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Satellite-based communication technology regains much attention in the past few years, where satellites play mainly the supplementary roles as relay devices to terrestrial communication networks. Unlike previous work, we treat the low-earth-orbit (LEO) satellites as secure data storage mediums [1]. We focus on data acquisition from an LEO satellite-based data storage system (also referred to as the LEO based datacenters), which has been considered as a promising and secure paradigm on data storage. Under the LEO based datacenter architecture, one fundamental challenge is to deal with energy-efficient downloading from space to ground while maintaining the system stability. In this paper, we aim to maximize the amount of data admitted while minimizing the energy consumption, when downloading files from LEO based datacenters to meet user demands. To this end, we first formulate a novel optimization problem and develop an online scheduling framework. We then devise a novel coflow-like "Join the first K-shortest Queues (JKQ)" based job-dispatch strategy, which can significantly lower backlogs of queues residing in LEO satellites, thereby improving the system stability. We also analyze the optimality of the proposed approach and system stability. We finally evaluate the performance of the proposed algorithm through conducting emulator based simulations, based on real-world LEO constellation and user demand traces. The simulation results show that the proposed algorithm can dramatically lower the queue backlogs and achieve high energy efficiency.
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This paper has been accepted by the IEEE Transactions on Mobile Computing (TMC) and will appear in an upcoming issue with DOI:
10.1109/TMC.2019.2936202. This is the author-reserved complete version with appendix. Aug16, 2019
Coflow-like Online Data Acquisition from
Low-Earth-Orbit Datacenters
Huawei Huang Member, IEEE, Song Guo, Senior Member, IEEE, Weifa Liang, Senior Member, IEEE,
Kun Wang, Senior Member, IEEE, and Yasuo Okabe, Member, IEEE
Abstract—Satellite-based communication technology regains much attention in the past few years, where satellites play mainly the
supplementary roles as relay devices to terrestrial communication networks. Unlike previous work, we treat the low-earth-orbit (LEO)
satellites as secure data storage mediums [1]. We focus on data acquisition from a LEO satellite based data storage system (also
referred to as the LEO based datacenters), which has been considered as a promising and secure paradigm on data storage. Under
the LEO based datacenter architecture, one fundamental challenge is to deal with energy-efficient downloading from space to ground
while maintaining the system stability. In this paper, we aim to maximize the amount of data admitted while minimizing the energy
consumption, when downloading files from LEO based datacenters to meet user demands. To this end, we first formulate a novel
optimization problem and develop an online scheduling framework. We then devise a novel coflow-like “Join the first K-shortest
Queues (JKQ)” based job-dispatch strategy, which can significantly lower backlogs of queues residing in LEO satellites, thereby
improving the system stability. We also analyze the optimality of the proposed approach and system stability. We finally evaluate the
performance of the proposed algorithm through conducting emulator based simulations, based on real-world LEO constellation and
user demand traces. The simulation results show that the proposed algorithm can dramatically lower the queue backlogs and achieve
high energy efficiency.
Index Terms—LEO-based Datacenter, Online Job-Scheduling, Coflow, Drift-plus-Penalty, Energy Efficiency, Queue Stability.
F
1 INTRODUCTION
ALTHOUGH existing state-of-the-art storage systems
such as NoSQL, NewSQL Databases and Big Data
Querying Platforms [2], can meet the stringent requirements
of users on data storage and management, it is widely
admitted that those storage systems handling cloud op-
erations and data storage are prone to cyber attacks. To
mitigate the widespread global crisis of data insecurity,
several well known IT organizations and companies are
seeking new data storage paradigms to provide secure data
storage and management. For example, a startup company
named Cloud Constellation [3] intends to establish a space-
based cloud storage network SpaceBelt [1], which aims to
offer secure data storage for Internet service providers, large
enterprises, and government organizations [1], [3].
In this paper, we concentrate on space based datacenter
platforms like SpaceBelt that combine LEO satellites and
well-connected secure ground networks. This system allows
users to store their mission-critical data securely in space
H. Huang is with the School of Data and Computer Sci-
ence, Sun Yat-Sen University, 510006 Guangzhou, China. Email:
huanghw28@mail.sysu.edu.cn
S. Guo is with the Department of Computing and Research Institute
for Sustainable Urban Development (RISUD), The Hong Kong Poly-
technic University, Hung Hom, Kowloon, Hong Kong SAR. Email:
song.guo@polyu.edu.hk
W. Liang is with the Research School of Computer Science, Aus-
tralian National University, Canberra, ACT 0200, Australia. Email:
wliang@cs.anu.edu.au
K. Wang is with the Department of Electrical and Computer Engineer-
ing, University of California, Los Angeles, 90095, CA, USA. Email:
wangk@ucla.edu
Y. Okabe is with the Academic Center for Computing and Media Studies,
Kyoto University, 606-8501, Kyoto, Japan. Email: okabe@media.kyoto-
u.ac.jp
instead of ground. The advantages of such a system can
be easily recognized since it can isolate data completely
from the terrestrial Internet and address some jurisdictional
issues [1]. Inspired by the SpaceBelt project, we believe that
in the upcoming space based cloud era, LEO satellites will
undertake more critical roles than just performing as relay
devices for ground core communication networks.
In the LEO based datacenter infrastructure, the data-
storage system is built upon multiple LEO satellites with
each equipped with at least one data-storage server. A
dataset is distributedly stored across the data-storage sys-
tem with multiple duplications, according to a certain re-
dundancy policy. Under such an infrastructure, since the
contact window between a ground station and an LEO satel-
lite is intermitted and the power budget in LEO satellites
is limited, energy-efficient downloading original files from
LEO based datacenters to meet dynamic demands of users
poses a great challenge under time-varying channel condi-
tions. However, existing online algorithms for job schedul-
ing in terrestrial cloud datacenters [4]–[6] are not applicable
to LEO based infrastructures, as they did not consider time-
varying downloading opportunities in their system models.
Motivated by these concerns, we here study an online data-
acquisition problem in LEO based datacenters, while taking
both mobility of LEO satellites and time-varying downlinks
into account.
As energy supplies in LEO satellites are constrained by
limited energy budgets that keep satellites alive and ensure
communications [7], [8], we aim to (1) maximize the amount
of data admitted; and (2) reduce the energy consumption of
data transfer while serving admissions of user requests. To
this end, we first formulate a novel optimization problem
2
for file downloading from a system of LEO based datacen-
ters. We then propose an online scheduling algorithm by
exploiting the drift-plus-penalty optimization technique [9].
Particularly, we design a coflow-like parallel file-download
strategy “Join the first K-shortest Queues (JKQ)” for dis-
patching jobs to satellite queues. To accelerate data transfer
in datacenter networks, the technique of coflow [10], [11] is
invented recently, where a coflow is a collection of parallel
flows serving the same request, and the flow transfer does
not stop until the completion of all its constituent flows. One
advantage of utilizing the coflow-like strategy is shortening
the backlogs of queues residing in LEO satellites, where the
queue backlog is measured by the size (bit) of unfinished
jobs in a queue. Small backlogs in queues are indicators of
system stability. Inefficient control strategies will incur large
queue backlogs [9]. When the system stability is not well
ensured, the queues with large backlogs may lead to packet
overflowing and thus packet losses.
The main contributions of this paper are summarized as
follows.
We study the data-acquisition problem under the
infrastructure of mobile LEO based datacenters, to
meet user requests with security concerns.
To maximize the amount of data admitted while mini-
mizing the energy consumption, we propose an on-
line scheduling algorithm, in which a novel coflow-
like job dispatch scheme is devised to lower queue
backlogs. The optimality of the proposed algorithm,
and its achieved queue stability are analyzed rigor-
ously, by adopting the drift-plus-penalty theory frame-
work.
We also conduct performance evaluation through an
emulator the Satellite Tool Kit. The real-world
trace driven simulations show that the proposed
algorithm achieves much lower queue backlogs and
higher energy efficiency than other the benchmark
algorithms for traditional datacenters.
The remainder of the paper is organized as follows.
Section 2 reviews the related works. Section 3 presents the
system model and problem statement. The online schedul-
ing algorithm is given in Section 4. Section 5 shows the
performance evaluation, and Section 6 concludes the paper.
2 RE LATED WORKS
2.1 Satellite based Communication Networks
Several studies on satellite based communication networks
have been conducted recently. For example, Wu et al. [12]
proposed a two-layer caching model for content delivery
services in satellite-terrestrial networks. Jia et al. [13] studied
data transmission and downloading by exploiting inter-
satellite links in LEO satellite based communication net-
works. Cello et al. [14] proposed a selection algorithm to
mitigate network congestion, using nano-satellites in LEO
based networks.
In industry, several representative LEO satellite based
projects have been announced recently. For example,
OneWeb satellite constellation aims to provide global Internet
broadband services to consumers as early as 2019 [15].
SpaceX has detailed its ambitious plan [16] to bring fast In-
ternet access to the world by deploying a new LEO satellite
system that offers greater speeds and lower latency than
existing satellite networks. Boeing plans to launch a project
GiSAT with 702 satellites [17], which can offer twice the
capacity of previous digital payload designs for Cayman-
Islands.
From these existing exploration efforts, we find that the
LEO satellites have been only considered as supplementary
extensive devices to terrestrial communication networks.
The data storage mechanism under the LEO based data-
centers has not been paid much attention yet. To the best of
our knowledge, together with our previous study [18], this
article is one of the first studies focusing on job scheduling
for such LEO based datacenter infrastructures.
2.2 Green Job Scheduling on Datacenters
Several existing works in literature are leveraging stochastic
optimization framework to study the energy-efficiency is-
sues on terrestrial datacenters [19]–[22]. For example, Deng
et. al. [19], [20] studied how to minimize the operational cost
of datacenters by utilizing multiple renewable energy re-
sources. A MultiGreen online scheduling algorithm [19] was
proposed by applying a two-stage Lyapunov optimization
techinque. Zhou et. al. [21] proposed a fuel-cell powered
cloud utility indexed maximization problem, which jointly
takes the energy cost, carbon emission and geographical
request routing into account. In their subsequent work [22],
they designed a carbon-aware online control framework
by exploiting Lyapunov optimization to find a balance on
the three-way tradeoff between energy consumption, ser-
vice level agreement requirement and emission reduction
budget. The common feature of these mentioned stochastic
optimization frameworks and together with this paper is
that the job scheduling is performed under an assumption
that a priori knowledge of system statistics is not given,
this ensures the practicality when deploying the proposed
online algorithms in the real-world environment.
In the perspective of job-dispatch, although there are
a number of online control solutions in literature for job
scheduling and resource allocation in cloud and datacenter
networks [4]–[6], [23], the work in this paper is essentially
different from them, due to the following reasons. These
existing approaches exploit the “Join in the Shortest Queue”
scheme when allocating jobs to queues under their online
control frameworks. However, if the system controller sends
all arrived jobs at the current time slot to a chosen queue,
such a scheme will increase the queue backlog sharply, thus
degrading the system stability. In contrast, we here develop
a new coflow-like JKQ based scheme that dispatches jobs
to different queues, aiming to jointly improve energy effi-
ciency and maintain lower queue backlogs throughout the
distributed satellites.
Although the proposed coflow-like JKQ based job-
dispatch scheme shares similarities with existing works such
as the “batch-sampling” [24] and “batch-filling” [25] load
balancing algorithms, it should be noticed that the proposed
coflow-like JKQ based scheme is unique under the LEO
based datacenter infrastructure. The essential differences
between them [24], [25] are summarized as follows. First,
3
the “batch-based” algorithms [24], [25] dispatch multiple
redundant copies of each job to a subset of least loaded
queues among the randomly sampled servers. However, due
to the randomness of sampling over all candidate servers,
the globally least loaded server may not be included in the
sampling of each round. In contrast, in the proposed JKQ
based scheme, the target Kleast loaded servers, i.e., the first
Kshortest queues, for each file-downloading request are se-
lected only from those containing the associated file chunks,
rather than from a randomly sampled subset. Second, under
the LEO based datacenter infrastructure, the arrival file-
downloading jobs at each time slot are dispatched to the first
K-shortest queues associated with the currently available
downlink channels. Thus, the set of K-shortest queues are
varying over time due to the mobility of LEO satellites.
This is significantly different from that of the batch-based
algorithms [24], [25].
3 SYSTEM MODEL & PROBLEM STATEMENT
3.1 System Model
Inspired by recent modeling studies on clouds [6], [26], we
consider a discrete time-slotted system, where time slots are
normalized to equal integral units t∈ {1,2, ...T }and the
length of each time slot (denoted by δ) may range from
hundreds of milliseconds to minutes [27] in reality.
We study an LEO-satellite based datacenter network G=
(SG, E(t)), where Sand Gare a set of LEO satellites
orbiting in specific planes and a set of terrestrial ground
stations, respectively. In particular, E(t)is a set of available
time-varying downlink channels at time slot t∈ {1,2, ...T }
between the satellites and the ground stations. Each LEO
satellite is equipped with at least one data storage server,
which is called a LEO server hereafter for brevity.
Referring to [13], [28], we elaborate the following prelim-
inaries of the LEO system considered in our system model.
Because the orbit of each LEO satellite is determined and
known in priori, ground stations periodically contact with a
mobile LEO satellite at predictable time slots. Multiple satel-
lites can be in view of a ground station, and multiple ground
stations could be in the footprint of a mobile satellite. Thus,
a satellite can transmit its data to multiple ground stations
at a time if there are sufficient downlink channels. The
ground station network consists of multiple well-connected
ground stations, which are located at different geographical
locations, and cooperatively download different chunks of a
file from different mobile satellites to meet its user demand.
Let (i, j)E(t)denote a downlink channel between
a LEO satellite iSand a ground station jG, and
let Ct
ij represent the channel state of (i, j)at time slot t.
Note that, the state of each time-varying channel can be
directly measured or predicted [23]. For example, channel
states can be accurately predicted up to one second in future
[29]. Thus, we consider that the channel state is known by
the system controller at the beginning of each time slot and
remains the same without changes at that time slot.
The total frequency bandwidth of each satellite is di-
vided into multiple beams, and each beam then is broken
into narrow channels via the Frequency Division Multiple
Access (FDMA) technology. The overall bandwidth within a
frequency band can increase, by using the frequency reuse
p1
p0p3
p2p4pmax
Under c1
Under c2
Under c3
µ=g(p,c)
Power level (p)
Transmission rate (µ)
µmax
c1, c2, and c3are channel
conditions (c), e.g.,
{“good”, “medium”, “bad”}.
Fig. 1. The classical piecewise rate-power curve [7], [23] with parame-
ters: power-supply level and channel condition.
Q1(t)
Qi(t)
Q|S|(t)
r
arki
iS
Jobs (r,k),
k =1,..,Ky(r)
Admission
control
If r=1
rR(t),
t=1,.. ,T
Arrival
requests
Job
generation
Job dispatch
(a) Admission control and job dispatch
Power allocation
prk (t) on (i,j)E(t)
Q1 (t)
Qi (t)
Q|S|(t)
Time-varying
channels: E(t)
jG
Arrival jobs
Jobs
Jobs
Jobs
ij
iS
Queue in
LEO Sat.
(b) Power allocation on time-varying downlinks
Fig. 2. Decisions for arrived file-acquisition requests: admission control,
job dispatch and power allocation on time-varying downlink channels.
technique such as the orthogonal polarization. The total
number of downlink channels in LEO satellite iSis
represented by σi. Furthermore, the Time Division Multiple
Access (TDMA) [30] has become a mature satellite commu-
nication technology, where a transmission channel is reused
by different transmitters at different time slots.
By defining
Cas a vector of observed channel conditions
of downlinks, the relationship between the power allocation
and the transmission rate can be described by referring a
classical concave rate-power curve g(p, c)[7], [23] as shown
in Fig. 1, where pis the allocated power, and c
Cdenotes
the current channel condition. In reality, linear piece-wise
power function with a finite set
P= [p1, p2, ..., pmax]
of discrete operating power-allocation levels rather than
a continuous concave function, is adopted [7], [23]. Thus,
the transmission rate of an LEO-satellite downlink is deter-
mined by the power level allocated and the current channel
condition. Furthermore, as shown in Fig. 1, the maximum
transmission rate of each downlink is µmax, i.e.,
g(p, c)µmax,p
P , c
C .
Many types of files Y={1,2, ..., Y }are assumed to
4
have been stored at LEO based datacenters in advance.
Each file is with a unique size and stored in multiple copies
throughout all LEO servers, following a certain redundancy
policy, such as repetition based or network coding mecha-
nisms. If the former is adopted, the duplications need to be
randomly distributed over LEO servers for parallel down-
loading; otherwise, the maximum-distance separable (MDS)
code [31] is an option. Under either of the mechanisms, we
define a pair of general storage parameters (Ny, Ky) for any
file yY: each file is duplicated to Nychunks, any Ky
(Ny) chunks among the Nychunks can reconstruct the
original file. Each of the Kychunks of the file is of size Zy.
At the beginning of each time slot t, all arrival data-
acquisition requests (denoted by R(t)) are sent to the sys-
tem controller. For each request rR(t), we define a
mapping function y(r)that returns the file type indicated
by r. The corresponding original file y(r)is with storage
parameters (Ny(r), Ky(r)). Then, all the file chunks with
size Zy(r)are randomly distributed to the |S|LEO servers.
Let f(r)represent the original size of a file y(r), we have
f(r) = Ky(r)·Zy(r).
System controller knows of the storage parameters of
each original file and the locations of its chunks. Specifically,
we use Iy(r)(S)to denote the set of LEO servers that con-
tain the chunks of file y(r). Thus, we have |Iy(r)|=Ny(r),
and any Ky(r)out of the |Iy(r)|chunks can be used to
reconstruct the original file y(r). In addition, to enforce the
Service Level Agreement (SLA) [32] between LEO based
datacenter providers and users, each data-acquisition re-
quest has a maximum tolerable downloading delay, which
is measured by time slots and denoted by Tr,rR(t).
Even if a chunk cannot be completely downloaded within
a contact window between an LEO satellite and a ground
station, the downloading job will continue in the next
contact opportunity through the seamless service handover
technology [33].
During each time slot, if a chunk is under download-
ing, we consider the tight Service Level Agreement (SLA)
[32] between the LEO based datacenter provider and its
users. Here SLA refers to as a contract between the service
provider and its users, serving as the foundation for ex-
pected QoS attributes such as the data amount downloaded
and traffic rate. In our system model, we consider that the
SLA as the desired downloading rate for each chunk should
not be violated while a downlink channel is being exploited
for a chunk-downloading.
3.2 Problem Statement
3.2.1 Three-Step Planning for Each Request
As shown in Fig. 2(a), an arrived file-acquisition request
rR(t)is first filtered by an admission control strategy.
Only if request ris admitted, the system controller will
generate Ky(r)equal-sized chunk-downloading jobs (r, k),
k= 1,2, ..., Ky(r),rR(t)for it. For brevity, we denote
by Kr={1,2, ..., Ky(r)}the job indices for request r. Next,
jobs need to be dispatched to queues, each of which resides
in an LEO satellite. Particularly, to download file-chunks for
each request in parallel, we perform a coflow-like policy on
dispatching jobs to queues. That is, jobs (r, k),kKr,
generated for a same request rR(t)must be dispatched
TABLE 1
Notations and Variables
S;Gthe set of LEO data storage servers;
ground stations
E(t)
the set of time-varying downlink channels
available in time slot tbetween LEO satellites
and ground stations
δ;Tthe length of a time slot; the # of all time slots
Y={1,2,...,Y}, all file types in storage system
R(t)
the set of all arrival requests at the beginning
of time slot t, each wants to access its
associated original file
(Ny, Ky)
storage parameters of an original file yY,
which is duplicated into Nychunks, only Ky
out of Nychunks can recover the original file
Zysize of each chunk for file yY
Trdata acquisition deadline required by r
R(t), measured by time slots
y(r)function that returns the file type demanded
by rR(t)
Kr={1,2, ..., Ky(r)}, the set of job indices for
request r
Iy(r)S, the set of LEO servers containing the file
chunks of original file type y(r),|Iy(r)|=Ny(r)
(r, k)the kth (k= 1, ..., Ky(r)) job generated for
request r
(i, j)E(t), downlink channel between iS
and jG
σitotal number of channels in LEO satellite iS
P;
Cvector of power levels; vector of channel
conditions
αrbinary variable denoting admission control
of rR(t)
f(r)function returning the size of the original file
y(r),f(r) = Ky(r)Zy(r)
arki
binary variable indicating the event that
dispatches job (r, k)to the queue Qi(iS)
at the beginning of t
f(arki )function returning the size of the job (r, k)
if arki = 1; 0 otherwise. f(arki) = Zy(r)·arki .
prk
ij (t)
P, the variable indicating the power
allocated on channel (i, j)E(t), for job (r, k)
g(p, c)transmission-rate function of satellite channels,
with parameters of power level p
Pand
channel state c
C
1{Π}a binary indicator that returns 1 if condition Π
is met; 0 otherwise
to Ky(r)different queues for parallel chunk-downloading.
Notice that, we here consider the preemptive scheduling at
each queue, which implies that a chunk-downloading job
can be interrupted by another job at two consecutive time
slots. The preemptive model also implies that every down-
loading job allocated in each queue will be rescheduled at
the beginning of each time slot until its downloading is
finished. As shown in Fig. 2(b), the third step is to allocate
power to time-varying downlink channels to decide their
transmission rates.
5
3.2.2 Problem Formulation
Now under the aforementioned system model, we need to
make crucial control decisions: (1) admission control to all
file-acquisition requests; (2) workload scheduling for chunk-
downloading jobs; and (3) power allocations for downlink
channels.
Variables: To determine whether a request rR(t)is
admitted, we first define a binary variable αr, which is 1 if
the request is admitted; 0 otherwise. Further, let b
Qi(t)(i
S) denote the set of jobs dispatched to the queue that resides
in satellite iSat time slot t, we define another binary
variable arki (rR(t),kKr)to represent the event
that chunk-downloading job (r, k)is allocated to b
Qi(t). If
arki = 1, we have b
Qi(t)b
Qi(t)∪ {(r, k)}. Each assigned
job (r, k)will be removed from b
Qi(t)once its maximum
tolerant delay Tris violated. That is, the file acquisition of
request ris unsuccessful. In the control of power allocation,
for a job (r, k)b
Qi(t), we define a real-valued variable
prk
ij (t), which is chosen from a vector
P, to indicate the
power allocation level on the downlink channel (i, j)E(t)
at time slot t.
Performance Metrics: For cloud and datacenter net-
works, system throughput is an important performance
metric [5], [6], [8]. Particularly, under the LEO based dat-
acenter platform, we consider a metric that is equivalent to
throughput, i.e., the amount of data admitted in each time slot
t. We denote this meteric by φ(t), which is calculated as
follows.
φ(t) = X
rR(t)
αrf(r) = X
rR(t)
αrKy(r)Zy(r).(1)
black
As mentioned, the data-transmission in satellites is con-
strained by a pre-defined power-budget [7], [8]. If the power
allocation on transmission channels cannot be carefully
scheduled, e.g., allocating too large power level to a down-
link with a bad channel condition, much energy will be
wasted, thus degrading the amount of data admitted. There-
fore, the energy consumption should be minimized when
satellites are transmitting their data to ground stations. The
total energy consumption ζ(t)on data transmission of all
satellites at time slot tis then defined as follows.
ζ(t) = X
iSX
(r,k)
b
Qi(t)X
(i,j)E(t)
δ·prk
ij (t).(2)
Objectives: In order to maximize overall the amount of
data admitted while minimizing the energy consumption si-
multaneously, we define a penalty function. Because we aim
to describe an online system, the objective is to minimize a
time-average penalty that is denoted by P en.
To make the formulation concise, let Πrepresent the
condition g(prk
ij (t), c(t)) >0, which indicates that the down-
loading rate of downlink (i, j)E(t)is larger than 0
with the allocated power prk
ij (t)and channel condition c(t)
at time slot t. Furthermore, since the concept of mean-rate
stability of a queue is used in problem formulation, we give
its definition as follows.
Definition 1. A queue b
Q(t)is mean-rate stable [9] if it
satisfies
lim
t→∞ sup E{| b
Q(t)|}
t= 0,
where |b
Q(t)|denotes the backlog of queue b
Q(t).
We then have the following penalty-minimization for-
mulation.
min P en = lim
T→∞
1
T
T
X
t=1
{β·ζ(t)φ(t)}(3)
s.t. X
kKr
arki αr,rR(t), i Iy(r).(4)
g(prk
ij (t), c(t)) f(r)
δT r
,(r,k)
b
Qi(t),(i,j)E(t),iS. (5)
X
(i,j)E(t)
1{Π}1,(r, k)b
Qi(t), i S. (6)
X
(r,k)
b
Qi(t)X
(i,j)E(t)
1{Π}σi,iS. (7)
X
(r,k)
b
Qi(t)X
(i,j)E(t)
prk
ij (t)pbgt
i,iS. (8)
b
Qi(t)is mean-rate stable,iS. (9)
Variable: αr∈ {0,1}, arki ∈ {0,1}, prk
ij (t)
P ,
rR(t), k Kr,(i, j )E(t),t= 1, ..., T,
where the coefficient βin Eq. (3) represents the weight
(or price) of each unit of energy consumption. Tuning β
also implies changing the relative weighting of the energy
consumption against the amount of data admitted.
Constraint (4) specifies the aforementioned coflow-like
policy, i.e., the number of chunk-downloading jobs dis-
patched to each of its associated satellite iIy(r)is either
1, if αr= 1; or 0 otherwise.
To enforce the SLA described in system model, Con-
straint (5) claims that the download rate at each time slot for
job (r, k)b
Qi(t)needs to be guaranteed, by the required
average downloading rate represented in its right-hand-
side, where a time slot is referred to as a valid one to a
job (r, k)only if the downlink (i, j)E(t)for job (r, k)is
allocated with power, i.e., prk
ij (t)>0and g(prk
ij (t), c(t)) >0.
Further, Constraint (5) also includes the following important
implications. Since the number of downlinks is limited in
each contact window between the satellites and the ground
stations, each downlink channel should be fully exploited
by allocating sufficient power. Thus, an extremely slow
speed to download a chunk in a time slot is not allowed.
Constraint (5) is also to enforce the fact that the system needs
to download the desired file size of each admitted request
rR(t)in a long run. Notice that, the second arguments
c(t)of function g(.)represents the current channel condition
of downlink (i, j)E(t).
Constraint (6) implies that the number of downlink
serving the job (r, k)dispatched to b
Qi(t)should be no more
than 1. Here, 1{Π}is a binary indicator that returns 1 if
condition Πis met; or 0 otherwise. Constraint (7) specifies
that the total number of exploited downlinks at each satellite
iSshould be limited by its total number of channels
σi. Let pbgt
idenote the total power budget of LEO satellite
iSat any time slot, constraint (8) indicates that the total
6
power capacity should be conserved at each satellite while
transmitting data to ground stations. Finally, Constraint (9)
specifies that all queues residing in the LEO satellites need
keeping the mean-rate stable.
4 ONLINE SCHEDULING FRAMEWORK
In this section, we first transform the original problem by
applying the drift-plus-penalty optimization technique [9]
to construct an online scheduling framework, which will
deliver a near-optimal solution to the problem. We then
analyze the optimality of the proposed approach and its
achieved system stability rigorously.
4.1 Problem Transformation
4.1.1 Dynamics of Actual Queues
Denote by Qi(t)the queue backlog as the total size measured
in bits that has not been yet transmitted for jobs in b
Qi(t).
Initially, Qi(1) = 0,iS. The queue dynamics over time for
each satellite is expressed as follows.
Qi(t+ 1) = max[Qi(t)bi(t),0] + Ai(t),iS, (10)
where
bi(t) = X
(i,j)E(t)X
(r,k)
b
Qi(t)
δg(pr k
ij (t), c(t)).(11)
Here bi(t)represents the total diminishing bits of the
backlog in b
Qi, and
Ai(t) = X
rR(t)X
kKr
f(arki ),(12)
denotes the total size of all arrived jobs at time slot twhen
dispatching jobs to queue iS. Note that, f(arki )is a
function returning the size of the job (r, k)if arki= 1; 0
otherwise. That is, f(arki ) = Zy(r)·arki.
4.1.2 Virtual Queues
Next, we transform the original optimization objective
min P en with its constraints into a queue-stability problem
[9].
To enforce all constraints on the optimization objective
min P en, we define the following virtual queues: Mri(t),
rR(t), i Iy(r);Hrk
ij (t),rR(t);Urki (t),(r, k)
b
Qi(t),iS;Di(t)and Xi(t),iScorresponding
to constraints (4)-(8), respectively. Particularly, the virtual
queues need to be updated in the end of each time slot, and
the update equations are defined as follows.
Λ(t+ 1) = max[Λ(t) + λ(t),0], t = 1, ..., T, (13)
where Λrepresents virtual queues Mri,Hr,Urki ,Diand Xi,
respectively. And λdenotes mri,hr,urki ,diand xi, respec-
tively. For brevity, we still use Πto represent the condition
g(prk
ij (t), c(t)) >0when using function 1{g(prk
ij (t),c(t))>0}in
the following. In particular, t= 1, ..., T ,
mri(t) = X
kKr
arki αr,rR(t), i Iy(r),(14)
hrk
ij (t) = f(r)
δT r
g(prk
ij (t), c(t)),(r,k)
b
Qi(t),(i,j)E(t),iS, (15)
urki (t) = X
(i,j)E(t)
1{Π}1,(r, k)b
Qi(t), i S, (16)
di(t) = X
(r,k)
b
Qi(t)
X
(i,j)E(t)
1{Π}σi,iS, (17)
and
xi(t) = X
(r,k)
b
Qi(t)
X
(i,j)E(t)
prk
ij (t)pbgt
i,iS. (18)
We consider the initial conditions satisfying Λ(1) = 0 for
all virtual queues.
Insight: The virtual queues Λ(t)are used to enforce the
constraint λ(t)0, i.e., inequalities (4) to (8). By summing
Λ(t)over time slots t= 1, ..., T , we have Λ(T)
TΛ(1)
T
1
TPT
1λ(t). With Λ(1) = 0, taking expectations on both
sides and letting T→ ∞, it yields: limT→∞ sup E{Λ(T)}
T
limT→∞ sup λ(t), where λ(t)is the time-average expecta-
tion of λ(t)over t= 1, ..., T . If Λ(t)is mean-rate stable,
according to Definition 1, we have limT→∞ sup E{Λ(T)}
T= 0,
which implies that limT→∞ sup λ(t)0. This means that
the desired constraints for λ(t)are satisfied.
We then define Q(t) = {Qi(t),iS},M(t) =
{Mri(t),rR(t), i Iy(r)},H(t) = {Hrk
ij (t),(r, k)
b
Qi(t),(i, j)E(t), i S},U(t) = {Urki (t),(r, k)
b
Qi(t), i S},D(t) = {Di(t),iS}and X(t) =
{Xi(t),iS}as the set of all actual and virtual queues.
Let Θ(t) = [Q(t),M(t),H(t),U(t),D(t),X(t)] represent a
concatenated vector of all actual and virtual queues under
update equations (10) and (13), we define a Lyapunov
function of the LEO based datacenter system as follows.
L(Θ(t)) ,1
2[X
iS
Qi(t)2+X
rR(t),
iIy(r)
Mri(t)2+X
iSX
(r,k)
b
Qi(t),
(i,j)E(t)
Hrk
ij (t)2
+X
(r,k)
b
Qi(t),
iS
Urki (t)2+X
iS
Di(t)2+X
iS
Xi(t)2].(19)
In fact, L(Θ(t)) calculates a scalar volume of queue
congestion in the LEO based datacenters. Intuitively, a small
value of the Lyapunov function implies small backlogs of
both actual queues and virtual queues, and the holistic
system tends to be stable consequently.
4.1.3 Drift-plus-Penalty Expression
To make the system stable, the Lyapunov function (19) needs
to be controlled at each time step to maintain lower conges-
tion in queues. Denoted by ∆(Θ(t)) the one-slot conditional
Lyapunov drift [9], which is defined as
∆(Θ(t)) = E{L(Θ(t+ 1)) L(Θ(t))|Θ(t)}.(20)
Given the current state Θ(t), this drift is the expectation
of changes in the Lyapunov function (19) over one time
slot. Under the Lyapunov optimization framework [9], the
supremum bound of drift-plus-penalty expression is expected
to be minimized at each time slot to achieve the optimal
solution to the proposed original optimization problem.
That is,
min ∆(Θ(t)) + VE{βζ (t)φ(t)|Θ(t)},(21)
7
where Vis a tunable knob denoting the weight of penalty.
We can observe that a positive Vin the objective function
(21) is to minimize the energy consumption and maximize
the amount of data admitted, while maintaining the stability
of holistic system simultaneously. A large positive Vimplies
that the system operator desires a small penalty, i.e., a small
energy consumption and a large amount of data admitted.
We then have the following Lemma.
Lemma 1. Given that the arrival request set R(t), the avail-
able downlink channel set E(t), all the backlogs of both
actual and virtual queues, as well as the job queue b
Qi(t)
(iS)are observable at each slot t, for arbitrary Θ(t),
the Lyapunov drift ∆(Θ(t)) of a storage system in the
LEO based datacenters under arbitrary control policies
satisfies the following result:
∆(Θ(t)) B(t) + X
iS
Qi(t)E{Ai(t)bi(t)|Θ(t)}
+X
iIy(r)X
rR(t)
Mri(t)E{mr i(t)|Θ(t)}
+X
iSX
(r,k)
b
Qi(t),
(i,j)E(t)
Hrk
ij (t)E{hrk
ij (t)|Θ(t)}
+X
(r,k)
b
Qi(t),
iS
Urki (t)E{urki(t)|Θ(t)}
+X
iS
(Di(t)E{di(t)|Θ(t)}+Xi(t)E{xi(t)|Θ(t)}),(22)
where B(t),1
2P
iS
{(P
rR(t)
Zy(r))2+|b
Qi(t)|2σ2
i(δ2µ2
max +
p2
max +1) +|b
Qi(t)|(( f(r)
δT r)2-σ2
i2σi(1+pmax ·pbgt
i)+1) +σ2
i
+(pbgt
i)2}+1
2P
rR(t)
Ny(r)K2
y(r)is a time-varying positive
constant in each time slot. Note that, |.|returns the size
of a set.
The proof of Lemma 1 can be seen in Appendix A.
We then show the upper bound on the drift-plus-penalty
expression of the storage system, by combining objective
function (21) and inequality (22).
∆(Θ(t)) + VE{βζ (t)φ(t)|Θ(t)}
B(t) + X
iS
[X
(r,k)
b
Qi(t),
(i,j)E(t)
Hrk
ij (t)·f(r)
TrδX
(r,k)
b
Qi(t)
Urki (t)
Di(t)σiXi(t)pbgt
i](23)
+X
iS
Qi(t)E{Ai(t)|Θ(t)}(24)
+X
rR(t)
αrE{−V f(r)X
iIy(r)
Mri(t)|Θ(t)}(25)
+X
rR(t)X
kKrX
iIy(r)
E{Mri(t)ar ki|Θ(t)}(26)
+X
iSX
(r,k)
b
Qi(t),
(i,j)E(t)
E{(V βδ +Xi(t))pr k
ij (t)[Hrk
ij (t) +δQi(t)]
×g(prk
ij (t), c(t)) + (Urki (t) + Di(t))1{Π}|Θ(t)}.(27)
4.2 Online Scheduling Algorithm
We notice that, it is impractical to assume the arrival rate
of requests is known in a realistic system setting, because it
is difficult to predict the precise arriving time of a request.
Therefore, existing offline solutions based on known arriv-
ing rates of requests are not applicable to the problem here.
Using an emerging technology such as Software-defined
Satellite Networks [34]–[36] based centralized control mech-
anism, we can design a near-optimal online scheduling
algorithm that yields a solution for the system controller
without a-priori statistical knowledge of arrival rates, while
maintaining low backlogs in all queues, and thus stabilizes
the system in a long run.
Through observing the upper bound of drift-plus-penalty
expression shown from term (23) to term (27), we found that
term (23) yields a constant at time slot t. Thus, minimizing
the objective function (21) is equivalent to minimizing from
terms (24) to (27) meanwhile.
In particular, we first analyze the Ai(t)appeared in the
term (24). Let Ar
i(t)denote the job size for request rR(t)
that is dispatched to queue iS, we have
Ai(t) = X
rR(t)
Ar
i(t),iS. (28)
According to the location of original file indicated by each
request,
Ar
i(t) = PkKrf(arki ) = PkKrarkiZy(r),if iIy(r);
0,otherwise if iS\Iy(r).
(29)
And taking into account constraint (4), we then have
X
iS
Qi(t)Ai(t) = X
iS
Qi(t)X
rR(t)
Ar
i(t)
X
rR(t)X
iIy(r)
Qi(t)X
kKr
arki Zy(r)(30)
X
rR(t)X
iIy(r)
Qi(t)Zy(r)·αr.(31)
Through terms (30) and (31), it can be seen that term (24)
involves both arki and αr, respectively. Furthermore, the
variables αr,arki and prk
ij (t)appear in separate terms (25),
(26) and (27) in the right-hand-side of the drift-plus-penalty
expression, respectively. Therefore, when minimizing terms
(25) and (26), the term (24) can be viewed as an auxiliary.
We then decouple the minimization over drift-plus-
penalty function (21) into a four-phase online scheduling
framework:
1) admission control over arrival requests;
2) job dispatch control;
3) power allocation to downlink channels;
4) and queue update.
Recall that as mentioned in Lemma 1, the online schedul-
ing algorithm needs online observations of all actual and
virtual queues. In the following, we start with the first phase
of online scheduling framework, i.e., admission control of
requests, given an arriving request set R(t)at time slot t.
4.2.1 Admission Control
Notice that, the admission decision variables αr(rR(t))
are independent of each other among the arrival requests.
8
Algorithm 1: Join in the first K-shortest queues (JKQ)
Input : rR(t),Krand αr(obtained from (33))
Output : ar ki (kKr, i Iy(r))
1if αr= 1 then
2Ψr← ∅
3for iIy(r)do
4ψri Qi(t)Zy(r)+Mri (t)
5ΨrΨr∪ {ψri}
6initialize arki 0,kKr, i Iy(r)
7for k= 1 to Ky(r)do
8ψriarg min(Ψr)
9ΨrΨr− {ψri}
10 arki1, where iarg ψri
11 b
Qi(t)b
Qi(t)∪ {(r, k)}
Thus, we have the following subproblem (32) based on the
joint minimization over the terms (24) and (25):
min αr[P
iIy(r)
(Qi(t)Zy(r)Mri(t)) V f (r)] (32)
s.t. αr∈ {0,1},rR(t).
Differentiating the objective function (32) with respect
to αryields the following simple threshold-based admission
control strategy:
αr=
1 : P
iIy(r)
(Qi(t)Zy(r)Mri(t)) V f (r);
0 : otherwise.
(33)
When V > 0, it can be observed that a large Vwill
benefit to admission ratio.
4.2.2 Coflow-like JKQ based Job Dispatch
If a request is admitted, system generates its associated jobs
(r, k), which should be dispatched to the selected queues.
We decide the job-dispatch decisions by reducing the mini-
mization of term (26) to the following subproblem (34). Since
the job-dispatch decisions arki (iIy(r), k Kr, r R(t))
are independent among different requests, the job dispatch
can be conducted for different requests concurrently in a
complete distributed manner.
min arki [Qi(t)Zy(r)+Mri(t)] (34)
s.t. arki ∈ {0,1},rR(t), k Ky(r), i Iy(r).
Recall that the coflow-like parallel download policy is
implied in the definition of virtual queue Mri(t). Thus,
subproblem (34) results in a JKQ scheme for the job dispatch
phase, which is described as Algorithm 1.
The basic idea is to find the first Ky(r)shortest queues in
terms of their backlogs out of the candidate queue set Iy(r)
for the admitted request r, and dispatch Ky(r)jobs to Ky(r)
different chosen queues eventually.
4.2.3 Power Allocation on Downlinks
In each time slot, the overall energy consumption of chan-
nels on all satellites iScan be determined by minimizing
term (27). Because the decision of power allocation on
downlink channels is independent among the satellites, the
energy-minimization can be also realized by the system
controller for each satellite in a distributed manner: the
power allocation at each satellite is implemented individ-
ually without knowing anything from other satellites. Let
(p, c)represent (prk
ij (t), c(t)), we then have the following
subproblem (35).
min Γ(p, c)(35)
s.t. prk
ij (t)
P , (r, k)b
Qi(t),(i, j)E(t), i S,
where Γ(p, c)=(V βδ +Xi(t))prk
ij (t)- [Hrk
ij (t)+δQi(t)]
g(p, c)+ [ Urki (t)+Di(t)]1{g(p,c)>0}.
Problem (35) is a simple linear programming. By par-
tially differentiating Γ(p, c)with respect to pand rearrang-
ing terms, it yields
Γ(p, c)
∂p =V βδ +Xi(t)(Hrk
ij (t) + δQi(t)) g(p, c)
∂p .(36)
Recall that, the rate-power curve g(p, c)is a given
function over power supply levels and channel conditions.
Thus, the values of the term ∂g (p,c)
∂p in each piecewise
power supply level p
Pcan be calculated under the
observed channel condition c. Specifically, let pvary within
P= [p1, p2, ..., pmax], and by Eq. (36), we obtain a vector of
derivative values:
D= [Γ(p, c)
∂p1
,Γ(p, c)
∂p2
, ..., Γ(p, c)
∂pmax
].
Furthermore, the concave function g(p, c)implies that
Γ(p, c)is a convex function. Based on Eq. (36), we have the
valley point (p, c(t)) of Γ(p, c)such that
∂g(p, c(t))
∂p=V βδ +Xi(t)
(Hrk
ij (t) + δQi(t)) .(37)
From Eq. (37), we can see that a large Vimplies a large
slope in the rate-power curve g(p, c), i.e., a large ∂g(p,c(t))
∂p.
On the other hand, through observing from the curve g(p, c)
shown in Fig. 1, a large slope indicates a small power level.
Therefore, equation (37) tells that a large Vleads to a small
optimal power level p.
Now, we can make the power-allocation decisions by
discussing the condition of elements (ele.) in
D:
prk
ij (t)=
pmin,if ele. in
Dare non-negative;
pmax,if ele. in
Dare non-positive;
por p+:arg min{Γ(p, c(t)),Γ(p+, c(t))},if ele.
in
Dvary from negative to positive,
where pand p+are two successive discrete power levels
such that ppp+, where p, p+
P, and pis the
optimal power level denoted by the valley point (p, c(t))
mentioned above.
4.2.4 Queue Update
In the end of each time slot, the actual queues in Q(t)should
be updated by Eq. (10) based on the optimal solutions arki
and prk
ij (t). Similarly, the virtual queues M(t),H(t),U(t),
D(t)and X(t)need to be updated according to Eq. (13) using
all the optimal solutions derived.
9
4.3 Analysis on Optimality and Queue Stability
We now show the optimality and stability of the proposed
online scheduling algorithm. Notice that, the optimality
means the performance gap between the proposed online
algorithm and the theoretical optimum, while the system
stability implies that all the actual and virtual queues resid-
ing the system are stable.
Theorem 1. Given that V > 0, for arbitrary arrival requests
rR(t),t, the proposed online scheduling framework yields
a solution ensuring that:
(a) the gap between the achieved time-average penalty and
the optimal one P enopt is within
e
B
V, i.e.,
lim
T→∞ sup 1
T
T
X
t=1
{βζ (t)φ(t)} − P enopt e
B
V,(38)
where P enopt = lim
T→∞ inf 1
TPT
t=1{βζ(t)φ(t)},
ζ(t)and φ(t)are the resulted energy consumption
and amount of data admitted of the admitted requests
indicated by the optimal solution to the original
optimization (3), and e
B= lim
T→∞
1
TPT
t=1 B(t);
(b) all actual and virtual queues are mean-rate stable.
Recall that Vdenotes the weight of penalty in the
objective function (21). From inequality (38), we can see
that a large positive Vcan lead to a small gap between the
achieved time-average penalty and the optimal one P enopt.
Before we proceed to prove Theorem 1, we have the
following Lemma.
Lemma 2. (Existence of an optimal randomized stationary
policy) For any arrival requests rR(t),t, and for any
 > 0, there is a randomized stationary control policy
ωthat indicates feasible control decisions α
r,a
rki and
prk
ij for i, j, r, k, t, independent of the current queue
backlogs, and gives the following steady state values:
E{d
P en(hα
r, a
rki i, ω(t))} ≤ P enopt +(39)
E{b
mri(hα
r, a
rki i, ω(t))} ≤ , rR(t),iIy(r)(40)
E{b
hrk
ij (prk
ij , ω(t))} ≤ , (r,k)
b
Qi(t),(i,j)E(t)(41)
E{b
urki (prk
ij , ω(t))} ≤ , (r,k)
b
Qi(t),(i,j)E(t)(42)
E{b
di(prk
ij , ω(t))} ≤ , iS(43)
E{b
xi(prk
ij , ω(t))} ≤ , iS(44)
E{b
Ai(a
rki , ω(t))} ≤ E{b
bi(prk
ij , ω(t))}+, iS,(45)
where d
P en,b
Ai,b
bi,b
mri,b
hrk
ij ,b
urki ,b
diand b
xiare the
resulting penalty, arrival rate, service capability, and
other attributes under policy ω.
Lemma 2 can be proved by adopting the similar tech-
niques in the proof body of Theorem 4.5 in [9]. We now
prove Theorem 1 as the follows.
Proof: The proposed online scheduling algorithm
finds a solution that can minimize the right-hand-side of the
inequation (22) over all feasible control decisions, including
the policy ω, in each time slot, we thus have:
∆(Θ(t)) + VE{P en(t)|Θ(t)}
B(t) + VE{P en(t)|Θ(t)}
+X
rR(t)X
iIy(r)
Mri(t)E{m
ri(t)|Θ(t)}
+X
iS
E{[Qi(t)(A
i(t)b
i(t)) + X
(r,k)
b
Qi(t),
(i,j)E(t)
Hrk
ij (t)·hrk
ij (t)+
X
(r,k)
b
Qi(t)
Urki (t)u
rki (t)+Di(t)d
i(t)+Xi(t)x
i(t)]|Θ(t)},(46)
where P en(t),d
P en (hα
r,a
rki i,ω(t)),
A
i(t),b
Ai(a
rki , ω(t)),b
i(t),b
bi(prk
ij , ω(t)),
m
ri(t),b
mri(hα
r, a
rki i, ω(t)),hrk
ij (t),b
hrk
ij (prk
ij , ω(t)),
u
rki (t),b
urki (prk
ij , ω(t)),d
i(t),b
di(prk
ij , ω(t)),
x
i(t),b
xi(prk
ij , ω(t)).
Letting  > 0, and having Lemma 2, the resulting values
of P en(t),A
i(t),b
i(t),m
ri(t),hr k
ij (t),u
rki (t),d
i(t)and
x
i(t)are independent of the current queue backlogs Θ(t).
We then have
E{P en(t)|Θ(t)}=E{P en(t)} ≤ P enopt +(47)
E{A
i(t)b
i(t)|Θ(t)}=E{A
i(t)b
i(t)} ≤ , iS(48)
E{m
ri(t)|Θ(t)}=E{m
ri(t)} ≤ , iS,r R(t)(49)
E{hrk
ij (t)|Θ(t)}=E{hrk
ij (t)} ≤ , (r,k)
b
Qi(t),(i,j)E(t)(50)
E{u
rki (t)|Θ(t)}=E{u
rki (t)} ≤ , (r,k)
b
Qi(t)(51)
E{d
i(t)|Θ(t)}=E{d
i(t)} ≤ , iS(52)
E{x
i(t)|Θ(t)}=E{x
i(t)} ≤ , iS(53)
Plugging (47)-(53) into the right-hand-side of (46) and
taking 0, we get
∆(Θ(t)) + VE{P en(t)|Θ(t)} ≤ B(t) + V·P enopt.(54)
Taking expectations of both sides of (54) and using the
law of iterated expectations,
E{L(Θ(t+ 1)) L(Θ(t))}+VE{P en(t)}
B(t) + V·P enopt.(55)
Summing over t∈ {1,2, ..., T }for T > 1and using the
law of telescoping sums, we have
E{L(Θ(T)) L(Θ(1)}+V
T
X
t=1
E{P en(t)}
T
X
t=1
B(t) + V T ·P enopt.(56)
Rearranging terms and neglecting L(Θ(T)) in the
right-hand-side, we can obtain the inequality for T > 1:
1
T
T
X
t=1
E{P en(t)} ≤ P enopt+1
V T
T
X
t=1
B(t)+ 1
V T E{L(Θ(1))}.
(57)
Then, taking limits of (57) by T→ ∞ proves the part (a).
To prove part (b), we have the following inequation from
10
(56), for all time slots T > 1:
E{L(Θ(T))} − E{L(Θ(1)} ≤
T
X
t=1
B(t) + V T P enopt.(58)
Referring the definition of L(Θ(T)), we know
1
2E{X
iS
Qi(T)2} ≤ E{L(Θ(1)}+
T
X
t=1
B(t) + V T P enopt.
(59)
Then, for iS, we have
E{Qi(T)2} ≤ 2E{L(Θ(1)}+ 2
T
X
t=1
B(t)+2V T P enopt .(60)
Because |Qi(T)|is non-negative, we have E{Qi(T)2} ≥
E{|Qi(T)|}2. Thus, for all slots T > 1:
E{|Qi(T)|} ≤ [2E{L(Θ(1)}+ 2
T
X
t=1
B(t)+2V T P enopt ]1
2.
(61)
Dividing by Tand taking a limit as T→ ∞, we hvae
lim
T→∞
E{|Qi(T)|}
T
lim
T→∞[2E{L(Θ(1)}
T2+2
T2
T
X
t=1
B(t) + 2
TV P enopt]1
2
= 0.(62)
Thus, all actual queues Qi(iS) are mean-rate stable
according to Definition 1. Similarly, the mean-rate stability
of all virtual queues can be proved following the same
routine. This concludes part (b).
5 PERFORMANCE EVALUATION
In this section, we first elaborate the methodology of per-
formance evaluation, including the emulator, trace, metrics
and benchmark algorithms used in simulations. We then
demonstrate the simulation results that can prove the high
efficiency of the proposed algorithm.
5.1 Settings
5.1.1 Emulator of LEO Satellites
We conduct the trace-driven simulations based on the com-
mercial emulator Satellite Tool Kit (STK) to evaluate the
performance of the proposed online algorithm. The STK [37]
designed by AGI (Analytical Graphics, Inc.) is an analytical
tool enabling engineers and scientists to analyze the com-
plex land, sea, air and space assets. Our simulations are
performed on the Globalstar LEO constellation (a typical
system of Walker delta constellation [38]), in which 48
satellites are organized into 8 equal-separated orbital planes
with 6 satellites in each. Satellites in the same plane are
separated from each other with equal angular distance. The
orbital period is 114 minutes.
Through selecting 108 locations globally, we first deploy
ground stations under the Globalstar LEO constellation.
Then, we generate the synthetic channel-state traces with
three states (i.e., good, medium and bad), according to the
weather conditions in all locations obtained from the Inter-
net. The LEO constellation mission starts from 12 July 2017
00:00:00 UTCG (Gregorian Coordinated Universal Time)
and terminates 24 hours later. The length of each time slot,
i.e., δ, is set as 10 seconds. The contact window between any
satellite and any ground station is recorded and analyzed in
each time slot.
5.1.2 Request Trace
Without loss of generality, we adopt YouTube traffic traces
in [39] as user request traces. To integrate the traces with the
Globalstar LEO constellation, we extract a subset of traces
with 48 data-storage servers, ranging in a 24-hour duration.
This set of traces includes 731 file-downloading requests
originated from 430 users. The servers are equally attached
to the 48 LEO satellites. The features of the YouTube traffic
traces can be observed in Fig. 4 that user requests arrive
with drastically different volumes at different time in one
day. The size of files in small-scale ranges between 11,680
bytes and 26,511,812 bytes. In particular, each traffic has
a duration attribute, which is viewed as the download
deadline, i.e., Trin our system model. On the other hand,
the duration of file-downloading task ranges from 0.16
seconds to 625 seconds, and 90% of them are lower than
200 seconds. Notice that, when the number of the user
requests is too few, it can be observed from Fig. 4(a) that
the number of requests on average in each time slot is
less than 20. Thus, the original traces are not suitable to
evaluate the job-allocation performance of algorithms. We
then generate a large-scale of synthesized request traces
based on the original one. For example, the file size and
downloading duration are randomly generated according
to the corresponding features of the original traces. We thus
obtain a synthesized trace set, which includes 7,310 requests
originating from 430 users. In the following, we show the
performance evaluations using the synthesized traces.
5.1.3 Channel Attenuation Coefficient
The number of downlink channels in each satellite is fixed
at 100. The bandwidth of each downlink channel is set
at 1 Megahertz (MHz). To calculate the transmission rate
of downlinks, we adopt the rate-power function g(p, c) =
1MHz ·log(1 + v(c)·p)presented in [7], where v(c)repre-
sents the channel attenuation coefficients determined by the
channel state c. Viewing that the three-state condition model
[29] is adopted for a single downlink, we vary v(c)within
three representative combinations, i.e., {5.03, 3.46, 1.0},{10,
2, 0.1}and {16, 1, 0.01}, to evaluate how the different varying
scales of channel attenuation rate impact the system perfor-
mance. The three values in each combination correspond
to the channel condition cwhen it is observed as “good”,
“medium” and “bad”, respectively. Note that, the varying-
scale of channel attenuation rate describes the changing degree
of transmission rate on downlinks due to the “medium” and
“bad” weather conditions. We can see that the varying-scale
of channel attenuation rate become from weak to strong when
v(c)is set from {5.03, 3.46, 1.0}to {16, 1, 0.01}.
5.1.4 Other Parameters
Furthermore, referring to the parameter settings shown in
[7], the power budget at each satellite is set to 100 Watts.
11
Jobs
Scheduler
Select the first K-
shortest queues to
dispatch one job to
each queue
After dispatch
Dispatch
(a) JKQ based algorithm
Scheduler
Select the shortest
queue and dispatch
Kjobs together
Jobs
After dispatch
Dispatch
(b) JSQ based algorithm [4]–[6]
Scheduler
Select Kqueues
randomly and
dispatch one job
to each queue
Jobs
After dispatch
Dispatch
(c) RJQ based algorithm
Fig. 3. Comparison of three algorithms while dispatching 3 chunk-downloading jobs for an admitted request r, with Ky(r)=3, Ny(r)=6. Notice that,
all the 6 candidate LEO satellites in the right hand side of each illustrative figure hold the required chunks associated with this request.
02468
Time (second) ×104
0
50
100
Num. of request
Synthesized trace
Original trace
(a) Number of requests.
0 10 20 30
File Size (Megabytes)
0
0.5
1
CDF
Original trace
(b) CDF of file size.
Fig. 4. The extracted original YouTube file-download request trace and
its synthesized request trace, which involve 48 data-storage servers and
last for 24 hours in (a). The cumulative distribution function (CDF) of the
original file size requested by users is shown in (b).
The power values in
Pare averagely divided into 10 levels
ranging from 0.1 Watt to 1 Watt. We then deploy redundant
duplications of each file according to the storage parameters
(Ny, Ky)randomly over all LEO servers. Before running
each round of simulation, we randomly shuffle the file
chunks for each file downloading task.
5.2 Metrics
We view the energy consumption and queue backlog as the
major metrics to evaluate the performance of the pro-
posed algorithm. The energy implies the cumulative en-
ergy consumption induced by all jobs. It is measured in
kiloWatt·Second (KW·s). Notice that, the two metrics in-
cluded in the objective function of the original minimiza-
tion problem (3), i.e., amount of data admitted and energy
consumption, are conflict with each other. Therefore, it is
not fair to compare any single perspective of those two
metrics. We then design an integrated performance metric
that is associated with both of them. We call it Watt·Sec per
bit, which denotes the energy consumed by each bit of file
chunks downloaded. It is easy to find that the Watt·Sec per
bit is reversely related to the energy efficiency. A low Watt·Sec
per bit indicates a high energy efficiency of an algorithm.
The length of queue backlogs is an indicator of the queue
stability in system. Thus, a low backlog performance implies
strong stability that an algorithm can bring to system.
In addition, by running at least 20 rounds of simulation
under each parameter setting, we also explore the job com-
pletion ratio (JCR), packet loss, and job waiting time (JWT) in
Jobs
Scheduler
Step2: select the shortest queue
among the ncandidates
Step1: sample n(=3) candidate
queues randomly
A job
After
dispatch
...
Large backlogs can be
induced in some queues.
Dispatch the next
(a) Principle of each job-dispatch in the batch-
based algorithm [24], [25]
(b) Job Completion Ratio (JCR) v.s. batch-size
Fig. 5. Principle and Job Completion Ratio performance of batch based
algorithm [24], [25].
queues as important metrics to evaluate the performance of
each algorithm.
5.3 Benchmark Algorithms
In addition to the aforementioned batch based algorithm [24],
[25], another benchmark named “Join in the Shortest Queue
(JSQ)” based algorithm is used to compare the performance
with the proposed JKQ based algorithm. The JSQ based
online algorithm [4]–[6] has been widely adopted on dy-
namic job scheduling in cloud computing and datacenter
networks. Under our LEO data-acquisition framework, we
implement a JSQ based algorithm, in which job allocation is
12
(a) Admission ratio (b) Energy consumption.
(c) Penalty (d) Watt·Sec per bit
Fig. 6. Time-varying performance comparison among three algorithms,
with 7310 synthesized requests, 48 LEO servers, under β= 1,V= 10,
v(c)={10, 2, 0.1}while cis {“Good”, “Medium”, “Bad”}, respectively.
conducted by the JSQ mechanism. As illustrated in Fig. 3(b),
we argue that the JSQ based algorithm potentially brings
a sharp increase of backlog in the chosen queue for job
dispatching under certain circumstances. In our simulation,
we show this through the comparison of the queue backlogs
yielded by both algorithms.
The other benchmark algorithm is called Randomly Join
KQueues (RJQ) based algorithm. Although RJQ is a random
selection based algorithm, it does not arbitrarily select any
random satellite queues as the job-dispatch destinations
for chunk-downloading jobs. As shown in Fig. 3(c), based
on the (Ny(r),Ky(r)) file-storage strategy, only Ky(r)out
of the Ny(r)satellites containing the encoded file chunks
associated with a file-download request rcan be selected as
the job-dispatch destinations.
5.4 Simulation Results
5.4.1 Job Completion Ratio of Batch based Algorithm
As mentioned in Section 2, the job-dispatch mechanism
of the proposed JKQ based algorithm has significant dif-
ferences from that of the batch-based algorithm [24], [25].
However, we still implement the job-dispatch approach of
the original batch-based algorithm under the emphasized
LEO based datacenter infrastructure. Fig. 5(a) illustrates the
basic idea of the batch-based algorithm, which includes
randomly sampling a specified number (i.e., the batch size
[24], [25]) of candidate queues for each arrived job, and
selecting the shortest queue among the sampled candidates
as the job-dispatch destination. Through varying the batch
size from 1 to 48, and setting the β,V,Nyand Kyto 1, 10, 6
and 3, respectively, we evaluate the job completion ratio (JCR)
performance of the batch-based algorithm. In addition, v(c)
is set to 10, 2, and 0.1 corresponding to “good”,“medium”
and “bad” weather conditions, respectively.
The JCR results of the batch-based algorithm are shown
in Fig. 5(b). We can see that the original batch-based algo-
rithm exhibits a very low JCR performance while varying
the batch size from 1 to 48. Notice that, once the batch
size reaches to 48, all LEO servers will be sampled as the
candidates to choose the least loaded server for job dispatch
in the batch based algorithm. It means that even though all
the LEO servers are examined for finding the queue-shortest
destination server for each job, the JCR has only around
11 % on average. This is because the queue-shortest server
chosen from the sampled set may not contain the required
file-chunk of a specified request.
Since the JCR of the original batch based algorithm is
too low, we omit its performance comparison with other
algorithms in the subsequent results.
5.4.2 Time Varying Performance
In this group of simulations, under the same parameter
settings as we did for Fig. 5, we examine the admission ratio
and energy efficiency yielded by the three online algorithms
illustrated in Fig. 3.
From Fig. 6(a), we find that the admission ratios of
all three algorithms are 100% in the end. This is because
the current parameter settings match the admission control
represented by equation (33). Thus, the amount of data
admitted of all algorithms are same.
Fig. 6(b) demonstrates the cumulative time-varying en-
ergy consumption of the three algorithms while download-
ing data from satellites. It can be seen that the proposed JKQ
based algorithm consumes the least energy comparing with
the other two algorithms.
Fig. 6(c) shows the penalty performance, which is the
objective of the original minimization problem (3). In the
transformed problem (21), not only is the penalty needed to
be minimized, but also the Lyapunov drift ∆(Θ(t)) must be
minimized as well. Interestingly, on one hand, we observe
that the panalties by the JSQ based algorithm grow over
time, showing a contrary descending performance under
the other two algorithms. The reason behind is as follows.
Under the JSQ based algorithm, the chunk downloading
jobs are always dispatched to the shortest queues, where the
queue backlog increases dramatically. Thus, the JSQ based
algorithm has to devote much great efforts to maintain
the Lyapunov drift ∆(Θ(t)) in a low level and to sacrifice
the penalty performance, even though the current weight
of penalty Vis set at 10 while the weight of Lyapunov
drift ∆(Θ(t)) is only 1. On the other hand, the proposed
JKQ based algorithm shows descending and much lower
penalties than that of the other two algorithms.
Fig. 6(d) illustrates the energy efficiency of algorithms.
Recall that energy efficiency is reversely related to Watt·Sec
per bit. From which, we observe that JKQ based algorithm
achieves lower time-varying Watt·Sec per bit than that of the
JSQ and RJQ based algorithms. This observation implies
that the proposed JKQ based algorithm has the highest
energy efficiency against the other two benchmarks. The
insight behind the high energy-efficiency of our proposed
algorithm is that the coflow-like JKQ based job-dispatch
strategy dispatches jobs to a larger number of satellites that
are with good weather conditions for its downlinks or with
lower queue backlogs in a high probability than JSQ and
RJQ do.
5.4.3 Impact of Varying-Scale of Channel Attenuation Rate
As aforementioned, we vary v(c)within three combinations,
i.e., {5.03, 3.46, 1.0},{10, 2, 0.1}and {16, 1, 0.01}, to
evaluate the impact of different varying scales of channel
13
(a) Watt·Sec per bit (b) JCR (c) CDF of packet loss rate (d) CDF of backlog
Fig. 7. Metrics of algorithms when βis fixed at 1, with 7310 synthesized requests, 48 LEO servers, under v(c)={5.03, 3.46, 1.0}if cis {“Good”,
“Medium”, “Bad”}, respectively.
(a) Watt·Sec per bit (b) JCR (c) CDF of packet loss rate (d) CDF of backlog
Fig. 8. Metrics of algorithms when βis fixed at 1, with 7310 synthesized requests, 48 LEO servers, under v(c)={10, 2, 0.1}if cis {“Good”,
“Medium”, “Bad”}, respectively.
(a) Watt·Sec per bit (b) JCR (c) CDF of packet loss rate (d) CDF of backlog
Fig. 9. Metrics of algorithms when βis fixed at 1, with 7310 synthesized requests, 48 LEO servers, under v(c)={16, 1, 0.01}if cis {“Good”,
“Medium”, “Bad”}, respectively.
(a) v(c)={5.03, 3.46, 1}(b) v(c)={10, 2, 0.1}(c) v(c)={16, 1, 0.01}
Fig. 10. Job Waiting Time (JWT) of algorithms when βis fixed at 1 and Vis fixed at 10, under different varying scales of channel attenuation rate.
attenuation rate caused by three types of weather condition.
As illustrated by Fig. 7, 8 and 9, we show the performance
of three algorithms in terms of energy efficiency, JCR, Cu-
mulative Distribution Function (CDF) of packets lost and
CDF of backlog, under three attenuation rate combinations,
respectively.
First, by comparing Fig. 7(a), 8(a) and 9(a), we can see
that the difference of energy efficiency of three algorithms is
small under low varying-scale of channel attenuation rate,
i.e., when v(c)={5.03, 3.46, 1.0}if cis {“Good”, “Medium”,
“Bad”}, respectively. However, under large varying-scale
of channel attenuation rate combinations, i.e., when v(c)
={10, 2, 0.1}and {16, 1, 0.01}, the energy efficiency of
our proposed JKQ based algorithm shows growing benefits
than the other two benchmarks. This feature proves the
robustness of our JKQ based algorithm, because it has the
best energy efficiency under the channel transmission rate is
super sensitive to the weather conditions when v(c)={16,
1, 0.01}if cis {“Good”, “Medium”, “Bad”}, respectively.
Second, from Fig. 7(b), 8(b) and 9(b), we observe that the
job completion ratios of all three algorithms perform very
close to each other. On the other hand, when the varying-
scale of channel attenuation rate becomes large, the JCR of
algorithms degrades a little bit. The reason can be attributed
to that the transmission rate becomes very low when a
channel meets the bad weather condition under the large
varying-scale of channel attenuation rate. Thus, there are
more jobs, which cannot complete their chunk-downloading
14
(a) v(c)={5.03, 3.46, 1}(b) v(c)={10, 2, 0.1}(c) v(c)={16, 1, 0.01}
Fig. 11. Penalty performance of algorithms when βis fixed at 1 and Vis fixed at 10, under different varying scales of channel attenuation rate.
(a) v(c)={5.03, 3.46, 1}(b) v(c)={10, 2, 0.1}(c) v(c)={16, 1, 0.01}
Fig. 12. Watt·Sec per bit performance of algorithms when βis fixed at 1 and Vis fixed at 10, under different varying scales of channel attenuation
rate.
(a) Energy consum. (KW·s). (b) Watt·Sec per bit. (c) Job completion ratio (%). (d) Packet loss rate (%).
Fig. 13. Metric examination among the three algorithms with 7310 requests and 48 LEO servers, while varying βfrom 1 to 10, and the channel
attenuation rate v(c)is set to {10, 2, 0.1}while cis {“Good”, “Medium”, “Bad”}, respectively.
(a) β=1 (b) β=5 (c) β=10
Fig. 14. Backlog comparison of three algorithms while varying βwithin {1, 5, 10}, and setting the channel attenuation rate v(c)to {10, 2, 0.1}if c
is {“Good”, “Medium”, “Bad”}, respectively.
under this situation, than that under a milder varying-scale
of channel attenuation rate.
Third, Fig. 7(c), 8(c) and 9(c) show the CDFs of packet-
loss rates. It can be observed that: (1) the JSQ based algo-
rithm has a lowest packet-loss performance among the three
algorithms; (2) the packet-loss performance of the JKQ based
algorithm is similar to that of the RJQ based algorithm. This
is because the possibility of encountering bad transmission
conditions under JKQ and RJQ based algorithms is higher
than that under the JSQ based algorithm. Associated with
the JCR performance, the packet-loss amount grows when
the varying-scale of channel attenuation rate becomes large.
The reason is same with that as analyzed for the JCR
performance.
We show the CDFs of queue backlogs of algorithms
in Fig. 7(d), 8(d) and 9(d), under three varying scales of
channel attenuation rate, respectively. We see that there is
almost no difference among the three CDF figures, which
indicate that the backlog performance yielded by the three
algorithms is not affected by the varying scales of channel
attenuation rate. It is also worth noting that the proposed
JKQ based algorithm has the lowest backlog performance
among the three algorithms. The reason is very clearly
illustrated in Fig. 3 and omitted here.
Next, by recording all the job waiting time (JWT) of each
job allocated to LEO queues, we compare the JWT perfor-
15
(a) Energy consum. (KW·s). (b) Watt·Sec per bit. (c) Job completion ratio (%). (d) Packet loss rate (%).
Fig. 15. Metric examination among the three algorithms with 7310 requests and 48 LEO servers, while varying Kyfrom 3 to 6, fixing Ny=6, and
the channel attenuation rate v(c)is set to {10, 2, 0.1}while cis {“Good”, “Medium”, “Bad”}, respectively.
(a) Ky= 3. (b) Ky= 4. (c) Ky= 5. (d) Ky= 6.
Fig. 16. Job-waiting-time (JWT) performance among the three algorithms with 7310 requests and 48 LEO servers, while varying Kyfrom 3 to 6,
fixing Ny=6, and the channel attenuation rate v(c)is set to {10, 2, 0.1}while cis {“Good”, “Medium”, “Bad”}, respectively.
(a) Ky= 3. (b) Ky= 4. (c) Ky= 5. (d) Ky= 6.
Fig. 17. Backlog comparison of three algorithms while varying Kyfrom 3 to 6, fixing Ny=6, and setting the channel attenuation rate v(c)to {10, 2,
0.1}if cis {“Good”, “Medium”, “Bad”}, respectively.
mance of three algorithms under different combinations of
channel attenuation rate in Fig. 10. These three CDF figures
show that: (1) the JWT of all three algorithms performs the
same under each group of simulation setting; (2) the overall
JWT grows when the varying-scale of channel attenuation
rate changes from small to large. The first observation
indicates that the JWT performance is not affected by the
job-dispatch schemes. The reason of the second observation
is that the large varying-scale of channel attenuation rate,
where v(c)={10, 2, 0.1}or {16, 1, 0.01}, makes the packet
transmission in downlinks very difficult under the non-
good weather conditions. Thus, the jobs waiting in queues
need to stay for longer durations than that under a milder
varying-scale of channel attenuation rate.
We then evaluate the penalty performance under the
different varying scales of channel attenuation rate through
Fig. 11, from which we see different performance curves
under different varying scales of V(c). For example,
penaltiesintend to descend in Fig. 11(a), ascend in Fig. 11(c),
and mixtured in Fig. 11(b). As we have explained in Fig.
6(c), the penalty is only a part of the transformed penalty-
plus-drift minimization problem (21), where the Lyapunov
drift ∆(Θ(t)) is minimized for short queues throughout the
LEO satellites as well. Under different channel attenuation
rates where the short queues are easily maintained when
V(c)={5.03, 3.46, 1}, a low penalty (indicates a high overall
data amount downloaded, or a low cumulative energy
consumption, or both) is easier to acheive. In contrast, under
large varying-scale of channel attenuation rate, e.g., when
V(c)={10, 2, 0.1}and {16, 1, 0.01}, the data transmission
via the downlinks will heavily be impacted by the bad
weather conditions, and large queue backlogs are easily to
be incurred. Thus, algorithms tend to ensure the system
stability by sacrificing the penalty performance. That is why
we see the penalty ascending trends in Fig. 11(b) and 11(c).
Finally, we study the impact of varying-scale of chan-
nel attenuation rate on the performance of Wat-Sec per bit
under three algorithmes. The comparison is shown in Fig.
12. From which, we can see that the proposed JKQ based
algorithm significantly outperforms the other two on energy
consumptions. On the other hand, it is can be seen that
under the large varying-scale of channel attenuation rates,
e.g., when v(c)={10, 2, 0.1}and {16, 1, 0.01}, the energy
consumption of per bit of downloaded data becomes higher
than that under a small varying-scale of channel attenuation
rate when v(c)={5.03, 3.46, 1}.
5.4.4 Impact of Varying β
We then evaluate the impact of the weight of energy con-
sumption by varying βfrom 1 to 10, using the synthesized
16
trace file associated with 7310 requests and 48 LEO servers.
The channel attenuation rate v(c)is set to {10, 2, 0.1}while c
is {“Good”, “Medium”, “Bad”}, respectively. In this group
of simulations, the admission ratios of all algorithms are
always 100% and thus omitted here. We mainly examine the
performance of algorithms in terms of the energy consump-
tion, energy efficiency, job completion ratio and packet loss
rate.
Fig. 13(a) and 13(b) illustrate the overall cumulative en-
ergy consumption and the energy efficiency versus varying
β, respectively. We can see that: (1) the performance trends
shown in these two figures are same; (2) the proposed JKQ
based algorithm exhibits the best energy efficiency against
the other two, especially much higher than that of the JSQ
based algorithm; (3) the increasing βmakes the cumulative
energy consumption decreasing and the energy efficiency
increasing. The reason of the third observation is that a
large βimplies a large weight of energy consumption in
the objective function of the original penalty-minimization
problem. Thus, the growing βdegrades the energy con-
sumption. When βis larger than 8, the benefit of large
energy-consumption weight becomes saturated gradually.
Furthermore, a coin always has two sides. A large weight
of energy-consumption, i.e., a large β, also induces nega-
tive effects under our file acquisition system. Because once
the weight of energy-consumption grows bigger, the file
acquisition system tends to save energy. However, this may
damage the job completion ratio and increase packet loss
rate. These two concerns are verified by Fig. 13(c) and Fig.
13(d), respectively. Fig. 13(c) shows that the job completion
ratio performance of JKQ based algorithm is slightly lower
than that of the JSQ based algorithm, while βincreases to
10. In Fig. 13(d), the packet loss rate of JKQ based algorithm
is a little bit higher than that of the JSQ based algorithm.
Therefore, setting an appropriate βneeds to consider the
nontrivial tradeoff between the energy-consumption and the
job completion ratio.
Finally, under the same parameter settings with Fig. 13,
Fig. 14(a), 14(b) and 14(c) exhibit the backlog comparison of
the three algorithms while setting βto 1, 5, and 10. We then
have the following two observations. (1) Under each β, the
proposed JKQ based algorithm outperforms the JSQ based
algorithm overwhelmingly in terms of the queue backlog
size. Furthermore, since the RJQ based algorithm randomly
selects the target Kqueues to allocate Kjobs for each
request, its backlog performance is much better than that
of the JSQ based, but still worse than that of the JKQ based.
(2) The varying βhas no effect on the distribution of queue
backlog size for all three algorithms.
5.4.5 Impact of Varying Storage Parameters Ky
In this part, we study the impact of storage parameter Ky
by varying it from 3 to 6, while fixing Nyat 6. From the
four metrics shown in Fig. 15, we can observe that the
energy consumption, Watt·Sec per bit, and the job com-
pletion ratio grow nearly linearly with the growth of Ky,
whereas the packet loss rate drops. From Fig. 15(b), we also
see that the Wat·Sec per bit performance distance between
the proposed JKQ and JSQ algorithms enlarges from 1.4e-
7 to 1.8e-7 while Kygrows from 3 to 6. We attribute
this result to the following reason. When Kygrows larger,
the proposed JKQ algorithm will dispatch the Kychunk-
downloading jobs of a file-download request to Kysatellite
queues, much more than the JSQ does. Thus the merit of
JKQ will become more apparent comparing with that of JSQ.
Fig. 16 shows that the job-waiting-time of all downloading
jobs shrinks while Kyenlarges. This is because the size of
each chunk-downloading job becomes smaller when each
file was divided into more chunks. Due to the same reason,
Fig. 17 illustrates that the queue backlogs of satellites keep
decreasing while Kygrows from 3 to 6.
Through all trace-driven simulation results, we can sum-
marize the following facts. The proposed JKQ algorithm
outperforms the batch-based dispatch algorithm [24], [25]
significantly in terms of job completion ratio. Under differ-
ent varying scales of channel attenuation rate, the proposed
JKQ based algorithm outperforms JSQ and RJQ in terms of
energy efficiency. JKQ is also able to yield shorter queue
backlogs than that under the other two algorithms.
6 CONCLUSION
In this paper, we studied how to maximize the overall
amount of data admitted while minimizing the energy con-
sumption when transmitting data from satellites to ground.
We proposed an online scheduling framework. Particularly,
we devised a novel coflow-like JKQ based algorithm, which
can drastically reduce backlogs of queues in satellites. We
also throughly analyzed the optimality gap between the so-
lution delivered by the proposed algorithm and the theoreti-
cal optimal solution, and the queue stability. We finally eval-
uated the performance of the proposed algorithm through
experimental simulations using the real-world traces. The
evaluation results show that the proposed online algorithm
exhibits its merits in terms of short queue backlogs and high
energy efficiency.
7 ACKNOWLEDGEMENT
This work is partially supported by NSFC under research
grant no. 61872310, 61872195, 61572262, the Kyoto Univer-
sity Research Fund for Young Scientists (Start-up) FY-2018,
and the Start-up Research Fund (67000-18841220) from Sun
Yat-Sen University, China.
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APPENDIX A
PROOF OF LEMMA 1
Proof: Because the actual queues Qi(t),iS, are
updated according to Eq. (10), and based on the fact that
max[qb, 0]2(qb)2, we obtain:
Qi(t+ 1)2(Qi(t)bi(t))2+Ai(t)2
+ 2 max[Qi(t)bi(t),0]Ai(t)
= (Qi(t)bi(t))2+Ai(t)2+ 2(Qi(t)e
bi(t))Ai(t),(63)
where e
bi(t) = min[Qi(t), bi(t)].
Next, we have:
Qi(t+ 1)2Qi(t)2Qi(t)22Qi(t)bi(t) + Ai(t)2
+ 2Qi(t)Ai(t)2e
bi(t)Ai(t)Qi(t)2
=Ai(t)2+bi(t)2+ 2Qi(t)(Ai(t)bi(t)) 2e
bi(t)Ai(t).
That is,
∆(Qi(t)) X
iS
E{Ai(t)2+bi(t)2
2|Qi(t)}
+X
iS
Qi(t)E{Ai(t)bi(t)|Qi(t)}.(64)
Similarly, we have the following one-slot conditional
Lyapunov drift for all virtual queues.
∆(Mri(t)) = 1
2X
rR(t)X
iIy(r)
[Mri(t+ 1)2Mr i(t)2]
1
2X
rR(t)X
iIy(r)
E{mri(t)2|Mr i(t)}
+X
rR(t)X
iIy(r)
E{Mri(t)mr i(t)|Mri (t)}.(65)
18
∆(Hrk
ij (t)) = 1
2X
iSX
(r,k)
b
Qi(t),
(i,j)E(t)
[Hr(t+ 1)2Hrk
ij (t)2]
1
2X
iSX
(r,k)
b
Qi(t),
(i,j)E(t)
E{hrk
ij (t)2|Hrk
ij (t)}
+X
iSX
(r,k)
b
Qi(t),
(i,j)E(t)
E{Hrk
ij (t)hrk
ij (t)|Hrk
ij (t)}.(66)
∆(Urki (t)) = 1
2X
iSX
(r,k)
b
Qi(t)
[Urki (t+ 1)2Urki(t)2]
1
2X
iSX
(r,k)
b
Qi(t)
E{urki (t)2|Urki(t)}
+X
iSX
(r,k)
b
Qi(t)
E{Urki (t)urki(t)|Ur ki(t)}.(67)
∆(Di(t)) = 1
2X
iS
[Di(t+ 1)2Di(t)2]
1
2X
iS
E{di(t)2|Di(t)}+X
iS
E{Di(t)di(t)|Di(t)}.(68)
∆(Xi(t)) = 1
2X
iS
[Xi(t+ 1)2Xi(t)2]
1
2X
iS
E{xi(t)2|Xi(t)}+X
iS
E{Xi(t)xi(t)|Xi(t)}.(69)
We then have the following inequalities to show the
upper bound of each square terms in the drift-expression
from (64) to (69).
Taking (28) and constraint (4) into consideration,
we know that Ai(t)PrR(t)PkKrarki Zy(r)
PrR(t)αrZy(r)PrR(t)Zy(r). Thus,
X
iS
Ai(t)2X
iS
(X
rR(t)
Zy(r))2.(70)
Because bi(t) = P(i,j)E(t)P(r,k)
b
Qi(t)δg(pr k
ij (t), c(t))
P(r,k)
b
Qi(t)σiδµmax , we know that
X
iS
bi(t)2X
iS
[X
(r,k)
b
Qi(t)
σiδµmax ]2=X
iS
(|b
Qi(t)|σiδµmax )2.
(71)
We proceed to derive the upper bounds of the square
terms related to virtual queues as follows.
mri(t)2= ( X
kKr
αrki αr)2
(( X
kKr
1) 0)2=K2
y(r).(72)
hrk
ij (t)2= [f(r)
δT r
g(prk
ij (t), c(t))]2
[f(r)
δT r
µmin]2(f(r)
δT r
)2.(73)
urki (t)2= [( X
(i,j)E(t)
1{Π})1]2
[( X
(i,j)E(t)
1) 1]2(σi1)2.(74)
di(t)2= [( X
(r,k)
b
Qi(t)X
(i,j)E(t)
1{Π})σi]2
[( X
(r,k)
b
Qi(t)
σi)σi]2
=σ2
i(( X
(r,k)
b
Qi(t)
1) 1)2
= (|b
Qi(t)| − 1)2σ2
i.(75)
xi(t)2= [ X
(r,k)
b
Qi(t)X
(i,j)E(t)
prk
ij (t)pbgt
i]2
(X
(r,k)
b
Qi(t)
σipmax pbgt
i)2
= (|b
Qi(t)|σipmax pbgt
i)2.(76)
Finally, combining the one-slot conditional Lyapunov
drift defined in (20) and inequalities (64)-(69), we can obtain
the inequality (22) and B(t)as shown in Lemma 1. This
concludes the proof.
Huawei Huang (M’16) received his Ph.D in
Computer Science and Engineering from the
University of Aizu, Japan. He is currently an
associate professor at School of Data and Com-
puter Science, Sun Yat-Sun University, China.
His research interests mainly include SDN/NFV,
edge computing, and blockchain. He received
the best paper award of TrustCom-2016. He
used to be a visiting scholar at the Hong Kong
Polytechnic University (2017-2018), a post-
doctoral research fellow of JSPS (2016-2018),
an assistant professor at Kyoto University, Japan (2018-2019). He is a
member of the IEEE.
Song Guo (M’02-SM’11) is a Full Professor with
the Department of Computing, Hong Kong Poly-
technic University, Hong Kong. He received his
PhD degree in computer science from Univer-
sity of Ottawa. He has authored or coauthored
over450 papers in major conferences and jour-
nals. His current research interests include big
data, cloud and edge computing, mobile com-
puting, and distributed systems. Prof. Guo was
a recipient of the 2019 TCBD Best Conference
Paper Award, the 2018 IEEE TCGCC Best Mag-
azine Paper Award, the 2017 IEEE SYSTEMS JOURNAL Annual Best
Paper Award, and six other Best Paper Awards from IEEE/ACM con-
ferences. He was an IEEE Communications Society Distinguished Lec-
turer. He has served as an Associate Editor of IEEE TPDS, IEEE TCC,
IEEE TETC, etc. He also served as the general and program chair
for numerous IEEE conferences. He currently serves in the Board of
Governors of the IEEE Communications Society.
19
Weifa Liang (M’99-SM’01) received the PhD
degree from the Australian National University
in 1998, the ME degree from the University of
Science and Technology of China in 1989, and
the BSc degree from Wuhan University, China
in 1984, all in computer science. He is currently
a professor in the Research School of Computer
Science at the Australian National University. His
research interests include design and analysis
of energy-efficient routing protocols for wireless
ad hoc and sensor networks, cloud computing,
software-defined networking, virtualized network function services, de-
sign and analysis of parallel and distributed algorithms, approximation
algorithms, combinatorial optimization, and graph theory. He is a senior
member of the IEEE.
Kun Wang (M’13-SM’17) received two Ph.D. de-
grees in computer science from Nanjing Univer-
sity of Posts and Telecommunications, Nanjing,
China, in 2009, and from the University of Aizu,
Aizuwakamatsu, Japan, in 2018. He was a Post-
Doctoral Fellow in UCLA, USA from 2013 to
2015, where he is a Senior Research Professor.
He was a Research Fellow in the Hong Kong
Polytechnic University, Hong Kong, from 2017
to 2018, and a Professor in Nanjing University
of Posts and Telecommunications. His current
research interests are mainly in the area of big data, wireless com-
munications and networking, energy Internet, and information security
technologies. He is the recipient of IEEE GLOBECOM 2016 Best Paper
Award, IEEE TCGCC Best Magazine Paper Award 2018, IEEE TCBD
Best Conference Paper Award 2019, and IEEE ISJ Best Paper Award
2019. He serves/served as an Associate Editor of IEEE Access, an
Editor of Journal of Network and Computer Applications, and a Guest
Editor of IEEE Network, IEEE Access, Future Generation Computer
Systems, Peer-to-Peer Networking and Applications, IEICE Transac-
tions on Communications, Journal of Internet Technology, and Future
Internet.
Yasuo Okabe received M.E. and Ph.D in En-
gineering from Department of Information Sci-
ence, Kyoto University in 1988 and 1994 re-
spectively. He joined Kyoto University as an in-
structor of Faculty of Engineering in 1988. He
advanced to an associate professor of Data Pro-
cessing Center in 1994 and moved to Graduate
School of Informatics in 1998. Since 2002 he
has been a professor of Division of Networking
Research, Academic Center for Computing and
Media Studies. His current research interest in-
cludes Internet architecture, distributed algorithms and network security.
He is a member of IEICE, IPSJ. ISCIE, JSSST, IEEE and ACM.
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