coflow-like online data acquisition from low-earth-orbit...

1536-1233 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMC.2019.2936202, IEEETransactions on Mobile Computing

1

Coflow-like Online Data Acquisition fromLow-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 thesupplementary 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 (alsoreferred to as the LEO based datacenters), which has been considered as a promising and secure paradigm on data storage. Underthe LEO based datacenter architecture, one fundamental challenge is to deal with energy-efficient downloading from space to groundwhile maintaining the system stability. In this paper, we aim to maximize the amount of data admitted while minimizing the energyconsumption, when downloading files from LEO based datacenters to meet user demands. To this end, we first formulate a noveloptimization problem and develop an online scheduling framework. We then devise a novel coflow-like “Join the first K-shortestQueues (JKQ)” based job-dispatch strategy, which can significantly lower backlogs of queues residing in LEO satellites, therebyimproving the system stability. We also analyze the optimality of the proposed approach and system stability. We finally evaluate theperformance of the proposed algorithm through conducting emulator based simulations, based on real-world LEO constellation anduser demand traces. The simulation results show that the proposed algorithm can dramatically lower the queue backlogs and achievehigh energy efficiency.

Index Terms—LEO-based Datacenter, Online Job-Scheduling, Coflow, Drift-plus-Penalty, Energy Efficiency, Queue Stability.

F

1 INTRODUCTION

A LTHOUGH existing state-of-the-art storage systemssuch as NoSQL, NewSQL Databases and Big Data

Querying Platforms [2], can meet the stringent requirementsof users on data storage and management, it is widelyadmitted that those storage systems handling cloud op-erations and data storage are prone to cyber attacks. Tomitigate the widespread global crisis of data insecurity,several well known IT organizations and companies areseeking new data storage paradigms to provide secure datastorage and management. For example, a startup companynamed Cloud Constellation [3] intends to establish a space-based cloud storage network SpaceBelt [1], which aims tooffer secure data storage for Internet service providers, largeenterprises, and government organizations [1], [3].

In this paper, we concentrate on space based datacenterplatforms like SpaceBelt that combine LEO satellites andwell-connected secure ground networks. This system allowsusers 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:[email protected]

• S. Guo is with the Department of Computing and Research Institutefor Sustainable Urban Development (RISUD), The Hong Kong Poly-technic University, Hung Hom, Kowloon, Hong Kong SAR. Email:[email protected]

• W. Liang is with the Research School of Computer Science, Aus-tralian National University, Canberra, ACT 0200, Australia. Email:[email protected]

• K. Wang is with the Department of Electrical and Computer Engineer-ing, University of California, Los Angeles, 90095, CA, USA. Email:[email protected]

• Y. Okabe is with the Academic Center for Computing and Media Studies,Kyoto University, 606-8501, Kyoto, Japan. Email: [email protected]

instead of ground. The advantages of such a system canbe easily recognized since it can isolate data completelyfrom the terrestrial Internet and address some jurisdictionalissues [1]. Inspired by the SpaceBelt project, we believe thatin the upcoming space based cloud era, LEO satellites willundertake more critical roles than just performing as relaydevices for ground core communication networks.

In the LEO based datacenter infrastructure, the data-storage system is built upon multiple LEO satellites witheach equipped with at least one data-storage server. Adataset is distributedly stored across the data-storage sys-tem with multiple duplications, according to a certain re-dundancy policy. Under such an infrastructure, since thecontact window between a ground station and an LEO satel-lite is intermitted and the power budget in LEO satellitesis limited, energy-efficient downloading original files fromLEO based datacenters to meet dynamic demands of usersposes 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 applicableto 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 takingboth mobility of LEO satellites and time-varying downlinksinto account.

As energy supplies in LEO satellites are constrained bylimited energy budgets that keep satellites alive and ensurecommunications [7], [8], we aim to (1) maximize the amountof data admitted; and (2) reduce the energy consumption ofdata transfer while serving admissions of user requests. Tothis end, we first formulate a novel optimization problem



2

for file downloading from a system of LEO based datacen-ters. We then propose an online scheduling algorithm byexploiting the drift-plus-penalty optimization technique [9].Particularly, we design a coflow-like parallel file-downloadstrategy “Join the first K-shortest Queues (JKQ)” for dis-patching jobs to satellite queues. To accelerate data transferin datacenter networks, the technique of coflow [10], [11] isinvented recently, where a coflow is a collection of parallelflows serving the same request, and the flow transfer doesnot stop until the completion of all its constituent flows. Oneadvantage of utilizing the coflow-like strategy is shorteningthe backlogs of queues residing in LEO satellites, where thequeue backlog is measured by the size (bit) of unfinishedjobs in a queue. Small backlogs in queues are indicators ofsystem stability. Inefficient control strategies will incur largequeue backlogs [9]. When the system stability is not wellensured, the queues with large backlogs may lead to packetoverflowing and thus packet losses.

The main contributions of this paper are summarized asfollows.

• We study the data-acquisition problem under theinfrastructure of mobile LEO based datacenters, tomeet 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 queuebacklogs. 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 anemulator − the Satellite Tool Kit. The real-worldtrace driven simulations show that the proposedalgorithm achieves much lower queue backlogs andhigher energy efficiency than other the benchmarkalgorithms for traditional datacenters.

The remainder of the paper is organized as follows.Section 2 reviews the related works. Section 3 presents thesystem model and problem statement. The online schedul-ing algorithm is given in Section 4. Section 5 shows theperformance evaluation, and Section 6 concludes the paper.

2 RELATED WORKS

2.1 Satellite based Communication Networks

Several studies on satellite based communication networkshave been conducted recently. For example, Wu et al. [12]proposed a two-layer caching model for content deliveryservices in satellite-terrestrial networks. Jia et al. [13] studieddata transmission and downloading by exploiting inter-satellite links in LEO satellite based communication net-works. Cello et al. [14] proposed a selection algorithm tomitigate network congestion, using nano-satellites in LEObased networks.

In industry, several representative LEO satellite basedprojects have been announced recently. For example,OneWeb satellite constellation aims to provide global Internetbroadband 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 satellitesystem that offers greater speeds and lower latency thanexisting satellite networks. Boeing plans to launch a projectGiSAT with 702 satellites [17], which can offer twice thecapacity of previous digital payload designs for Cayman-Islands.

From these existing exploration efforts, we find that theLEO satellites have been only considered as supplementaryextensive 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 ofour knowledge, together with our previous study [18], thisarticle is one of the first studies focusing on job schedulingfor such LEO based datacenter infrastructures.

2.2 Green Job Scheduling on Datacenters

Several existing works in literature are leveraging stochasticoptimization framework to study the energy-efficiency is-sues on terrestrial datacenters [19]–[22]. For example, Denget. al. [19], [20] studied how to minimize the operational costof datacenters by utilizing multiple renewable energy re-sources. A MultiGreen online scheduling algorithm [19] wasproposed by applying a two-stage Lyapunov optimizationtechinque. Zhou et. al. [21] proposed a fuel-cell poweredcloud utility indexed maximization problem, which jointlytakes the energy cost, carbon emission and geographicalrequest routing into account. In their subsequent work [22],they designed a carbon-aware online control frameworkby exploiting Lyapunov optimization to find a balance onthe three-way tradeoff between energy consumption, ser-vice level agreement requirement and emission reductionbudget. The common feature of these mentioned stochasticoptimization frameworks and together with this paper isthat the job scheduling is performed under an assumptionthat a priori knowledge of system statistics is not given,this ensures the practicality when deploying the proposedonline algorithms in the real-world environment.

In the perspective of job-dispatch, although there area number of online control solutions in literature for jobscheduling and resource allocation in cloud and datacenternetworks [4]–[6], [23], the work in this paper is essentiallydifferent from them, due to the following reasons. Theseexisting approaches exploit the “Join in the Shortest Queue”scheme when allocating jobs to queues under their onlinecontrol frameworks. However, if the system controller sendsall arrived jobs at the current time slot to a chosen queue,such a scheme will increase the queue backlog sharply, thusdegrading the system stability. In contrast, we here developa new coflow-like JKQ based scheme that dispatches jobsto different queues, aiming to jointly improve energy effi-ciency and maintain lower queue backlogs throughout thedistributed satellites.

Although the proposed coflow-like JKQ based job-dispatch scheme shares similarities with existing works suchas the “batch-sampling” [24] and “batch-filling” [25] loadbalancing algorithms, it should be noticed that the proposedcoflow-like JKQ based scheme is unique under the LEObased datacenter infrastructure. The essential differencesbetween them [24], [25] are summarized as follows. First,

3

the “batch-based” algorithms [24], [25] dispatch multipleredundant copies of each job to a subset of least loadedqueues among the randomly sampled servers. However, dueto the randomness of sampling over all candidate servers,the globally least loaded server may not be included in thesampling of each round. In contrast, in the proposed JKQbased scheme, the target K least loaded servers, i.e., the firstK shortest 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, underthe LEO based datacenter infrastructure, the arrival file-downloading jobs at each time slot are dispatched to the firstK-shortest queues associated with the currently availabledownlink channels. Thus, the set of K-shortest queues arevarying over time due to the mobility of LEO satellites.This is significantly different from that of the batch-basedalgorithms [24], [25].

3 SYSTEM MODEL & PROBLEM STATEMENT

3.1 System ModelInspired by recent modeling studies on clouds [6], [26], weconsider a discrete time-slotted system, where time slots arenormalized to equal integral units t ∈ {1, 2, ...T} and thelength of each time slot (denoted by δ) may range fromhundreds of milliseconds to minutes [27] in reality.

We study an LEO-satellite based datacenter network G =(S ∪ G,E(t)), where S and G are a set of LEO satellitesorbiting in specific planes and a set of terrestrial groundstations, respectively. In particular, E(t) is a set of availabletime-varying downlink channels at time slot t ∈ {1, 2, ...T}between the satellites and the ground stations. Each LEOsatellite 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 andknown in priori, ground stations periodically contact with amobile LEO satellite at predictable time slots. Multiple satel-lites can be in view of a ground station, and multiple groundstations could be in the footprint of a mobile satellite. Thus,a satellite can transmit its data to multiple ground stationsat a time if there are sufficient downlink channels. Theground station network consists of multiple well-connectedground stations, which are located at different geographicallocations, and cooperatively download different chunks of afile from different mobile satellites to meet its user demand.

Let (i, j) ∈ E(t) denote a downlink channel betweena LEO satellite i ∈ S and a ground station j ∈ G, andlet Ct

ij represent the channel state of (i, j) at time slot t.Note that, the state of each time-varying channel can bedirectly measured or predicted [23]. For example, channelstates can be accurately predicted up to one second in future[29]. Thus, we consider that the channel state is known bythe system controller at the beginning of each time slot andremains 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 brokeninto narrow channels via the Frequency Division MultipleAccess (FDMA) technology. The overall bandwidth within afrequency band can increase, by using the frequency reuse

p1p0 p3p2 p4 pmax…

Under c1

Under c2

Under c3

µ=g(p, c)

Power level (p)

Tran

smiss

ion

rate

(µ)

µmax

c1, c2, and c3 are 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)

…

⍺rarki

…

i∈S

Jobs (r, k),k =1,..,Ky(r)

Admission control

If ⍺r=1r∈R(t),t =1,..,T

Arrivalrequests

Jobgeneration

Job dispatch

(a) Admission control and job dispatch

Power allocationprk (t) on (i, j)∈E(t)

Q1 (t)

Qi (t)

Q|S|(t)

…

Time-varyingchannels: E(t)

…

j∈G

Arrival jobs

Jobs

Jobs

Jobs

ij

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 totalnumber of downlink channels in LEO satellite i ∈ S isrepresented by σi. Furthermore, the Time Division MultipleAccess (TDMA) [30] has become a mature satellite commu-nication technology, where a transmission channel is reusedby different transmitters at different time slots.

By defining−→C as a vector of observed channel conditions

of downlinks, the relationship between the power allocationand the transmission rate can be described by referring aclassical concave rate-power curve g(p, c) [7], [23] as shownin Fig. 1, where p is the allocated power, and c ∈

−→C denotes

the current channel condition. In reality, linear piece-wisepower function with a finite set

−→P = [p1, p2, ..., pmax]

of discrete operating power-allocation levels rather thana 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 channelcondition. Furthermore, as shown in Fig. 1, the maximumtransmission rate of each downlink is µmax, i.e.,

g(p, c) ≤ µmax,∀p ∈−→P , c ∈

−→C .

Many types of files Y = {1, 2, ..., Y } are assumed to



4

have been stored at LEO based datacenters in advance.Each file is with a unique size and stored in multiple copiesthroughout all LEO servers, following a certain redundancypolicy, such as repetition based or network coding mecha-nisms. If the former is adopted, the duplications need to berandomly distributed over LEO servers for parallel down-loading; otherwise, the maximum-distance separable (MDS)code [31] is an option. Under either of the mechanisms, wedefine a pair of general storage parameters (Ny,Ky) for anyfile y ∈ Y: each file is duplicated to Ny chunks, any Ky

(≤ Ny) chunks among the Ny chunks can reconstruct theoriginal file. Each of the Ky chunks 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 amapping function y(r) that returns the file type indicatedby r. The corresponding original file y(r) is with storageparameters (Ny(r),Ky(r)). Then, all the file chunks withsize Zy(r) are randomly distributed to the |S| LEO servers.Let f(r) represent the original size of a file y(r), we havef(r) = Ky(r) · Zy(r).

System controller knows of the storage parameters ofeach 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 toreconstruct the original file y(r). In addition, to enforce theService Level Agreement (SLA) [32] between LEO baseddatacenter providers and users, each data-acquisition re-quest has a maximum tolerable downloading delay, whichis measured by time slots and denoted by T r , ∀r ∈ R(t).Even if a chunk cannot be completely downloaded withina contact window between an LEO satellite and a groundstation, the downloading job will continue in the nextcontact opportunity through the seamless service handovertechnology [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 itsusers. Here SLA refers to as a contract between the serviceprovider and its users, serving as the foundation for ex-pected QoS attributes such as the data amount downloadedand traffic rate. In our system model, we consider that theSLA as the desired downloading rate for each chunk shouldnot be violated while a downlink channel is being exploitedfor a chunk-downloading.

3.2 Problem Statement

3.2.1 Three-Step Planning for Each RequestAs shown in Fig. 2(a), an arrived file-acquisition requestr ∈ R(t) is first filtered by an admission control strategy.Only if request r is admitted, the system controller willgenerate Ky(r) equal-sized chunk-downloading jobs (r, k),∀k = 1, 2, ...,Ky(r),∀r ∈ R(t) for it. For brevity, we denoteby Kr = {1, 2, ...,Ky(r)} the job indices for request r. Next,jobs need to be dispatched to queues, each of which residesin an LEO satellite. Particularly, to download file-chunks foreach request in parallel, we perform a coflow-like policy ondispatching jobs to queues. That is, jobs (r, k), ∀k ∈ Kr ,generated for a same request r ∈ R(t) must be dispatched

TABLE 1Notations and Variables

S; G the set of LEO data storage servers;ground stations

E(t)the set of time-varying downlink channelsavailable in time slot t between LEO satellitesand ground stations

δ;T the length of a time slot; the # of all time slotsY ={1,2,...,Y}, all file types in storage system

R(t)the set of all arrival requests at the beginningof time slot t, each wants to access itsassociated original file

(Ny,Ky)storage parameters of an original file y ∈ Y,which is duplicated into Ny chunks, only Ky

out of Ny chunks can recover the original fileZy size of each chunk for file y ∈ Y

T rdata acquisition deadline required by r∈ R(t), measured by time slots

y(r)function that returns the file type demandedby r ∈ R(t)

Kr= {1, 2, ...,Ky(r)}, the set of job indices forrequest r

Iy(r)⊂ S, the set of LEO servers containing the filechunks of original file type y(r), |Iy(r)| = Ny(r)

(r, k)the kth (k = 1, ...,Ky(r)) job generated forrequest r

(i, j)∈ E(t), downlink channel between i ∈ Sand j ∈ G

σi total number of channels in LEO satellite i ∈ S−→P ;−→C

vector of power levels; vector of channelconditions

αrbinary variable denoting admission controlof r ∈ R(t)

f(r)function returning the size of the original filey(r), f(r) = Ky(r)Zy(r)

arki

binary variable indicating the event thatdispatches 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.

prkij (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 ∈

−→P and

channel state c ∈−→C

1{Π}a binary indicator that returns 1 if condition Πis met; 0 otherwise

to Ky(r) different queues for parallel chunk-downloading.Notice that, we here consider the preemptive scheduling ateach queue, which implies that a chunk-downloading jobcan be interrupted by another job at two consecutive timeslots. The preemptive model also implies that every down-loading job allocated in each queue will be rescheduled atthe beginning of each time slot until its downloading isfinished. As shown in Fig. 2(b), the third step is to allocatepower to time-varying downlink channels to decide theirtransmission rates.



5

3.2.2 Problem Formulation

Now under the aforementioned system model, we need tomake crucial control decisions: (1) admission control to allfile-acquisition requests; (2) workload scheduling for chunk-downloading jobs; and (3) power allocations for downlinkchannels.

Variables: To determine whether a request r ∈ R(t) isadmitted, we first define a binary variable αr, which is 1 ifthe request is admitted; 0 otherwise. Further, let Qi(t) (i ∈S) denote the set of jobs dispatched to the queue that residesin satellite i ∈ S at time slot t, we define another binaryvariable arki (∀r ∈ R(t), ∀k ∈ Kr) to represent the eventthat chunk-downloading job (r, k) is allocated to Qi(t). Ifarki = 1, we have Qi(t) ← Qi(t) ∪ {(r, k)}. Each assignedjob (r, k) will be removed from Qi(t) once its maximumtolerant delay T r is violated. That is, the file acquisition ofrequest r is unsuccessful. In the control of power allocation,for a job (r, k) ∈ Qi(t), we define a real-valued variableprkij (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 performancemetric [5], [6], [8]. Particularly, under the LEO based dat-acenter platform, we consider a metric that is equivalent tothroughput, i.e., the amount of data admitted in each time slott. We denote this meteric by φ(t), which is calculated asfollows.

φ(t) =∑

r∈R(t)

αrf(r) =∑

r∈R(t)

αrKy(r)Zy(r). (1)

blackAs mentioned, the data-transmission in satellites is con-

strained by a pre-defined power-budget [7], [8]. If the powerallocation on transmission channels cannot be carefullyscheduled, e.g., allocating too large power level to a down-link with a bad channel condition, much energy will bewasted, thus degrading the amount of data admitted. There-fore, the energy consumption should be minimized whensatellites are transmitting their data to ground stations. Thetotal energy consumption ζ(t) on data transmission of allsatellites at time slot t is then defined as follows.

ζ(t) =∑i∈S

∑(r,k)∈Qi(t)

∑(i,j)∈E(t)

δ · prkij (t). (2)

Objectives: In order to maximize overall the amount ofdata admitted while minimizing the energy consumption si-multaneously, we define a penalty function. Because we aimto describe an online system, the objective is to minimize atime-average penalty that is denoted by Pen.

To make the formulation concise, let Π represent thecondition g(prkij (t), c(t)) > 0, which indicates that the down-loading rate of downlink (i, j) ∈ E(t) is larger than 0with the allocated power prkij (t) and channel condition c(t)at time slot t. Furthermore, since the concept of mean-ratestability of a queue is used in problem formulation, we giveits definition as follows.

Definition 1. A queue Q(t) is mean-rate stable [9] if it

satisfies

limt→∞

supE{|Q(t)|}

t= 0,

where |Q(t)| denotes the backlog of queue Q(t).We then have the following penalty-minimization for-

mulation.

min Pen = limT→∞

1

T

T∑t=1

{β · ζ(t)− φ(t)} (3)

s.t.∑k∈Kr

arki ≤ αr, ∀r ∈ R(t), i ∈ Iy(r). (4)

g(prkij (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) ∈ Qi(t), i ∈ S. (6)

∑(r,k)∈Qi(t)

∑(i,j)∈E(t)

1{Π} ≤ σi, ∀i ∈ S. (7)

∑(r,k)∈Qi(t)

∑(i,j)∈E(t)

prkij (t) ≤ pbgti , ∀i ∈ S. (8)

Qi(t) is mean-rate stable, ∀i ∈ S. (9)

Variable: αr ∈ {0, 1}, arki ∈ {0, 1}, prkij (t) ∈−→P ,

∀r ∈ R(t), k ∈ Kr,∀(i, j) ∈ E(t),∀t = 1, ..., T,

where the coefficient β in Eq. (3) represents the weight(or price) of each unit of energy consumption. Tuning βalso implies changing the relative weighting of the energyconsumption against the amount of data admitted.

Constraint (4) specifies the aforementioned coflow-likepolicy, i.e., the number of chunk-downloading jobs dis-patched to each of its associated satellite i ∈ Iy(r) is either1, 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 forjob (r, k) ∈ Qi(t) needs to be guaranteed, by the requiredaverage downloading rate represented in its right-hand-side, where a time slot is referred to as a valid one to ajob (r, k) only if the downlink (i, j) ∈ E(t) for job (r, k) isallocated with power, i.e., prkij (t) > 0 and g(prkij (t), c(t)) > 0.Further, Constraint (5) also includes the following importantimplications. Since the number of downlinks is limited ineach contact window between the satellites and the groundstations, each downlink channel should be fully exploitedby allocating sufficient power. Thus, an extremely slowspeed to download a chunk in a time slot is not allowed.Constraint (5) is also to enforce the fact that the system needsto download the desired file size of each admitted requestr ∈ R(t) in a long run. Notice that, the second argumentsc(t) of function g(.) represents the current channel conditionof downlink (i, j) ∈ E(t).

Constraint (6) implies that the number of downlinkserving the job (r, k) dispatched to Qi(t) should be no morethan 1. Here, 1{Π} is a binary indicator that returns 1 ifcondition Π is met; or 0 otherwise. Constraint (7) specifiesthat the total number of exploited downlinks at each satellitei ∈ S should be limited by its total number of channelsσi. Let pbgti denote the total power budget of LEO satellitei ∈ S at any time slot, constraint (8) indicates that the total



6

power capacity should be conserved at each satellite whiletransmitting data to ground stations. Finally, Constraint (9)specifies that all queues residing in the LEO satellites needkeeping the mean-rate stable.

4 ONLINE SCHEDULING FRAMEWORK

In this section, we first transform the original problem byapplying the drift-plus-penalty optimization technique [9]to construct an online scheduling framework, which willdeliver a near-optimal solution to the problem. We thenanalyze the optimality of the proposed approach and itsachieved system stability rigorously.

4.1 Problem Transformation

4.1.1 Dynamics of Actual QueuesDenote by Qi(t) the queue backlog as the total size measuredin bits that has not been yet transmitted for jobs in Qi(t).Initially, Qi(1) = 0,∀i ∈ S. The queue dynamics over time foreach satellite is expressed as follows.

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

where

bi(t) =∑

(i,j)∈E(t)

∑(r,k)∈Qi(t)

δg(prkij (t), c(t)). (11)

Here bi(t) represents the total diminishing bits of thebacklog in Qi, and

Ai(t) =∑

r∈R(t)

∑k∈Kr

f(arki), (12)

denotes the total size of all arrived jobs at time slot t whendispatching jobs to queue i ∈ S. Note that, f(arki) is afunction returning the size of the job (r, k) if arki= 1; 0otherwise. That is, f(arki) = Zy(r) · arki.

4.1.2 Virtual QueuesNext, we transform the original optimization objectiveminPen with its constraints into a queue-stability problem[9].

To enforce all constraints on the optimization objectiveminPen, 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 ∈ S correspondingto constraints (4)-(8), respectively. Particularly, the virtualqueues need to be updated in the end of each time slot, andthe update equations are defined as follows.

Λ(t+ 1) = max[Λ(t) + λ(t), 0], t = 1, ..., T, (13)

where Λ represents virtual queuesMri,Hr , Urki,Di andXi,respectively. And λ denotes mri, hr , urki, di and xi, respec-tively. For brevity, we still use Π to represent the conditiong(prkij (t), c(t)) > 0 when using function 1{g(prk

ij (t),c(t))>0} inthe following. In particular, ∀t = 1, ..., T ,

mri(t) =∑k∈Kr

arki − αr, ∀r ∈ R(t), i ∈ Iy(r), (14)

hrkij (t) =f(r)

δT r− g(prkij (t), c(t)), ∀(r,k)∈Qi(t),(i,j)∈E(t),i∈S, (15)

urki(t) =∑

(i,j)∈E(t)

1{Π} − 1,∀(r, k) ∈ Qi(t), i ∈ S, (16)

di(t) =∑

(r,k)∈Qi(t)

∑(i,j)∈E(t)

1{Π} − σi,∀i ∈ S, (17)

and

xi(t) =∑

(r,k)∈Qi(t)

∑(i,j)∈E(t)

prkij (t)− pbgti ,∀i ∈ S. (18)

We consider the initial conditions satisfying Λ(1) = 0 forall virtual queues.

Insight: The virtual queues Λ(t) are used to enforce theconstraint λ(t) ≤ 0, i.e., inequalities (4) to (8). By summingΛ(t) over time slots t = 1, ..., T , we have Λ(T )

T − Λ(1)T ≥

1T

∑T1 λ(t). With Λ(1) = 0, taking expectations on both

sides and letting T → ∞, it yields: limT→∞ sup E{Λ(T )}T ≥

limT→∞ supλ(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→∞ supλ(t) ≤ 0. This means thatthe 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 underupdate equations (10) and (13), we define a Lyapunovfunction of the LEO based datacenter system as follows.

L(Θ(t)) ,1

2[∑i∈S

Qi(t)2 +

∑r∈R(t),i∈Iy(r)

Mri(t)2 +∑i∈S

∑(r,k)∈Qi(t),(i,j)∈E(t)

Hrkij (t)2

+∑

(r,k)∈Qi(t),i∈S

Urki(t)2 +

∑i∈S

Di(t)2 +

∑i∈S

Xi(t)2]. (19)

In fact, L(Θ(t)) calculates a scalar volume of queuecongestion in the LEO based datacenters. Intuitively, a smallvalue of the Lyapunov function implies small backlogs ofboth actual queues and virtual queues, and the holisticsystem tends to be stable consequently.

4.1.3 Drift-plus-Penalty ExpressionTo make the system stable, the Lyapunov function (19) needsto be controlled at each time step to maintain lower conges-tion in queues. Denoted by ∆(Θ(t)) the one-slot conditionalLyapunov 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 expectationof changes in the Lyapunov function (19) over one timeslot. Under the Lyapunov optimization framework [9], thesupremum bound of drift-plus-penalty expression is expectedto be minimized at each time slot to achieve the optimalsolution to the proposed original optimization problem.That is,

min ∆(Θ(t)) + V E{βζ(t)− φ(t)|Θ(t)}, (21)



7

where V is a tunable knob denoting the weight of penalty.We can observe that a positive V in the objective function(21) is to minimize the energy consumption and maximizethe amount of data admitted, while maintaining the stabilityof holistic system simultaneously. A large positive V impliesthat the system operator desires a small penalty, i.e., a smallenergy 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 bothactual and virtual queues, as well as the job queue Qi(t)(i ∈ S) are observable at each slot t, for arbitrary Θ(t),the Lyapunov drift ∆(Θ(t)) of a storage system in theLEO based datacenters under arbitrary control policiessatisfies the following result:

∆(Θ(t)) ≤ B(t) +∑i∈S

Qi(t)E{Ai(t)− bi(t)|Θ(t)}

+∑

i∈Iy(r)

∑r∈R(t)

Mri(t)E{mri(t)|Θ(t)}

+∑i∈S

∑(r,k)∈Qi(t),(i,j)∈E(t)

Hrkij (t)E{hrkij (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) , 12

∑i∈S{(

∑r∈R(t)

Zy(r))2 + |Qi(t)|2σ2

i (δ2µ2max +

p2max +1) + |Qi(t)|(( f(r)

δTr)2 - σ2

i −2σi(1+pmax ·pbgti )+1) + σ2i

+ (pbgti )2} + 12

∑r∈R(t)

Ny(r)K2y(r) is a time-varying positive

constant in each time slot. Note that, |.| returns the sizeof a set.

The proof of Lemma 1 can be seen in Appendix of [34].We then show the upper bound on the drift-plus-penalty

expression of the storage system, by combining objectivefunction (21) and inequality (22).

∆(Θ(t)) + V E{βζ(t)− φ(t)|Θ(t)}

≤ B(t) +∑i∈S

[∑

(r,k)∈Qi(t),(i,j)∈E(t)

Hrkij (t) · f(r)

Trδ−

∑(r,k)∈Qi(t)

Urki(t)

−Di(t)σi −Xi(t)pbgti ] (23)

+∑i∈S

Qi(t)E{Ai(t)|Θ(t)} (24)

+∑

r∈R(t)

αrE{−V f(r)−∑

i∈Iy(r)

Mri(t)|Θ(t)} (25)

+∑

r∈R(t)

∑k∈Kr

∑i∈Iy(r)

E{Mri(t)arki|Θ(t)} (26)

+∑i∈S

∑(r,k)∈Qi(t),(i,j)∈E(t)

E{(V βδ +Xi(t))prkij (t)− [Hrk

ij (t) +δQi(t)]

×g(prkij (t), c(t)) + (Urki(t) +Di(t))1{Π}|Θ(t)}. (27)

4.2 Online Scheduling AlgorithmWe notice that, it is impractical to assume the arrival rateof requests is known in a realistic system setting, because itis 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-definedSatellite Networks [35]–[37] based centralized control mech-anism, we can design a near-optimal online schedulingalgorithm that yields a solution for the system controllerwithout a-priori statistical knowledge of arrival rates, whilemaintaining low backlogs in all queues, and thus stabilizesthe system in a long run.

Through observing the upper bound of drift-plus-penaltyexpression shown from term (23) to term (27), we found thatterm (23) yields a constant at time slot t. Thus, minimizingthe objective function (21) is equivalent to minimizing fromterms (24) to (27) meanwhile.

In particular, we first analyze the Ai(t) appeared in theterm (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) =∑

r∈R(t)

Ari (t),∀i ∈ S. (28)

According to the location of original file indicated by eachrequest,

Ari (t) =

{∑k∈Kr

f(arki) =∑

k∈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) =∑i∈S

Qi(t)∑

r∈R(t)

Ari (t)

≤∑

r∈R(t)

∑i∈Iy(r)

Qi(t)∑k∈Kr

arkiZy(r) (30)

≤∑

r∈R(t)

∑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, thevariables αr , arki and prkij (t) appear in separate terms (25),(26) and (27) in the right-hand-side of the drift-plus-penaltyexpression, 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 schedulingframework:

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 andvirtual queues. In the following, we start with the first phaseof online scheduling framework, i.e., admission control ofrequests, given an arriving request set R(t) at time slot t.

4.2.1 Admission ControlNotice that, the admission decision variables αr (∀r ∈ R(t))are independent of each other among the arrival requests.



8

Algorithm 1: Join in the first K-shortest queues (JKQ)Input : r ∈ R(t), Kr and αr (obtained from (33))Output : arki (∀k ∈ Kr, i ∈ Iy(r))

1 if αr = 1 then2 Ψr ← ∅3 for i ∈ Iy(r) do4 ψri ← Qi(t)Zy(r) +Mri(t)5 Ψr ← Ψr ∪ {ψri}6 initialize arki ← 0, ∀k ∈ Kr, i ∈ Iy(r)

7 for k = 1 to Ky(r) do8 ψri∗ ← arg min(Ψr)9 Ψr ← Ψr − {ψri∗}

10 arki∗ ← 1, where i∗ ← argψri∗

11 Qi∗(t)← Qi∗(t) ∪ {(r, k)}

Thus, we have the following subproblem (32) based on thejoint minimization over the terms (24) and (25):

min αr[∑

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 respectto αr yields the following simple threshold-based admissioncontrol strategy:

αr =

1 :∑

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 V willbenefit to admission ratio.

4.2.2 Coflow-like JKQ based Job DispatchIf 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). Sincethe job-dispatch decisions arki (∀i ∈ Iy(r), k ∈ Kr, r ∈ R(t))are independent among different requests, the job dispatchcan be conducted for different requests concurrently in acomplete 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 isimplied in the definition of virtual queue Mri(t). Thus,subproblem (34) results in a JKQ scheme for the job dispatchphase, which is described as Algorithm 1.

The basic idea is to find the first Ky(r) shortest queues interms 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 DownlinksIn each time slot, the overall energy consumption of chan-nels on all satellites i ∈ S can be determined by minimizingterm (27). Because the decision of power allocation ondownlink channels is independent among the satellites, the

energy-minimization can be also realized by the systemcontroller for each satellite in a distributed manner: thepower allocation at each satellite is implemented individ-ually without knowing anything from other satellites. Let(p, c) represent (prkij (t), c(t)), we then have the followingsubproblem (35).

min Γ(p, c) (35)

s.t. prkij (t) ∈−→P , (r, k) ∈ Qi(t), (i, j) ∈ E(t), i ∈ S,

where Γ(p, c) = (V βδ + Xi(t))prkij (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 p and 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 givenfunction over power supply levels and channel conditions.Thus, the values of the term ∂g(p,c)

∂p in each piecewise

power supply level p ∈−→P can be calculated under the

observed channel condition c. Specifically, let p vary within−→P = [p1, p2, ..., pmax], and by Eq. (36), we obtain a vector ofderivative values:

−→D = [

∂Γ(p, c)

∂p1,∂Γ(p, c)

∂p2, ...,

∂Γ(p, c)

∂pmax].

Furthermore, the concave function g(p, c) implies thatΓ(p, c) is a convex function. Based on Eq. (36), we have thevalley point (p∗, c(t)) of Γ(p, c) such that

∂g(p∗, c(t))

∂p∗=

V βδ +Xi(t)

(Hrkij (t) + δQi(t))

. (37)

From Eq. (37), we can see that a large V implies a largeslope 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 V leads to a smalloptimal power level p∗.

Now, we can make the power-allocation decisions bydiscussing the condition of elements (ele.) in

−→D :

prkij (t)=

pmin, if ele. in

−→D are non-negative;

pmax, if ele. in−→D are 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 levelssuch 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) shouldbe updated by Eq. (10) based on the optimal solutions arkiand prkij (t). Similarly, the virtual queues M(t), H(t), U(t),D(t) and X(t) need to be updated according to Eq. (13) usingall the optimal solutions derived.



9

4.3 Analysis on Optimality and Queue Stability

We now show the optimality and stability of the proposedonline scheduling algorithm. Notice that, the optimalitymeans the performance gap between the proposed onlinealgorithm and the theoretical optimum, while the systemstability implies that all the actual and virtual queues resid-ing the system are stable.

Theorem 1. Given that V > 0, for arbitrary arrival requestsr ∈ R(t), ∀t, the proposed online scheduling framework yieldsa solution ensuring that:

(a) the gap between the achieved time-average penalty andthe optimal one Penopt is within B

V , i.e.,

limT→∞

sup1

T

T∑t=1

{βζ(t)−φ(t)}−Penopt ≤ B

V, (38)

where Penopt = limT→∞

inf 1T

∑Tt=1{βζ∗(t) − φ∗(t)},

ζ∗(t) and φ∗(t) are the resulted energy consumptionand amount of data admitted of the admitted requestsindicated by the optimal solution to the originaloptimization (3), and B = lim

T→∞1T

∑Tt=1B(t);

(b) all actual and virtual queues are mean-rate stable.

Recall that V denotes the weight of penalty in theobjective function (21). From inequality (38), we can seethat a large positive V can lead to a small gap between theachieved time-average penalty and the optimal one Penopt.

Before we proceed to prove Theorem 1, we have thefollowing Lemma.

Lemma 2. (Existence of an optimal randomized stationarypolicy) For any arrival requests r ∈ R(t), ∀t, and for anyε > 0, there is a randomized stationary control policyω that indicates feasible control decisions α∗r , a∗rki andprk

∗

ij for ∀i, j, r, k, t, independent of the current queuebacklogs, and gives the following steady state values:

E{P en(〈α∗r , a∗rki〉, ω(t))} ≤ Penopt + ε (39)E{mri(〈α∗r , a∗rki〉, ω(t))} ≤ ε, ∀r∈R(t),i∈Iy(r)

(40)

E{hrkij (prk∗

ij , ω(t))} ≤ ε, ∀(r,k)∈Qi(t),∀(i,j)∈E(t) (41)

E{urki(prk∗

ij , ω(t))} ≤ ε, ∀(r,k)∈Qi(t),∀(i,j)∈E(t) (42)

E{di(prk∗

ij , ω(t))} ≤ ε, ∀i∈S (43)

E{xi(prk∗

ij , ω(t))} ≤ ε, ∀i∈S (44)

E{Ai(a∗rki, ω(t))} ≤ E{bi(prk

∗

ij , ω(t))}+ ε, ∀i∈S , (45)

where P en, Ai, bi, mri, hrkij , urki, di and xi are theresulting penalty, arrival rate, service capability, andother 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 nowprove Theorem 1 as the follows.

Proof: The proposed online scheduling algorithmfinds a solution that can minimize the right-hand-side of the

inequation (22) over all feasible control decisions, includingthe policy ω, in each time slot, we thus have:

∆(Θ(t)) + V E{Pen(t)|Θ(t)}≤ B(t) + V E{Pen∗(t)|Θ(t)}+

∑r∈R(t)

∑i∈Iy(r)

Mri(t)E{m∗ri(t)|Θ(t)}

+∑i∈S

E{[Qi(t)(A∗i (t)− b∗i (t)) +

∑(r,k)∈Qi(t),(i,j)∈E(t)

Hrkij (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 Pen∗(t) , P en (〈α∗r , a∗rki〉, ω(t)),A∗i (t) , Ai(a

∗rki, ω(t)), b∗i (t) , bi(p

rk∗

ij , ω(t)),m∗ri(t) , mri(〈α∗r , a∗rki〉, ω(t)), hrk∗ij (t) , hrkij (prk

∗

ij , ω(t)),u∗rki(t) , urki(p

rk∗

ij , ω(t)), d∗i (t) , di(prk∗

ij , ω(t)),x∗i (t) , xi(p

rk∗

ij , ω(t)).

Letting ε > 0, and having Lemma 2, the resulting valuesof Pen∗(t), A∗i (t), b∗i (t), m∗ri(t), hrk∗ij (t), u∗rki(t), d∗i (t) andx∗i (t) are independent of the current queue backlogs Θ(t).We then have

E{Pen(t)|Θ(t)} = E{Pen(t)} ≤ Penopt + ε (47)E{A∗i (t)− b∗i (t)|Θ(t)}=E{A∗i (t)− b∗i (t)} ≤ ε, ∀i∈S (48)E{m∗ri(t)|Θ(t)} = E{m∗ri(t)} ≤ ε, ∀i∈S,r∈R(t) (49)

E{hrk∗ij (t)|Θ(t)} = E{hrk∗ij (t)} ≤ ε, (r,k)∈Qi(t),(i,j)∈E(t) (50)

E{u∗rki(t)|Θ(t)} = E{u∗rki(t)} ≤ ε, ∀(r,k)∈Qi(t)(51)

E{d∗i (t)|Θ(t)} = E{d∗i (t)} ≤ ε, ∀i∈S (52)E{x∗i (t)|Θ(t)} = E{x∗i (t)} ≤ ε, ∀i∈S (53)

Plugging (47)-(53) into the right-hand-side of (46) andtaking ε→ 0, we get

∆(Θ(t)) + V E{Pen(t)|Θ(t)} ≤ B(t) + V · Penopt. (54)

Taking expectations of both sides of (54) and using thelaw of iterated expectations,

E{L(Θ(t+ 1))− L(Θ(t))}+ V E{Pen(t)}≤ B(t) + V · Penopt. (55)

Summing over t ∈ {1, 2, ..., T} for T > 1 and using thelaw of telescoping sums, we have

E{L(Θ(T ))− L(Θ(1)}+ VT∑

t=1

E{Pen(t)}

≤T∑

t=1

B(t) + V T · Penopt. (56)

Rearranging terms and neglecting −L(Θ(T )) in theright-hand-side, we can obtain the inequality for ∀T > 1:

1

T

T∑t=1

E{Pen(t)} ≤ Penopt+ 1

V T

T∑t=1

B(t)+1

V TE{L(Θ(1))}.

(57)

Then, taking limits of (57) by T →∞ proves the part (a).To prove part (b), we have the following inequation from



10

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

E{L(Θ(T ))} − E{L(Θ(1)} ≤T∑

t=1

B(t) + V TPenopt. (58)

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

1

2E{∑i∈S

Qi(T )2} ≤ E{L(Θ(1)}+T∑

t=1

B(t) + V TPenopt.

(59)

Then, for ∀i ∈ S, we have

E{Qi(T )2} ≤ 2E{L(Θ(1)}+ 2T∑

t=1

B(t) + 2V TPenopt. (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)}+ 2T∑

t=1

B(t) + 2V TPenopt]12 .

(61)

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

limT→∞

E{|Qi(T )|}T

≤ limT→∞

[2E{L(Θ(1)}

T 2+

2

T 2

T∑t=1

B(t) +2

TV Penopt]

12

= 0. (62)

Thus, all actual queues Qi (∀i ∈ S) are mean-rate stableaccording to Definition 1. Similarly, the mean-rate stabilityof all virtual queues can be proved following the sameroutine. This concludes part (b).

5 PERFORMANCE EVALUATION

In this section, we first elaborate the methodology of per-formance evaluation, including the emulator, trace, metricsand benchmark algorithms used in simulations. We thendemonstrate the simulation results that can prove the highefficiency of the proposed algorithm.

5.1 Settings5.1.1 Emulator of LEO SatellitesWe conduct the trace-driven simulations based on the com-mercial emulator Satellite Tool Kit (STK) to evaluate theperformance of the proposed online algorithm. The STK [38]designed by AGI (Analytical Graphics, Inc.) is an analyticaltool enabling engineers and scientists to analyze the com-plex land, sea, air and space assets. Our simulations areperformed on the Globalstar LEO constellation (a typicalsystem of Walker delta constellation [39]), in which 48satellites are organized into 8 equal-separated orbital planeswith 6 satellites in each. Satellites in the same plane areseparated from each other with equal angular distance. Theorbital period is 114 minutes.

Through selecting 108 locations globally, we first deployground stations under the Globalstar LEO constellation.Then, we generate the synthetic channel-state traces withthree 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 201700:00:00 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 anysatellite and any ground station is recorded and analyzed ineach time slot.

5.1.2 Request TraceWithout loss of generality, we adopt YouTube traffic tracesin [40] as user request traces. To integrate the traces with theGlobalstar LEO constellation, we extract a subset of traceswith 48 data-storage servers, ranging in a 24-hour duration.This set of traces includes 731 file-downloading requestsoriginated from 430 users. The servers are equally attachedto the 48 LEO satellites. The features of the YouTube traffictraces can be observed in Fig. 4 that user requests arrivewith drastically different volumes at different time in oneday. The size of files in small-scale ranges between 11,680bytes and 26,511,812 bytes. In particular, each traffic hasa duration attribute, which is viewed as the downloaddeadline, i.e., Tr in our system model. On the other hand,the duration of file-downloading task ranges from 0.16seconds to 625 seconds, and 90% of them are lower than200 seconds. Notice that, when the number of the userrequests is too few, it can be observed from Fig. 4(a) thatthe number of requests on average in each time slot isless than 20. Thus, the original traces are not suitable toevaluate the job-allocation performance of algorithms. Wethen generate a large-scale of synthesized request tracesbased on the original one. For example, the file size anddownloading duration are randomly generated accordingto the corresponding features of the original traces. We thusobtain a synthesized trace set, which includes 7,310 requestsoriginating from 430 users. In the following, we show theperformance evaluations using the synthesized traces.

5.1.3 Channel Attenuation CoefficientThe number of downlink channels in each satellite is fixedat 100. The bandwidth of each downlink channel is setat 1 Megahertz (MHz). To calculate the transmission rateof 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 thechannel state c. Viewing that the three-state condition model[29] is adopted for a single downlink, we vary v(c) withinthree representative combinations, i.e., {5.03, 3.46, 1.0}, {10,2, 0.1} and {16, 1, 0.01}, to evaluate how the different varyingscales of channel attenuation rate impact the system perfor-mance. The three values in each combination correspondto the channel condition c when it is observed as “good”,“medium” and “bad”, respectively. Note that, the varying-scale of channel attenuation rate describes the changing degreeof transmission rate on downlinks due to the “medium” and“bad” weather conditions. We can see that the varying-scaleof channel attenuation rate become from weak to strong whenv(c) is set from {5.03, 3.46, 1.0} to {16, 1, 0.01}.

5.1.4 Other ParametersFurthermore, referring to the parameter settings shown in[7], the power budget at each satellite is set to 100 Watts.

11

Jobs

Scheduler

Select the firstK-shortest queues to dispatch one job to

each queue

After dispatch

Dispatch

(a) JKQ based algorithm

Scheduler

Select the shortestqueue and dispatch K jobs together

Jobs

After dispatch

Dispatch

(b) JSQ based algorithm [4]–[6]

Scheduler

SelectK queuesrandomly and

dispatch one job to each queue

Jobs

After dispatch

Dispatch

(c) RJQ based algorithm

Fig. 3. Comparison of three algorithms while dispatching 3 chunk-downloading jobs for an admitted request r, with Ky(r)=3, Ny(r)=6. Notice that,all the 6 candidate LEO satellites in the right hand side of each illustrative figure hold the required chunks associated with this request.

0 2 4 6 8

Time (second) ×104

0

50

100

Nu

m.

of

req

ues

t

Synthesized trace

Original trace

(a) Number of requests.

0 10 20 30

File Size (Megabytes)

0

0.5

1

CD

F

Original trace

(b) CDF of file size.

Fig. 4. The extracted original YouTube file-download request trace andits synthesized request trace, which involve 48 data-storage servers andlast for 24 hours in (a). The cumulative distribution function (CDF) of theoriginal file size requested by users is shown in (b).

The power values in−→P are averagely divided into 10 levels

ranging from 0.1 Watt to 1 Watt. We then deploy redundantduplications of each file according to the storage parameters(Ny,Ky) randomly over all LEO servers. Before runningeach round of simulation, we randomly shuffle the filechunks for each file downloading task.

5.2 Metrics

We view the energy consumption and queue backlog as themajor 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 inkiloWatt·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 energyconsumption, are conflict with each other. Therefore, it isnot fair to compare any single perspective of those twometrics. We then design an integrated performance metricthat is associated with both of them. We call it Watt·Sec perbit, which denotes the energy consumed by each bit of filechunks downloaded. It is easy to find that the Watt·Sec perbit is reversely related to the energy efficiency. A low Watt·Secper bit indicates a high energy efficiency of an algorithm.The length of queue backlogs is an indicator of the queuestability in system. Thus, a low backlog performance impliesstrong stability that an algorithm can bring to system.

In addition, by running at least 20 rounds of simulationunder 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 queueamong the n candidates

Step1: sample n (=3) candidate queues randomly

A job

Afterdispatch

...

Large backlogs can be induced in some queues.

Dispatch the next

(a) Principle of each job-dispatch in the batch-based algorithm [24], [25]

13 6 10 24 36 48Size of sample set (batch-size)

0

5

10

15

Job

com

pl. r

atio

(%)

Batch based [24, 25]

(b) Job Completion Ratio (JCR) v.s. batch-size

Fig. 5. Principle and Job Completion Ratio performance of batch basedalgorithm [24], [25].

queues as important metrics to evaluate the performance ofeach algorithm.

5.3 Benchmark AlgorithmsIn 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 performancewith the proposed JKQ based algorithm. The JSQ basedonline algorithm [4]–[6] has been widely adopted on dy-namic job scheduling in cloud computing and datacenternetworks. Under our LEO data-acquisition framework, weimplement a JSQ based algorithm, in which job allocation is



12

0 2000 4000 6000 8000Time slots

0.00.20.40.60.81.0

Adm

issio

n ra

tio JKQ basedJSQ basedRJQ based

(a) Admission ratio

0 2000 4000 6000 8000Time slots

0.00.20.40.60.8

Ener

gy c

onsu

mp. 1e6

JKQ basedJSQ basedRJQ based

8000 85006.2

8.21e5

(b) Energy consumption.

0 2000 4000 6000 8000Time slots

7.5

2.5

2.5

7.5

Pena

lty

1e4


(c) Penalty

0 2000 4000 6000 8000Time slots

0.8

0.9

1.0

Wat

tSe

c pe

r bit 1e 6

JKQ based (Proposed)JSQ based [4]-[6]RJQ based

(d) Watt·Sec per bit

Fig. 6. Time-varying performance comparison among three algorithms,with 7310 synthesized requests, 48 LEO servers, under β = 1, V = 10,v(c)={10, 2, 0.1} while c is {“Good”, “Medium”, “Bad”}, respectively.

conducted by the JSQ mechanism. As illustrated in Fig. 3(b),we argue that the JSQ based algorithm potentially bringsa sharp increase of backlog in the chosen queue for jobdispatching under certain circumstances. In our simulation,we show this through the comparison of the queue backlogsyielded by both algorithms.

The other benchmark algorithm is called Randomly JoinK Queues (RJQ) based algorithm. Although RJQ is a randomselection based algorithm, it does not arbitrarily select anyrandom satellite queues as the job-dispatch destinationsfor chunk-downloading jobs. As shown in Fig. 3(c), basedon the (Ny(r), Ky(r)) file-storage strategy, only Ky(r) outof the Ny(r) satellites containing the encoded file chunksassociated with a file-download request r can be selected asthe job-dispatch destinations.

5.4 Simulation Results5.4.1 Job Completion Ratio of Batch based AlgorithmAs mentioned in Section 2, the job-dispatch mechanismof 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 ofthe original batch-based algorithm under the emphasizedLEO based datacenter infrastructure. Fig. 5(a) illustrates thebasic idea of the batch-based algorithm, which includesrandomly sampling a specified number (i.e., the batch size[24], [25]) of candidate queues for each arrived job, andselecting the shortest queue among the sampled candidatesas the job-dispatch destination. Through varying the batchsize from 1 to 48, and setting the β, V , Ny and Ky to 1, 10, 6and 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 shownin Fig. 5(b). We can see that the original batch-based algo-rithm exhibits a very low JCR performance while varyingthe batch size from 1 to 48. Notice that, once the batchsize reaches to 48, all LEO servers will be sampled as thecandidates to choose the least loaded server for job dispatch

in the batch based algorithm. It means that even though allthe LEO servers are examined for finding the queue-shortestdestination server for each job, the JCR has only around11 % on average. This is because the queue-shortest serverchosen from the sampled set may not contain the requiredfile-chunk of a specified request.

Since the JCR of the original batch based algorithm istoo low, we omit its performance comparison with otheralgorithms in the subsequent results.

5.4.2 Time Varying PerformanceIn this group of simulations, under the same parametersettings as we did for Fig. 5, we examine the admission ratioand energy efficiency yielded by the three online algorithmsillustrated in Fig. 3.

From Fig. 6(a), we find that the admission ratios ofall three algorithms are 100% in the end. This is becausethe current parameter settings match the admission controlrepresented by equation (33). Thus, the amount of dataadmitted 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 JKQbased algorithm consumes the least energy comparing withthe other two algorithms.

Fig. 6(c) shows the penalty performance, which is theobjective of the original minimization problem (3). In thetransformed problem (21), not only is the penalty needed tobe minimized, but also the Lyapunov drift ∆(Θ(t)) must beminimized as well. Interestingly, on one hand, we observethat the panalties by the JSQ based algorithm grow overtime, showing a contrary descending performance underthe other two algorithms. The reason behind is as follows.Under the JSQ based algorithm, the chunk downloadingjobs are always dispatched to the shortest queues, where thequeue backlog increases dramatically. Thus, the JSQ basedalgorithm has to devote much great efforts to maintainthe Lyapunov drift ∆(Θ(t)) in a low level and to sacrificethe penalty performance, even though the current weightof penalty V is set at 10 while the weight of Lyapunovdrift ∆(Θ(t)) is only 1. On the other hand, the proposedJKQ based algorithm shows descending and much lowerpenalties 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·Secper bit. From which, we observe that JKQ based algorithmachieves lower time-varying Watt·Sec per bit than that of theJSQ and RJQ based algorithms. This observation impliesthat the proposed JKQ based algorithm has the highestenergy efficiency against the other two benchmarks. Theinsight behind the high energy-efficiency of our proposedalgorithm is that the coflow-like JKQ based job-dispatchstrategy dispatches jobs to a larger number of satellites thatare with good weather conditions for its downlinks or withlower queue backlogs in a high probability than JSQ andRJQ do.

5.4.3 Impact of Varying-Scale of Channel Attenuation RateAs 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}, toevaluate the impact of different varying scales of channel



13

8.15 8.25 8.35Watt Sec per bit 1e 7

0.00.20.40.60.81.0

CD

F JKQ basedJSQ basedRJQ based

(a) Watt·Sec per bit

94 96 98 100Job completion ratio (%)

0.250.500.751.00

CD

F


(b) JCR

1 2 3 4 5Packet loss rate (%)

0.250.500.751.00

CD

F


(c) CDF of packet loss rate

0 100 200 300 400Queue backlog (Mbits)

0.0

0.5

1.0

CD


(d) CDF of backlog

Fig. 7. Metrics of algorithms when β is fixed at 1, with 7310 synthesized requests, 48 LEO servers, under v(c) = {5.03, 3.46, 1.0} if c is {“Good”,“Medium”, “Bad”}, respectively.

7.9 8.3 8.7 9.1 9.5Watt Sec per bit 1e 7

0.00.20.40.60.81.0

CD

F




0.250.500.751.00

CD

FJKQ basedJSQ basedRJQ based

(b) JCR


0.250.500.751.00

CD

F




0.0

0.5

1.0

CD


(d) CDF of backlog

Fig. 8. Metrics of algorithms when β is fixed at 1, with 7310 synthesized requests, 48 LEO servers, under v(c) = {10, 2, 0.1} if c is {“Good”,“Medium”, “Bad”}, respectively.

8.8 8.9 9.0 9.1 9.2 9.3 9.4Watt Sec per bit 1e 7

0.00.20.40.60.81.0

CD

F




0.250.500.751.00

CD


(b) JCR


0.250.500.751.00

CD

FJKQ basedJSQ basedRJQ based



0.0

0.5

1.0

CD


(d) CDF of backlog

Fig. 9. Metrics of algorithms when β is fixed at 1, with 7310 synthesized requests, 48 LEO servers, under v(c) = {16, 1, 0.01} if c is {“Good”,“Medium”, “Bad”}, respectively.

0 10 20 30 40 50Job waiting time (sec)

0.20.40.60.81.0

CDF


(a) v(c) = {5.03, 3.46, 1}


0.20.40.60.81.0

CDF JKQ basedJSQ basedRJQ based

(b) v(c) = {10, 2, 0.1}


0.20.40.60.81.0

CDF JKQ based

JSQ basedRJQ based

(c) v(c) = {16, 1, 0.01}

Fig. 10. Job Waiting Time (JWT) of algorithms when β is fixed at 1 and V is 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 performanceof three algorithms in terms of energy efficiency, JCR, Cu-mulative Distribution Function (CDF) of packets lost andCDF of backlog, under three attenuation rate combinations,respectively.

First, by comparing Fig. 7(a), 8(a) and 9(a), we can seethat the difference of energy efficiency of three algorithms issmall under low varying-scale of channel attenuation rate,i.e., when v(c) = {5.03, 3.46, 1.0} if c is {“Good”, “Medium”,“Bad”}, respectively. However, under large varying-scaleof channel attenuation rate combinations, i.e., when v(c)= {10, 2, 0.1} and {16, 1, 0.01}, the energy efficiency ofour proposed JKQ based algorithm shows growing benefits

than the other two benchmarks. This feature proves therobustness of our JKQ based algorithm, because it has thebest energy efficiency under the channel transmission rate issuper sensitive to the weather conditions when v(c) = {16,1, 0.01} if c is {“Good”, “Medium”, “Bad”}, respectively.

Second, from Fig. 7(b), 8(b) and 9(b), we observe that thejob completion ratios of all three algorithms perform veryclose to each other. On the other hand, when the varying-scale of channel attenuation rate becomes large, the JCR ofalgorithms degrades a little bit. The reason can be attributedto that the transmission rate becomes very low when achannel meets the bad weather condition under the largevarying-scale of channel attenuation rate. Thus, there aremore jobs, which cannot complete their chunk-downloading



14

0 2000 4000 6000 8000Time slots

43210

Pena

lty1e4


(a) v(c) = {5.03, 3.46, 1}

0 2000 4000 6000 8000Time slots

7.5

2.5

2.5

7.5

Pena

lty

1e4


(b) v(c) = {10, 2, 0.1}

0 2000 4000 6000 8000Time slots

0.00.20.40.60.81.0

Pena

lty

1e5


(c) v(c) = {16, 1, 0.01}

Fig. 11. Penalty performance of algorithms when β is fixed at 1 and V is fixed at 10, under different varying scales of channel attenuation rate.

0 2000 4000 6000 8000Time slots

0.8

0.9

1.0

Wat

tSe

c pe

r bit 1e 6


100 700 1300 19008.0

8.5 1e 7

(a) v(c) = {5.03, 3.46, 1}

0 2000 4000 6000 8000Time slots

0.8

0.9

1.0

Wat

tSe

c pe

r bit 1e 6


100 700 1300 19000.80.9

1e 6

(b) v(c) = {10, 2, 0.1}

0 2000 4000 6000 8000Time slots

0.8

0.9

1.0

Wat

tSe

c pe

r bit 1e 6


100 300 5000.850.900.95

1e 6

(c) v(c) = {16, 1, 0.01}

Fig. 12. Watt·Sec per bit performance of algorithms when β is fixed at 1 and V is fixed at 10, under different varying scales of channel attenuationrate.

2 4 6 8 100.4

0.6

0.8

1.0

Ener

gy c

ons.

(KW

S) 1e3


(a) Energy consum. (KW·s).

2 4 6 8 100.6

0.7

0.8

0.9

1.0

Wat

tSec

per

bit

1e 6


(b) Watt·Sec per bit.

2 4 6 8 1060

70

80

90

100

Job

com

pl. r

atio

(%)


(c) Job completion ratio (%).

2 4 6 8 102

4

6

8

10

Pack

et lo

ss ra

te (%

)


(d) Packet loss rate (%).

Fig. 13. Metric examination among the three algorithms with 7310 requests and 48 LEO servers, while varying β from 1 to 10, and the channelattenuation rate v(c) is set to {10, 2, 0.1} while c is {“Good”, “Medium”, “Bad”}, respectively.


0.0

0.5

1.0

CD

F JKQ based, =1JSQ based, =1RJQ based, =1

(a) β=1


0.0

0.5

1.0

CD


(b) β=5


0.0

0.5

1.0

CD


(c) β=10

Fig. 14. Backlog comparison of three algorithms while varying β within {1, 5, 10}, and setting the channel attenuation rate v(c) to {10, 2, 0.1} if cis {“Good”, “Medium”, “Bad”}, respectively.

under this situation, than that under a milder varying-scaleof 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 threealgorithms; (2) the packet-loss performance of the JKQ basedalgorithm is similar to that of the RJQ based algorithm. Thisis because the possibility of encountering bad transmissionconditions under JKQ and RJQ based algorithms is higherthan that under the JSQ based algorithm. Associated withthe JCR performance, the packet-loss amount grows whenthe 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 ofchannel attenuation rate, respectively. We see that there isalmost no difference among the three CDF figures, whichindicate that the backlog performance yielded by the threealgorithms is not affected by the varying scales of channelattenuation rate. It is also worth noting that the proposedJKQ based algorithm has the lowest backlog performanceamong the three algorithms. The reason is very clearlyillustrated in Fig. 3 and omitted here.

Next, by recording all the job waiting time (JWT) of eachjob allocated to LEO queues, we compare the JWT perfor-



15

3 4 5 6Ky

0.7

0.9

1.1En

ergy

con

s. (K

WS) 1e3

JKQJSQRJQ

(a) Energy consum. (KW·s).

3 4 5 6Ky

0.8

0.9

1.0

Wat

tSec

per

bit

1e 6

Distance is:1.4e-07

Distance is:1.6e-07 Distance is:

1.7e-07

Distance is:1.8e-07

JKQJSQ

RJQ

(b) Watt·Sec per bit.

3 4 5 6Ky

91

94

97

100

Job

com

pl. r

atio

(%)

JKQJSQRJQ

(c) Job completion ratio (%).

3 4 5 6Ky

1

2

3

4

Pack

et lo

ss ra

te (%

)

JKQJSQRJQ

(d) Packet loss rate (%).

Fig. 15. Metric examination among the three algorithms with 7310 requests and 48 LEO servers, while varying Ky from 3 to 6, fixing Ny =6, andthe channel attenuation rate v(c) is set to {10, 2, 0.1} while c is {“Good”, “Medium”, “Bad”}, respectively.

0 5 10 15 20 25 30Job waiting time (sec)

0.20.40.60.81.0

CD

F JKQ, Ky=3JSQ, Ky=3RJQ, Ky=3

(a) Ky = 3.


0.2

0.4

0.6

0.8

1.0C

DF JKQ, Ky=4

JSQ, Ky=4RJQ, Ky=4

(b) Ky = 4.


0.2

0.4

0.6

0.8

1.0

CD


(c) Ky = 5.


0.4

0.6

0.8

1.0

CD


(d) Ky = 6.

Fig. 16. Job-waiting-time (JWT) performance among the three algorithms with 7310 requests and 48 LEO servers, while varying Ky from 3 to 6,fixing Ny =6, and the channel attenuation rate v(c) is set to {10, 2, 0.1} while c is {“Good”, “Medium”, “Bad”}, respectively.

0 20 40 60 80 100Queue backlog (Mbits)

0.0

0.5

1.0

CD


(a) Ky = 3.


0.0

0.5

1.0

CD


(b) Ky = 4.


0.0

0.5

1.0C

DF JKQ, Ky=5

JSQ, Ky=5RJQ, Ky=5

(c) Ky = 5.


0.0

0.5

1.0

CD


(d) Ky = 6.

Fig. 17. Backlog comparison of three algorithms while varying Ky from 3 to 6, fixing Ny =6, and setting the channel attenuation rate v(c) to {10, 2,0.1} if c is {“Good”, “Medium”, “Bad”}, respectively.

mance of three algorithms under different combinations ofchannel attenuation rate in Fig. 10. These three CDF figuresshow that: (1) the JWT of all three algorithms performs thesame under each group of simulation setting; (2) the overallJWT grows when the varying-scale of channel attenuationrate changes from small to large. The first observationindicates that the JWT performance is not affected by thejob-dispatch schemes. The reason of the second observationis that the large varying-scale of channel attenuation rate,where v(c) = {10, 2, 0.1} or {16, 1, 0.01}, makes the packettransmission in downlinks very difficult under the non-good weather conditions. Thus, the jobs waiting in queuesneed to stay for longer durations than that under a mildervarying-scale of channel attenuation rate.

We then evaluate the penalty performance under thedifferent varying scales of channel attenuation rate throughFig. 11, from which we see different performance curvesunder 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 Lyapunovdrift ∆(Θ(t)) is minimized for short queues throughout theLEO satellites as well. Under different channel attenuationrates where the short queues are easily maintained when

V (c)={5.03, 3.46, 1}, a low penalty (indicates a high overalldata amount downloaded, or a low cumulative energyconsumption, or both) is easier to acheive. In contrast, underlarge varying-scale of channel attenuation rate, e.g., whenV (c) = {10, 2, 0.1} and {16, 1, 0.01}, the data transmissionvia the downlinks will heavily be impacted by the badweather conditions, and large queue backlogs are easily tobe incurred. Thus, algorithms tend to ensure the systemstability by sacrificing the penalty performance. That is whywe 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 bitunder three algorithmes. The comparison is shown in Fig.12. From which, we can see that the proposed JKQ basedalgorithm significantly outperforms the other two on energyconsumptions. On the other hand, it is can be seen thatunder the large varying-scale of channel attenuation rates,e.g., when v(c) = {10, 2, 0.1} and {16, 1, 0.01}, the energyconsumption of per bit of downloaded data becomes higherthan that under a small varying-scale of channel attenuationrate when v(c) = {5.03, 3.46, 1}.

5.4.4 Impact of Varying βWe then evaluate the impact of the weight of energy con-sumption by varying β from 1 to 10, using the synthesized



16

trace file associated with 7310 requests and 48 LEO servers.The channel attenuation rate v(c) is set to {10, 2, 0.1}while cis {“Good”, “Medium”, “Bad”}, respectively. In this groupof simulations, the admission ratios of all algorithms arealways 100% and thus omitted here. We mainly examine theperformance of algorithms in terms of the energy consump-tion, energy efficiency, job completion ratio and packet lossrate.

Fig. 13(a) and 13(b) illustrate the overall cumulative en-ergy consumption and the energy efficiency versus varyingβ, respectively. We can see that: (1) the performance trendsshown in these two figures are same; (2) the proposed JKQbased algorithm exhibits the best energy efficiency againstthe other two, especially much higher than that of the JSQbased algorithm; (3) the increasing β makes the cumulativeenergy consumption decreasing and the energy efficiencyincreasing. The reason of the third observation is that alarge β implies a large weight of energy consumption inthe objective function of the original penalty-minimizationproblem. Thus, the growing β degrades the energy con-sumption. When β is larger than 8, the benefit of largeenergy-consumption weight becomes saturated gradually.Furthermore, a coin always has two sides. A large weightof energy-consumption, i.e., a large β, also induces nega-tive effects under our file acquisition system. Because oncethe weight of energy-consumption grows bigger, the fileacquisition system tends to save energy. However, this maydamage the job completion ratio and increase packet lossrate. These two concerns are verified by Fig. 13(c) and Fig.13(d), respectively. Fig. 13(c) shows that the job completionratio performance of JKQ based algorithm is slightly lowerthan that of the JSQ based algorithm, while β increases to10. In Fig. 13(d), the packet loss rate of JKQ based algorithmis a little bit higher than that of the JSQ based algorithm.Therefore, setting an appropriate β needs to consider thenontrivial tradeoff between the energy-consumption and thejob completion ratio.

Finally, under the same parameter settings with Fig. 13,Fig. 14(a), 14(b) and 14(c) exhibit the backlog comparison ofthe three algorithms while setting β to 1, 5, and 10. We thenhave the following two observations. (1) Under each β, theproposed JKQ based algorithm outperforms the JSQ basedalgorithm overwhelmingly in terms of the queue backlogsize. Furthermore, since the RJQ based algorithm randomlyselects the target K queues to allocate K jobs for eachrequest, its backlog performance is much better than thatof the JSQ based, but still worse than that of the JKQ based.(2) The varying β has no effect on the distribution of queuebacklog 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 Ny at 6. From thefour metrics shown in Fig. 15, we can observe that theenergy 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 alsosee that the Wat·Sec per bit performance distance betweenthe proposed JKQ and JSQ algorithms enlarges from 1.4e-7 to 1.8e-7 while Ky grows from 3 to 6. We attributethis result to the following reason. When Ky grows larger,

the proposed JKQ algorithm will dispatch the Ky chunk-downloading jobs of a file-download request to Ky satellitequeues, much more than the JSQ does. Thus the merit ofJKQ will become more apparent comparing with that of JSQ.Fig. 16 shows that the job-waiting-time of all downloadingjobs shrinks while Ky enlarges. This is because the size ofeach chunk-downloading job becomes smaller when eachfile was divided into more chunks. Due to the same reason,Fig. 17 illustrates that the queue backlogs of satellites keepdecreasing while Ky grows from 3 to 6.

Through all trace-driven simulation results, we can sum-marize the following facts. The proposed JKQ algorithmoutperforms the batch-based dispatch algorithm [24], [25]significantly in terms of job completion ratio. Under differ-ent varying scales of channel attenuation rate, the proposedJKQ based algorithm outperforms JSQ and RJQ in terms ofenergy efficiency. JKQ is also able to yield shorter queuebacklogs than that under the other two algorithms.

6 CONCLUSION

In this paper, we studied how to maximize the overallamount 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, whichcan drastically reduce backlogs of queues in satellites. Wealso 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 throughexperimental simulations using the real-world traces. Theevaluation results show that the proposed online algorithmexhibits its merits in terms of short queue backlogs and highenergy efficiency.

7 ACKNOWLEDGEMENT

This work is partially supported by NSFC under researchgrant 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 SunYat-Sen University, China.

REFERENCES

[1] “Spacebelt: The global cloud platform above all others,” 2016.[Online]. Available: http://spacebelt.com/

[2] M. Strohbach, J. Daubert, H. Ravkin, and M. Lischka, Big DataStorage. Springer International Publishing, 2016, pp. 119–141.

[3] “The information ultra-highway for enterprises and govern-ments,” 2017. [Online]. Available: http://cloudconstellation.com/

[4] S. Maguluri, R. Srikant, and L. Ying, “Stochastic models of loadbalancing and scheduling in cloud computing clusters,” in Proc.of IEEE Conference on Computer Communications (INFOCOM), 2012,pp. 702–710.

[5] S. Maguluri and R. Srikant, “Scheduling jobs with unknownduration in clouds,” IEEE/ACM Transactions on Networking (TON),vol. 22, no. 6, pp. 1938–1951, 2014.

[6] F. Liu, Z. Zhou, H. Jin, B. Li, B. Li, and H. Jiang, “On arbitratingthe power-performance tradeoff in saas clouds,” IEEE Transactionson Parallel and Distributed Systems (TPDS), vol. 25, no. 10, pp. 2648–2658, 2014.

[7] M. J. Neely, E. Modiano, and C. E. Rohrs, “Power allocationand routing in multibeam satellites with time-varying channels,”IEEE/ACM Transactions on Networking (TON), vol. 11, no. 1, pp.138–152, 2003.



17

[8] Y. Yang, M. Xu, D. Wang, and Y. Wang, “Towards energy-efficientrouting in satellite networks,” IEEE Journal on Selected Areas inCommunications, vol. 34, no. 12, pp. 3869–3886, 2016.

[9] M. J. Neely, “Stochastic network optimization with applicationto communication and queueing systems,” Synthesis Lectures onCommunication Networks, vol. 3, no. 1, pp. 1–211, 2010.

[10] Q. Liang and E. Modiano, “Coflow scheduling in inputqueuedswitches: Optimal delay scaling and algorithms,” in Proc. of IEEEInternational Conference on Computer Communications (INFOCOM),2017, pp. 1–9.

[11] W. Wang, S. Ma, B. Li, and B. Li, “Coflex: Navigating the fair-nessefficiency tradeoff for coflow scheduling,” in Proc. of IEEEInternational Conference on Computer Communications (INFOCOM),2017, pp. 1–9.

[12] H. Wu, J. Li, H. Lu, and P. Hong, “A two-layer caching model forcontent delivery services in satellite-terrestrial networks,” in IEEEGlobal Communications Conference (GLOBECOM), 2016, pp. 1–6.

[13] X. Jia, T. Lv, F. He, and H. Huang, “Collaborative data download-ing by using inter-satellite links in leo satellite networks,” IEEETransactions on Wireless Communications, vol. 16, no. 3, pp. 1523–1532, 2017.

[14] M. Cello, M. Marchese, and F. Patrone, “Coldsel: A selectionalgorithm to mitigate congestion situations over nanosatellite net-works,” in IEEE Global Communications Conference (GLOBECOM),2016, pp. 1–6.

[15] “Oneweb satellite constellation,” March 2017. [Online]. Available:https://en.wikipedia.org/wiki/OneWeb satellite constellation

[16] “Spacex satellite constellation.” [Online]. Available:https://en.wikipedia.org/wiki/SpaceX satellite constellation

[17] “Gisat-1.” [Online]. Available:https://en.wikipedia.org/wiki/GiSAT-1

[18] H. Huang, S. Guo, and K. Wang, “Envisioned wireless big datastorage for low-earth-orbit satellite-based cloud,” IEEE WirelessCommunications, vol. 25, no. 1, pp. 26–31, 2018.

[19] W. Deng, F. Liu, H. Jin, C. Wu, and X. Liu, “Multigreen: Cost-minimizing multi-source datacenter power supply with onlinecontrol,” in Proceedings of the fourth international conference on Futureenergy systems. ACM, 2013, pp. 149–160.

[20] W. Deng, F. Liu, H. Jin, B. Li, and D. Li, “Harnessing renewableenergy in cloud datacenters: opportunities and challenges,” IEEENetwork, vol. 28, no. 1, pp. 48–55, 2014.

[21] Z. Zhou, F. Liu, B. Li, B. Li, H. Jin, R. Zou, and Z. Liu, “Fuelcell generation in geo-distributed cloud services: A quantitativestudy,” in 2014 IEEE 34th International Conference on DistributedComputing Systems (ICDCS). IEEE, 2014, pp. 52–61.

[22] Z. Zhou, F. Liu, R. Zou, J. Liu, H. Xu, and H. Jin, “Carbon-awareonline control of geo-distributed cloud services,” IEEE Transactionson Parallel and Distributed Systems (TPDS), vol. 27, no. 9, pp. 2506–2519, 2016.

[23] M. J. Neely, E. Modiano, and C. E. Rohrs, “Dynamic powerallocation and routing for time-varying wireless networks,” IEEEJournal on Selected Areas in Communications, vol. 23, no. 1, pp. 89–103, 2005.

[24] K. Ousterhout, P. Wendell, M. Zaharia, and I. Stoica, “Sparrow:distributed, low latency scheduling,” in Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles. ACM,2013, pp. 69–84.

[25] L. Ying, R. Srikant, and X. Kang, “The power of slightly morethan one sample in randomized load balancing,” Mathematics ofOperations Research, 2017.

[26] M. Lin, A. Wierman, L. L. Andrew, and E. Thereska, “Dynamicright-sizing for power-proportional data centers,” IEEE/ACMTransactions on Networking (TON), vol. 21, no. 5, pp. 1378–1391,2013.

[27] D. Xu and X. Liu, “Geographic trough filling for internet data-centers,” in Proc. of IEEE Conference on Computer Communications(INFOCOM), 2012, pp. 2881–2885.

[28] J. Castaing, “Scheduling downloads for multi-satellite, multi-ground station missions,” in Proc. Small Satellite Conf. (SSC), 2014,pp. 1–12.

[29] J. Choi and V. Chan, “Predicting and adapting satellite chan-nels with weather-induced impairments,” IEEE Transactions onAerospace and Electronic Systems, vol. 38, no. 3, pp. 779–790, 2002.

[30] L. J. Ippolito and L. J. Ippolito Jr, Satellite communications systemsengineering: atmospheric effects, satellite link design and system perfor-mance. John Wiley & Sons, 2017.

[31] B. Li, A. Ramamoorthy, and R. Srikant, “Mean-field-analysis ofcoding versus replication in cloud storage systems,” in Proc. ofIEEE Conference on Computer Communications (INFOCOM), 2016,pp. 1–9.

[32] P. Patel, A. H. Ranabahu, and A. P. Sheth, “Service level agreementin cloud computing,” in Conference on Object Oriented Program-ming Systems Languages and Applications, Orlando, Florida, Orlando,Florida, USA, Oct. 2009, pp. 1–10.

[33] B. Yang, Y. Wu, X. Chu, and G. Song, “Seamless handover insoftware-defined satellite networking,” IEEE Communications Let-ters, vol. 20, no. 9, pp. 1768–1771, 2016.

[34] [Online]. Available: https://drive.google.com/file/d/1-YtdLytVO2y2p yvCF51cuFZ-po LNtC/view?usp=sharing

[35] J. Bao, B. Zhao, W. Yu, Z. Feng, C. Wu, and Z. Gong, “Opensan:a software-defined satellite network architecture,” in ACM SIG-COMM Computer Communication Review, vol. 44, no. 4, 2014, pp.347–348.

[36] L. Bertaux, S. Medjiah, P. Berthou, S. Abdellatif, A. Hakiri,P. Gelard, F. Planchou, and M. Bruyere, “Software defined net-working and virtualization for broadband satellite networks,”IEEE Communications Magazine, vol. 53, no. 3, pp. 54–60, 2015.

[37] J. Nobre, D. Rosario, C. Both, E. Cerqueira, and M. Gerla, “Towardsoftware-defined battlefield networking,” IEEE CommunicationsMagazine, vol. 54, no. 10, pp. 152–157, 2016.

[38] [Online]. Available: https://en.wikipedia.org/wiki/Systems Tool Kit/[39] J. Wang, L. Li, and M. Zhou, “Topological dynamics characteriza-

tion for leo satellite networks,” Computer Networks, vol. 51, no. 1,pp. 43–53, 2007.

[40] M. Zink, K. Suh, Y. Gu, and J. Kurose, “Watch global, cachelocal: Youtube network traffic at a campus network-measurementsand implications,” Computer Science Department Faculty PublicationSeries, p. 177, 2008.

Huawei Huang (M’16) received his Ph.D inComputer Science and Engineering from theUniversity of Aizu, Japan. He is currently anassociate 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 receivedthe best paper award of TrustCom-2016. Heused to be a visiting scholar at the Hong KongPolytechnic University (2017-2018), a post-doctoral research fellow of JSPS (2016-2018),

an assistant professor at Kyoto University, Japan (2018-2019). He is amember of the IEEE.

Song Guo (M’02-SM’11) is a Full Professor withthe Department of Computing, Hong Kong Poly-technic University, Hong Kong. He received hisPhD degree in computer science from Univer-sity of Ottawa. He has authored or coauthoredover450 papers in major conferences and jour-nals. His current research interests include bigdata, cloud and edge computing, mobile com-puting, and distributed systems. Prof. Guo wasa recipient of the 2019 TCBD Best ConferencePaper Award, the 2018 IEEE TCGCC Best Mag-

azine Paper Award, the 2017 IEEE SYSTEMS JOURNAL Annual BestPaper 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 chairfor numerous IEEE conferences. He currently serves in the Board ofGovernors of the IEEE Communications Society.



18

Weifa Liang (M’99-SM’01) received the PhDdegree from the Australian National Universityin 1998, the ME degree from the University ofScience and Technology of China in 1989, andthe BSc degree from Wuhan University, Chinain 1984, all in computer science. He is currentlya professor in the Research School of ComputerScience at the Australian National University. Hisresearch interests include design and analysisof energy-efficient routing protocols for wirelessad hoc and sensor networks, cloud computing,

software-defined networking, virtualized network function services, de-sign and analysis of parallel and distributed algorithms, approximationalgorithms, combinatorial optimization, and graph theory. He is a seniormember 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 to2015, where he is a Senior Research Professor.He was a Research Fellow in the Hong KongPolytechnic University, Hong Kong, from 2017to 2018, and a Professor in Nanjing Universityof Posts and Telecommunications. His current

research interests are mainly in the area of big data, wireless com-munications and networking, energy Internet, and information securitytechnologies. He is the recipient of IEEE GLOBECOM 2016 Best PaperAward, IEEE TCGCC Best Magazine Paper Award 2018, IEEE TCBDBest Conference Paper Award 2019, and IEEE ISJ Best Paper Award2019. He serves/served as an Associate Editor of IEEE Access, anEditor of Journal of Network and Computer Applications, and a GuestEditor of IEEE Network, IEEE Access, Future Generation ComputerSystems, Peer-to-Peer Networking and Applications, IEICE Transac-tions on Communications, Journal of Internet Technology, and FutureInternet.

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. Headvanced to an associate professor of Data Pro-cessing Center in 1994 and moved to GraduateSchool of Informatics in 1998. Since 2002 hehas been a professor of Division of NetworkingResearch, Academic Center for Computing andMedia 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.

coflow-like online data acquisition from low-earth-orbit...

Documents