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Coflow-Like Online Data Acquisition from Low-Earth-Orbit Datacenters

August 2019
IEEE Transactions on Mobile Computing

DOI:10.1109/TMC.2019.2936202

Authors:

Huawei Huang

Sun Yat-sen University

Song Guo

Hong Kong University of Science and Technology

Weifa Liang

City University of Hong Kong

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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.

a) Decisions for arrived file-acquisition requests: admission control, and job dispatch.

…

b) Decisions for arrived file-acquisition requests: queue update and power allocation on time-varying downlink channels.

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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.

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

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,

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=

(S∪G, 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 i∈Sand a ground station j∈G, 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

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

…

i∈S

Jobs (r,k),

k =1,..,Ky(r)

Admission

control

If ⍺r=1

r∈R(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)

…

j∈G

Arrival jobs

Jobs

i∈S

…

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 i∈Sis

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

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 y∈Y: 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 r∈R(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,∀r∈R(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

r∈R(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),∀r∈R(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),∀k∈Kr,

generated for a same request r∈R(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 y∈Y,

which is duplicated into Nychunks, only Ky

out of Nychunks can recover the original ﬁle

Zysize of each chunk for ﬁle y∈Y

Trdata acquisition deadline required by r

∈R(t), measured by time slots

y(r)function that returns the ﬁle type demanded

by r∈R(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 i∈S

and j∈G

σitotal number of channels in LEO satellite i∈S

−→

P;−→

Cvector of power levels; vector of channel

conditions

αrbinary variable denoting admission control

of r∈R(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(i∈S)

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∈−→

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.

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 r∈R(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 i∈Sat time slot t, we deﬁne another binary

variable arki (∀r∈R(t),∀k∈Kr)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

r∈R(t)

αrf(r) = X

r∈R(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

i∈SX

(r,k)∈

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→∞

t=1

{β·ζ(t)−φ(t)}(3)

s.t. X

k∈Kr

arki ≤αr,∀r∈R(t), i ∈Iy(r).(4)

g(prk

ij (t), c(t)) ≥f(r)

δT r

,∀(r,k)∈

Qi(t),(i,j)∈E(t),i∈S. (5)

(i,j)∈E(t)

1{Π}≤1,∀(r, k)∈b

Qi(t), i ∈S. (6)

(r,k)∈

Qi(t)X

(i,j)∈E(t)

1{Π}≤σi,∀i∈S. (7)

(r,k)∈

Qi(t)X

(i,j)∈E(t)

prk

ij (t)≤pbgt

i,∀i∈S. (8)

Qi(t)is mean-rate stable,∀i∈S. (9)

Variable: αr∈ {0,1}, arki ∈ {0,1}, prk

ij (t)∈−→

P ,

∀r∈R(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 i∈Iy(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

r∈R(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

i∈Sshould be limited by its total number of channels

σi. Let pbgt

idenote the total power budget of LEO satellite

i∈Sat any time slot, constraint (8) indicates that the total

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,∀i∈S. The queue dynamics over time for

each satellite is expressed as follows.

Qi(t+ 1) = max[Qi(t)−bi(t),0] + Ai(t),∀i∈S, (10)

where

bi(t) = X

(i,j)∈E(t)X

(r,k)∈

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

r∈R(t)X

k∈Kr

f(arki ),(12)

denotes the total size of all arrived jobs at time slot twhen

dispatching jobs to queue i∈S. 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),

∀r∈R(t), i ∈Iy(r);Hrk

ij (t),∀r∈R(t);Urki (t),∀(r, k)∈

Qi(t),i∈S;Di(t)and Xi(t),∀i∈Scorresponding

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

k∈Kr

arki −αr,∀r∈R(t), i ∈Iy(r),(14)

hrk

ij (t) = f(r)

δT r

−g(prk

ij (t), c(t)),∀(r,k)∈

Qi(t),(i,j)∈E(t),i∈S, (15)

urki (t) = X

(i,j)∈E(t)

1{Π}−1,∀(r, k)∈b

Qi(t), i ∈S, (16)

di(t) = X

(r,k)∈

Qi(t)

(i,j)∈E(t)

1{Π}−σi,∀i∈S, (17)

and

xi(t) = X

(r,k)∈

Qi(t)

(i,j)∈E(t)

prk

ij (t)−pbgt

i,∀i∈S. (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)

T−Λ(1)

T≥

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),∀i∈S},M(t) =

{Mri(t),∀r∈R(t), i ∈Iy(r)},H(t) = {Hrk

ij (t),∀(r, k)∈

Qi(t),(i, j)∈E(t), i ∈S},U(t) = {Urki (t),∀(r, k)∈

Qi(t), i ∈S},D(t) = {Di(t),∀i∈S}and X(t) =

{Xi(t),∀i∈S}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

i∈S

Qi(t)2+X

r∈R(t),

i∈Iy(r)

Mri(t)2+X

i∈SX

(r,k)∈

Qi(t),

(i,j)∈E(t)

Hrk

ij (t)2

(r,k)∈

Qi(t),

i∈S

Urki (t)2+X

i∈S

Di(t)2+X

i∈S

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)

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)

(i∈S)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

i∈S

Qi(t)E{Ai(t)−bi(t)|Θ(t)}

i∈Iy(r)X

r∈R(t)

Mri(t)E{mr i(t)|Θ(t)}

i∈SX

(r,k)∈

Qi(t),

(i,j)∈E(t)

Hrk

ij (t)E{hrk

ij (t)|Θ(t)}

(r,k)∈

Qi(t),

i∈S

Urki (t)E{urki(t)|Θ(t)}

i∈S

(Di(t)E{di(t)|Θ(t)}+Xi(t)E{xi(t)|Θ(t)}),(22)

where B(t),1

i∈S

{(P

r∈R(t)

Zy(r))2+|b

Qi(t)|2σ2

i(δ2µ2

max +

max +1) +|b

Qi(t)|(( f(r)

δT r)2-σ2

i−2σi(1+pmax ·pbgt

i)+1) +σ2

+(pbgt

i)2}+1

r∈R(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

i∈S

(r,k)∈

Qi(t),

(i,j)∈E(t)

Hrk

ij (t)·f(r)

Trδ−X

(r,k)∈

Qi(t)

Urki (t)

−Di(t)σi−Xi(t)pbgt

i](23)

i∈S

Qi(t)E{Ai(t)|Θ(t)}(24)

r∈R(t)

αrE{−V f(r)−X

i∈Iy(r)

Mri(t)|Θ(t)}(25)

r∈R(t)X

k∈KrX

i∈Iy(r)

E{Mri(t)ar ki|Θ(t)}(26)

i∈SX

(r,k)∈

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 r∈R(t)

that is dispatched to queue i∈S, we have

Ai(t) = X

r∈R(t)

i(t),∀i∈S. (28)

According to the location of original ﬁle indicated by each

request,

i(t) = Pk∈Krf(arki ) = Pk∈KrarkiZy(r),if i∈Iy(r);

0,otherwise if i∈S\Iy(r).

(29)

And taking into account constraint (4), we then have

i∈S

Qi(t)Ai(t) = X

i∈S

Qi(t)X

r∈R(t)

i(t)

≤X

r∈R(t)X

i∈Iy(r)

Qi(t)X

k∈Kr

arki Zy(r)(30)

≤X

r∈R(t)X

i∈Iy(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(∀r∈R(t))

are independent of each other among the arrival requests.

Algorithm 1: Join in the ﬁrst K-shortest queues (JKQ)

Input : r∈R(t),Krand αr(obtained from (33))

Output : ar ki (∀k∈Kr, i ∈Iy(r))

1if αr= 1 then

2Ψr← ∅

3for i∈Iy(r)do

4ψri ←Qi(t)Zy(r)+Mri (t)

5Ψr←Ψr∪ {ψri}

6initialize arki ←0,∀k∈Kr, i ∈Iy(r)

7for k= 1 to Ky(r)do

8ψri∗←arg min(Ψr)

9Ψr←Ψr− {ψri∗}

10 arki∗←1, where i∗←arg 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

i∈Iy(r)

(Qi(t)Zy(r)−Mri(t)) −V f (r)] (32)

s.t. αr∈ {0,1},∀r∈R(t).

Differentiating the objective function (32) with respect

to αryields the following simple threshold-based admission

control strategy:

αr=





1 : P

i∈Iy(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 (∀i∈Iy(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},∀r∈R(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 i∈Scan 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 −→

prk

ij (t)=









pmin,if ele. in−→

Dare non-negative;

pmax,if ele. in−→

Dare non-positive;

p−or p+:arg min{Γ(p−, c(t)),Γ(p+, c(t))},if ele.

in−→

Dvary from negative to positive,

where p−and p+are two successive discrete power levels

such that p−≤p∗≤p+, where p−, p+∈−→

P, and p∗is 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.

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

r∈R(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

V, i.e.,

lim

T→∞ sup 1

t=1

{βζ (t)−φ(t)} − P enopt ≤e

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→∞

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 r∈R(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))} ≤ , ∀r∈R(t),i∈Iy(r)(40)

E{b

hrk

ij (prk∗

ij , ω(t))} ≤ , ∀(r,k)∈

Qi(t),∀(i,j)∈E(t)(41)

E{b

urki (prk∗

ij , ω(t))} ≤ , ∀(r,k)∈

Qi(t),∀(i,j)∈E(t)(42)

E{b

di(prk∗

ij , ω(t))} ≤ , ∀i∈S(43)

E{b

xi(prk∗

ij , ω(t))} ≤ , ∀i∈S(44)

E{b

Ai(a∗

rki , ω(t))} ≤ E{b

bi(prk∗

ij , ω(t))}+, ∀i∈S,(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)}

r∈R(t)X

i∈Iy(r)

Mri(t)E{m∗

ri(t)|Θ(t)}

i∈S

E{[Qi(t)(A∗

i(t)−b∗

i(t)) + X

(r,k)∈

Qi(t),

(i,j)∈E(t)

Hrk

ij (t)·hrk∗

ij (t)+

(r,k)∈

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)} ≤ , ∀i∈S(48)

E{m∗

ri(t)|Θ(t)}=E{m∗

ri(t)} ≤ , ∀i∈S,r ∈R(t)(49)

E{hrk∗

ij (t)|Θ(t)}=E{hrk∗

ij (t)} ≤ , (r,k)∈

Qi(t),(i,j)∈E(t)(50)

E{u∗

rki (t)|Θ(t)}=E{u∗

rki (t)} ≤ , ∀(r,k)∈

Qi(t)(51)

E{d∗

i(t)|Θ(t)}=E{d∗

i(t)} ≤ , ∀i∈S(52)

E{x∗

i(t)|Θ(t)}=E{x∗

i(t)} ≤ , ∀i∈S(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=1

E{P en(t)}

≤

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:

t=1

E{P en(t)} ≤ P enopt+1

V T

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

(56), for all time slots T > 1:

E{L(Θ(T))} − E{L(Θ(1)} ≤

t=1

B(t) + V T P enopt.(58)

Referring the deﬁnition of L(Θ(T)), we know

2E{X

i∈S

Qi(T)2} ≤ E{L(Θ(1)}+

t=1

B(t) + V T P enopt.

(59)

Then, for ∀i∈S, we have

E{Qi(T)2} ≤ 2E{L(Θ(1)}+ 2

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=1

B(t)+2V T P enopt ]1

(61)

Dividing by Tand taking a limit as T→ ∞, we hvae

lim

T→∞

E{|Qi(T)|}

≤lim

T→∞[2E{L(Θ(1)}

T2+2

t=1

B(t) + 2

TV P enopt]1

= 0.(62)

Thus, all actual queues Qi(∀i∈S) 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]

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.

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

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

100

Num. of request

Synthesized trace

Original trace

(a) Number of requests.

0 10 20 30

File Size (Megabytes)

0.5

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

(a) Admission ratio (b) Energy consumption.

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

(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

(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-

(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

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),∀i∈S, are

updated according to Eq. (10), and based on the fact that

max[q−b, 0]2≤(q−b)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)2−Qi(t)2≤Qi(t)2−2Qi(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

i∈S

E{Ai(t)2+bi(t)2

2|Qi(t)}

i∈S

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

r∈R(t)X

i∈Iy(r)

[Mri(t+ 1)2−Mr i(t)2]

≤1

r∈R(t)X

i∈Iy(r)

E{mri(t)2|Mr i(t)}

r∈R(t)X

i∈Iy(r)

E{Mri(t)mr i(t)|Mri (t)}.(65)

∆(Hrk

ij (t)) = 1

i∈SX

(r,k)∈

Qi(t),

(i,j)∈E(t)

[Hr(t+ 1)2−Hrk

ij (t)2]

≤1

i∈SX

(r,k)∈

Qi(t),

(i,j)∈E(t)

E{hrk

ij (t)2|Hrk

ij (t)}

i∈SX

(r,k)∈

Qi(t),

(i,j)∈E(t)

E{Hrk

ij (t)hrk

ij (t)|Hrk

ij (t)}.(66)

∆(Urki (t)) = 1

i∈SX

(r,k)∈

Qi(t)

[Urki (t+ 1)2−Urki(t)2]

≤1

i∈SX

(r,k)∈

Qi(t)

E{urki (t)2|Urki(t)}

i∈SX

(r,k)∈

Qi(t)

E{Urki (t)urki(t)|Ur ki(t)}.(67)

∆(Di(t)) = 1

i∈S

[Di(t+ 1)2−Di(t)2]

≤1

i∈S

E{di(t)2|Di(t)}+X

i∈S

E{Di(t)di(t)|Di(t)}.(68)

∆(Xi(t)) = 1

i∈S

[Xi(t+ 1)2−Xi(t)2]

≤1

i∈S

E{xi(t)2|Xi(t)}+X

i∈S

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)≤Pr∈R(t)Pk∈Krarki Zy(r)≤

Pr∈R(t)αrZy(r)≤Pr∈R(t)Zy(r). Thus,

i∈S

Ai(t)2≤X

i∈S

r∈R(t)

Zy(r))2.(70)

Because bi(t) = P(i,j)∈E(t)P(r,k)∈

Qi(t)δg(pr k

ij (t), c(t)) ≤

P(r,k)∈

Qi(t)σiδµmax , we know that

i∈S

bi(t)2≤X

i∈S

(r,k)∈

Qi(t)

σiδµmax ]2=X

i∈S

(|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

k∈Kr

αrki −αr)2

≤(( X

k∈Kr

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≤(σi−1)2.(74)

di(t)2= [( X

(r,k)∈

Qi(t)X

(i,j)∈E(t)

1{Π})−σi]2

≤[( X

(r,k)∈

Qi(t)

σi)−σi]2

=σ2

i(( X

(r,k)∈

Qi(t)

1) −1)2

= (|b

Qi(t)| − 1)2σ2

i.(75)

xi(t)2= [ X

(r,k)∈

Qi(t)X

(i,j)∈E(t)

prk

ij (t)−pbgt

i]2

≤(X

(r,k)∈

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.

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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Jan 2023

Internet-of-Things (IoT) applications from many industries, such as transportation (maritime, road, rail, air) and fleet management, offshore monitoring, and farming are located in remote areas without cellular connectivity. Such IoT applications continuously generate stream data with hidden values that need to unveiled in real time. Streaming analytics is emerging as a popular type of Big Data analytics to process large volume of stream data for IoT applications in remote regions. Built upon terrestrial-satellite integrated networks, Satellite Edge Computing (SEC) equipped with computing resource in satellites has been envisioning as a key enabling technology to timely analyze stream data of IoT applications in remote regions on the Earth. Considering the dynamically-moving property of satellites in an SEC network, it is vital to optimize the responsiveness of each Big Data analytical query, such that none of such queries takes much longer time to wait for available satellites with sufficient computing resource. Furthermore, the uncertain data volumes of Big Data queries in SEC networks make the resources in satellites fragmented, particularly when the collaboration among satellites is intermittent. Therefore, directly application of existing methods may not guarantee the timelineness of streaming analytics in an SEC network. To address the afore-mentioned unique challenges of streaming analytics in SEC networks, it is urgent to design new algorithms and methods for timely Big Data processing. Specifically, we use the flow time to capture the responsiveness of streaming analytics in satellite edge computing, which is the time between the generation of the first unit of a dataset and the finish time of the data processing. We consider the flow time minimization problem for query evaluation of Big Data analytics in an SEC network with the aim of minimizing the average flow time of Big Data analytical queries, under an assumption of uncertain volumes of datasets. To this end, we first propose an approximation algorithm with a provable approximation ratio for the offline version of the flow time minimization problem. We then devise an online learning algorithm, referred to the customized Lipschitz bandit learning algorithm, with a bounded regret for the online version of the problem. We finally evaluate the performance of the proposed algorithms in a real SEC network topology. Experiment results show that the performance of the proposed algorithm outperforms its counterparts by at least 13% in terms of flow time.

Quality of Service Optimization for Satellite-Borne Router With Multi-Priority Scheduling Queues

Article

Nov 2023

Yan Zhu

The efficiency of the multi-priority queue scheduling of the satellite-borne router determines the latency quality of service (QoS) guarantee capability of the traffic frame. However, the existing scheduling methods do not consider the impact of the traffic arrival rates of multi-priority queues on the queuing latency of different priority queues, which results in a low QoS guarantee ratio. Therefore, we construct an multi-priority scheduling model of satellite-borne routers and a performance optimization problem of the latency QoS guarantee. In the solving process, the intractable nonconvex primal optimization problem is subtly reformulated into a tractable knapsack problem with convex constraints. On this basis, we propose a priority programming algorithm to optimize the traffic arrival rates, which achieves the optimality. The simulation results verify that our algorithm can effectively and rapidly converge to the optimal solution, and achieve a 30% performance gain in terms of the QoS guarantee ratio.

How to Address Storage Issues for Metaverse? Blockchains and Distributed File Systems

Chapter

May 2023

Constructing globally distributed file systems (DFS) has received great attention. Traditional peer-to-peer (P2P) distributed file systems have inevitable drawbacks such as instability and lacking auditing and incentive mechanisms. Thus, Inter-Planetary File Systems (IPFS) and Swarm, as the representative DFSs which integrate with blockchain technologies, are proposed and becoming a new generation of distributed file systems. Although the blockchain-based DFS successfully provides adequate incentives and security guarantees by exploiting the advantages of blockchain, a series of challenges, such as scalability and privacy issues, are also constraining the development of the new generation of DFSs. Mainly focusing on IPFS and Swarm, this chapter conducts an overview of the principle, layered structure, and cutting-edge studies of blockchain-based DSFs. Furthermore, we also identify their challenges, open issues, and future directions. We anticipate that this survey can shed new light on the subsequent studies related to blockchain-based distributed file systems.KeywordsBlockchainDistributed file systemsPeer-to-peerSwarmConsensus algorithmsScalabilityStorage optimization

Envisioned Wireless Big Data Storage for Low-Earth-Orbit Satellite-Based Cloud

Article

Full-text available

Feb 2018

Satellite-based communication technology regains much attention in the past few years, where the satellites mainly play the role as relay devices to the communication networks. In this article, we focus on the data storage leveraging the low-earth-orbit (LEO) satellite based datacenter (also called space based cloud), which has been considered as a very promising secure paradigm to data storage, especially in the big data era. We first propose a layered architecture for the space based cloud infrastructure. Then, a novel management framework is devised to enable the operability of the proposed architecture. Finally, some challenging open issues are revealed from both academic and industrial perspectives.

Service Level Agreement in Cloud Computing

Book

Full-text available

Jan 2009

Cloud computing that provides cheap and pay-as-you-go computing resources is rapidly gaining momentum as an alternative to traditional IT Infrastructure. As more and more consumers delegate their tasks to cloud providers, Service Level Agreements(SLA) between consumers and providers emerge as a key aspect. Due to the dynamic nature of the cloud, continuous monitoring on Quality of Service (QoS) attributes is necessary to enforce SLAs. Also numerous other factors such as trust (on the cloud provider) come into consideration, particularly for enterprise customers that may outsource its critical data. This complex nature of the cloud landscape warrants a sophisticated means of managing SLAs. This paper proposes a mechanism for managing SLAs in a cloud computing environment using the Web Service Level Agreement(WSLA) framework, developed for SLA monitoring and SLA enforcement in a Service Oriented Architecture (SOA). We use the third party support feature of WSLA to delegate monitoring and enforcement tasks to other entities in order to solve the trust issues. We also present a real world use case to validate our proposal.

A Two-Layer Caching Model for Content Delivery Services in Satellite-Terrestrial Networks

Conference Paper

Full-text available

Dec 2016

ColdSel: A Selection Algorithm to Mitigate Congestion Situations over Nanosatellite Networks

Conference Paper

Full-text available

Dec 2016

Nanosatellites offer a solution to provide Internet access in areas where there is no ICT infrastructure, such as rural and remote areas, keeping low construction and maintenance costs. A nanosatellite constellation is composed of a certain number of nanosatellites distributed in one or more orbital planes. In most cases, this network cannot ensure an end-to-end connection between sources and destinations, because not all satellite links are up at the same time. The Delay and Disruption Tolerant Networking (DTN) paradigm is so necessary to deal with predictable disruptions and large delays, allowing nanosatellites, Internet gateways (also called hot spots), and rural gateways (also called cold spots) to keep data stored in their buffers also for tens of minutes waiting to be forwarded. We focused our attention on a possible selection strategy which indicates to all nanosatellites how many bundles (PDUs of the DTN protocol) they can upload from rural gateways during each contact. The decision is made by considering the maximum amount of data that nanosatellites and cold spots can exchange during each contact (quantity related to contact durations) and the possible presence of congestion situations in rural and remote areas or in nanosatellites. The proposed strategy is called ColdSel: it calculates the amount of bundles that each cold spot has to upload on the nanosatellite in contact with in order to mitigate congestion situations in rural areas and nanosatellites and to reduce the nanosatellite buffer occupancies so improving the performance in terms of data delivery time.

Stochastic Network Optimization with Application to Communication and Queueing Systems

Article

Jan 2010

Michael J. Neely

Coflex: Navigating the fairness-efficiency tradeoff for coflow scheduling

Conference Paper

May 2017

Coflow scheduling in input-queued switches: Optimal delay scaling and algorithms

Conference Paper

May 2017

Satellite Communications Systems Engineering: Atmospheric Effects, Satellite Link Design and System Performance

Article

Aug 2008

Louis J. Ippolito

Half-Title PageWiley Series PageTitle PageCopyright PageTable of ContentsList of AcronymsPreface

The Power of Slightly More than One Sample in Randomized Load Balancing

Article

Feb 2017

In many computing and networking applications, arriving tasks have to be routed to one of many servers, with the goal of minimizing queueing delays. When the number of processors is very large, a popular routing algorithm works as follows: select two servers at random and route an arriving task to the least loaded of the two. It is well known that this algorithm dramatically reduces queueing delays compared to an algorithm, which routes to a single randomly selected server. In recent cloud computing applications, it has been observed that even sampling two queues per arriving task can be expensive and can even increase delays due to messaging overhead. So there is an interest in reducing the number of sampled queues per arriving task. In this paper, we show that the number of sampled queues can be dramatically reduced by using the fact that tasks arrive in batches (called jobs). In particular, we sample a subset of the queues such that the size of the subset is slightly larger than the batch size (thus, on average, we only sample slightly more than one queue per task). Once a random subset of the queues is sampled, we propose a new load-balancing method called batch-filling to attempt to equalize the load among the sampled servers. We show that, asymptotically, our algorithm dramatically reduces the sample complexity compared to previously proposed algorithms.

Collaborative Data Downloading by using Inter-Satellite Links in Satellite Networks

Article

Jan 2017

Satellite systems have attracted great attention from academic and industrial communities in the recent years. There are many satellites that have been launched for weather forecast, environment monitoring, and target surveillance. One important task of the satellites is to download the data they have collected in the space to the ground servers via Earth Stations (ESs). Since satellites move at high speed along their own orbits and have very limited contact time with ESs, satellites may not be able to download all the data they have to the ground on time. In this paper, we propose a collaborative scheme that allows satellites to offload data among themselves using intersatellite links (ISLs) before they come to the contact with the ES, such that satellites will carry the right amount of data according to the length of their contact time with the ES and the throughput of data downloading at ES is maximized. We develop an iterative optimization algorithm that jointly schedules data offload among the satellites and data downloading from satellites to the ES. Extensive simulations have been conducted to evaluate the effectiveness of our proposed method. The simulation results show that the data downloading throughput by using ISL data offload can be increased significantly. In many cases, the throughput reaches close to 100% of the capacity of the ES.

Coflow-Like Online Data Acquisition from Low-Earth-Orbit Datacenters

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