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p2Charging: Proactive Partial Charging for Electric

Taxi Systems

Yukun Yuan, Desheng Zhang†, Fei Miao§, Jiming Chen∗, Tian He‡, and Shan Lin

Stony Brook University, †Rutgers University, §University of Connecticut, ∗Zhejiang University, ‡University of Minnesota

Abstract—Electric taxis (e-taxis) have been increasingly de-

ployed in metropolitan cities due to low operating cost and

reduced emissions. Compared to conventional taxis, e-taxis re-

quire frequent recharging and each charge takes half an hour

to several hours, which may result in unpredictable number of

working taxis on the street. In current systems, E-taxi drivers

usually charge their vehicles when the battery level is below

a certain threshold, and then make a full charge. Although

this charging strategy directly decreases the number of charges

and the time to visit charging stations, our study reveals that

it also signiﬁcantly reduces the availability of number of taxis

during busy hours with our data driven analysis. To meet

dynamic passenger demand, we propose a new charging strategy:

proactive partial charging (p2Charging), which allows an e-taxi

to get partially charged before its remaining battery level is

running too low. Based on this strategy, we propose a charging

scheduling framework for e-taxis to meet dynamic passenger

demand in spatial-temporal dimensions as much as possible

while minimizing idle time to travel to charging stations and

waiting time at charging stations. This work implements and

evaluate our solution with large datasets that consist of (i) 7,228

regular internal combustion engine taxis and 726 e-taxis, (ii) an

automatic taxi payment transaction collection system with total

62,100 records per day, (iii) charging station system, including

37 working charging stations over the city. The evaluation results

show that p2Charging improves the ratio of unserved passengers

by up to 83.2% on average and increases e-taxi utilization by

up to 34.6% compared with ground truth and existing charging

strategies.

I. INTRODUCTION

Electric taxis have been deployed in large scale in many

cities for public transit with local governments’ support and

incentives, e.g., Chicago [1], New York City [2] and Los An-

geles [3]. For example, in Shenzhen, a city in China, an e-taxi

ﬂeet has passed the business breakeven point since 2013 [4].

Compared to conventional internal combustion engine taxis

which have an average of around 300 miles on a full tank

of gas, e-taxis travel between 60 and 200 miles on a full

charge [5]. So, e-taxis require more frequent recharges. Our

study with real e-taxi data traces shows that an e-taxi recharges

more than three times per day on average. Also, different from

conventional taxis which only need several minutes to ﬁll their

tanks, a full charge of an e-taxi takes as little as 30 minutes

or up to several hours. Moreover, e-taxis usually have to wait

for an available charging point at a charging station, given the

limited number of charging points and stations. As a result,

each e-taxi spends a signiﬁcant amount of idle time at the

charging stations. In fact, [6] shows that 48.75% of e-taxi

drivers spend more than 3 hours at charging stations per day.

Such long idle time at charging stations reduces the avail-

ability of e-taxi service, resulting in unbalanced taxi supply

and passenger demand. Especially, this happens during busy

hours when passengers are waiting on the streets, but e-taxis

are getting charged or waiting to be charged. Therefore, the

timing and duration of each charge of e-taxis are critical to

the quality of the e-taxi service. Our analysis reveals that

most e-taxi drivers charge their vehicles only when their

batteries are low, and more than half of taxi drivers charge

their batteries to full on each charge. Although conducting

full charge reactively can reduce the total number of charges,

it also misses opportunities to serve more passengers, since

during busy hours an e-taxi can ﬁnd a passenger quickly if

it stops charging when its battery is charged sufﬁciently high

but not necessarily full.

To satisfy dynamic passenger demand, we propose a new

charging strategy: proactive partial charging. Proactive partial

charging suggests that an e-taxi can get partially charged rather

than fully charged and get charged before its remaining energy

is running too low. This strategy allows much more temporal

ﬂexibility for scheduling charging tasks so that we can allocate

the taxi supply to match passenger demand and also reduce

waiting time at charging stations. In this paper, we formu-

late the Electric Taxis Proactive Partial Charging Scheduling

Problem and propose a proactive partial charging (p2Charging)

framework to schedule and coordinate when and where to

charge, and how much energy to charge for each e-taxi. The

objectives of our formulation include maximizing satisﬁed

passenger demand and minimizing the cost of charging that

includes the total driving time to charging stations and waiting

time at charging stations for all e-taxis. Our solution utilizes

predicted passenger demand and estimated waiting time at

charging stations to ﬁnd the global optimal charging decisions.

There are a number of research works on electric vehicles

and scheduling algorithms [7], [8], [9], [10], [11], [12]. These

works provide valuable insights into EV charging problems.

For example, Dong et al. [13] provides a scheduling algorithm

to achieve bounded waiting time in the charging station.

However, it adopts the reactive charging strategy, which sched-

ules an e-taxi when its battery is below a ﬁxed level; some

other works [8], [9], [7], [14], [15], [16] employ the full

charging strategy, which assumes every charge is a full charge.

Compared to existing charging solutions, including reactive

full charging [13], reactive partial charging [10], and proactive

full charging [15] strategies, our solution can better balance

Fig. 1: Charging behaviors analysis Fig. 2: Mismatch between Passenger

Demand and E-Taxi Supply

Fig. 3: Charging demand distribution

taxi supply with passenger demand with little overhead.

To the best of our knowledge, our work is the ﬁrst to

schedule e-taxis charges with a proactive partial charging

strategy. Compared to previous charging solutions that use

ﬁxed thresholds to decide the timing and duration for each

charge, actually proactive partial charging is a more generic

type of charging strategy, which can be reduced to reactive

and full charging with special parameter settings.

One issue for conducting partial charge is the increased

number of charges, but actually, the rapid advancements

of battery technology allow for more and more recharges

[17], [18], [19]. Moreover, recent research [20], [21] shows

that deep discharge and high charge current actually shorten

lithium battery life; on the contrary, taking a discharge rate

consistently to 50% can improve the battery life expectancy

to 3 or 4 times compared with 100% discharge.

The contributions of this paper are listed as follows:

•To the best of our knowledge, we are the ﬁrst to pro-

pose the proactive partial strategy for charging e-taxis.

Proactive partial charging allows full charging tasks to be

divided into small partial charging tasks, enabling more

ﬂexible charging schedules and better taxi services with

little overhead.

•We formulate the Electric Taxis Proactive Partial Charg-

ing Scheduling Problem, and model variable battery lev-

els in our formulation. Different from previous taxi charg-

ing works that only consider binary battery levels (empty

and full), our variable battery level modeling provides a

new dimension for scheduling algorithm design.

•The charging process of e-taxis is tightly coupled with the

dispatch process of taxi service. To integrate our charging

solution with existing taxi dispatch systems, we propose

the p2Charge framework that employs a receding hori-

zon optimization approach to coordinate both processes

simultaneously with real-time multi-source data.

•Our study is based on one of the most comprehensive

datasets for taxis that consist of (i) 7,228 regular internal

combustion engine taxis and 726 e-taxis, (ii) an automatic

taxi deal collection system with a total 62,100 records per

day, (iii) charging station system, including 37 working

charging stations over the city, Shenzhen, where our

data is collected. Our data-driven evaluation shows that

compared to ground truth and existing charging strategies,

including reactive full charging [13], reactive partial

charging, and proactive full charging [15] strategies,

p2Charging improves the ratio of unserved passengers by

up to 83.2% on average and improve e-taxi utilization by

up to 34.6% on average.

II. DATA-DRIVEN CHARGING STR ATEG Y ANALYSI S

In existing e-taxi systems, an e-taxi typically requires multi-

ple recharges per day. E-taxi drivers choose when, where, and

how long to charge the car battery based on their experiences.

In this section, we reveal that most drivers practice the reactive

full charging: get a full charge only when the remaining

energy is low. Our data driven analysis shows that such an

uncoordinated greedy charging strategy is inefﬁcient, which

results in mismatch between passenger demand and e-taxi

supply especially during rush hours. The details of the datasets

we used is shown in Section V-A.

We use 20 minutes time slots to partition the datasets. If one

e-taxi driver charges his vehicle when its battery level is below

20% [22], then we consider it as reactive charging. While if

a vehicle’s battery level is above 80% after charging, it is

considered to have a full charge. We calculate the battery level

of each e-taxi by applying an energy consumption model [23].

Figure 1 plots the percentage of reactive and full charging

vehicles of one day. We can see that on average 63.9% of

drivers practice reactive charging and on average 77.5% of

drivers practice full charging. We can also observe that some

drivers’ charging behaviors change during the day that. Most

drivers conduct reactive and full charging in the morning and

evening of a day, possibly due to low passenger demand; while

during 10 am to 12 pm, the percentage of reactive charging

vehicles increases and that of full charging vehicles decreases.

This is because taxis nearly use up energy after trips in the

morning, and drivers can only charge the battery during limited

lunch time, which also conﬁrms the results in research [4].

We also analyze the dynamics of passenger demand and the

percentage of charging e-taxis over time. Figure 2 plots the

number of passengers and the percentage of charging vehicles

over three days, here we use the number of passengers who

were picked up to represent the passenger demand. We have

several observations of Figure 2. The ﬁrst one is the daily

passenger demand and vehicle charging patterns are similar

2

0

Remaining

Energy

Passenger

demand

Time

Time

100%

Inactive period

Proactive partial charging

Reactive full charging

Fig. 4: Comparison of reactive full and proactive partial

charging

over these days, most e-taxis get charged at night and get

on the road during the day. The second observation is while

the passenger demand is consistently high during the day, the

percentage of charging vehicles varies signiﬁcantly over the

day. We can see clear mismatches between passenger demand

and working taxi supply in the afternoon and evening hours, as

highlighted in grey in the Fig. 2. This is because many e-taxis

get complete discharged after the morning hours, then they

have to get charged one by one at limited charging stations.

In addition, every one of 37 working charging stations is

regarded as the center of one region and any location in the

city belongs to the region with the nearest center. We analyze

the geographical distribution of charging demand. Since the

number of charging points varies in different regions, we

use the ratio between total charging requests and the number

of charging points in the region as a metric, called average

charging load. Figure 3 plots the average charging load in

all the regions. We can see charging load varies a lot among

regions, e.g., the average charging load of region 5 is nearly 5.1

times larger than that of region 25. This suggests that charging

demand is unbalanced in different regions, it is also important

to balance the charging demand across different regions to

reduce e-taxis’ waiting time at charging stations.

III. p2CHARGING OVE RVIEW

A. Proactive Partial Charging Strategy

To address the mismatch between passenger demand and e-

taxi supply, it is essential to employ a new charging strategy:

proactive partial charging. Proactive partial charging divides

full charging tasks into small partial charging tasks and allows

ﬂexible charging schedules to adapt taxi supply to spatiotem-

poral dynamic passenger demand, therefore improving e-taxis

ﬂeet’s service quality with little overhead.

Figure 4 shows an example to demonstrate the key idea

of proactive partial based charging schedules. We can see that

with the reactive full charging strategy (straight line), an e-taxi

operates until its battery depletes and then goes to a charging

station to get a full charge. But when the passenger demand

starts rising during the rush hours, the taxi is receiving a

full charge and stays inactive, missing opportunities to pick

up more passengers while reducing taxi supply on the street.

On the contrary, with the proactive partial charging strategy

(dashed line), a taxi does not need to wait long periods until

Taxi supply &

passenger demand

model

Charging

supply & demand

model

Charging Taxi SupplyCharging Demand

Taxi Dispatch and Charging Scheduler

Passenger Demand

Passenger

Mobility

Passengers

Charging Supply

Charging Stations E-Taxis

Pickup & Delivery

Taxi

Mobility

&Status

Real-time

Charging

Decisions

Fig. 5: p2Charging framework

its battery depletes or is fully charged. To prepare for the rush

hour, it can get charged for a period even before its battery

is not depleted. So, it will have a sufﬁcient amount of energy

to operate through the rush hours to pick up more passengers.

Plus, it can stop charging when passenger demand increases

even when its battery is not fully charged. Compared to

reactive full charging, the ﬂexible timing and variable duration

of charging allows us to make much more efﬁcient charging

schedules, to match taxi supply with passenger demand. We

note that an individual e-taxi can be carefully scheduled to

match passenger demand in rush hours even with reactive full

strategy. However, when all e-taxis practice this strategy, they

have to queue up at a charging station, which has a limited

number of charging points, resulting in an even longer inactive

period and reduced taxi supply due to the long waiting period.

B. p2Charging Architecture

Based on the proactive partial charging strategy, we design a

p2Charging framework to schedule and coordinate the charg-

ing tasks of all e-taxis. Figure 5 shows an overview of the

p2Charging architecture. This architecture is designed based

on the existing e-taxis systems of metropolitan cities, in which

e-taxis are equipped with networked GPS, fare meter, and

communication devices to upload real-time status, e.g., current

location and occupancy status to a dispatching center for

monitoring and dispatching purposes [24], [25], [26], [27].

In p2Charging, taxi scheduler periodically updates the status

of current working e-taxis, e.g., location, remaining energy and

occupancy status, according to the uploaded e-taxis’ status and

then schedules when, where and how long to charge them

to meet spatiotemporal passenger demand. E-taxis follow the

charging decisions obtained from the taxi scheduler to charge

their battery. The taxi scheduler uses both passenger demand

and taxi supply model and charging supply/demand model to

make scheduling decisions.

p2Charging is driven by real-time multi-source data, which

is provided by existing infrastructures, including e-taxi system

and charging stations. These datasets contain rich spatiotem-

poral information about passenger mobility patterns and the

demand and supply in either urban taxi serivce or charging

system. To integrate this information into real-time scheduling,

3

p2Charging employs a receding horizon control (RHC) frame-

work to adapt charging decisions based on both current and

future passenger demand and charging supply. Our framework

allows taxi scheduler to specify multi-objective optimization

goals under the charging system constraints and taxi system

requirements. p2Charging makes decisions for a group of

e-taxis simultaneously by solving an optimization problem

repeatedly at each iteration step of the RHC framework and

then updates charging commands periodically. The objectives

of p2Charging are: (i) meeting dynamic passenger demand

with supply in both spatial and temporal dimensions; (ii) min-

imizing the charging cost, e.g., idle driving time to charging

stations and waiting time at charging stations.

IV. PROACTIVE PARTIAL CHARGING PROB LE M

FOR MU LATI ON A ND ALGORITHM DESIGN

In this section, we formulate the e-taxi proactive partial

charging problem that decides charging schedules for each

e-taxi. Informally, our goal is to meet dynamic passenger

demand in spatial-temporal dimensions as much as possible

and minimize cost related to scheduling e-taxis for charging.

To address this problem, we design a receding horizon based

scheduling algorithm that utilizes predicted passenger demand

and waiting time at charging stations to ﬁnd the global optimal

charging schedules for all e-taxis.

Deﬁnition 1 (Proactive Partial Charging Scheduling Problem

(P2CS P )).Given the spatiotemporal distribution of passen-

ger demand, the location of charging stations and the number

of charging points at each charging station, and initial energy

status of all e-taxis in a city, how to decide when, where and

how long each e-taxi should be charged for serving as many

passenger as possible while minimizing the idle time to travel

to charging stations and waiting time for free charging points

at charging stations.

The formal objectives, constraints and mathematical formu-

lation will be introduced in the following subsections.

A. E-taxi network

We discretize time and space. Given current time slot t, we

consider future mtime slots for e-taxis charging scheduling,

where one time slot is indexed by k,(k=t, ..., t +m−1).

Suppose that the entire area of a city is partitioned into n

regions according to some speciﬁc methods, such as adminis-

trative sub-districts [28], grid ﬁle [29] and quad-tree [30].

Each e-taxi has one of three states at any time slot: working,

waiting, and charging, where working means the e-taxi is on

the road to search or deliver passengers, waiting indicates the

e-taxi is waiting for a free charging point at a charging station,

and charging represents that the e-taxi connects to a charging

point to charge its battery.

Here the remaining energy of an e-taxi is discretized into

Llevels. If an e-taxi works for one time slot, its remaining

energy will decrease L1levels. L2represents the number of

energy level increase if an e-taxi is charged for one time slot.

The remaining energy does not change under waiting state.

Decision variables: In our problem, taxi scheduler needs to

decide when, where and how long to charge the battery, which

should be reﬂected on the decision variables. To represent

when and where to charge, we deﬁne Xk

i,j as the number of

e-taxis dispatched from region ito jduring time slot kfor

charging. The e-taxis with different initial energy level have a

different range of charging duration. Given the initial energy

level l, the maximum energy level Land the number of energy

level increased when charged for one time slot L2, the possible

charging duration qis within [1,⌊(L−l)/(L2)⌋], meaning that

if the initial energy level is larger than L−L2, the taxi will not

be charged for one time slot. Finally, we extend the decision

variables from Xk

i,j to Xl,k,q

i,j to describe how many l-th energy

level e-taxis are dispatched from region ito jduring time slot

kfor charging qfuture time slots.

Xl,k,q

i,j shows the consideration of proactive and partial

charging simultaneously. The range of l,[1, L], demonstrates

that e-taxis with any energy level are considered for charging,

showing proactive charging. Given the initial energy level l,

all possible charging duration is considered, reﬂecting partial

charging.

B. Passenger demand and taxi supply

The key objective of e-taxi service is to meet passenger

demand with sufﬁcient taxi supply. In e-taxi networks, taxi

supply varies since e-taxis become out of service during its

charging duration. In this subsection, we model passenger

demand, taxi supply, and how charging schedules affect taxi

supply.

Passenger demand: With historical dataset of taxi GPS and

passenger transaction, we extract dynamic passenger demand

information, such as passenger demand during rush or non-

rush hours and in busy areas. We assume that during time

slot k, the passenger demand that we want to serve by current

available e-taxis at region iis denoted by rk

i. These are the

demands that we want to meet during time slot t, ..., t +m−1

with current available e-taxis.

Taxi supply: We study how taxi supply changes with

charging decisions. Vl,k

i, Ol,k

i∈R+are deﬁned as the number

of vacant and occupied l-th level e-taxis at region iat the

beginning of time slot kbefore being dispatched for charging

respectively. At each step of iteration, we ﬁrst update the real-

time sensing information, such as GPS locations, occupancy

status, and energy status of all e-taxis, and Vl,t

iand Ol,t

iare

provided by real-time data. Let Sl,k

ibe the total number of

available e-taxis at the l-th level within region iduring time

slot kafter scheduling.

Sl,k

i=Vl,k

i−

n

j=1

⌊(L−l)/L2⌋

q=1

Xl,k,q

i,j , k =t, ..., t +m−1

Vl,k+1

i=

n

j=1

P vk

j,iSl+L1,k

j+

n

j=1

Qvk

j,iOl+L1,k

j+Ul,k+1

i

Ol,k+1

i=

n

j=1

P ok

j,iSl+L1,k

j+

n

j=1

Qok

j,iOl+L1,k

j(1)

4

where P vk

j,i, P ok

j,i, Qvk

j,i, Qok

j,i ∈[0,1] are region transition

matrices describing the taxis’ mobility pattern between dif-

ferent regions during time slot k:P vk

j,i(P ok

j,i)describe the

probability that one vacant taxi starting from region jat the

beginning of time slot kwill travel to region iand become

vacant (occupied) at the beginning of time slot k+1. Similarly,

Qvk

j,i(Qok

j,i)describe the probability that one occupied taxi

starting from region jat the beginning of time slot kwill travel

to region iand become vacant (occupied) at the beginning

of time slot k+ 1. Both current free and occupied e-taxis

are considered for charging during future mtime slots. The

region transition matrices are learned from historical data by

frequency theory of probability, and satisfy that:

n

i=1

P vk

j,i +P ok

j,i = 1,

n

i=1

Qvk

j,i +Qok

j,i = 1

Note that previous work has developed multiple ways to

learn passenger demand and taxi mobility patterns [31], [32],

[33]. With perfect knowledge of passenger demand and taxi

mobility patterns, we can set a large receding control horizon

to control charging behaviors in a long time period. However,

it is hard to have perfect predictions practically, since large

accumulated prediction error over time may affect the perfor-

mance negatively.

In Equation 1, Ul,k

i∈R+is the number of e-taxis which

ﬁnish charging at the beginning of time slot kin region iwith

energy level l. Here, we assume that once an e-taxi ﬁnishes

charging in region i, it will be ready to pick up passenger

at the beginning of next time slot. It is clear that Ul,k

iis

related to charging demand Xl,k,q

i,j and charging supply pk

i,

and taxi supply is considered with charging demand/supply

simultaneously. We will introduce how to calculate Ul,k

iin

the following charging demand/supply part.

C. Charging demand and supply model

With limited charging infrastructure distributed in the city,

an e-taxi’s waiting time is affected by the number of e-taxis in

front of it at the charging station and their charging duration.

In this subsection, we model the relation between charging

demand and supply, and how to derive waiting time based on

charging demand and schedules.

Charging supply: Although there are ﬁxed number of

charging points located in each region, the number of free

charging points may vary from time slot tto t+m−1due

to existing waiting or charging e-taxis at charging stations.

Let pk

idenote the number of free charging points in region

iduring time slot k. At the beginning of time slot t, taxi

scheduler updates the existing charging demand from current

waiting or charging e-taxis in each region according to e-

taxis’ GPS trajectory and previous charging decisions. Then

pk

iis equal to total number of charging points minuses existing

charging demand in region iduring time slot k. We note that

in existing infrastructure, charging stations are built over the

city according to the same standard and each charging station

may have different number of charging points.

Charging demand: With the assumption that all e-taxis

follow charging decisions, charging demand consists of ex-

isting charging demand in each region and future charging

demand decided by taxi scheduler at the beginning of time

slot t,i.e.,Xl,k,q

i,j . The existing charging demand is considered

when updating charging supply, and our problem decides the

future charging demand with constrained charging supply pk

i.

According to the charging decision Xl,k,q

i,j , we deﬁne Dl,k,q

i

as the number of l-th energy level e-taxis dispatched to region

iduring time slot kwith qtime slots charging duration, where

Dl,k,q

i=

n

j=1

Xl,k,q

j,i (2)

Waiting time estimation: Due to a limited number of

charging points in each region, e-taxis may need to wait

for a free charging point. Here we consider all the charging

points homogeneous, since currently local authorities built all

charging points and e-taxis with the same standards [34], [35].

According to existing charging practices, if e-taxis are

dispatched to the same region during different time slots, they

are scheduled by ﬁrst-come, ﬁrst-serve. In the same time slot,

they are scheduled by the shortest task ﬁrst, meaning that

the e-taxi with shorter charging duration is scheduled with

higher priority. For simplicity, we assume that if one e-taxi is

dispatched to one region at the beginning of a time slot, it will

arrive within this time slot. Later we introduce one constraint

to make sure that e-taxis will not be dispatched to a region

that they cannot arrive within one time slot.

To represent the charging ﬁnish time of e-taxis, we deﬁne

Yl,k,q,k′

ias the number of e-taxis that are dispatched to

region iduring time slot kand ﬁnish charging qtime slots

by the beginning of time slot k′. For l-th energy level e-

taxis dispatched to region iat time slot kfor charging

qtime slots, they may not ﬁnish charging by the end of

optimization time horizon, and this number is denoted as

Dul,k,q

i=Dl,k,q

i−t+m

k′=k+qYl,k,q,k′

i. Then we constrain that

Dul,k,q

i≥0, meaning:

Dl,k,q

i−

t+m

k′=k+q

Yl,k,q,k′

i≥0,

n

j=1

Xl,k,q

j,i −

t+m

k′=k+q

Yl,k,q,k′

i≥0

For e-taxis that satisfying the deﬁnition of Yl,k,q,k′

i, ac-

cording to the scheduling discipline, some e-taxis should be

charged before them, and we deﬁne the number of e-taxis with

higher charging priority than them as Dbk,q

i:

Dbk,q

i=

k−1

k1=t

L

l=1

⌊(L−l)/L2⌋

q1=1

Dl,k1,q1

i+

L

l=1

˜q

q1=1

Dl,k,q1

i(3)

where ˜q= min{q−1,(L−l)/L2}. The ﬁrst part represents

the number of e-taxis dispatched to region ibefore time slot k

and the second part denotes the number of e-taxis dispatched

to the same region iduring the same time slot kwith shorter

charging duration.

If some e-taxis reach region iat time slot kwith charging

length qand ﬁnish charging at time slot k′, there should be

an amount of e-taxis which ﬁnish charging before time slot

k′−qand arrive at region ino later than time slot k. Such

5

amount of e-taxis is denoted as Df k,q,k′

iand calculated by:

Df k,q,k′

i=

L

l=1

k−1

k1=t

ˆq

q1=1

k′−q

k′

1=k1+q1

Yl,k1,q1,k′

1

i

+

L

l=1

¯q

q1=1

k′−q

k′

1=k+q1

Yl,k,q1,k′

1

i(4)

where ˆq= min{⌊(L−l)/L2⌋, k′−q−k1}and ¯q=

min{⌊(L−l)/L2⌋, k′−q−k, q −1}. In Equation 4, the ﬁrst and

second part represent the number of e-taxis that ﬁnish charging

before (k′−q)and are dispatched to region ibefore and at k

respectively. In summary, for e-taxis satisfying Yl,k,q,k′

i, at the

beginning of time slot (k′−q), the number of e-taxis that are

still connected with one charging point is: Dbk,q

i−Df k,q,k′

i.

Considering the limited number of charging points, we have

the following constraint:

Dbk,q

i−Df k,q,k′

i+

L−q×L2

l=1

Yl,k,q,k′

i≤pk′−q

i(5)

Therefore, we consider the taxi supply provided by charged

e-taxis, Ul,k

iin the previous passenger demand and taxi supply

model:

Ul,k

i=

⌊(l−1)/L2⌋

q=1

k−q

k1=t

Yl−q×L2,k1,q,k

i(6)

D. Problem formulation

According to the problem statement in Deﬁnition 1, we

want to schedule e-taxis for charging with satisfying as many

passengers as possible and minimizing the idle driving time

and waiting time for a free charging points. The decision vari-

ables have already been studied previously and we formulate

the objectives, constraints and mathematical description of our

problem in the following part.

Objective: Satisfying the demand by allocating taxi supply

across the network in spatial-temporal dimensions is one type

of service quality metric in taxi dispatching system [36], au-

tonomous mobility-on-demand system [25], [37] and subway-

bus scheduling [38]. Whereas, because of the large pas-

senger demand during peak hours, such as 8:00∼9:00 and

17:00∼19:00, the supply that taxi network can provide may

not satisfy the passenger demand. In this work, we consider

the number of unsatisﬁed passengers in each region during

each time slot as the measurement of meeting demand with

supply, denoted by max{0, rk

i−Sk

i}, where Sk

i=L

l=1 Sl,k

i.

The objective of meeting demand with supply in both spatial

and temporal dimensions is formulated as:

Js=

t+m−1

k=t

n

i=1

max{0, rk

i−

L

l=1

Sl,k

i}(7)

We aim to minimize this objective function.

Besides satisfying passenger demand, we also consider min-

imizing the cost of scheduling e-taxis for charging, including

the idle driving time to charging stations and waiting time for a

free charging point. Given the spatial structure of one city, we

deﬁne Wk

i,j ∈Ras the weight matrix describing the driving

time from region ito region jduring time slot k, which can

be estimated more precisely by incorporating historical and

real-time data [39], [40]. Then the total idle driving time to

charging stations is:

Jidle =

t+m−1

k=t

L

l=1

n

i,j=1

⌊(L−l)/L2⌋

q=1

Xl,k,q

i,j Wk

i,j (8)

For e-taxis satisfying Yl,k,q,k′

i, their waiting time for one

free charging point is k′−q−k. Meanwhile, for the e-taxis

which do not ﬁnish charging by the end of time slot t+m−1

(the beginning of time slot t+m), we use t+m−k−q+1, the

lower bound of waiting time of these e-taxis as their waiting

time. In conclusion, the total waiting time is:

Jwait =

i,l,k,q,k′

Yl,k,q,k′

i×(k′−q−k)

+

i,l,k,q

Dul,k,q

i×(t+m−k−q+ 1)

Constraints: The distance every e-taxi can travel during one

bounded time slot is also bounded, due to limited speed and

trafﬁc conditions. We deﬁne one constraint parameter, ck

i,j ∈

{0,1}, such that ck

i,j = 0, if region jcan be reached from

region iwithin time slot k, otherwise, ck

i,j = 1. Then the

following constraint

Xl,k,q

i,j ck

i,j = 0, l = 1, ..., L (9)

represents that if region jcannot be reached from region

iduring time slot k, the number of scheduled e-taxis for

charging should be 0.

For the e-taxis, the operation sustainability is one major

concern. E-taxis’ batteries discharge while driving and they

should have enough energy to be operated on the road.

With the assumption that the charging behaviors of each

e-taxi follow the decisions of our charging scheduler, our

scheduling decisions should ensure that the low energy e-taxis

are charged. The following constraint

Sl,k

i= 0, l = 1, ..., L1(10)

ensures that the low energy e-taxis l≤L1at each region

during each time slot are not used to pick up passengers in

case of using up energy during one time slot on the road.

We deﬁne one weight parameter βwhen summing up the

two objectives: (i) serving as many passengers as possible

and (ii) reducing the idle driving time to charging stations

and waiting time for a free charging point. To summarize,

we formulate the following problem based on the previous

deﬁnitions of decision variables, constraints, and objectives:

min

Xl,k,q

i,j ,Y l,k,q,k′

i

J=Js+β(Jidle +Jwait)(11)

s.t. Xl,k,q

i,j ck

i,j = 0,

Sl,k

i= 0,(1) ∼(6)

E-taxis partial proactive charging scheduling problem, Equa-

tion 11, is a mixed-integer linear programming problem

(MILP) which can be solved by branch-and-bound [41] and

6

Algorithm 1: E-taxi charging algorithm with real-time

information for taxi scheduler

Input: Duration of one time slot: t1minutes; time horizon

mtime slots; parameter L, L1, L2, β

Output: Control decision: Xl,t,q

i, i ∈[i, n], l ∈[1, L], t ∈

[0,24 ∗60/t1], q ∈[1,⌊(L−l)/L2⌋]

1: while At the beginning of each t1-minutes time slot do

2: Update current time slot as t, sensor information for

initial positions and energy status of vacant e-taxis

Vl,t

iand occupied e-taxis Ol,t

i;

Update the charging supply pk

i, driving time matrix

Wkand driving distance constraint parameters , ck

i,j ;

Update the passenger demand of every region to

region pair based on historical data and real-time

sensor information.

3: Solve the charging scheduling problem, Equation 11

to get the charging scheduling decision.

4: Send current time slot’s charging decisions: Xl,t,q

i.

5: end while

6: return Charging decision

cutting-plan [42] algorithms. In our evaluation experiment, the

global optimal solution can be obtained within 2 minutes using

one multi-core PC by an existing solver, Gurobi [43].

E. Charging Scheduling Algorithm

Passenger demand and taxi mobility pattern can be learned

from historical data, but they are not sufﬁcient to calculate

a charging scheduling solution due to dynamic positions of

e-taxis and uncertainty of e-taxis’ remaining energy. Hence,

we design one receding horizon control (RHC) framework to

adjust charging scheduling solutions and incorporate historical

model with real-time sensing information.

The pseudo-code of RHC algorithm is shown in Alg. 1.

Since we only calculate the number of a group of e-taxis,

we assume that e-taxis with the same parameter, i.e., region

i, energy level l, are identical and randomly select one of

them for charging based on the charging decisions. We update

remaining energy of each e-taxi based on one energy consump-

tion model [23] due to lacking such information in our dataset.

However, remaining energy has already been displayed on

the dashboard and e-taxis have communication devices. We

argue that it is easy for an e-taxi company to collect real-

time remaining energy information in the future. To update

charging supply, we ﬁrst infer the current charging demand

based on the charging duration of current charging e-taxis and

charging supply is equal to total number of charging points in

each region minuses the charging demand.

We note that receding horizon control [44] has been used as

a mathematical framework in some of the recent works [25],

[37], [45] to adapt control decisions with real-time informa-

tion. Although we use receding horizon control, the decision

variables, objectives, and constraints are different from pre-

vious research, as they are deﬁned by the speciﬁc charging

scheduling problem that we study. Moreover, our problem con-

siders multiple energy levels and charging duration for each

e-taxi to conduct proactive partial charging which is totally

different from previous work [36], [30] that only dispatching

taxis to different regions for picking up passengers.

V. EVAL UATION

A. Data Description

The datasets we used consists of three parts as follows.

Existing charging station data: the geographical distribution

of existing charging stations is shown in [13]. Within the city,

there are a total of 37 charging stations deployed and in use,

and there is a different number of charging points at each

charging station. We know the GPS location and number of

charging points of each charging station.

Taxis’ trajectory data: every taxi, including e-taxis and

conventional taxis, has networked GPS device that can upload

real-time location information every 30 seconds. One record

in this dataset contains a plate number, a time stamp in

seconds, GPS coordinates and an occupancy status. Based on

this dataset and charging station information, we can infer

when one e-taxi arrives at and leaves which charging station,

and then all e-taxis’ charging behaviors are mined.

Passengers’ transaction dataset: it contains the informa-

tion of each trip, such as when one passenger is picked

up and dropped off, and the plate number of the taxi. By

combining taxis’ trajectory and passengers’ transaction data,

we can estimate the passenger demand in each region over the

city during the different time slot of one day.

B. Methodology

To evaluate p2Charging in a real-world scenario, we use the

dataset described previously to conduct a trace-driven analysis.

We partition the city into regions based on the location of

charging stations, i.e., each charging station is the center of one

region and each location belongs to the region with the nearest

center. From the dataset, we extract the origin/destination

information of each trip, and then get the passenger mobility

information between two regions in each time slot.

Since the dataset contains the GPS trajectory and pick-up

and drop-off information of both regular and e-taxis, we use

the number of passengers each regular taxi picks up to estimate

the passenger demand of e-taxis for any two regions pair in

each time slot. Due to lacking direct information of remaining

energy of each e-taxi, we infer such remaining energy infor-

mation by adopting an energy consumption model [23].

To show the effectiveness of p2Charging, we compare it

with the following existing solutions: (i) Ground: the ground

truth extracted from the dataset; (ii) REC [13]: one reactive full

charging solution whose charging threshold is 15% and one

e-taxi is scheduled to the charging station with the minimum

waiting time; (iii) proactive full charging [15]: given a group

of e-taxis and charging stations, it always selects the e-taxi

and charging station pair with the minimum idle driving time

and waiting time; (iv) reactive partial charging: since [10]

considers electricity price to adjust charging scheduling which

is not considered in our problem, we reduce our p2Charging

with ﬁxed charging threshold (20%) to this category.

7

Fig. 6: Performance improvment over ground truth Fig. 7: Idle and waiting time, and e-taxi utilization

The performance metrics include: (i) ratio of unserved

passengers: the number of unserved passengers over the total

number of passenger demand; (ii) idle time: the sum of the

idle driving time and the waiting time for each e-taxi; (iii) E-

taxi utilization: 1-(idle time+total charging time)/total work-

ing time; (iv) improvement of ratio of unserved passengers:

the performance improvement when comparing the ratio of

unserved passengers by any one of four solutions and that in

ground truth.

C. Results

In the experiment, the length of each time slot is 20 minutes

and then the time horizon is 6 time slots. We assume that the

driving time after one full charge is ﬁxed (300 minutes) and

set the parameters as β= 0.1,L= 15,L1= 1 and L2= 3.

1) Comparison of solutions: Figure 6 plots the performance

improvement of ratio of unserved passengers over time. The

average improvement of REC, proactive full, reactive partial

and p2Charging is 53.6%, 56.8%, 74.8% and 83.2%, respec-

tively. If all taxis are e-taxis and drivers follow the charging

scheduling of p2Charging in the city where our data was

collected, nearly 45,000 more passengers will be served per

day based on the total passenger demand described in [46].

We also have several observations. The ﬁrst one is partial

charging provides the opportunity for more e-taxis to prepare

well for the upcoming high passenger demand duration. A

large number of e-taxis go to charge the battery after the

operation in the morning from 12:00, and p2Charging and

reactive partial charging outperforms the other two solutions

during high passenger demand period, 13:00∼15:00. The

reason is due to partial charging, the ﬁrst arriving charging

e-taxis end charging before 13:00, which also reduces the

waiting time of waiting e-taxis to get enough energy as early

as possible. The second observation is by proactive charging,

e-taxis can charge during low passenger demand period to

be ready for the following rush hours. All four solutions have

similar performance during 7:00∼8:00, and proactive charging

allows some e-taxis to charge the battery during such low

passenger demand period, and then offer more supply during

rush hour, after 9:00. The last observation is considering the

charging decisions of all e-taxis rather than conducting local

optimal decisions can coordinate the charging behaviors of all

e-taxis to achieve better global performance.

Figure 7 plots the idle time length, charging time length

and improvement of e-taxi utilization compared with ground

truth. p2Charging reduces the idle driving time and waiting

time by 81.2%, 75.4% and 64.1% compared with the other

three solutions, respectively. We can conclude that: (i) partial

charging reduces the waiting time of e-taxis by ending the

charging process as early as possible; (ii) proactive charging

decreases the number of waiting e-taxis at charging stations

during high charging demand period. At the beginning of one

day, most e-taxis are close to full energy after charging during

the ﬁrst hours of one day, and they may reach the charging

threshold simultaneously during daytime by reactive charging.

Compared with ground truth, the four solutions achieve a

performance improvement of -0.4%, 10.0%, 19.6% and 34.6%

respectively, meaning that by p2Charging, an e-taxi has 135.4

minutes more on the road to serve passengers compared with

the ground truth if one driver works 12 hours per day.

2) Remaining energy before and after charging: Figure 8

and 9 plot the CDF of remaining energy before and after

charging respectively. Reactive full/partial charging and proac-

tive/reactive full charging are not shown in two ﬁgures, since

they use one ﬁxed threshold to start or end charging, which

will be a curve jump from 0 to 1 at a speciﬁed threshold. For

ground truth, 80% e-taxis’ remaining energy before charging

is no more than 0.28, whereas, that of p2Charging is 0.43.

By p2Charging, 40% e-taxis’ remaining energy after charging

is no more than 0.58 and that of ground truth is 0.8. It

is concluded that compared with ground truth, p2Charging

achieves higher remaining energy before charging and lower

energy after charging by proactive partial charging.

3) Overhead of p2Charging: The overhead of p2Charging

is measured by number of charges. Figure 10 shows the

number of charges of ground truth and by four solutions. We

can see that one e-taxi needs to be charged nearly 9.7 times

on average by p2Charging, which is 2.78 times compared with

that in ground truth. Considering the total energy needed to

be charged for one e-taxi each day does not ﬂuctuate between

different charging strategies, both p2Charging and reactive

partial charging introduce a greater number of charges due

to partial charging, while they introduce less idle time and

higher e-taxi utilization as shown in Figure 7.

4) Impact of β:In Fig. 11 and 12, we show the impact of

parameter βon the amount of picked-up passengers and the

8

Fig. 8: CDF of remaining energy be-

fore charging

Fig. 9: CDF of remaining energy after

charging

Fig. 10: Overhead of p2Charging

Fig. 11: Impact of βon ra-

tio of unserved passengers

Fig. 12: Impact of βon idle

time

Fig. 13: Impact of time

horizon

Fig. 14: Impact of update

period

idle time for charging, including idle driving and waiting time.

We set the βas 0.01, 0.5 and 1.0, the time slot as 20 minutes

and the time horizon as 6 time slots. The observation is that

the performance improvement of β= 0.01 outperforms that

of β= 0.5and 1.0 with average improvement by 4.3% and

13.8% respectively over the day. With the increase of β, the

average idle time decreases, e.g.,β= 1.0reduces the average

idle time by 16.6% and 67.6% compared with β= 0.5and

0.01. It is observed that there is a trade-off between serving

more passengers and reducing idle time duration. To minimize

the idle time duration, i.e., increasing β, e-taxis are scheduled

to charging station deployed in the suburban area, where the

idle waiting time decreases a lot, but few passengers are served

due to low passenger demand in such areas.

One important observation is that the performance improve-

ment of β= 0.01 is worse than that of β= 0.5and 1.0

during 6:00∼8:00 and 12:00∼13:00. The reason behind this

is there exists high passenger demand during 8:00∼11:00

and 14:00∼16:00 and p2Charging focuses on satisfying more

passengers during high passenger demand time periods which

sacriﬁces the performance before such periods with a small β.

5) Time horizon: Figure 13 plots the performance improve-

ment of p2Charging with a different prediction time horizon:

1, 2 and 4 time slots (20, 40 and 80 minutes). The observation

is that the performance improvement of 4 time slots horizon

outperforms that of 1 and 2 time slots horizon with average

24.5% and 4.1% more performance improvement respectively

over the day. The reason for this observation is that a shorter

time horizon means that only passenger demand and vehicles’

energy status in the very recent future is considered, which

misses opportunities to achieve better control. Speciﬁcally,

long time horizon provides the opportunity to prepare the up-

coming rush hours, 8:00∼10:00 and 14:00∼17:00, proactively.

6) Control update period: Figure 14 plots the performance

improvement of p2Charging with different update periods: 10,

20 and 30 minutes. The prediction time horizon is set to be 120

minutes. We can see that shorter update periods can increase

the performance of p2Charging, as it allows more frequent

control decisions for passenger demand, and e-taxis’ dynamic

energy status and location changes: when update period length

is 10 minutes, it achieves 10.3% and 36.3% more improvement

on average compared with 20 and 30 minutes.

7) Evaluation Discussion: Due to charging e-taxis partially,

it may exist that some e-taxis have no enough energy to

bring passengers from origin to destination and then get stuck

somewhere middle of the path. In the simulation, given the

pickup time slot and region, we observe that there are at least

98.0% of e-taxis that can serve all passenger trips.

We assume that all e-taxis have the same battery capacity,

charging speed and energy consumption model, which is

supported by our data that e-taxis are the same car model in

the city where our data was collected, and previous work also

makes the same assumptions [13], [23], [11]. We can extend

our problem formulation with different battery, charging and

energy consumption models to describe each e-taxi.

In our dataset, the number of available e-taxis varies with

time, i.e., new e-taxis joining or leaving the system based on

their working schedules. If such scenario exists during one

time slot, our system can handle it by updating the number

of available e-taxis and recomputing scheduling decisions for

current available e-taxis at the beginning of the next time slot.

We use trajectory to infer the energy consumption of e-taxis.

When one e-taxi is at one charging station, its status, waiting

or being charged is estimated by queueing model described in

the previous waiting time estimation part of section IV-C.

In the evaluation, we estimate the passenger demand for

e-taxis based on the passengers that served by both regular

9

and electric taxis in each time slot. We note that our system

performance is affected by the ratio between number of e-taxis

and number of charging points. The beneﬁts of p2charging will

increase if the ratio decreases.

VI. DISCUSSION

Implementation of p2Charging: We focus on the tech-

nical approach for e-taxis dispatching, instead of providing

incentives for drivers to participate in our dispatching effort.

In practice, based on our interactions with Shenzhen trans-

portation committee (which oversees all taxi companies and

controls taxi medallion), we believe most of the drivers will

participate this effort since all drivers are currently under the

dispatching platform to pick up passengers using smartphones

to make taxi reservations. Since our goal is to reduce the total

charging time for all taxis, the drivers have the obligation for

their taxi companies to follow their dispatching. If most drivers

do not follow our dispatching, we can utilize the concept of

virtual electricity inspired [47] for incentivzing them.

Battery lifetime: Battery lifetime is one concern of e-taxis’

drivers. We adapt proactive partial charging which increases

charging times but will not shorten the lifetime of battery.

Based on [20], [21], deep discharges shorten lithium battery

life and taking a discharge rate consistently to 50% can

improve the battery life expectancy to 3 to 4 times compared

with 100% discharge. [48] shows that partial charging is better

than full charging and deep discharge wears the battery down.

Lesson learned: Based on our results, we learned a few

valuable lessons: (i) partial charging can reduce the waiting

time and offer more ready e-taxis for rush hours; (ii) proac-

tive charging takes the opportunity to charge some extra e-

taxis during non-rush hours to prepare for rush hours; (iii)

coordination of e-taxis charging scheduling can improve the

system efﬁciency by considering global optimal rather than

local optimal solution one by one.

Potential impact: A charging scheduling coordination sys-

tem is beneﬁcial for promoting e-taxis service quality. With the

development of autonomous vehicles, e-taxi companies will

operate and dispatch a group of autonomous e-taxis around

a city to deliver passengers. Hence, our charging scheduling

system is valuable to improve the proﬁt of e-taxi companies

by reducing the impact of charging on serving passengers.

Future work: One of the future works will be incorporating

passenger capacity of each vehicle and ride-sharing scenarios.

The other direction is to consider shared charging infrastruc-

ture among different types of electric vehicles.

VII. REL ATED WORK

There are many works on electric vehicle charging, most

of these works use ﬁxed parameters such as battery levels to

decide when to start and ﬁnish a charge.

In many other works [7], [14], [15], [16], every charge is

considered as a full charge. [7] designs a real-time charging

station recommendation system for e-taxis by large-scale GPS

data mining, where one vehicle is scheduled if it sends a

request no matter the remaining energy. [14] schedules charg-

ing activities spatially and temporally to minimize charging

Reactive Proactive

Partial [10] p2Charging (Our work)

Full [7], [8], [9], [13] [14], [15], [16]

TABLE I: Electric taxis charging strategy comparison

waiting time, where one vehicle is scheduled if minimal

waiting time is achieved. [15] proposes electric vehicles

charging scheduling algorithms to reduce the total charging

time, in which vehicles with distinct remaining energy. [16]

investigates the operations of an e-taxi ﬂeet that accommodates

only those trips for which advance reservations are made and

decides the changeable remaining battery time on arrival at

one charging station. These works provide valuable insights

to the electric charging problem but having the full charge

assumption missing opportunities to serve more passengers

when vehicles are sufﬁcient high but not fully charged, which

is represented by our approach.

There are several papers allows a vehicle to be charged

opportunistically. [10] considers the time-varying electricity

price and electric taxis’ future charging behaviors and then

proposes one charging scheduler to minimize the charging cost

of electric taxis. Each taxi is charged only when electricity

price is below a given threshold and repeats deciding whether

charging the battery every time unit. [11] and [49] consider

the wireless power transmission technology that allows electric

vehicles to be charged going through road segments where

charging devices are installed. A route planner system is

designed to enable in-motion charging for electric vehicles.

In summary, we classify the related work into four different

classes as shown in Table I. Our work is the only one that

proposes a novel proactive and partial charging scheduling for

e-taxis that enable ﬂexible charge schedules and provide better

service quality for taxi passengers. Compared to previous

charging solutions that use ﬁxed thresholds to decide the

timing and duration for each charge, proactive partial charging

is a more generic type of charge strategy, which can be reduced

to reactive and full charging with special parameter settings.

VIII. CONCLUSION

We investigate charging behaviors for e-taxi ﬂeets with

real-world datasets and identiﬁed that most e-taxis conduct

reactive full charges, which misses opportunities to serve

more passengers during busy hours and leads to long idle

time at charging stations. To address this problem, we design

a novel proactive partial charging strategy and show that

much more efﬁcient charging schedules can be realized with

centralized dispatch. So, we design, implement and evaluate

the p2Charging framework for e-taxi ﬂeet to meet dynamic

passenger demand with real-time multi-source data. Trace-

driven simulation demonstrates our solution achieves up to

83.2% performance improvement of the ratio of unserved

passengers and increases e-taxi utilization by up to 34.6%

compared with ground truth and existing charging strategies.

ACKNOWLEDGMENT

This work was funded in part by NSF CNS 1553273, NSF

1849238 and NSFC 61629302 .

10

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