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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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