Abstract: Vehicle electrification is a promising approach towards attaining green transportation. However, the absence of charging stations limits the penetration of electric vehicles. Current approaches for optimizing the locations of charging stations suffer from challenges associated with spatial-temporal dynamic travel demands and the lengthy period required for the charging process. The present article uses the electric taxi (ET) as an example to develop a spatial-temporal demand coverage approach for optimizing the placement of ET charging stations in the space-time context. To this end, public taxi demands with spatial and temporal attributes are extracted from massive taxi GPS data. The cyclical interactions between taxi demands, ETs, and charging stations are modeled with a spatial-temporal path tool. A location model is developed to maximize the level of ET service on the road network and the level of charging service at the stations under spatial and temporal constraints such as the ET range, the charging time, and the capacity of charging stations. The reduced carbon emission generated by used ETs with located charging stations is also evaluated. An experiment conducted in Shenzhen, China demonstrates that the proposed approach not only exhibits good performance in determining ET charging station locations by considering temporal attributes, but also achieves a high quality trade-off between the levels of ET service and charging service. The proposed approach and obtained results help the decision-making of urban ET charging station siting. Keyword: facility location; spatial-temporal demand; maximum coverage; big data; electric vehicle Currently, the transportation sector contributes 20% to 30% of the total production of greenhouse gases (GHGs) such as oxocarbons (CO 2 and CO) and (IPCC, 2013) . The reduction of GHGs in the transportation sector has therefore gained much attention from with respect to technical innovation and scientific research. Among various alternatives, vehicle electrification is a promising approach towards attaining green transportation (IEA, 2014a). However, relative to alternative fuel vehicles, electric vehicles (EVs) generally have a shorter range that is compounded by the requirements of an extended charging period (IEA, 2013), which, with the absence of charging infrastructure, inspires a severe degree of anxiety regarding the allowable vehicle range (i.e., range anxiety). Meanwhile, the return of the considerable investment required for charging stations is exceedingly meager under conditions of low EV penetration (Carpenter et al., 2014) . Therefore, the EV market is dropping into a kind of "egg-chicken" paradox (Hiwatari et al., 2011; Xi et al., 2013; Jung et al., 2014) . Clearly, the relationship between active EVs and available EV charging stations must be carefully coordinated (Nie and Ghamami, 2013; Sathaye, 2014) . Public transportation, such as bus and taxi, are an appropriate first step towards electrification (IEA, 2013), and various cities have made efforts in this direction (IEA, 2013). For example, London plans to substitute all taxis in the city with EVs with the aim of low carbon emissions (IEA, 2014b). New York issues roadmap for electrifying one-third of the city's taxi fleet by 2020 (NYC TLC, 2013) . In China, the city of Shenzhen plans to add 3000 electric taxis (ETs) by 2015 (Shenzhen Transportation Administration, 2012). Therefore, the emerging question is where to locate charging stations to serve the various charging demands of a city. Location approaches are used to address the facility location problem to serve geographically distributed demands (Church, 2002) . These methods typically consist of two main components: a demand representation and a location model. Usually, the demand is represented as points, polygons, or flow in a spatial context (Miller, 1996) . The magnitude of the demand is generated by a synthetic method based on population or travel surveys. Demand is defined as being covered (i.e., fullfilled) if it is within a certain travel distance/time to a facility (Church and ReVelle, 1974) . A location model is designed to select the best locations that achieve maximum system utility, minimum cost, or other objective(s). Based on various demand representations and objectives, a number of location models have been proposed such as the p-Median (Hakimi, 1964 ), p-Center (Hakimi, 1964, the maximum coverage location problem (MCLP; Church and ReVelle, 1974) , and the flow capture location model (FCLM; Hodgson, 1990) . With the aid of geographic information systems (GISs) in the integration of spatial data management, visualization, and analysis, location models and optimization methods have been implemented and widely applied for facility location in public and private sectors (Thill, 2000; Church, 2002; Drezner and Hamacher, 2004; Church and Murray, 2009; Gentili, M., Mirchandani, P.B., 2012) . For appropriately locating ET charging stations, however, time is a crucial factor. Firstly, daily taxi demand exhibits spatial-temporal variations from hour to hour and from place to place (Wong et al., 2014; Qian and Ukkusuri, 2015) . This type of spatial-temporal dynamic feature is quite difficult to capture using a synthetic demand approach, and has therefore been ignored in current demand representation methods (Miller, 1996; Church, 2002) . This feature also creates a substantial challenge for defining the conditions whereby a charging demand is fulfilled, or formally, is covered (Zhou and Lin, 2012) . The acquisition of spatial-temporal variations in taxi demand is a basic issue. Secondly, the required duration for ET charging at charging stations can be quite long, where, depending on the charging mode, the charging duration can be from 5 minutes to several hours (IEA, 2013). Such an extensive duration will heavily affect the interaction between taxi demand and available ETs. Moreover, the capacity of a charging station is limited, depending upon the number of charging stakes, and only a limited number of ETs can be charged simultaneously at a given charging station. Any ETs in excess of the maximum service number arriving at a station for charging must therefore wait for service (Qin and Zhang, 2013), which would also affect subsequent ET service on the roads. However, traditional location models cannot address these temporal issues at a facility. Clearly, an extension of the conventional location model is needed. Detailed-rich space-time data is an aid to decision-making and policy analysis. Recently, taxis with GPS that track real-time vehicle positions have been widely applied in transportation (Tu et al., 2010; Li et al., 2011; Fang et al., 2011; Zhang et al., 2013; Yue et al., 2014) . Data regarding taxi service with corresponding time information in a city could be extracted from raw taxi GPS data. This information would not only contribute to traffic monitoring , travel time estimation (Zhan et al., 2013; Rahmani et al., 2015) , etc., but also deepen our understanding of travel patterns (Liu et al., 2010) , urban taxi service (Qian and Ukkusuri, 2015) , use of critical infrastructure (Fang et al., 2013(Fang et al., , 2015, etc. Such time rich information also provides an opportunity to capture city-wide spatial-temporal variations in taxi demands, which could serve as the cornerstone for the optimal siting of ET charging stations. The present article develops a spatial-temporal demand coverage approach using big spatial-temporal data to facilitate charging station siting. To this end, actual spatial-temporal taxi demands in the city of Shenzhen, China has been extracted from large volume raw taxi GPS data. Using the spatial-temporal path concept, the cyclical taxi demand serving on the roads, ET charging, and possible additional ET waiting at charging stations are modeled in a spatial-temporal context. A spatial-temporal demand coverage location model is proposed according to considerations of EV range, the requirements of charging and waiting at charging stations, and the competition of taxies. Only the taxi demand covered by an ET is included in the presented model. Analysis of the obtained results for Shenzhen, China indicates the good performance of the proposed ET charging station siting approach obtained by taking the time dimension into account. The daily reduced carbon emission (RCE) generated by the ETs with located charging stations is also mapped to evaluate the green effect. The remainder of this article is organized as follows. The next section reviews existing location approaches and their applications to charging station siting. Section 3 describes the study area and associated data. Section 4 presents the proposed spatial-temporal demand coverage approach. Section 5 illustrates the obtained results, and analyzes the environmental effect of used ETs with located charging stations. In the final section, we discuss and conclude the study. Facility location begins with a representation of human demands and locates facilities at the places best suited to serve those demands. According to the demand representation, current location approaches are divided into two approaches: point demand and flow demand. This section briefly reviews the two approaches and their implementations in charging station siting. For comprehensive reviews related to facility location, please refer to Church (2002) , ReVelle & Eiselt (2005) , and Murray (2010). The point demand location approach assumes that demand is located at distinct places, such as residential areas, working places, and shopping centers. The basic demand unit is a polygonal area based spatial object in a geographical space (Church and Murray, 2009 ). The demand count or the demand density is usually derived from demographic data, topographic data, cadastral data, survey data, etc. Because a polygonal area is much too complex for geocomputing, the representation of the demand is usually simplified as a point at the center of the polygon by abstracting and aggregating (Tong and Murray, 2009) . The inherent assumption is that dedicated travels between demand locations and facilities are made to fulfill geographical distributed needs. Therefore, the travel distance/time is defined as the key system utility index. The demand unit is defined as covered if it is within a certain travel distance/time to facilities. The objective is to either minimize the total travel cost between demands and facilities (the p-Median; Hakimi, 1964) Although the point demand location approach has achieved success in many applications, it still faces a number of challenges in transportation such as fuel station siting and charging station locating, e.g., the demand occurring during a trip rather than a fixed place, the cost index, etc. Rather than engaging in dedicated travels between individual facilities and customer locations to procure services, drivers may prefer to fulfill side needs during a long trip (Wang and Wang, 2010) . Also, travel distance/time as the cost in the point demand location approach is not an appropriate measure for the system cost in location modeling in transportation. Therefore, both the point demand representation and the covering definition are inaccurate in this scenario. A new location model is therefore needed to effectively handle this type of location problem. The flow demand location approach assumes that consumers search for a service during the travel to their destination locations (Hodgson, 1990; Kuby, 2006) . In this approach, the basic demand unit is not a polygon-based or a point-based spatial object representing aggregated human needs, but, rather, demand is represented as a flow passing along consumer routes of travel (Upchurch and Kuby, 2010) . Formally, this location approach is denoted as the FCLM (Hodgson, 1990) , which seeks to locate some facilities to intercept as many demand flow pathways as possible. In this method, an origin-destination matrix is typically first generated to model the demand distribution in the study area. The demand is defined as covered when a facility is located at any point along a consumer travel pathway. Because the objective is to locate facilities to maximize the passing demand flow, the FCLM is well suited for the types of facilities where consumers are served on their routes to travel destinations (Upchurch and Kuby, 2010; Zeng et al., 2010) . With considerations for limited travel distance, the FCLM has been extended to the flow-refueling location model (FRLM; Kuby et al., 2009 ) that locates a given number of stations to maximize the number of trips that can be refueled during a long travel. Because refueling is also considered, this model is more effective for a larger study area (Capar et al., 2013) . Both FCLM and FRLM have been successfully applied to the transportation sector in the optimal siting of conventional and alternative fuel stations (Goodchild and Noronha, 1987; Kuby, 2006; Kuby et al., 2009; Lim and Kuby, 2010; Kim and Kuby, 2013) . However, these methods consider only the spatial dimension of demand, and the temporal dimension of demand is ignored, such as the time of demand, service duration, and the possible waiting at a facility. Recently, both location approaches have been used for charging station siting. Nevertheless, potential waiting at the facility was not modeled. To date, Jung et al. (2014) have conducted the only study where the potential waiting time of ETs, based on random itinerary information over an 8 hour period in Seoul, Korea, was considered to optimize the configuration of charging stations for ETs. However, the stochastic demand data were synthesized using transportation planning software, which deviates substantially from reality. Detailed spatial-temporal taxi demand data is expected to obtain better results. The present study extracted actual taxi travel demand from massive taxi GPS data to model the space-time interaction between taxi demands, ETs, and charging stations. A spatial-temporal demand coverage location model is developed to site ET charging stations in a space-time GIS environment, which benefits decision-making regarding ET charging station. The research was conducted in Shenzhen, a metropolitan area in South China, as shown in Fig. 1 . To reduce carbon emission in the transportation sector, the local administration of Shenzhen plans to implement the use of ETs. Numerous ET charging stations are expected to be built. In this study, we propose a spatial-temporal demand coverage location approach using massive taxi GPS data to facilitate the siting decision-making. Raw taxi GPS data, the transportation network, the ET, and charging station data are used. The details of the data are described as follows. -Taxi GPS data. Every day in Shenzhen, about 15,000 taxis are actively engaged in transferring people between various locations such as homes, workplaces, shopping centers, the airport, and parks. According to transportation statistics, about 420,000 to 460,000 trips are conducted daily by taxis, which is about 5% of the travel occurring in Shenzhen. Each taxi has been installed with a smart terminal connected with a GPS receiver, which records data concerning the vehicle identification, time, position, speed, and working status with a sampling interval between 40 to 80 seconds. Table 1 describes the taxi GPS format, and provides an example. In particular, the working status is a binary variable indicating whether or not the taxi is serving a client at a given time, where the status is recorded as 1 if the taxi is occupied, and 0 otherwise when the taxi is vacant. Therefore, both the times and locations at which passengers are picked-up and dropped-off can be identified from the taxi GPS data. In the present study, we employed raw taxi GPS data for a seven-day period from Oct. 12, 2013 to Oct. 18, 2013 to extract historical spatial-temporal dynamic taxi demands.  The presented location approach for ET charging station siting extends the demand representation and the location model into a spatial-temporal context. It makes use of massive taxi GPS data for optimizing the placement of ET charging station. Fig. 2 illustrates the workflow of the approach. Firstly, dynamic taxi demands are extracted from the raw GPS data in conjunction with the transportation network data. The cyclical interaction between taxi demands, ETs, and charging stations in the spatial-temporal context is modeled with a spatial-temporal path tool which depicts an individual's sequential activities at various locations over a time period (Hägerstrand, 1970) . Then, a spatial-temporal demand coverage location model (STDCLM) is proposed to maximize ET service on the roads and charging service at the stations. A genetic algorithm is used to solve the STDCLM. Finally, the obtained results are analyzed, including the spatial pattern of covered demands, the temporal pattern of demand serving, charging and waiting behaviors, the impact of charging speed, the marginal utility, and the daily RCE estimation. Basic assumptions about ETs and charging stations are: (1) all ETs have the identical electricity capacity, E; (2) with full capacity electricity, all ETs have the same maximum travel distance, D max ; (3) the charging speed CS for all ETs in any located station are identical. It indicates that time E/CS will be cost to recharge an ET from the zero-electricity state to the full capacity electricity. It also specifies that all charging stations provide the same charging service; (4) once a charging process begins, it can't be interrupted or stopped until the charging need is completely fulfilled; (5) the travelable distance d is proportional to the remaining capacity e (Dong et al., 2014), as given in equation (1), where . In other words, the remaining electricity is linearly reduced with the traveled distance. (1) [place Fig. 2 about here] In contrast to point demand or flow demand, taxi demand is based on a client's plan to travel from some origin to a given destination at some time. Formally, the taxi demand can be defined as the triplet , where t o denotes the beginning time of the demand, (x o , y o ) denotes the spatial location of the origin, and To accommodate a travel demand, a taxi picks up a client at the origin, makes a dedicated transit to the destination, and drops off the client. Formally, taxi travel can be represented by extending the taxi demand to the quintuplet , where the path denotes the driving route from the origin to the destination, and t d is the arrival time at the destination. All taxi demands and taxi travels in the city are extracted from the massive raw taxi GPS data. To this end, spatial-temporal trajectories are firstly recovered using the map-matching algorithm of Li et al. (2011) . Then, in accordance with changes in a taxi's working status, the origin and the destination of a taxi demand is identified. Based on the time-series GPS records for a taxi listed in The sequence of road links traversed from the origin to the destination is the path, which preserves the effect of numerous factors, such as road conditions, traffic congestion, and drivers' personal preferences. After processing of all raw GPS data, all taxi demands and taxi travel data with exact spatial-temporal information are stored in a database for charging station siting. When substituting a number of ETs into the current oil-based fuel taxi system, both ET drivers and oil-based fuel taxi drivers explore dynamically changing demands to provide good taxi service to the public. If a taxi demand is serviced by an ET, we define the taxi demand as covered by the ET. To identify taxi demands covered by ETs, we model the daily ET lifecycle using the spatial-temporal path tool, which illustrates the spatial-temporal interaction between taxi demands, ETs and charging stations. Fig. 3 gives an example of the spatial-temporal paths of ETs. Following the sequence of ET driver's activities, an ET continues serving taxi demands (TD 1 , …, TD n in Fig.3 ) when the remaining electricity is enough (e.g., after serving TD i in Fig.3) . Otherwise, the ET goes to a charging station. According the charging state of charging station at the arrival time, the charging will be done immediately (l 1 in Fig.3 ) or after an essential waiting (l 3 in Fig.3 ). The details of interactions are described below. [place Fig. 3 about here] With sufficient electrical power, the ET serves emerging taxi demands for the public. An idle ET at a position (x, y) at a time t rationally seeks a taxi request from the emerging demands nearby its current location. To model the competition between taxis, we identify the covered demand from a set of spatially near demands. The roulette wheel selection rule is used to determine which demand will be served by the ET to simulate the uncertainty in actual taxi service. An uncovered demand neighbor list nearby (x, y) after time t is first filled according to distance criteria. Then, a random value within [0, 1] is generated to select the ith nearest demand TD i from the list to serve, as given by equation (2), where a i is the accumulated probability that the ith nearest demand is served in historical taxi serving. Whether or not the current charge state of the ET is sufficient to serve the selected demand TD i is examined before initiation of taxi travel. If the ET's current charge state e to is greater than the threshold required for traveling to the nearest charging station after serving TD i , the demand will be covered. (3), where d td is the length of the corresponding driving path. Otherwise, the taxi demand is rejected and the ET travels to the nearest charging station for battery recharging. The remaining charge capacity when arriving a charging station will be updated according to the travel to the charging station. The charging of an ET at a station is decided by the arrival time and current charge state at the station. If an idle charging stake is found at the station, the charging action will begin at once when ET v arrives at time . The charging duration is determined by the remaining charge capacity , the expected charge capacity and CS. In this paper, we set as a random value within [0.95E, E] to model the diversity of charging decisions. The charging duration tc v of v is given by equation (4). The charging of v will be end at time . Finally, the ET's charge state e v is updated with the value . After charging, the ET will return to serving the taxi demand in the city. In the absence of an idle charging stake at the station, ET v must wait until a charging ET in the station completes its charging action and releases a stake. In this case, the wait time t w for v is equal to the difference between the arrival time and the earliest charging completion time at the station , as given by equation (5), where u denotes a charging ET at a station s and V s denotes the set of charging ETs at s at time T v a . Based upon equations (4) and (5), the charging for v will end at time . After charging, the ET leaves the station and proceeds to serve taxi demands on the roads. Owing to the cyclical demand serving, vehicle charging, and waiting, the siting of charging stations will heavily affect public ET service and the charging service for ET drivers. The STDCLM aims to locate a set of ET charging stations to maximize both the ET service level and the charging service level. The ET service level is indicated by the ET covered taxi demands, and we measure it according to the total distances of the taxi travel of all ET covered taxi demands. The longer the total distances, the better is the level of ET service. The charging service level is indicated by the extent to which ET drivers must wait to charge at charging stations, and we measure it according to the total wait time at all charging stations. The lower the total wait time, the better is the level of charging service. It should be mentioned that travel distance/time to located stations is not explicitly included in the STDCLM. Reasons are from two aspects. Firstly, a survey of ETs on taxi drivers in Shenzhen, China, indicates that, because of the lengthy period required for the charging process, drivers care more about the waiting time at stations than the travel time to/from stations. Secondly, as Fig. 3 illustrates, in order to calculate the total taxi travel distances of all ET covered demands, the travel distances to charging stations (D n to the charging station in Fig.3) have been subtracted from the total travel distances. The mathematical formulation of the STDCLM is as below. Subject to: Here, S is the set of candidate locations to site charging stations, Q is the set of spatial-temporal taxi demands, V is the set of ETs, T is the time period, n is the number of stakes in a charging station, M is the number of charging stations to be The objective of (6) is to maximize the ET service level and the charging service level. The expression (km) is the total taxi travel distance of all ET covered taxi demands, indicating the ET service level, and (h) is the value of total waiting time for all ETs, indicating the charging service level. The negative sign and the weight coefficient before are used to adjust the relationship between the ET service and charging service. In this research, we set to the average travel speed of all roads across a whole day in the city reported by the Shenzhen transportation administration, which is 26 (km/h), with the goal to transform waiting time into travel distances for the second objective. Constraint (7) indicates that each taxi demand can be covered once only by a single ET. Constraint (8) requires that the total number of charging ETs at a given station and time cannot exceed the number of stakes at that station. This constraint introduces the temporal competition between ET charging actions. Constraint (9) specifies that the charging service at a station is available only when that charging station is chosen to be located. Constraint (10) requires that the number of charging stations to be located is equal to M. Constraint (11) indicates that the travel distance of v between consecutive charging events is proportional to the cost electricity over the time period in accordance with the assumption in equation (1). Because and are in the range [0, E], the limitation of the ET range is also specified. Constraints (12), (13), (14), and (15) impose integrality conditions on decision variables. Location problems are difficult to solve due to their inherent complexity. The heuristic algorithm is a promising method for complex location problems. Genetic algorithms evolve to globally optimal solutions for complex optimization problems by simulating natural behavior (Mitchell and Melanie, 1996) . Therefore, this method has been successfully applied to many location problems (Xiao, 2008; Tong and Murray, 2009 ). In the present study, we employ a genetic algorithm to solve the STDCLM. Genetic algorithms involve several components, namely, genome coding, population generation, fitness function, and selection, crossover, mutation, and stopping criteria. For the STDCLM, we use an integer representation to encode sited locations as a chromosome. The code length of a genome is equal to the number of located stations. The bit value indicates which the candidate places has been selected for a charging station. The objective function of the STDCLM (equation (6)) serves as the fitness function of each individual. An initial population of selected locations is randomly generated. At each generation, the roulette wheel selection is conducted according to the fitness value. Crossover is accomplished by the single point crossover operator. Mutation is employed at some random bits. Simulated evolution is repeated until the maximum number of iterations have been reached or the objective (equation (6)) has not been improved over a fixed number of iterations . Finally, the optimal results are reported, and the corresponding charging stations are displayed. Details concerning the demand coverage, ET charging, and essential waiting at the located stations are also obtained. Before optimizing the STDCLM, the parameters of genetic algorithm, such as the population size p, the selection rate , the mutation rate , , and , are established after intensive experiments using the parameter tuning method of Coy et al. (2001) . The top-k locations with the greatest taxi demands are generated as candidate places. According to the performance of used ET BYD E6 in Shenzhen, China, we set the maximum travel distance D max to 250 km, the charging speed CS to E/120 min -1 . An initial scenario (S0) with 12 charging stations and 2,000 ETs was designed to assess the proposed approach. The obtained result is analyzed from both spatial and temporal perspective, including the spatial distribution of covered taxi demands, and the temporal patterns of ET serving, charging and waiting behaviors. The impact of charging speed is investigated by solving the scenario S0 with different settings of the parameter CS, from E/240 min -1 to E/60 min -1 . To evaluate the marginal utility of various numbers of sited charging stations, another four scenarios (S1-S4) were also designed and solved. Scenarios S1 and S2 are with 4 and 8 stations, respectively, whereas S3 and S4 are with 16 and 20 stations, respectively. The setting of each scenario, including the name, the number of ETs, the number of located stations, the number of stakes, and the ratio between ETs and stakes, is presented in Table 2 . To evaluate the environmental effect of the ET service, the daily RCE is also estimated using the evaluation model of Barth and Boriboonsomsin (2008) , which estimates the carbon emission per mile of a light-duty internal combustion vehicle according to the running speed. As the ET releases zero carbon emission to air, we measured the ET's RCE with the carbon emission generated by an oil-taxi travelling the same route. So, with the speed information and the travel path obtained from the taxi GPS data, the amount of RCE owing to ET covered taxi demands is calculated. By accumulating all the RCE on road segments, we map the green effect of the ET system based on the number of ETs and the located charging stations. [place Tab. 2 about here]  Experiment and results Spatial-temporal distribution of taxi demands The obtained results from the scenario S0 are summarized in  The spatial distribution of the covered taxi demands by ETs is displayed in Fig. 7 . The results indicate that a relatively small number of stations can support the ET service for the entire city. Most of these demands are spatially aggregated in the downtown area. Some places, like the airport, the railway stations, and ports to Hong Kong also have intensive covered demands. However, much dispersed covered demands are observed in other areas like the north and east Shenzhen. Fig. 8 displays the spatial distribution of the ET covered ratio obtained by dividing the count of ET covered taxi demands to the total demands in the same place in the city, based on Fig.   4b . In contrast to the spatial aggregation observed for the covered taxi demands, the ratio distribution is quite spatially homogeneous. The ratios over most areas of the city are in the range [10%, 20%]. A ratio of less than 10% is observed in a small area in northeast Shenzhen. Ratios greater than 20% are observed for only a few areas at the border of the covered area, where taxi demands are quite few, as shown in Fig. 4b . Therefore, in these places, when two or three demands are covered by ETs, as shown in Fig. 7 , the ratios will be high as shown in Fig. 8 . In addition to the spatial dynamics, the ET service on the road and the charging service at the stations also exhibit highly temporal dynamics. while the total charging time per day decreases from 11,758.3 h to 4,172.5 h and the total waiting time sharply decreases from 4507.7 h to 17.8 h. As the ET spends will spend more time on the roads, the improvement of charging service at stations generates a better ET service on the roads. Total travel distance of covered demands increases from 476, 469.7 km to 662, 930.8 km. [place Tab. 4 about here] Fig. 10 and Table 5 depict the objectives of each scenario and their tendencies as a function of the located stations. With the charging service supply increasing from S1 to S4, the obtained solutions exhibit a uniform improvement in both the ET service on the roads and the charging service at stations. For the ET service, the total length of ET covered travel increases from 403,707.3 km (S1) to 659,167.1 km (S4). For the charging service, the total waiting time reduces from 8,930.3 h with 1,939 waiting actions (S1) to 121.1 h with 498 actions (S4). Meanwhile, the total charging time increases from 4,448.4 h (S1) to 9,836.6 h (S4). The total number of charging actions increases from 2,733 (S1) to 5,777 (S4). The average charging time at the stations also increases from 1.63 h to 1.70 h, which is due to the reduced distance to a station with a greater number of charging stations. It is noteworthy that new stations may induce an increase in the number of waiting actions. As shown in Table 5 , the number of waiting actions at stations is nearly doubled between scenarios S1 (1,939 waiting actions) and S2 (3,619 waiting actions). This is mainly due to the inadequate charging service supply under the conditions in S1, in which each ET charges 1.367 times (i.e., 2,733/2,000) on average with 4 charging stations. With the addition of 4 more stations in S2, the charging service supply increases, and each ET charges an average of 2.52 times (i.e., 5,040/2,000) per day, which also generates an increased number of waiting actions at the stations. Nevertheless, the total waiting time still decreases from 8,930 h (S1) to 4,379 h (S2), as illustrated in Fig. 10 . The average waiting time is also significantly improved from 4.61 (i.e., 8,930.3/1,939) h to 1.21 (i.e., 4,379/3,619) h between scenarios S1 and S2. This truth validates the improvement of the objectives with more charging stations. However, the marginal utility of more located charging stations diminishes. Between scenarios S1 (4 stations) and S2 (8 stations initially appear along main roads in S1 (Fig. 11a) . With increasing number of charging stations, new stations tend to be located in the high density taxi demand areas in S2 (Fig. 11b) and S0 (Fig. 11c) . Finally, new stations are sited at the airport or low density taxi demand areas in northern Shenzhen in S3 (Fig. 11d) and S4 (Fig.   11e ). [place Tab Fig. 12 illustrates the spatial distribution of the daily RCE. In accordance with the ET footprint, reduced RCE is observed over nearly the entire road network. The most prominent effects occur in the downtown area (A), corridors to the downtown area (B), and the highway to the airport (C). Once again, the green effect obtained with more located charging stations diminishes. Between scenarios S1 (4 stations) and S2 (8 stations), the total RCE increases by 104,999.7 kg, and a more uniformly distributed green effect is generated. However, the total RCE only increases by 1,275.1 kg between scenarios S3 (16 stations) and S4 (20 stations) because the charging supply provided by 16 stations in S3 is nearly sufficient for the 2000 ETs used. Differences between the spatial RCE distributions in Fig. 12d and Fig. 12e are also very slight. [place Tab  The electrification of public transportation has been a pioneer in attaining the goal of green transportation. With respect to the electric taxi (ET), one key to success lies in the location of charging stations to provide a high quality ET service for the public and a convenient charging service for ET drivers (Jung et al., 2014) . However, in the dynamics of taxi demand and ET charging, time becomes a crucial factor, which is neglected in current location approaches that consider only spatial issues. In recognition of this limitation, this article has addressed the location problem The main contributions of this research are three fold, as follows. Firstly, a novel location model was presented from the spatial-temporal perspective, which extends current location approach to address dynamic demand rather than static demand. Additionally, the complex interaction between travel demand and transportation service supply has been handled in a spatial-temporal context. Secondly, this research makes use of massive GPS data to support public policy making in transportation sectors, which acknowledges the value of big data and advances towards smart decisions in a highly dynamic environment. Thirdly, the problem of optimizing siting of ET charging stations has been addressed. This work can not only support short-term decision making regarding the use of ETs as a public utility, but can also help to promote the long-term development of the electric vehicle (EV) market. Clearly, the results offered by the proposed approach are of great practical use for ET charging station siting. Nevertheless, the approach also demonstrates some notable limitations. Firstly, the located stations are only aimed at servicing ETs, and private EVs are not considered. In the future, the presented work should be extended towards the fulfillment of the charging requests of all EVs. The second limitation is the neglect of the variability of taxi demand. If taxi service is absent for a time, taxi demand nearby bus stations or metro stations may transfer to the bus or the metro system. Therefore, more public transportation data must be collected and be further involved in the presented work. The third limitation is the disregard for the relation between charging stations and grids. More data regarding grid infrastructure should be collected, and the candidate ET charging station sites should be adjusted accordingly. The last limitation is about the parameter , which is set to the mean travel speed of all roads across a whole day. However, urban traffic varies significantly across space and time , leading to quite different reduced travel distances of the waiting. Hence, a spatial-temporal dependent value should be set according to historical traffic information in the further. This research was supported in part by the National Science Foundation of China
A spatial-temporal demand coverage location approach is used in REF to address the location problem of electric taxi charging stations.
Optimizing the locations of electric taxi charging stations: A spatial–temporal demand coverage approach
Transportation Research Part C-emerging Technologies
Engineering