-33.png
Fichier image/png, 9,5k
Titre Figure 17: Choropleth map (left: alpha index, right: gamma index)
Légende *Spatial unit for aggregating v and e: an encircled area.**Green colored links and black colored links mean wide roads and roads in an encircled area, respectively.
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-34.jpg
Fichier image/jpeg, 88k
Titre Figure 18: Connectivity of road networks in FEA without cul-de-sacs by using the gamma index
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-35.png
Fichier image/png, 92k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-36.png
Fichier image/png, 9,2k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-37.png
Fichier image/png, 12k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-38.png
Fichier image/png, 11k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-39.png
Fichier image/png, 9,7k
URL http://journals.openedition.org/cybergeo/docannexe/image/23825/img-40.png
Fichier image/png, 9,4k
Haut de page

Pour citer cet article

Référence électronique

Hiroyuki Usui et Yasushi Asami, « An Evaluation of Road Network Patterns Based on the Criteria for Fire-Fighting », Cybergeo: European Journal of Geography [En ligne], Systèmes, Modélisation, Géostatistiques, document 542, mis en ligne le 29 juin 2011, consulté le 28 novembre 2021. URL : http://journals.openedition.org/cybergeo/23825 ; DOI : https://doi.org/10.4000/cybergeo.23825

Haut de page

Auteurs

Hiroyuki Usui

Institution: Ministry of Land, Infrastructure, Transport and Tourism, Japan, E-mail: usui-h2ym[at]milt.go.jp

Yasushi Asami

Institution: Center for Spatial Information Science, The University of Tokyo, Japan, E-mail: asami[at]csis.u-tokyo.ac.jp

Haut de page

Droits d’auteur

Licence Creative Commons
La revue Cybergeo est mise à disposition selon les termes de la Licence Creative Commons Attribution 4.0 International.

Haut de page
Rechercher dans OpenEdition Search

Vous allez être redirigé vers OpenEdition Search