Population-weighted efficiency in transportation networks

ABSTRACT Transportation efficiency is critical for the operation of cities and is attracting great attention worldwide. Improving the transportation efficiency can not only decrease energy

consumption, reduce carbon emissions, but also accelerate people’s interactions, which will become more and more important for sustainable urban living. Generally, traffic conditions in

less-developed countries are not so good due to the undeveloped economy and road networks, while this issue is rarely studied before, because traditional survey data in these areas are

scarce. Nowadays, with the development of ubiquitous mobile phone data, we can explore the transportation efficiency in a new way. In this paper, based on users’ call detailed records

(CDRs), we propose an indicator named population-weighted efficiency (PWE) to quantitatively measure the efficiency of the transportation networks. PWE can provide insights into

transportation infrastructure development, according to which we identify dozens of inefficient routes at both the intra- and inter-city levels, which are verified by several ongoing

construction projects in Senegal. In addition, we compare PWE with excess commuting indices and the fitting result of PWE is better than excess commuting index, which also proves the

validity of our method. SIMILAR CONTENT BEING VIEWED BY OTHERS IMPACT OF BUILT ENVIRONMENT ON COMMUTING CARBON EMISSIONS USING BIG DATA: A CASE STUDY OF JINAN’S MAIN URBAN AREA Article Open

access 15 May 2025 EXPLORING THE INTERPLAY BETWEEN POPULATION PROFILE AND OPTIMAL ROUTES IN U.S. CITIES Article Open access 08 May 2025 A UNIFIED DATASET FOR THE CITY-SCALE TRAFFIC

ASSIGNMENT MODEL IN 20 U.S. CITIES Article Open access 29 March 2024 INTRODUCTION Almost all of the dynamical processes we concern within cities, such as human mobility1,2,3,4, epidemic

spreading5,6,7,8 and socio-economic activities, are driven by population interactions and based on transportation networks. In a broad sense, almost all urban flows (e.g. population,

products, energy, information) are carried by “transportation networks”. After realizing the importance, most cities are stretching their transportation networks to promote urban

development, but it is too costly to build new routes to reach every part of a city. Thus, analyzing and improving the efficiency of transportation networks are of great importance, since

the efficiency improvement can not only decrease energy consumption and CO2 emissions9, but also accelerate urban flows, which are critical for the sustainability and effective operation of

cities10. Previous researches on transportation efficiency mainly focus on three separate ways: one is about the topology of networks, which is devoted to a general network efficiency, which

can be applied to information exchange and transportation by treating the inverse of distance between node pairs as local measure of efficiency between them11. Another is about the

geometric properties of spatial networks12,13 and develops an indicator named _route factor_ (denote as ) to measure the network efficiency by calculating the mean ratio of the distance

along edges (_l__i_0) and Euclidean straight line (_d__i_0)14,15. The other one concentrates on the job-housing balance16 or excess commuting [i.e., the difference between the average actual

commuting time (or distance) and the theoretical minimum average commuting time (or distance)]17,18. The first two do not consider the real population distribution, while the third one

suffers from the use of statistically improbable variable (minimum average commuting distance) as a benchmark18 and is limited in finding local inefficient routes. Some recent work uses

hypergraphs to study transferability of collective transportation line network and begins to concern with passenger system level19. In addition, these methods need either road network data

(e.g. ordnance survey) or transportation survey data, which are costly and time consuming and might not be available in less-developed countries. The data scarcity problem adds up many

difficulties to the empirical analysis of transportation efficiency in these areas, where the traffic conditions are usually not so good due to the undeveloped economy and infrastructure.

Today, we leave tremendous “digital footprints” (geo-located data collected by electronic equipment) in cities due to the increasing penetration rate of mobile phones20, social media21,

transportation cards22 and credit cards23, among others. These “digital footprints” give us a dynamical perspective of the ongoing phenomena in cities24,25 and provide us new data source to

explore the transportation efficiency. Among these data, call detailed records (CDRs) of mobile phone users are considered to be of the highest quality to estimate the population/traffic

dynamics due to the high penetration rate and lower usage bias than social media data. In this paper, based on mobile phone CDRs and other open accessed data, we overcome the above-mentioned

shortcomings and develop a new indicator called population-weighted efficiency (PWE) to quantitatively measure the road network performance. The population weight factor is based on

home-work matrices, which will be our Origin-Destination (OD) matrices, extracted from CDRs and the road network data are based on Google Map Application Programming Interface (API). The

contributions of our work are as follows: First, the real population distribution is imported as the weight to the _route factor_. Cities with the same road network structure (_route

factor_) but different population distribution may have different efficiencies, they can be captured by our method rather than the traditional way. Second, mobile phone data and Google Maps

are used as proxy variables for population and road networks separately, they are quite useful for empirical research in African cities26,27,28,29, where the urbanization is fast but the

population census are costly and not timely updated and road network data of the OpenStreetMap (OSM)30 are sparse. Third, our method can be applied to detect inefficient routes and provide

suggestions for infrastructure development and improvement. For example, route pairs with a high volume of commuters and abnormal low PWE would be considered as in need of improvement or

reconstruction. As a case study, for Dakar, we identify the most inefficient route pairs at both intra- and inter-city levels and our results are partially verified by several ongoing

construction projects (e.g., the Dakar-Diamniadio highway31,32). In addition, we study ten main cities in Senegal and compare their PWEs with the most commonly used excess commuting index

and find that there is a significantly correlation between PWE and the average commuting time and the fitting result of PWE is better than excess commuting index, which further proves the

validity of our method. RESULTS DATA DESCRIPTION Our analysis is based on anonymous mobile phone datasets of CDRs and text exchanges at antenna resolution between more than 9 million users

of the Orange/Sonatel Group in Senegal from January 1, 2013, to December 31, 201333. The data are preprocessed33 and provided by D4D Challenge organizers and are systematized into

sub-datasets: dataset 1 includes the hourly voice and text exchange between mobile phone towers and dataset 2 includes fine-grained anonymized individual mobility data at the antenna level

of approximately 300,000 randomly sampled users for each fortnight. See ref. 33 for a full detailed description of the dataset and more related works based on D4D data can be found in ref.

34. We focus on ten main cities of Senegal, especially Dakar, which is the capital and the largest city in Senegal. The locations of the mobile phone towers and studied cities are displayed

in Fig. 1a and the averaged call density of Dakar is shown in Fig. 1b. According to the CDRs, we find that: i) on average, in each fortnight, there are more than 170,000 users within the

region of Dakar, which accounts for almost 60% of the total sampled users (300,000); ii) Plateau and Médina are two of the most active regions during the daytime, which is also in agreement

with the situation observed in reality. Instead of using the administration city boundary, we define the city boundary by the following criteria: i) divide the whole country into sub-regions

by Voronoi tessellation, which are calculated according to the geographical coordinates of the antennas (see Fig. 1a); ii) calculate the population density of each cell based on WorldPop

data35 and select all cells with a population density over 100 people/km2; and iii) combine the data with Google earth remote sensing data to filter out cells of non-built-up areas

(artificial recognition). The first four columns of Table 1 show the names, population and population density of the studied cities. POPULATION-WEIGHTED EFFICIENCY (PWE) If two places are

geometrically close (with a small geometric distance, assigned as _d__e_), but the route distance (_d__r_) between them is large (Fig. 2a shows the difference between the geometric distance

and route distance), then we can assume that this route’s structural efficiency _d__e_/_d__r_ is low and requires improvement. Here, the definition of structural efficiency is similar to the

_route factor_ proposed in refs 14,15. After repeating the process of calculating _d__e_/_d__r_ for every route and average the results, we can get the efficiency of the whole road

networks. This way weights each route equally, but in practice, the traffic volumes of routes are expected to be very different from one another, due to the uneven distribution of

population. Therefore, if we weight the route factor by the proportion of population flows along each route, we can then obtain a more practical indicator, the population-weighted efficiency

(PWE) for road networks, defined as: where _P_(_i_,_j_) stands for the number of persons commuting from place _i_ to _j_ and is the total size of the population flows, _d__r_(_i_,_j_) is

the route distance between _i_ and _j_ and _d__e_(_i_,_j_) is the geometric distance. It is easy to calculate _d__e_(_i_,_j_) between any two locations according to their (longitude,

latitude)s and _d__r_(_i_,_j_) could be acquired from Google Map API (see the Methods and Fig. 2b). By integrating the PWEs of each route pair, we can obtain the overall PWE of a city: Based

on our definition, η = 1 is the most efficient situation (there’s a direct route between any commuting pairs); the smaller η is, the less efficient it is. USERS’ BEHAVIORAL PATTERNS AND OD

DETECTION To understand the PWE of a city, the first step is to identify the dynamic population distribution, _P__i_,_j_, i.e., (at least) where people live and work, which is also called OD

matrices and usually collected by field transportation survey. While for many developing or less-developed countries, the transportation survey is not available. Even for developed

countries, the survey is usually conducted by the government once a year (or longer) for transportation planning purposes. Here, we use mobile phone call data to estimate the OD matrices,

which has been widely accepted in academia36,37. However, unlike previous related works on OD analysis, which assume working hours according to practical experience28,36, we detect OD

matrices by analyzing users’ behavioral patterns. For a closer look at the temporal patterns of the mobile phone calls, we find some common features of the calling patterns compared with

cities in developed countries: there are two peaks in phone call activities, one at noon (about 12:00) and another at night (about 21:00–22:00, see Fig. 3a,b) and the second peak in Senegal

is a little later than in most Spanish cities25. An attractive finding is that the average call duration during the day is about 60 seconds (Fig. 3c), which may be influenced by the charging

mode or may be merely a reflection of the daytime work character, which is short, frequent and brief. Additionally, people in Senegal are quite active during nights: the call duration is

long (see Fig. 3a) and the number of short messages is very high at night (especially late night, see Fig. 3d). Based on these user behavioral patterns, we identify that the actual working

hours are from 10:00 to 19:00. It is because the existence of a rapid increase in average call duration before and after this period, which corresponds to different active patterns. In Fig.

3d, we observe a striking peak in short messaging service (SMS) behavior at approximately 23:00, when the total call duration also peaks (see Fig. 3a,d), which implies another important

behavior feature that usually occurs during leisure time (i.e., at home). Therefore, we set the home hours as 21:00 to 06:00 of the next day. For a user, we identify the most frequently

visited location (tower) over the two periods mentioned above as his or her work/home places, respectively (see the Methods). Therefore, we can extract an OD pair as the home to work place

of each user at antenna resolution. By going through all of the users’ records, we obtain the OD matrices at both the intra- (see Fig. 4a,b and Supplementary Fig. S1, at antenna resolution)

and inter-city levels (see Fig. 5b, at city levels, i.e., treat all the antennas within one city as a node). Figure 4 shows the OD matrices in Dakar (Fig. 4a) and Thies (Fig. 4b): it implies

that a lot of people commute from west to east in Dakar, whereas the commuting pattern in Thies is from the center to the suburbs. It should be noted that these plots only show the

geometric links between two places, rather than the real routes. PWE AND ITS APPLICATIONS After obtaining the OD matrices, we can query each OD pair’s locations to Google Map API, which can

return the route distance and travel time between two locations. Figure 4c shows the scatter plots of route distance and geometric distance of Dakar and Fig. 4d exhibits Thies. The left-top

points of Fig. 4c,d indicate routes with high route distances and low geometric distances, which implies that paths between these points are zigzags or complicated and of inefficiencies. The

PWE of each road can be obtained by plugging the OD matrices and the ratio of the real route distance and the geometric distance into Eq. (1). As an improved indicator for road networks

efficiency, PWE has essentially three applications: i) detect inefficient routes within cities and ii) at inter-city level; iii) calculate overall commuting efficiency of each city. In the

following, we will show the viability and effectiveness of the PWE. First, as a case study in Dakar, according to the PWE of each road, we identify dozens of the most critical inefficient

routes (see Fig. 5a and Supplementary Table S1 gives the values of top ten inefficient routes). An attractive finding is that almost all of these critical inefficient routes are south-north

trending and can be divided into three groups (colored in red, blue and green separately in Fig. 5a). The existence of the red group in the east region may be mainly caused by the separation

of the west-east trending highway, people are forced to detour the way from home to work. The blue group in the west region is mainly caused by the high weight of commuting volume,

_P_(_i_,_j_)/_P__tot_ and the detour. And the green group is another representative type that crosses an enclosed space (the airport in Dakar). The pattern of detected inefficient routes

implies the necessity of constructing some fast transits between the north and south regions. Second, PWE can be applied to inter-city level by considering the entire antennas within a city

to be a node. Figure 5b shows the commuting flows between the ten main cities. We find that many people commute between Dakar and its surrounding cities, especially Thies, Mbour and Touba,

which indicates that the agglomeration degree of the urban population is very high in Senegal and that most of its population live near the Dakar region. With a similar calculation for PWE

within the city, we can obtain the PWEs for city pairs. We find that there are several routes connecting Dakar, Thies and Mbour that are of the lowest PWEs, which indicates that we may need

to build better roads between these city pairs. Our results are also partially verified by the ongoing construction of the Dakar-Diamniadio highway, which makes transit faster between Dakar,

Thies and Mbour31,32 (see inset of Fig. 5b). Third, we compute the overall PWE for all ten main Senegalese cities (see the fourth column of Table 1), from which we find that Dakar is the

most inefficient city with η = 0.683, whereas most city PWEs are about 0.73–0.78. The low efficiency of Dakar is mainly due to the lack of fast south-north trending transits and the high

work-home separation, which could also be inferred from CDRs (see the Methods). In Dakar, We find that most of the users are distributed in Dakar Plateau, Grand Dakar, Médina and Parcelles

Assainies during the daytime (Fig. 6a) and Parcelles Assainies at night (Fig. 6b). Figure 6c depicts the work-home user differences in Dakar. For each department, we obtain a day/night

population ratio, which evaluates the work-home separation situation (see Fig. 6d). We compare the separation degree of each _Region_ and find that Dakar and Kaolack are the two _Regions_

that have the highest separation degree (see Supplementary Table S2 for the calculation of the separation degree). COMPARISON BETWEEN PWE AND EXCESS COMMUTING INDEX There are many indicators

could be used to measure commuting efficiency and job-housing balance in transportation literature18. In this section, we want to compare the most commonly used one, excess commuting, with

PWE. First proposed by Hamilton38, the concept of excess commuting is used to measure the difference between the actual commuting distance (or time) and the theoretical minimum average

commuting distance (or time). Mathematically, the equation of excess commuting could be expressed as follows: where _C__act_ is the actual commuting distance, which is similar to _d__e_ at

individual level if measured by geometric distance, or _d__r_ by route distance (see Supplementary Fig. S2). _C__min_ is the minimum commuting distance when all working and living places are

fixed in urban area, workers in a city choose work places that is closest to their living places. In other words, the assumptions of this transportation problem are: 1) the volume of

origins, destinations of each area and the total flows between them are fixed; 2) individuals choose living and working places to minimize the total travel distance. The most optimal

commuting flows could be derived by optimizing: where _c__if_ is the distance (or time) between area _i_ and area _j_, _O__i_ is the total number of people living in area _i_ and _D__j_ is

the total number of people working in area _j. n__ij_ is the commuting flow from area _i_ to _j_. The minimum commuting flows (_n__ij_) are calculated using _Scipy_._optimize_ package in

_Python_ and the average minimum commuting distance (_C__min_) is shown in the fifth column of Table 1. Since _C__act_ varies for different definitions, here we calculate both geometric

distance and route distance and depict them in the sixth and seventh columns of Table 1 respectively. Obviously, _C__act_1 (geometric distance) is smaller than _C__act_2 (route distance).

Combining with Eq. 3, we could get excess commuting indices, _C__ex_1 and _C__ex_2 (see Table 1). To compare PWE and excess commuting, a third benchmark is needed. Here, we choose average

commuting time, which is a direct reflection of the transportation efficiency. We calculate the average commuting time in each city (see the Methods) and find that both PWE and excess

commuting indices highly correlate with average commuting time (by OLS regression), which indicates both of them could be used to measure the efficiency of a city, however, PWE is better

because its correlation coefficient is much higher (_R_2 = 0.87, see Fig. 5c) than the ones of _C__ex_1 (_R_2 = 0.24) or _C__ex_2 (_R_2 = 0.42). Excess commuting can offer valuable insights

in evaluating job-housing balance and the overall efficiency of a city. However, the minimized commuting flows are obtained by the global optimum solution, making excess commuting index

unable to find local inefficient routes, which could be improved by our PWE method. A NULL MODEL To explain why most ηs lie in (0.73, 0.78) (see Table 1), we build a null model to compare

the simulation with empirical results. Let us assume a monocentric city, where all the people work at the center of the city and live uniformly around the city space. The road network of the

city is in the form of a lattice (e.g. Manhattan grids, see Fig. 2a); therefore, the route distance from the location (_x_, _y_) to the city center (0, 0) is |_x_| + |_y_| and the geometric

distance is (_x_2 + _y_2)1/2. Under these assumptions, we could easily get η = 0.77 by simulation (see the Methods). Because the population distribution is not uniform within the city in

reality, we also test for normal and exponential population density decay from the city center, which are observed in many cities39. The PWEs of the normal and exponential distributions are

0.79 and 0.80, which implies the concentration at the city center leads to higher efficiency. The empirical results for monocentric cities in Senegal are well fitted by simulation except for

Dakar. In fact, the urban form of Dakar is irregular narrow strip and cannot be treated as a monocentric city. From both the model and empirical results, we could find that PWE is mainly

influenced by the road network structure and the population distribution. The more direct routes between OD pairs of high traffic volumes, the higher efficiency the road network is.

Similarly, increasing the ratio of jobs-housing balance may reduce overall commuting distance and improve the transportation efficiency. DISCUSSION In this paper, basing on CDRs, we

introduce a new indicator, the population-weighted efficiency, which tells us how efficient the city is and provides a quantitative measurement to guide transportation infrastructure

development. This indicator is helpful for evaluation of urban planning and designing and could be applied to other spatial networks easily. Besides, our method to obtain the OD matrices is

more objective which is based on users’ behavior patterns rather than practical sense. We prove that the PWE is a proper indicator for evaluating the efficiency in two ways. First, according

to the PWE, we identify the most inefficient roads both within Dakar and between cities, which are partially verified by ongoing constructed roads. Second, we compare PWE with excess

commuting, the most commonly used commuting efficiency index in transportation literature and find that PWE is highly correlated with the average commuting time and has a better fitting

result than excess commuting. After comparing the PWE indicator of all ten main cities in Senegal, We discover that Dakar is the most inefficient city, which is mainly due to the lack of

fast south-north trending transit and the high degree of work-home separation. Another finding is that most Senegalese cities’ average PWE value are approximately 0.73–0.78 and we believe

that this is a reflection of the monocentric feature and Manhattan road networks (i.e., lattice networks), which can be explained by the simple model that we propose. In fact, the efficiency

and extendibility of a city is strongly influenced by its terrain, current road network and population distribution and suitable planning strategies are required for special terrain. For

example, Dakar may need to build cross-sea transportation, but another possibility may lead to the redistribution of land use for the historical heart of the city. In addition, different

types of people may tend to have quite different mobility patterns. The mobility dynamics for local and non-local users may not be similar (see Supplementary Fig. 4) as well as for people

with different income24,40. For future studies, it will be critical to distinguish between different dynamics for different types of users41, which could be helpful when performing

simulations for policy impact evaluations or urban planning and real-estate development. One more possible exploration is assessing the infrastructure development within a region by

comparing the infrastructure density (e.g., road density) and population density within the same region (see Supplementary Fig. 4). METHODS OD DETECTION By integrating the CDR data records,

we obtain a list of places a user visited with information of both when and how many times these visits occurred. Then, we count the locations at which the user appears at both night and day

and consider the places that appear with the highest frequencies to be the home and workplace. When we fail to detect the work or home location, we assign it as UNKNOWN. If a user’s home is

unknown but work is known (or vice verse), we still accumulate the data point as the daytime population and draw it out together in Fig. 6. We obtain an extended OD matrix with an extra row

and column for users without a detected home or work place, respectively. There’s no user with both unknown home and work place, but the non-local users in Dakar are easily absent of a home

location (see discussion in Supplementary Fig. 3), which also happens in developed countries37. ROAD NETWORK DATA AND EFFICIENCY The Google Map API (http://maps.googleapis.com/maps/api/)

can return the travel time (by car, in seconds) and route distance between two locations and the geometric distance between these two locations can be easily calculated according to their

(longitude, latitude)s. In addition, the Google API can return real-time data on travel time in big cities, which could be used to compute the average commuting time in cities. SIMULATION

FOR THE NULL MODEL The simulation is performed as follows. We split the entire _L_ × _L_ space into _L_2 lattices, which represent Manhattan road networks. We uniformly generate 100,000

points, which are located at the intersections of the road network. Therefore, we calculate the geometric distance (_x_2 + _y_2)1/2 and route distance (|_x_| + |_y_|) to the center of the

_L_ × _L_ space, where the central lattice represents the working place. The PWEs of the uniform, normal and exponential distributions are 0.77(0.001), 0.79(0.001) and 0.80(0.001),

respectively. Each simulation was performed 10 times under the _R Environment_. ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Dong, L. _et al._ Population-weighted efficiency in

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sociodemographics on human mobility. Sci. Rep. 5 (2015). Download references ACKNOWLEDGEMENTS This study was performed using mobile communication data made available by ORANGE/SONATEL within

the framework of the D4D Challenge. We acknowledge the organizers of the D4D Challenge and ORANGE/SONATEL Group for permitting us to use the Senegal CDR dataset. R.L. acknowledges Guoyue Wu

from Beijing International Studies University for the helpful discussion on the general habits and behaviors of residents in Dakar. L.D. acknowledges Jianzhu Wang for the discussion on the

transportation situation in Africa. This work is supported by the Fundamental Research Funds for the Central Universities with the grant No. 2015KJJCB13. AUTHOR INFORMATION AUTHORS AND

AFFILIATIONS * School of Architecture, Tsinghua University, Beijing, 100084, China Lei Dong * School of Systems Science, Beijing Normal University, Beijing, 100875, China Ruiqi Li, Jiang

Zhang & Zengru Di Authors * Lei Dong View author publications You can also search for this author inPubMed Google Scholar * Ruiqi Li View author publications You can also search for this

author inPubMed Google Scholar * Jiang Zhang View author publications You can also search for this author inPubMed Google Scholar * Zengru Di View author publications You can also search

for this author inPubMed Google Scholar CONTRIBUTIONS L.D. and R.L. designed and performed the study. All the authors contributed to writing of the manuscript. ETHICS DECLARATIONS COMPETING

INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY MATERIAL SUPPLEMENTARY INFORMATION RIGHTS AND PERMISSIONS This work is licensed under a Creative

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this license, visit http://creativecommons.org/licenses/by/4.0/ Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Dong, L., Li, R., Zhang, J. _et al._ Population-weighted

efficiency in transportation networks. _Sci Rep_ 6, 26377 (2016). https://doi.org/10.1038/srep26377 Download citation * Received: 14 January 2016 * Accepted: 29 April 2016 * Published: 27

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