a Centro de F´ısica Teorica´ e Computacional, Faculdade de

The ubiquitous efficiency of going further how street networks affect travel speed

Gabriel L Maiaa Caio Pontea Carlos Caminhaa Lara Furtadoa Hygor P M Melob Vasco Furtadoa

aUniversity of Fortaleza Av Washington Soares 1321 - Bl J Sl 30 60811-905 Fortaleza BrazilbCentro de Fısica Teorica e Computacional Faculdade de Ciencias Universidade de Lisboa 1749ndash016 Lisboa Portugal

cUniversity of Masschusetts Amherst Amherst MA 01003 USA

Abstract

As cities struggle to adapt to more ldquopeople-centeredrdquo urbanism transportation planning and engineering must innovate toexpand the street network strategically in order to ensure efficiency but also to deter sprawl Here we conducted a study of over200 cities around the world to understand the impact that the patterns of deceleration points in streets due to traffic signs has intrajectories done from motorized vehicles We demonstrate that there is a ubiquitous nonlinear relationship between time anddistance in the optimal trajectories within each city More precisely given a specific period of time τ without any traffic one canmove on average up to the distance 〈D〉 sim τβ We found a super-linear relationship for almost all cities in which β gt 10 This pointsto an efficiency of scale when traveling large distances meaning the average speed will be higher for longer trips when comparedto shorter trips We demonstrate that this efficiency is a consequence of the spatial distribution of large segments of streets withoutdeceleration points favoring access to routes in which a vehicle can cross large distances without stops These findings show thatcities must consider how their street morphology can affect travel speed

1 Introduction

The growth of human mobility enabled by recent urbaniza-tion has created prosperous economical and social urban centersBettencourt et al (2007) Grimm et al (2008) On the otherhand urbanization can also have detrimental effects and posesparticular challenges to studies in mobility traffic and sustain-ability Boltze y Tuan (2016) Rutledge et al (2010) One suchissue is that of urban sprawl where urbanization takes placeat a fast pace consuming rural and green areas with no spe-cific planning mostly guided by speculative practices Laidley(2016) The expansion of the urban fabric brought by sprawlrequires an understanding of how to build efficient street net-works to absorb new vehicles coming from low density areas

Contemporary planning often led by New Urbanism princi-ples has staked claim against sprawl in favor of downtown ar-eas walkable neighborhoods smaller building blocks and denserconcentric cities in order to produce more sustainable and traffic-free environments Ewing y Bartholomew (2018) Calthorpe (2000)An understanding of individual and collective human mobilityis a particularly important aspect to understand the historicalevolution of cities and social aspects of urban life Makse et al(1995) Bettencourt et al (2007) Louf y Barthelemy (2014)Caminha et al (2017) It is essential for urban planning to de-sign urban networks that can improve wellbeing Ersoy (2016)Kraemer et al (2020) Caminha et al (2018) Furtado et al(2017) and optimize transport structures Liu et al (2017) Huang

et al (2018) Caminha et al (2016) Ponte et al (2018) Mas-troianni et al (2015) Biazzo et al (2019) However in thesprawl debate it remains unclear to which extent the expan-sion of cities and its street network are necessarily linked topoor traffic Ewing y Bartholomew (2018) Commuting timeand speed also can be related multiple factors such as the lo-cation of employment hubs Crane y Chatman (2003) housingcentrality or density Sarzynski et al (2006)

The complexity of the phenomenon of mobility has promptedstudies that investigate how multi-modal transport combine in-dividual vehicles bicycles buses and even airplanes to opti-mize human mobility Gallotti y Barthelemy (2014) Certainmodes of transport can make longer trips more time-efficientmoving from New York to London by plane takes less hours perkm than moving from New York to Boston by car for instanceIn this example the typical time to complete the trip does notincrease proportionally with the distance defining a non-lineartime gain which is a natural consequence of different modalspeeds Varga et al (2016) Recent studies reveal that the samenon-linearity can also be found on the time-distance scaling forurban travel even when using the same mode of transport Vargaet al (2016) Gallotti et al (2016) Mastroianni et al (2015) Bi-azzo et al (2019) Even though dwellers living in suburban ar-eas commute larger distances their travel time is in fact shorter(higher average speed) than that of those coming from an urbandowntown Kahn (2006) When driving is concentrated in morecompact areas it also leads to an increase in travel time which

2 METHODOLOGY 2

points to the importance of increasing street surface Ewing et al(2018)

The relationship between the street network and commut-ing time is particularly relevant for this study Jayasinghe et alJayasinghe et al (2019) developed a methodology to model ve-hicular traffic volume by using information on road segmentsbased on the notion of network centrality Their method didnot require extensive and expensive datasets commonly used intraffic modeling such as OD and vehicle tracking data How-ever the authors point to the study limitations since the methodwas not sufficient to model traffic volume at a macro level

Another study of street segments and traffic load over timeused GPS car data to identify geographic clusters based on driverrsquosbehavior Necula (2015) After crossing those clusters with speedvalues the authors found that greater road density implies loweraverage speed Loder et al (2019) investigated how networktopology determines the network systemrsquos critical point de-fined as the maximum number of vehicles in circulation whilemaintaining a continuous flow Since traffic planning seeks tooperate at a critical point the author apply concepts of central-ity to maximize travel speed The study was conducted with40 cities worldwide and they find a sub-linear relationship be-tween network size and critical accumulation This means thatthe smaller the network size the larger the accumulation of ve-hicles in an urban network Loder et al (2019)

Galloti and Barthelemy suggests that speed fluctuations in acarrsquos trajectory is what explains the non-linear relation betweentime and distance of trips Gallotti et al (2016) This bringsus to the important concept of free flow traffic conditions de-fined as rdquoconditions where vehicular traffic is typically char-acterized by low to medium vehicular density arbitrarily highmean speeds and stable flow over uninterrupted roadway seg-mentsrdquo Khabbaz et al (2012) Ensuring free flow is a challengein and of itself determined by density flow and speed Khabbazet al (2012) These variables have been assessed in differentcases with varying objectives

In Sweden for instance the Government introduced a traf-fic policy that reduced permitted speed limits in order to lowerthe overall traffic speed and the severity of traffic accidentsSimulations of the policy effects found that road characteris-tics and road environment such as design changes sidewalksand speed bumps were more efficient than actual posted speedlimitations in impacting free flow speed Silvano et al (2020)Physical conditions of the street network such as street connec-tivity can promote free flow traffic and reduce travel times anddelays Zlatkovic et al (2019)

There is still a lack of studies on how the expansion of theurban street footprint street signage and capacity can influencetrip efficiency of motorized vehicles within cities This researchcontributes to that gap and presents an empirical experimentthat simulates vehicle trips in order to measure time and dis-tance of trips considering the existing street layout Specifi-cally we employ data from the street network to investigatehow the spatial distribution of deceleration points - DP (iepoints where vehicles can potentially stop or lower speed) andthe street typology (correlated with specific permitted speeds)can influence tripsrsquo time and distance

We conducted simulations of motorized trips for 228 citiesworldwide by taking into account only variables pertaining tothe streetsrsquo built properties such as the existence of traffic lightsand stops street intersections and permitted driving speed foreach type of road (such as highway motorway residential toname a few) We did not consider dynamic aspects such as traf-fic and vehicle flow from specific origin-destination travel pat-terns and demands We found that for a given time the averagedistance traveled in each simulated trip increases proportionallyfaster than its duration As an example this means that a tripwith double the time will typically travel for more than doubleof the distance

We find that this phenomenon depends mostly on the amountof Segment Without Deceleration Points (SWDP) We coinedthat term to refer to a segment of one or more streets that containno points that force stopping or deceleration The size distri-bution and number of SWDP impacts a super-linear coefficient(described by a β exponent) meaning that longer SWDP withgood spatial coverage are easier to access and increase the gainof scale between the relation of time and distance A particu-lar empirical experiment we conducted supported that findingwhen we simulated the same amount of trips and routes withrandomly distributed SWDP we found the super-linearity to becompletely absent

It was also possible to classify cities based on their super-linear magnitude average street speed and city size (built foot-print or square footage) Mega-cities with extensive urban en-vironments of thousands of squared km tend to present higher βcoefficients (around 120) while small cities present lower val-ues (around 107) We find that some cities can have a goodcoverage of SWDP but their smaller extension in terms of areado not allow for long SWDP which leads to lower β values (LaPlata Argentina) Other small cities with less SWDP madeup of smaller street segments do not permit as much free flowand make that gain of scale less prominent (Copenhagen Den-mark) Larger cities known for having robust permeating high-way systems also enable higher βwith either low average speeds(Paris France) or high average speeds (Dubai Arabic Emi-rates) In short the distribution of SWDP and the urban foot-print are the explaining factors for how cities fare in terms of itslevel of economy of scale when driving further

2 Methodology

This empirical research analyzed cities and simulated op-timal travel routes based on the street footprint and permittedspeed and flows The routes are completed by automotive vehi-cles and drawn within the existing street layout extracted fromthe open and collaborative mapping tool OpenStreetMap Wedid not include traffic data in the simulations and focused onthe characteristics of the built street network such as signagespeed and intersections To represent cities we employed adirected graph G(V E) where nodes v (isin V) indicate streetintersections and edges e (isin E) represent directed street seg-ments between them We used the library osmnx to generatethe graph based on OpenStreetMap data Boeing (2017) We ex-tracted information on street lights street typology (motorway

2 METHODOLOGY 3

primary secondary etc) maximum street speed and length ofstreet segments for 228 cities in different continents

To simulate the routes we start with random origin pointsand generate routes in every possible direction following thestreet typology permitted direction flows and the decelerationpoints on the way We run the trip until a certain time thresh-old is achieved and estimate the speeds based on the maximumspeed provided by OpenStreetMap We then calculate the corre-lation between trip time and distance traveled for each optimalroute in different origin points

21 Deceleration Points

Deceleration points (DP) are street nodes that can poten-tially cause stops or significant reductions in vehicle speed Theyare not defined on the maps and are also not static since theychange based on the direction of the route Figure 1 shows partof a street network where the circles represent crossings andthe lines represent streets If the route begins from points Aor C the node B is highlighted as a DP If the vehicle beginsa trip from point D then it does not characterize as a DP Ifthe vehicle is moving from D to F it does not need to stop atB because the segment

minusminusrarrAB has lower preference than segment

minusminusminusminusminusrarrDBEF It is also possible to define Segments Without Decel-eration Points (SWDP) which are when the intermediate seg-ments of one or more streets are not DP Figure 1 shows threeSWDP the S WDPminusminusminusminusminusrarr

DBEF which starts at D and ends at F the

nodes B and E which are not DP and the segments S WDPminusminusrarrAB

and S WDPminusminusrarrBC

which present only a start and finish nodeIt is possible to find DP through a simulation of trips within

a city The preferential relation between intersecting streets de-pends on the street typology imported from OpenStreetMapservice ≺ residential ≺ tertiary ≺ secondary ≺ primary ≺ trunk≺ motorway Where B ≺ A means that street segment A haspriority over lane B and if C ≺ B then C ≺ A There is no pref-erential difference between lanes of a same typology in thatcase A = B Figure 2 shows the three rules applied to identifystreet DP We note that the DP are not fixed since they dependon the direction of the vehicle when passing a specific node andcan not be identified in a city without selecting a segment anddirection A certain intersection may be a DP for one routeand not for another route if the vehicle is passing through com-ing from a different direction as shown in Figure 1 Figure 2shows a simple schematic of the rules considering an existingcity street topology

22 Simulating Routes

Defining DPs is simultaneous to the calculus of time anddistance for several optimal routes simulated from graph G InG we simulated multiple routes with different origin pointsThe segments e have a weight w(e) equivalent to the averagetime it takes to travel the segment That time is calculated asw(e) = l(e)V(e) where l(e) is the segment length and V(e) is themaximum street speed permitted Since OpenStreetMap doesnot inform the speed for every single segment and street weemploy a method to input missing speeds which is detailed inSupplementary Materials A node v also gets assigned a weight

Figure 1 Identification of Deceleration Points (DP) and Segments WithoutDeceleration Points (SWDP) The figure presents an example of how to iden-tify a DP In the cross-shaped diagram the circles represent crossroads - streetintersections while the lines represent segments connecting these nodes Therelation of preference given to each street shown by (≺) indicates which nodesto classify as DP This classification is dynamic and depends on the route thevehicle takes For instance the node B highlighted is classified as a DP if thevehicle takes a route moving in direction

minusminusminusrarrABC while for the direction

minusminusminusminusminusrarrDBEF

the node B is not a DP This takes place becauseminusminusminusrarrABC ≺

minusminusminusminusminusrarrDBEF The drawing

style of lines in Figure help illustrate when node is a DP (dashed lines) andnot a DP (filled lines) Once the DP are established the SWDP can be definedby joining the segments between points The example presents three differentSWDP S WDPminusminusrarr

AB S WDPminusminusrarr

BCand S WDPminusminusminusminusminusrarr

DBEF The first and last nodes of the

SWDP will always be a DP and the intermediate nodes if existent will not beDP

wv(v) to represent the time a vehicle remains stopped at an in-tersection when it has to stop or slow down Nodes classifiedas DPs have wv(v) = 10 (in seconds) otherwise wv(v) = 0 Wediscuss how a variation in wv impacts the results in the Supple-mentary Material

The segment sizes depend on a time threshold (τ) which de-fines the maximum amount of time a vehicle can take to reada destination in other words the sum of the weights of nodesand edges must be smaller or equal to the specified τ We adaptthe algorithm from Dijkstra et al (1959) to obtain the optimalroutes (the pseudo-code is described in the Supplementary Ma-terial) In Dijkstra et al (1959) the algorithm stops runningwhen it finds the optimal path between two pre-defined pointsIn our adaptation the algorithm runs a shortest path from a ran-dom origin point during a time limit τ Thus there is no estab-lished final point and time is the limiting factor for the extent ofthe route as well as the nodes and segments weights

Figure 3(a) shows a point of origin O1 chosen to simu-late routes for a specific city region We simulate all optimal(fastest) routes that can be traveled starting from O1 during aspecified τ The green color exemplifies routes that start froman origin point and reach several destination points The edgepoints show the furthest destinations reached to shape an area

3 RESULTS 4

Figure 2 Rules to define Deceleration Points (DP) Rule 1 states that any node with a traffic light is a DP The other rules look at preferential streets to definewhich streets have priority to allow for vehicle passage and are represented by ldquo≺rdquo and ldquo=rdquo symbols Rule 2 establishes that if a vehicle hits a node with a segmente1 with equal priority among the incident segments (equal to e3) then this node gets classified as DP ie e1 = e3 Rule 3 states that a node will be DP ie e1 ≺ e2if the car reaches a node coming from a segment with lower preference e1 than the node used to continue e2The mapping figures present examples for how rulesdefine DP when the vehicle approaches an avenue roundabout or street junctions

that represent the region which can be accessed starting from O1considering the time limit τ When connected the edge pointsform an isochrone area Biazzo et al (2019) Such final pointsare not necessarily placed in city intersections and can also bepoints in the middle of a block since they must equate to placeswhere an optimal route has weight equal to τ When an edgecoordinate is not an intersection we can conduct a linear inter-polation in the node to find the edge coordinate

The time needed to reach one node from a cityrsquos network (tdwhere d is the node id) is calculated and stored from a singleexecution of the Dijkstra algorithm Once we obtain the valuesof td for a given origin and a value for τ we can find the edgepoints We generate 20 τ values for each city (τ1 τ2 τ3 τ20)where τ1 = 1 minute and τ20 = max(td) represent the amountof time it takes to get to a cityrsquos boundary from an initial pointThe other values for τrsquos (τ2 τ3 τ19) are generated to occupya logarithmic scale Each value for τi represents an area that canbe covered in the city starting from a shorter time until gettingto an area that covers the entire city The figure 3(b) presentsthe various isochrones generated for an origin point O1 and witheach of the 20 values for τ

23 Relation between Time and Distance

It is possible to establish a relation between the time anddistance traveled for each origin point Figure 3(c) shows therelation between time and distance for point O1 Each point in

the graph illustrates an isochrone area obtained from the vary-ing τ values The x axis represents the time for optimal routesin minutes which is also equal to the τ for that area and the yaxis represents the average distance of the optimal routes withinthe area 〈D〉 in Km given a single unique distance value foreach time limit The axis are plotted in log-log scale The cor-relation between τ and 〈D〉 helps to understand how routes withdifferent lengths take place within a city

The relation between time and distance is formally describedby a Power Law

〈D〉 = aτβ (1)

where τ is time 〈D〉 quantifies the distance run a is a pre-factorand β is the exponent we want to measure

The linear regression exponent between log(〈D〉) and log(τ)shows the efficiency of longer paths simulated within a city Ifa correlation coefficient is larger than 1 then a trip two timeslonger for example will reach an average distance more thantwice as long indicating a gain of scale

In the example from figure 3(c) the β1 exponent for the cor-relation between time and distance is associated to origin O1showing how β gets calculated from a single origin The expo-nent value 〈β〉 for the entire city with multiple p origin pointsis the average of all βi where i = 1 2 3 p

3 RESULTS 5

Figure 3 Method to estimate a cityrsquos β In (a) we show a city region wherewe simulated multiple optimal routes from all directions from a point of ori-gin O1 The routes are represented by different colors and take a shorter timethan τ From those points we define an area that can be reached in τ minutesrepresented by the area outlined in red In (b) for a same origin O1 we usemultiple values of τ The legend in (b) indicates how we chose τ values (c)shows how we establish a correlation between τ in the x-axis and the averagedistance reached 〈D〉 for the optimal fastest routes in the y-axis both in log-arithmic scale Each point of this x-y relation is associated to an area of (b)where the value from the y-axis is defined as the average distance of the opti-mal routes within an area and the value from the x-axis is the τ used to reachthat area The solid red line shows the regression with a better fit between thosepoints with an inclination of β1 The dashed line in black is a guideline withexponent equal to 10 In (d) we define the calculus used to obtain a cityrsquos 〈β〉which is the average of all βi values Each βi is associated to a point of originOi where the number of points defined is p (cf Fig 3d)

Figure 4 Correlation between time and distance and the distribution of〈β〉 In (a) we show the six average curves of the correlation between time τin x and distance 〈D〉 in y representing different cities In (b) we show thesame graph as in (a) but we scrambled the location of the DP with exponentsdescribed by βs The βs for these six cities are Cairo 140 New York 124Sao Paulo 117 Bengaluru 126 London 114 and Sydney 124 We addeddashed lines to the (a) and (b) plots to represent an exponent of 10 In (c) thefull line represents the NadarayandashWatson non-parametric regression of the 〈β〉and 〈βs〉 histograms

3 Results

This section verifies the correlation between the time thresh-old τ and the average distances that are reachable 〈D〉 for thecities selected As previously stated this paper encompasses228 cities from different continents and calculates a 〈β〉 valuefor each Table 1 details the non-linear relation between timeand distance measured by 〈β〉 largely superior to 10

We selected six mega-cities from different continents for adetailed analysis Figure 4(a) presents the regression of τ for〈D〉 showing a non-linear relation for all cities when comparedwith the dashed line of reference (〈β〉 = 1)

3 RESULTS 6

Figure 5 Spatial distribution of βprimes for different citiesIn (a-e) we calculate the values for 〈β〉 (on the left) and 〈βs〉 (on the right) for each of those six cities Wetake all the nodes from the street network as origin points The points are colored according to their exponent value and their color is painted by the color schemeat the center The black lines represent the larger SWDP The function for probability density for each experimentrsquos 〈βs〉 is shown in both sides of the color scale torepresent each result from the execution and a dashed line also shows its average distribution This figure also shows the linearity of the 〈βs〉 exponent for a randomexperiment which stays around 1 for all cities It also shows how SWDPs are important to ensure the non-linear characteristic of 〈βs〉rsquos indicating there is a spatialcorrelation between values with high exponents and SWDP

31 The role of the spatial distribution of DPs and SWDPs

To understand how the spatial structure of the DPs and SWDPimpact the 〈β〉 exponent we conducted an experiment by doinga random scrambling of of the wv(v) and w(e) values As aresult we created a completely random signaling structure tore-run the simulation for the optimal routes for each city Thescrambling process was conducted for every node triplex Atriplex A rarr B rarr C is a route between two nodes A rarr B eB rarr C The node A rarr B represents the current street wherethe vehicle is driving and B rarr C indicates the street wherethe vehicle wants to go to Depending on the priority of thestreets A rarr B and B rarr C the node B can be categorized asa DP or not according to the rules detailed in Figure 2 Afterclassifying which triplex are DP or not these classifications arescrambled to erase the spatial correlation between the DP in thecity The time τ and distances 〈D〉 were run again to calculate anew 〈βs〉 exponent for the random configuration of the DP Weconducted a similar process to randomly distribute the streetspeeds ie which also altered the node weights w(e)

Figure 4(b) shows the regression results for for the samecities when we scramble the DP and street speeds revealingthat the non-linear aspect evident in (a) disappears The exper-iment shows that the non-linear relation between τ and 〈D〉 isa consequence of the spatial correlation that exists between thestreet network and DP Figure 4(c) shows the kernel density es-timation for the distribution of 〈β〉 and 〈βs〉 for all 228 cities

When we compare the histograms we see that most cities have〈βs〉 greater than 10 and that the non-linear relation disappearswith the scrambling experiment

Figure 5 shows the spatial distribution of the values of β foreach of the six cities presented in Figures 4 (a) and (b) To cre-ate this example we use all the nodes for each city as originpoints and execute the proposed methodology to associate a βto each node represented by the node color We executed theexperiment twice for each city On the first run the routes simu-lated took into account the city signaling (shown to the left) andthe second run we employed the scrambling process previouslyexplained (shown to the right) We observe that the effects ofscrambling were i) to break continuity of free flow continuousstreet segments and (ii) to make the distribution of 〈β〉 expo-nents more homogeneous close to 1 in every city Both effectscan be witnessed on the maps to the right

32 The role of the large SWDPs

Figure 5 shows the more extensive (SWDP) highlighted inblack In this paper we selected the 20 longest SWDP of eachcity Next to the color bars we illustrate the density probabilityfunctions of the β to the left and βs to the right The resultspresented on the images to the left reveal the heterogeneity ofthe β values depending on the initial point where routes aresimulated Such heterogeneity is explained by the fact that our

4 CHARACTERIZATION OF CITIES BASED ON AVERAGE SPEED 7

method simulates routes from multiple random points of originto estimate the 〈β〉 for each city

We notice there are origin points which produce routes withhigh β around large SWDP In New York for instance Brook-lyn concentrates most of the smaller exponent values and practi-cally no large SWDP while that scenario is completely oppositefor Queens and Bronx Cairo is the city where such correlationcan be the hardest to visualize since it is the only city where thedistribution of β values is multimodal Still it is possible to no-tice that hot spots concentrate to the left along with most of thelarge SWDP In general Figure 5 shows that the large SWDPexplain the non-linearity since they boost the increase in speedand allow for a gain of scale by reducing time for longer tripswithin cities

Figure 6 shows another evidence of how SWDP are deter-mining to the phenomena of non-linearity presented in this pa-per We correlate the β exponent with the percentage of tripscompleted in SWDP for each city (δ

S WDP) This percentage il-lustrates how much gain of scale one can achieve with a routebased on two factors First the greater the SWDP the greaterthe gain of scale for a route in a trip Second the frequencywith which trips use SWDP also increases the possibility of again of scale and in turn an increase in β Thus we observefrom figure 6 that the higher the density of δ

S WDP the more βis exponentially higher for a specific city

10 11 12 13 14 in FFS

Figure 6 Correlation between δS WDP and β Each point represents a city

where δS WDP is in the x axis and the δ

S WDP is in the y axis The black lineshows a linear regression that establishes a relation between both axis

4 Characterization of cities based on average speed

Figure 7 represents every city analyzed (white dots) in fourquadrants according to their v and 〈β〉

The first blue quadrant on the lower-left has cities withlow average v and smaller gains of scale (〈β〉 low) for simu-lated trips These are generally smaller cities with few largearterial roadways and streets with lower maximum permittedspeeds Several are praised for being people-friendly and em-ploying good urban principles Copenhagen poster city for YanGehlrsquos rdquoCities for peoplerdquo (Gehl (2013)) Boulder known forimplementing a very successful Urban Growth Boundary and

β le 115v le 2883

β le 115v gt 2883

β gt 115v le 2883

β gt 115v gt 2883

10 11 12 13 14β

Cairo Egypt

Dubai United Arab Emirates

Yantai China

Bengaluru India

Norwich UKWilmington USA

Madrid Spain

Chandigarh IndiaCopenhagen Denmark

Figure 7 β exponent versus average speed Each point represents a citywhere the x axis presents the average exponent (β) and the y axis presentsthe average speed v achieved for each trip simulated The histograms for β andv values are shown in the upper and right-hand corner respectively The graphwas divided in four different colored quadrants according to their average β andv values

London are located in that group In general the streetscapeand urban planning in these cities is made up of smaller seg-ments that do not permit as much free flow and make that gainof scale less prominent Other cities in that quadrant includeMiami and Detroit which have fairly high street connectivityand density (America (2014)) and Buffalo known for Freder-ick Law Olmstedrsquos planned green-way system and accessiblestreets (Kowsky y Olenick (2013))

The upper-left green quadrant also shows cities with lowerscale efficiency but tend to generate trips with higher speeds forboth long and shorter trips These cities are less extensive citiesin terms of built footprint like Frankfurt La Plata Vancouverand Budapest These cities have connected streets that permithigher speeds but also large city blocks and small total areasFor instance Vancouver occupies a modest 115 kmˆ2 in com-parison to Toronto (630 kmˆ2) and Ottawa (2778 kmˆ2) LaPlata a planned city in Argentina is divided in a series of sixby six blocks cut by diagonal streets taking up only 27 kmˆ2Cities with such a small extension do not allow for long SWDPwhich explains its lower β values

The two other quadrants concentrate cities with larger βwhere longer trips tend to be completed proportionately fasterthan shorter trips Cities on the lower-right orange quadranthave lower average speeds and include places like Paris NewYork and Bogota These are larger cities known for their ro-bust highway systems that permeate the city which enable aneconomy of scale when driving further However these citiesare also constrained within dense urban environments This islikely due to the fact that these cities have taken strides to limitsprawl either naturally (such as NYC located on an island) orlegally (see Long et al (2015) for urban growth boundary inPortland) As a result smaller building blocks and a dense

Table 1 Exponent for all cities simulatedCity 〈β〉 City 〈β〉 City 〈β〉

Accra Ghana 113 plusmn002 Adelaide Australia 123 plusmn002 Akureyri Iceland 105 plusmn002Albuquerque USA 119 plusmn002 Amsterdam Netherlands 129 plusmn002 Antwerp Belgium 126 plusmn003Aracaju Brasil 116 plusmn002 Asuncion Paraguay 112 plusmn002 Atlanta USA 112 plusmn002Austin USA 12 plusmn002 Baltimore USA 107 plusmn001 Bamako Mali 116 plusmn002Barcelona Spain 114 plusmn002 Baton Rouge USA 115 plusmn002 Beira Mozambique 112 plusmn002Belgrade Serbia 114 plusmn002 Bengaluru India 125 plusmn002 Bergen Vestland Norway 122 plusmn002Bern Switzerland 121 plusmn003 Birmingham UK 109 plusmn001 Bogota Colombia 117 plusmn002Boston USA 106 plusmn002 Boulder USA 109 plusmn002 Brisbane Australia 118 plusmn002Bristol UK 108 plusmn002 Brussels Belgium 117 plusmn002 Bucharest Romania 114 plusmn002Budapest Hungary 113 plusmn002 Buenos Aires Argentina 116 plusmn002 Buffalo New York USA 109 plusmn002Cairo Egypt 136 plusmn002 Calgary Canada 124 plusmn002 Cali Colombia 113 plusmn002Cambridge UK 103 plusmn001 Campinas Brasil 12 plusmn003 Cancun Mexico 111 plusmn004Caracas Venezuela 118 plusmn003 Cartagena Colombia 119 plusmn002 Casablanca Morocco 128 plusmn002Cayenne France 101 plusmn002 Chandigarh India 12 plusmn002 Charlotte USA 113 plusmn002Chicago USA 115 plusmn002 Christchurch New Zealand 109 plusmn002 Ciudad del Este Paraguay 115 plusmn002Cologne Germany 124 plusmn002 Columbus USA 118 plusmn002 Conakry Guinea 121 plusmn002Copenhagen Denmark 106 plusmn001 Cork Ireland 122 plusmn003 Curitiba Brasil 116 plusmn002Dallas USA 12 plusmn002 Dar es Salaam Tanzania 111 plusmn002 DenverUSA 112 plusmn002Detroit USA 118 plusmn003 Dresden Germany 109 plusmn002 Dubai United Arab Emirates 129 plusmn002Dublin Ireland 105 plusmn001 Edinburgh UK 112 plusmn002 Edmonton Canada 12 plusmn002Eugene Oregon USA 108 plusmn002 Fes Morocco 123 plusmn002 Florianopolis Brasil 119 plusmn003Fortaleza Brasil 117 plusmn002 Frankfurt Germany 115 plusmn002 Geneva Switzerland 099 plusmn001Genoa Italy 116 plusmn002 Georgetown Guyana 102 plusmn002 Goiania Brasil 117 plusmn002Graz Austria 106 plusmn002 Guadalajara Mexico 114 plusmn002 Guayaquil Ecuador 124 plusmn003Hamilton New Zealand 111 plusmn002 Hanoi Vietnam 119 plusmn002 Ho Chi Minh City Vietnam 125 plusmn004Hong Kong 117 plusmn002 Honolulu USA 113 plusmn002 Houston USA 12 plusmn002Innsbruck Austria 106 plusmn002 Iquitos Peru 099 plusmn002 Jacksonville Florida USA 119 plusmn002Jersey City USA 101 plusmn001 Joensuu Finland 113 plusmn002 Joinville Brasil 117 plusmn002Joao Pessoa Brasil 114 plusmn002 Kampala Uganda 104 plusmn002 Kansas CityUSA 116 plusmn002Kolkata India 108 plusmn002 Kuala Lumpur Malaysia 124 plusmn003 Kyoto Kyoto Prefecture Japan 116 plusmn001La Plata Argentina 104 plusmn001 Las Vegas USA 124 plusmn002 Leipzig Germany 109 plusmn001Lisboa Portugal 122 plusmn002 Liverpool UK 115 plusmn002 Ljubljana Slovenia 122 plusmn003London UK 112 plusmn002 Londrina Brazil 117 plusmn002 Los Angeles USA 118 plusmn002Louisville USA 117 plusmn002 Luanda Angola 107 plusmn002 Lyon France 106 plusmn001Maceio Brasil 113 plusmn002 Madrid Spain 121 plusmn002 Manchester UK 111 plusmn002Manila Philippines 114 plusmn002 Maputo Mozambique 119 plusmn003 Mar del Plata Argentina 109 plusmn002Marrakesh Morocco 12 plusmn002 Marrakesh Morocco 12 plusmn002 Marseille France 116 plusmn003Medellın Colombia 112 plusmn002 Memphis USA 117 plusmn002 Mexico City Mexico 121 plusmn003Miami USA 115 plusmn002 Milan Italy 106 plusmn001 Milwaukee USA 11 plusmn002Minneapolis USA 109 plusmn002 Mombasa Kenya 111 plusmn002 Montevideo Uruguay 113 plusmn002Montreal Canada 112 plusmn002 Mumbai India 128 plusmn003 Munich Germany 115 plusmn002Merida Yucatan Mexico 12 plusmn002 NrsquoDjamena Chad 106 plusmn002 Nagpur India 115 plusmn002Nairobi Kenya 113 plusmn002 Nantes France 104 plusmn002 Nashville USA 117 plusmn002Natal Brasil 119 plusmn003 New Delhi India 118 plusmn002 New Orleans USA 116 plusmn002New York USA 119 plusmn002 Newark USA 103 plusmn002 Nice France 113 plusmn002Niteroi Brasil 107 plusmn003 Norwich UK 103 plusmn001 Nottingham UK 11 plusmn002Nouakchott Mauritania 113 plusmn002 Noumea New Caledonia 107 plusmn002 Nur-Sultan Kazakhstan 112 plusmn002Nuremberg Germany 117 plusmn002 Oakland California USA 12 plusmn003 Oklahoma City USA 12 plusmn002Orlando USA 116 plusmn002 OsloNorway 113 plusmn003 Ostrava Czechia 112 plusmn002Oxford UK 11 plusmn002 Papeete France 102 plusmn002 Paris France 115 plusmn002Philadelphia USA 114 plusmn002 Phoenix USA 118 plusmn002 Pittsburgh Pennsylvania USA 108 plusmn002Playa del Carmen Mexico 122 plusmn002 Pori Finland 111 plusmn002 Port Harcourt Nigeria 104 plusmn001Portland USA 118 plusmn002 Porto Alegre Brasil 111 plusmn002 Porto Velho Brasil 119 plusmn002Porto Portugal 119 plusmn003 Prague Czechia 12 plusmn002 Pyongyang North Korea 105 plusmn002Quebec City Canada 123 plusmn003 Rabat Morocco 115 plusmn002 Raleigh USA 112 plusmn002Reading USA 105 plusmn001 Recife Brasil 116 plusmn002 Reykjavik Iceland 127 plusmn003Ribeirao Preto Brazil 123 plusmn002 Richmond USA 11 plusmn002 Rijeka Croatia 108 plusmn002Rio de Janeiro Brasil 128 plusmn003 Saint Louis Illinois USA 117 plusmn002 Salt Lake City USA 105 plusmn003Salvador Brasil 126 plusmn003 Salzburg Austria 103 plusmn001 San Antonio USA 119 plusmn002San Diego USA 123 plusmn002 San Miguel de Allende Mexico 109 plusmn003 Santa Fe USA 111 plusmn002Santo Andre Brasil 112 plusmn002 Santos Brasil 111 plusmn001 Sapporo Japan 115 plusmn002Sarajevo Bosnia and Herzegovina 108 plusmn001 Saskatoon Canada 117 plusmn002 Scranton Pennsylvania USA 102 plusmn001Seattle USA 113 plusmn002 Seoul South Korea 129 plusmn003 Setubal Portugal 111 plusmn002Shenzhen China 123 plusmn002 Singapore 124 plusmn002 Sofia Bulgaria 11 plusmn002Sundsvall Sweden 11 plusmn003 Sydney Australia 123 plusmn002 Sao Bernardo do Campo Brasil 123 plusmn002Sao Luıs Brasil 119 plusmn003 Sao Paulo Brasil 118 plusmn002 Taipei Taiwan 118 plusmn002Teresina Brasil 114 plusmn002 The Hague Netherlands 119 plusmn002 Timisoara Romania 109 plusmn002Tirana Albania 114 plusmn003 Toronto Canada 124 plusmn003 Tripoli Libya 124 plusmn003Trondheim Troslashndelag Norway 121 plusmn002 Tulsa USA 121 plusmn002 Turin Italy 11 plusmn002Turku Finland 109 plusmn002 Ulaanbaatar Mongolia 114 plusmn002 Umea Sweden 114 plusmn002Utrecht Netherlands 12 plusmn002 Valencia Spain 118 plusmn002 Valparaıso Chile 121 plusmn003Vancouver Canada 102 plusmn001 Venice Italy 115 plusmn002 Vienna Austria 117 plusmn002Vila Velha Brasil 118 plusmn003 Vina del Mar Chile 114 plusmn002 Washington USA 10 plusmn001Wilmington USA 097 plusmn001 Winchester UK 119 plusmn002 Wollongong Australia 124 plusmn003Wuhan China 112 plusmn002 Yantai China 104 plusmn001 Yaounde Cameroon 104 plusmn001Zagreb Croatia 111 plusmn002 Zaragoza Spain 12 plusmn003 Zurich Switzerland 107 plusmn002

5 CONCLUSION 9

street network lead to more DP points and can reduce overallspeeds

Finally cities on the red quadrant have larger β but loweraverage speed It includes large mega-cities such as Rio deJaneiro Sao Paulo Los Angeles Mexico City Mumbai andSeoul This group or world metropolis have populations in themillions and an urban footprint that had to expand accordinglyIt comes as no coincidence that several cities that are able toachieve such higher β are also those most unsustainable witha high GHS emission due to on-road transportation (Wei et al(2021)) Other such cities include Houston known for havingvirtually no zoning laws Dubai built in the last two decadeson a megalomaniac model of ineffective freeway systems andShenzhen a new city founded in the 1980s and with one of theworst traffic conditions in China

It is important to note some remarks about these quadrantsFirst although an effort can be made to stifle city growth theeconomy of scale is still ubiquitous in every case The more acity presents large scale arterial roads with less DP the morethe β coefficient increases Second we present those exam-ples to make the coefficients tangible but we do not intend topresent and evaluate causality as to why cities are in a specificquadrant Lastly the quadrants are not tied to good or bad ur-ban planning principles A lower β value could pose no harmif a city is accessible with a homogeneous distribution of ser-vices and opportunities In that case citizens are able to livecomfortably with smaller trips On the other hand a city withno connecting transport infrastructure through SWDPrsquos can bequite limiting for the transportation of major goods What thisstudy does intend to show is that urban expansion inevitablygenerates a super-linear relationship between the urban streetmorphology and travel times

5 Conclusion

This article finds a non-linear relation between time and dis-tance for trips simulated for large cities worldwide The experi-ments reveal that city morphology allows for longer trips to takeproportionally less time than shorter trips within a city settingwhich supports previous studies that showed the same relationfor trips between cities and countries Varga et al (2016)

We identify that non-linearity takes place in virtually ev-ery city studied whether in small cities like Pori (Finland) andlarge mega-cities such as Sao Paulo (Brazil) with over 10 mil-lion inhabitants The β exponent for the correlation betweentime and distance indicates the magnitude of the efficiency forlonger trips within a city when compared to shorter trips mean-ing that cities with larger exponents tend to allow for propor-tionally faster trips the longer they are It is worth noting thatour findings do not suggest that cities with a higher exponentare more efficient than those with smaller exponents - the ac-curate statement is that cities with larger exponents have moreefficient longer trips than its shorter ones

We also present a method to select different points of ori-gin to simulate vehicle trips and explain how to define SWDPbased on DP where vehicles tend to stop or move slower Non-linearity depends on the spatial distribution of DP and street

speeds which create large SWDPs In general cities orga-nize in residential and commercial zones with a high densityof DP and smaller average permitted speeds which are con-nected by avenues with less DP and higher speeds The streetlayout creates large SWDPs which are segments that do not re-quire vehicles to stop or slow down and permit longer trips tobe completed with overall higher average speeds and conse-quently less time than shorter trips Simulations to randomlyreassign the DPs and maximum allowed street speeds made theSWDPs cease to exist which annulled the spatial correlationbetween those variables In short street topology determinesthe magnitude of the β exponent

This study has specific implications for urban studies andsustainable development Planning principles in favor of walk-ability small building blocks and high density emerge as goodstrategies the more cities seek to become ldquopeople-centeredrdquo andgreen Yet this study shows that streetways continue to growthrough a network of SWDP which makes driving longer dis-tances more advantageous We simulate and quantify why thereis a positive association between travel distance and time whichcontests the notion that sprawl is detrimental to the transporta-tion of human resources We show that the economy of scalewhen going further is a natural ubiquitous process and inviteurban planners and practitioners to consider how cities as com-plex systems get created over time

This finding begs the following question how can we deterthe expansion of the urban footprint if there is an economy ofscale when going further Since current urban guidelines strivefor sustainability by preserving rural open-space cutting backon fossil fuels and discouraging private vehicles planners mustanalyze the urban network carefully to attain those goals Inno-vative approaches to deter sprawl and change the transit infras-tructure require thinking about how scaling efficiency impactsthe distribution of goods and services and peoplersquos willingnessto drive Characteristics of the built environment play a key rolehere This study provides more evidence that physical changesto the transit infrastructure are adequate to increase travel timesand can consequently discourage suburban development anddriving New urban planning strategies must consider this dy-namic to fight against the natural urbanization process whichmakes growth and going further more advantageous

Acknowledgements

VF has been supported by FUNCAP and CNPQ (grant3075652020-3) CC CP LF and GLM has been sup-ported by FUNCAP HPMM acknowledges financial supportfrom the Portuguese Foundation for Science and Technology(FCT) under Contracts no PTDCFIS-MAC281462017(LISBOA-01-0145-FEDER-028146) UIDB006182020and UIDP006182020

References

America S G 2014 Measuring sprawlURL httpwwwsmartgrowthamericaorgmeasuring-sprawl(accessedFeb112021)

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Boeing G 2017 Osmnx New methods for acquiring constructing analyz-ing and visualizing complex street networks Computers Environment andUrban Systems 65 126ndash139

Boltze M Tuan V A 2016 Approaches to achieve sustainability in trafficmanagement Procedia engineering 142 205ndash212

Calthorpe P 2000 New urbanism and the apologists for sprawl [to rally dis-cussion] Places 13 (2)

Caminha C Furtado V Pequeno T H Ponte C Melo H P OliveiraE A Andrade Jr J S 2017 Human mobility in large cities as a proxy forcrime PloS one 12 (2) e0171609

Caminha C Furtado V Pinheiro V Ponte C 2018 Graph mining for thedetection of overcrowding and waste of resources in public transport Journalof Internet Services and Applications 9 (1) 22

Caminha C Furtado V Pinheiro V Silva C 2016 Micro-interventions inurban transportation from pattern discovery on the flow of passengers andon the bus network En 2016 IEEE International Smart Cities Conference(ISC2) IEEE pp 1ndash6

Crane R Chatman D G 2003 Traffic and Sprawl Evidence from US Com-muting from 1985-1997 Vol 6 University of Southern California

Dijkstra E W et al 1959 A note on two problems in connexion with graphsNumerische mathematik 1 (1) 269ndash271

Ersoy E 2016 Landscape ecology practices in planning landscape connec-tivity and urban networks Sustainable urbanization 291ndash316

Ewing R Tian G Lyons T 2018 Does compact development increase orreduce traffic congestion Cities 72 94ndash101URL httpwwwsciencedirectcomsciencearticlepiiS0264275116304498

DOI httpsdoiorg101016jcities201708010Ewing R H Bartholomew K 2018 Best practices in metropolitan trans-

portation planning RoutledgeFurtado V Furtado E Caminha C Lopes A Dantas V Ponte C Cav-

alcante S 2017 A data-driven approach to help understanding the prefer-ences of public transport users En 2017 IEEE International Conference onBig Data (Big Data) IEEE pp 1926ndash1935

Gallotti R Barthelemy M 2014 Anatomy and efficiency of urban multi-modal mobility Scientific reports 4 (1) 1ndash9

Gallotti R Bazzani A Rambaldi S Barthelemy M 2016 A stochasticmodel of randomly accelerated walkers for human mobility Nature commu-nications 7 (1) 1ndash7

Gehl J 2013 Cities for people Island pressGrimm N B Faeth S H Golubiewski N E Redman C L Wu J Bai

X Briggs J M 2008 Global change and the ecology of cities Science319 (5864) 756ndash760

Huang Z Ling X Wang P Zhang F Mao Y Lin T Wang F-Y 2018Modeling real-time human mobility based on mobile phone and transporta-tion data fusion Transportation research part C emerging technologies 96251ndash269

Jayasinghe A Sano K Abenayake C C Mahanama P K S 2019 Anovel approach to model traffic on road segments of large-scale urban roadnetworks MethodsX 6 1147ndash1163URL httpwwwsciencedirectcomsciencearticlepiiS2215016119301128

DOI httpsdoiorg101016jmex201904024Kahn M E 2006 The quality of life in sprawled versus compact cities pre-

pared for the OECD ECMT Regional Round Berkeley California 27ndash28Khabbaz M J Fawaz W F Assi C M 2012 A simple free-flow traffic

model for vehicular intermittently connected networks IEEE Transactionson Intelligent Transportation Systems 13 (3) 1312ndash1326DOI 101109TITS20122188519

Kowsky F R Olenick A 2013 The best planned city in the world OlmstedVaux and the Buffalo Park system University of Massachusetts Press

Kraemer M U Yang C-H Gutierrez B Wu C-H Klein B Pigott D MDu Plessis L Faria N R Li R Hanage W P et al 2020 The effectof human mobility and control measures on the covid-19 epidemic in chinaScience 368 (6490) 493ndash497

Laidley T 2016 Measuring sprawla new index recent trends and futureresearch Urban Affairs Review 52 (1) 66ndash97URL httpsjournalssagepubcomdoiabs1011771078087414568812

DOI 1011771078087414568812Liu Y Liu C Yuan N J Duan L Fu Y Xiong H Xu S Wu J

2017 Intelligent bus routing with heterogeneous human mobility patternsKnowledge and Information Systems 50 (2) 383ndash415

Loder A Ambuhl L Menendez M Axhausen K W 2019 Understandingtraffic capacity of urban networks Scientific Reports 9 (1) 16283URL httpsdoiorg101038s41598-019-51539-5DOI 101038s41598-019-51539-5

Long Y Han H Tu Y Shu X 2015 Evaluating the effectiveness of urbangrowth boundaries using human mobility and activity records Cities 46 76ndash84

Louf R Barthelemy M 2014 How congestion shapes cities from mobilitypatterns to scaling Scientific reports 4 (1) 1ndash9

Makse H A Havlin S Stanley H E 1995 Modelling urban growth pat-terns Nature 377 (6550) 608ndash612

Mastroianni P Monechi B Liberto C Valenti G Servedio V D LoretoV 2015 Local optimization strategies in urban vehicular mobility PloS one10 (12) e0143799

Necula E 2015 Analyzing traffic patterns on street segments based on gpsdata using r Transportation Research Procedia 10 276ndash285URL httpwwwsciencedirectcomsciencearticlepiiS2352146515002641

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Thought for food impacts of urbanisation trends on soil resource availabil-ity in new zealand En Proceedings of the New Zealand Grassland Associ-ation pp 241ndash246

Sarzynski A Wolman H L Galster G Hanson R 2006 Testing theconventional wisdom about land use and traffic congestion The more wesprawl the less we move Urban Studies 43 (3) 601ndash626URL httpsjournalssagepubcomdoiabs10108000420980500452441

DOI 10108000420980500452441Silvano A P Koutsopoulos H N Farah H 2020 Free flow speed estima-

tion A probabilistic latent approach impact of speed limit changes androad characteristics Transportation Research Part A Policy and Practice138 283ndash298URL httpwwwsciencedirectcomsciencearticlepiiS0965856420306066

DOI httpsdoiorg101016jtra202005024Varga L Kovacs A Toth G Papp I Neda Z 2016 Further we travel the

faster we go PloS one 11 (2) e0148913Wei T Wu J Chen S 2021 Keeping track of greenhouse gas emission

reduction progress and targets in 167 cities worldwide Frontiers in Sustain-able Cities 64

Zlatkovic M Zlatkovic S Sullivan T Bjornstad J Kiavash Fayyaz Sha-handashti S 2019 Assessment of effects of street connectivity on trafficperformance and sustainability within communities and neighborhoodsthrough traffic simulation Sustainable Cities and Society 46 101409URL httpwwwsciencedirectcomsciencearticlepiiS2210670718316676

DOI httpsdoiorg101016jscs201812037

1 Introduction

2 Methodology




3 Results




5 Conclusion