Quantifying Demand Dynamics for Supporting Optimal Taxi Services Strategies

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1 Available online at ScienceDirect Transportation Research Procedia 22 (2017) th EURO Working Group on Transportation Meeting, EWGT2016, 5-7 September 2016, Istanbul, Turkey Quantifying Demand Dynamics for Supporting Optimal Taxi Services Strategies Elena Kourti a, Christina Christodoulou a, Loukas Dimitriou a *, Symeon Christodoulou a,constantinos Antoniou b a Department of Civil and Environmental Engineering, University of Cyprus, 75 Kallipoleos Street P.O. Box Nicosia, Cyprus b School of Rural and Surveying Engineering, National Technical University of Athens, Heroon Polytechniou 9, Zografou, Greece Abstract In recent years, mobility patterns have reasonably attracted scientific interest, especially concerning Mega-Cities. The technological advances, especially concerning sensors, facilitates the collection and access on a massive amount of empirical data capturing in high-resolution urban mobility. The introduction and spread of location tracking devices and services provide the means for collecting reliable real-time data, particularly valuable for industrial as well as for personal applications. In this study, a complex and realistic dataset is monitored and analysed, that provide the real-time occupancy status and Global Positioning System (GPS) location for three taxi fleets during of New Year s Day. The scope of this paper is a preliminary identification of alternative Taxi-Services Strategies by means of dynamic clustering as well as heatmap analysis The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of EWGT2016. Keywords: Urban Mobility; Real-Time GPS Information; Taxi-services strategies; dynamic clustering; * Corresponding author. Tel.: /49; fax: address: lucdimit@ucy.ac.cy X 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of EWGT /j.trpro

2 676 Elena Kourti et al. / Transportation Research Procedia 22 (2017) Introduction Through the last decades, cities growth patterns have been undergoing qualitative changes. These changes (from monocentric to polycentric structures) have produced intense changes in mobility patterns in urban structure. Thus contemporary cities organization need to evolve and offer services effectively, efficiently and sustainable in all aspects (Ferreira et al. 2013) In order to optimize the transportation systems a crucial element stands for the understanding of what drives mobility and its patterns that in turn, is vital for demand and traffic modelling, simulation, forecasting and control (Peng et al. 2012, Veloso, Phithakkitnukoon & Bento 2011). Recent access to a variety of surveillance devices provides research community with an enormous amount of data, requiring new and valid methodological tools in order to take full advantage of these new opportunities. Taxi services stands for a vital demand-responsive transport mode, especially in Mega-Cities. The remarkable development of the Information and Communication Technology (ICT) provides powerful tools to monitor the time-resolved locations of individuals and makes it possible to understand the basic law of human motion. Although activities can easily appear to be random and unpredictable from the perspective of an observer who is unaware of the activity agenda, rarely perceive any of actions to be anomalous or stochastic. Traditional transportation systems in metropolitan areas often suffer from inefficiencies due to uncoordinated actions as system capacity and traffic demand change. With the pervasive deployment of networked sensors in modern vehicles, large amounts of information regarding traffic demand and system status can be collected in real-time. This information provides opportunities to perform various types of control and coordination for large scale intelligent transportation systems. Using commercial vehicle fleets as probes may be a cost-effective method for obtaining real-time traffic information. Because the taxi dispatch system automatically records the location of a taxi traveling in an urban network, large quantities of real-time travel data can be obtained at low cost. Although, the reliability of this information, about real-time traffic conditions, has not been investigated. However, Taxi service is an important mode of public transportation in most metropolitan areas since it provides door-to door convenience in the public domain. The aim of this paper is to identify alternative Taxi-Services Strategies by means of dynamic clustering. Through a complex and realistic dataset, preliminary analysis were done (spatial and temporary data) in order to develop challenging tests for Metropolitan cities. The study of large cities such as the New York City, particularly for the New Year s Day (2010), is a challenge. Due to high demand for taxies that special event day the result was large concentrations and fluctuations through that day. Spatial data were organized by performing clustering estimation and graphs of origin basis of destination, whereas, the temporal data were organized by performing dynamic analysis, separating the data into five minutes intervals. The ultimate scope of the paper is the understanding of taxi-services through various experiments, so as to identify the best strategies of taxi services. The strategies that will be close to 'optimal', may be used to create a decision support system that could be used by taxi-services companies. The paper is structured as follows: after this brief introduction, section 2 follows with a background review on urban mobility based on Global Positioning System-GPS information and taxi data analysis. In section 3 a dataset description is given by analysing the dataset with respect to various considerations. Next, the dataset is being processed and analytically presented, mainly providing GPS-based taxi traces distributed in time, both for pick-up as well as for drop-off locations in heatmaps. Section 4 follows with a clustering estimation, trying to detect and understand strategies followed by taxi drivers. Moreover an analysis of the data produces OD matrices and a brief processes of them is presented. Section 5 gives main conclusions and discusses some future research to improve the current work. 2. Background Review During the last years researchers has become more and more interested in the statistical analysis and process of transportation and human mobility pattern using the large amount of empirical data from location tracking devices (Castellano, Fortunato & Loreto 2009). Researchers provided evidence on the taxi industry organization, based on dynamic equilibrium assumptions quantified the impact of these policies on medallion prices and on the process that matches passengers with taxicabs in New York City (Lagos 2003). In (Ch, Briones 2006), a graphical approach

3 Elena Kourti et al. / Transportation Research Procedia 22 (2017) provided the characteristics of the cruising taxi market, in which taxi operator and passenger were taken as service producers. It was additionally analysed the relations among the free market equilibrium, social optimum and second best solution. In (Liang et al. 2012) data from more than taxis in Beijing were used in order to build models for trajectories with fine granularity. The observation was that in contrast with human mobility data that follow power-law distribution, taxi travelling displacements in urban areas tend to follow an exponential distribution. Movement data has recently received substantial attention in the visualization community (Andrienko, Andrienko 2012). Much of the work has focused on trajectory data, where the complete trace of the moving entities is recorded. Techniques have also been devised to visualize OD data. (Phan et al. 2005) proposed a method to automatically generate flow maps that show the movement between two locations. (Wood, Dykes & Slingsby 2010) proposed OD maps, which encode trips as a set of spatially ordered small multiples to avoid occlusion effects that occur when flow maps are applied to a large number of trips. While these two techniques consider only space, (Boyandin et al. 2011) proposed Flowstrates, which takes both space and time into account. These techniques are orthogonal and could be combined with our model. For example, in addition to the plots currently supported by the data summary view of our system, we could also display a Flowstrate visualization for users to explore the results of origindestination queries. Moreover, a large number of industrial application have been presented, the detailed presentation of which is omitted here for brevity. For instance, the experience of three Singapore-based taxi companies that implemented a GPS-based system for the automatic vehicle location and dispatch system (AVLDS), matching passengers with the nearest available cabs. The results of this approach enables the real-time cooperation of between call operators and individual taxi drivers, increasing productivity and customer satisfaction (Liao 2003). In (Ch, Briones 2006) a largescale and empirical evaluation of a dynamic and distributed taxi-sharing system is performed, aiming to achieve coordination between user requests (demand) and taxi fleet (supply). This service is designed to be dynamic, distributed, automatic, flexible, providing door to door and low cost services for passengers. Moving on the study of GPS traces from taxis in urban areas to understand and intervene to optimize urban mobility is a quite active research field (Veloso, Phithakkitnukoon & Bento 2011).(Liu et al. 2010) developed a methodology to analyse operational behaviour in a real urban environment of the taxi drivers, by classifying them into the top and standard drivers based on their performance. Processing data from 3,000 taxi drivers, it was observed that top drivers have the special proportion of operation zones, with an optimal balance between taxi travel demand and fluid traffic conditions, while ordinary drivers operate in fixed spots with few variations. (Ziebart et al. 2008), present a decision modelling framework for probabilistic reasoning from observed context-sensitive actions utilities rather than directly learning action sequences. Using data from 25 taxi drivers, the model is able to make decisions regarding intersections, route to known destination and destination prediction given partially travelled routes. (Yuan et al. 2010) propose to mine smart driving directions from a large number of real-world historical GPS trajectories generated by over 33,000 taxis in a period of three months. The purpose is to present the algorithm to compute the fastest path for a given destination and departure time. In order to model the knowledge of taxi drivers describe a three-layer architecture with the concept of landmark graph. (Chang, Tai & Hsu 2009) propose mining historical data in order to predict demand distributions taking in consideration the weather, time and taxi spatial position. It is a four step process including data filtering, clustering, semantic annotation, and hotness calculation. As a result it is shown that different clustering methods have different performances on distinct data distributions. (Qi et al. 2011), perform qualitative and quantitative analysis, to establish and confirm the relationship between pickup and dropoff locations characteristics of taxi passengers and the social function of city regions. The use of a simple classification method to recognize region s social function, suggests that the experimental results can be classified into three typical regional categories. (Veloso, Phithakkitnukoon & Bento 2001, Veloso et al. 2011, Veloso, Phithakkitnukoon & Bento 2011)also perform an exploratory analysis using data collected from taxi-gps traces in order to visualize the variations in GPS locations from the different taxi services, understand the relationship between pickup and dropoff, and analyse the pattern in downtime. At the end they try to perform a predictability analysis for the next pickup area given the history from the previous taxi trips. 3. Dataset Description In this study, a GPS dataset for taxi trips has been used for a whole day, particularly for the 1 st of January, 2010 (Donovan, Work 2015). The data are generated from taxis, taxi drivers and 3 different vendors operating in the urban area of New York, USA. The data are mostly for Manhattan Island and some parts from its

4 678 Elena Kourti et al. / Transportation Research Procedia 22 (2017) surrounding areas (Brooklyn, Queens, New Jersey), with a studying population of 8,336 million inhabitants in New York and 1, 63 million inhabitants for Manhattan Island (World Population Review ). The dataset contains raw information about the vendor, the vehicle identification and taxi driver license, the pickup/dropoff date and timestamp, the taxi trip duration, path distance, passengers capacity and the pickup/dropoff coordinates. The longitude and latitude location information are given in the WGS84 coordinate reference system. Moreover each pair of a pickup and a dropoff point is defined as a taxi trip, which corresponds to a total of taxi trips for the whole day, after a small process to the original dataset. Some additional information about the operation of the taxis in New York, are that they do not work for a taxi dispatching system but they cruise the road to find passengers. Most taxis run 24 hours with two shifts and some of them three depending on how many drivers each vendor employs. The original dataset contained taxi trips for the 1/1/2010 but after a data cleaning the taxi trips decreased 18%. There were some abnormal tracks that needed to be exclude from the dataset. The data filtering was performed by running queries in database, such as: The trip duration to be greater than 0,5 min, based on the hypothesis that a taxi trip last longer than half a minute. The path distance trip to be greater than 0,3 miles, for the purpose of the study shorter trips are not helpful. The Euclidean distance (calculated by the original information) to be shorter or equal to the path distance trip. It s a logical criterion to check the accuracy of the data. The pickup and dropoff longitude values to be between -74, < Longitude < -73, and the pickup and dropoff latitude values to be between 40, < Latitude < 40, The particular study selects to focus on trips that occur in this area. Subsequently, after cleaning the original data sample, the sample was divided by time intervals, five minutes and one hour respectively. For the better understanding of the dataset a histogram with taxi trip frequencies was created. Observing the Fig. 1 below, taxi trip frequencies are displayed for every 5 minutes of the day the first one starting at 12 o clock in the midnight. It s a temporal distrimbution with an enhrichment during late hours of the night (from 00:00-03:30) and a decrease during the early morning hours (from 05:00-10:00). It s not something that is expected, usually it s anticipated mobility movements to increase during the morning hours, people goes to work, andgo out to run errants or travel for leisure purposes and decrease during the late hours of the night. This strange phenomenon can be explained by the fact that the dataset is for taxi trips mostly in Manhattan s Island in the New Year s Evening, which also happens to be Friday. Considering the above fact it s not odd at all that movements increase during the late hours of the night, it s a holiday and a lot of people go out to celebrate. There is a pattern but as you break down the margins into smaller segments the results diverge.each hour is divided in twelve 5minutes margins that through them the results changes a lot, about a ±20% Number of Trips mins Intervals Fig.1: Frequencies for Taxi Trips per 5Minutes For the visual representation of the data, a Spreadsheet file, which contained data divide by five minutes interval as well as one hour interval, was imported in a Geographic information system software. A visual representation of

5 Elena Kourti et al. / Transportation Research Procedia 22 (2017) pickup and dropoff points for the whole day is necessary, in order to understand the data spatially. Pickup and dropoff coordinates maps were exported. Fig. 2 a) & b) shows all trips contacted through the day with its GPS location in origin and destination points. Fig.2: Pick-up (a) and Drop-off (b) coordinates map for 24 hours Taxi demand varies in time and space, according to the citizen s needs. Fig. 3 a) & b) presents the taxi service demand (based on pick-up and drop-off locations) during the New Year s Day. As shown in Fig. 3 heatmaps, the pickup points of each trip spreads into space, with significant concentrations in various areas of Manhattan, while the final destinations of trips (drop-off) are more spread out and have quite large concentrations in fewer areas. Furthermore as mentioned before pick-up and drop-off heatmaps created for the two different time intervals, 5- minutes and 1-hour. Fig.3: heatmap'-pick-up and drop-off locations for 24h For the paper purposes only an example will be presented and it was selected the heatmap from 00:00-01:00 and 01:00-02:00. Due to the fact that New Year s Day is studied, large population concentrations expected in central parts of Manhattan during the early hours. It s confirmed by Fig.4 a) & b) & c) & d) which shows the correlations between pick-ups and drop-off flows after midnight until 2 am. Fig.4: Heatmap -Pick-up (a, c) and drop-off (b, d) locations between 00:00-02:00 The mobilization to drop-off destinations is slightly greater than the corresponding pick-up and their maximum concentrations found in specific parts of the Centre (mainly in the area of Times Square), in contrast with the pick-

6 680 Elena Kourti et al. / Transportation Research Procedia 22 (2017) ups which are more divided in Manhattan s area. Additional information that was given in the original dataset and might reveals a specific pattern/behaviour, was the vendor for each taxi trip. Observing Fig.5 a pattern starts to reveal, all vendors had a high concentration of trips in the middle of Manhattan Island. Fig.5 a) & b) presents pickup and dropoff coordinates for every taxi trip that occur during 1/1/2010 categorized be vendor. (a) (b) Fig.5: a) Pickup and b) Dropoff Locations for the whole day by each vendor Three vendors are considered here: VTS, CMT, DDS. It s observed from both figures that VTS and CMT vendors secure the majority of the taxi trips during the day and also their taxi fleet are distributed widely into space in contrast to DDS vendor which its taxis are concentrated mostly in Manhattan s area. Additional dropoff points are more spread out into space than pickup points. In Fig. 6 a bivariate histogram for pickup and dropoff locations is shown. Through that kind of analysis it is possible to target and conclude into the most likely areas with taxi demand. Observing the pickup locations graph, it s noticeable that there is high concentration of taxi trips in the middle of Manhattan s Island and in smaller scale at the JFK airport and at the La Guardia airport. In contrast with pickup locations, dropoff is more spread out in the space but also with a high concentration in the middle of the Manhattan s Island. Comparing pickup with dropoff both for the whole day, it worth to mention that more people use taxi to leave from the airports than to go to, through the day. Fig.6: Bivariate Histogram for a) Pickup Locations and b) Dropoff Locations for the whole day Moving on, the scope of the paper is to identify strategies that Taxi-Services companies could use in order to organize and improve the existing system. Towards that it would be helpful to create OD matrices, which are combined information of the origin and destination for the dataset. Until now, dataset analysis was separate for origin and destination. OD Matrices are combined information with origin and destination. With OD estimation some gaps in the system can be observed and some strategies that are already applied incidentally may be identified in order to be more targeted. A clear and useful depiction of demand fluctuations can be captured by investigating demand matrices (structured in OD pairs). These matrices can be used for identifying places that produce sequences of trips with specific/desirable characteristics. Though, such information is also subjected to fluctuations and it is important to be

7 Elena Kourti et al. / Transportation Research Procedia 22 (2017) accompanied with a metric of stability. In Fig.7, OD matrices are plotted on a colour scale, exhibiting the completely different demand structure for two randomly selected 15-minutes intervals of the same day. As it can be observed, the OD matrices reproduce the different spatial distribution of demand and the corresponding complexity of identifying optimal taxi service organization Origin Origin Destination Destination Fig.7: Origin-Destination matrices in a resolution for two 15-minutes intervals Moreover for capturing the dynamics of fluctuation the metric of statistical entropy is used that lies in [0,1]. In Fig.8 a) the entropy of OD matrices is depicted for each 15-minutes interval (red line) and for the absolute difference between consecutive OD matrices (blue line). As it can be observed, the randomness of OD matrices follows total demand levels, as captured in both metrics and in particular the demand in low demand levels is almost three times more structured compared to increased demand levels. Furthermore, a more elaborated metric corresponds to the Structural Similarity Index-SSI that can capture the difference/similarity of complex signals like image signals. In brief, SSI is typically used for checking image/video information quality, based on reference images. Entropy Value 0,40 0,35 0,30 0,25 0,20 0,15 (a) 0, Structural Similarity Index min Interval 15-min Interval Fig.8: a) Statistical Entropy metric for the OD matrices (red line) and for their absolute difference (red line) b) Structural Similarity Index for the OD matrices for consecutive 15-minutes intervals (blue line) and for 1-hour intervals (red line). Here, this concept is used for checking the difference between consecutive OD signals. SSI lies in [0,1] where values closer to 1 reflect greater similarity. In Fig.8 b) the SSI for consecutive 15-minutes and 1-hour intervals are depicted. In the figure below the signal stability increase as far as total demand decrease. It is highlighted that the proposed combined dynamic randomness/stability analysis may provide necessary information for identifying benchmarking cases in estimating optimal taxi dispatching strategies. The results of further analysis go beyond the scope of the present study. An addition to previous analysis k-means clustering is performed. In order to study and identify optimal locations for picking taxi trips, initially a k-means clustering algorithm with (15 clusters/divisions) was applied, dividing NYC in regions based on their pickup and dropoff concentrations as shown in Fig. 9 a) & b) equally. Time intervals of 5 minutes were set for all day and the algorithm run for all of them. For example purposes hour 19:00-20:00 is selected for the figures. In Fig. 10 a), the results of the k-means clustering are depicted, in which areas with cluster (b)

8 682 Elena Kourti et al. / Transportation Research Procedia 22 (2017) numbers 2,3,5,8,9 and 12 are the areas with lowest trip concentration (see embedded histogram in Fig.10, while areas with cluster number 1,4,6,7,10,11,13,14 and 15 are the clusters with most trips generated. A more thorough analysis is necessary to reveal pattern and strategies that taxi drivers may use. Fig.9: Scatter plot with the centre of each cluster for five minutes intervals for a) Pickup Locations and b) Dropoff Locations for the whole day Using the classification in high profile demand areas provided by the clustering above as a map base, 7 different taxi drivers with their routes imprinted on. Taxi drivers were selected based on two main differences about their operation during the hour: Taxi drivers with more than 6 trips within the hour and taxi drivers with a large total trip time within the hour (but not necessarily a large number of trips). Interesting enough, taxis with more than 6 trips within the hour are shown in Fig.10 the figure shows k-means clustering of 19:00-20:00, based on pickup concentrations. On top of that are the trips for 7 taxis through the hour. Each taxi is symbolized with different colour line. Noticing the route that each taxi follows is kind of connected. The next pickup point near if not the same as the last dropoff point. This observation is valid for all hours of the day that had more than 5-6 trips in each hour, but for understanding purposes only one hour is shown. Fig.10: Cluster plot with 15 clusters for Pickup Locations for 19:00-20:00: taxi drivers with more than 6 trips Moreover taxies main activities are within high concentration clusters. Combining the observations from previous analysis also, it s suggested that targeted, short and frequent trips correspond to the optimal operation strategy within a complex Mega-city such as NYC. Fig.11 is the same as Fig 10 but with different taxi driver s route. Taxis here are taxis with large total trip time within the hour. Comparing the two figures, differences stands out. Here the route is not continuing, the last dropoff point is not the next pickup point, except in 1-2 random cases. In addition, taxis are moving in all clusters not only in high concentrations areas and as a result there is no return trip, therefor are forced to go back to high concentration clusters empty in order to find new trips. Interpreting the data this way suggests that random, long trips in time and distance are not the most smart and functional strategy.

9 Elena Kourti et al. / Transportation Research Procedia 22 (2017) Fig.11: Cluster plot with 15 clusters for Pickup Locations for 19:00-20:00: taxi drivers with large total time 4. Conclusions Modelling patterns of human mobility had drawn a lot of attention from researchers through the years, as a significant factor in urban traffic forecasting and prediction of epidemics. This paper contributes to this increasingly promising line of research, and in particular, Quantifying Demand Dynamics for Supporting Optimal Taxi Services Strategies, understanding through various forms of analysis, to identify the best strategies of taxi services in Mega- Cities. The dataset was for New Years Eve of New York City, and relationships such as pickup-dropoff locations and vendors, clustering and OD registers, were studied. The main purpose of selecting only one day and particularly the New Year's day data (in Manhattan, New York City) since it has distinctive and conceivable characteristics. The Taxi demand of such a special day, with large sample-size and composed of a variety of clients (tourists, locals) offers a suitable example for analysis. From the findings of the analysis descripted above it can be obsered that taxi trip frequencies during the day are not the expected as would be in any normal day, but are not unexpected for a special day such as New Years Day. There is increased mobility at midnight and dicreased in the morning. Observing pickup locations there is a consentration in the middle of the Manhattan and at the two airports (JFK and La Guardian). Dropoff locations are more distributed throghout the area. Also there are more pickup trips than dropoff trips to the airports. This may due to the fact that their arrival hours are not within the working hours of the public transport, are in a hurry and can t wait or they don t feel comfortable to use the public transport. Furthermore from the three vendors, DDS has the fewer taxi trips through the day and are concentrated mostly in Manhattan s Island. The other two are distributed widely through space. Moreover combining heatmaps, scatter plot with pickup-dropoff locations and the bivariate histogram, a pattern with the area with the highest probabilities start to reveal for the taxi driver to find a client. OD Matrices and k-means clustering can contribute to that. OD Matrices are plotted on colour scale image. As it can be observed, they reproduce the different spatial distribution of demand and corresponding complexity of identifying optimal taxi services optimization. Metric statistical entropy as shown in Fig.8 a) is used for capturing the dynamics of fluctuation. The randomness follows the demand levels. Additionally the difference or similarity of complex signals like image signals (OD Matrices image) can be captured from the Structural Similarity Index-SSI. In Fig. 8 b) signal Stability, increase as far as total demand decrease. Finally k-means clustering analysis shows that areas with high concentrations are the centre of Manhattans Island and the airports and suggests that targeted, short and frequent trips correspond to optimal operation strategy within a complex Mega-city such as NYC. Other topics for future studies could be further analysis of the data, or the analysis of any normal weekday. Moreover a development of a centralized optimal dispatching mechanism, incorporating advanced spatial optimization methods and technics, and maximize fleet utilization. References Andrienko, N. & Andrienko, G. 2012, Visual analytics of movement: An overview of methods, tools and procedures, Sage Publications,, pp

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