Time-Varying Resource Graph Based Resource Model for Space-Terrestrial Integrated Networks

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Time-Varying Resource Graph Based Resource
Model for Space-Terrestrial Integrated Networks
Long Chen†, Feilong Tang†, Zhetao Li‡, Laurence T. Yang§, Jiadi Yu†, Bin Yao†
†Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
‡College of Computer, Xiangtan University, Xiangtan, China
§Department of Computer Science, St. Francis Xavier University, Antigonish, Canada
Emails: nirver1994@sjtu.edu.cn, tang-fl@cs.sjtu.edu.cn, liztchina@hotmail.com,
ltyang@stfx.ca, jdyu@cs.sjtu.edu.cn, yaobin@cs.sjtu.edu.cn
Abstract—It is critical but difficult to efficiently model re-
sources in space-terrestrial integrated networks (STINs). Exist-
ing work is not applicable to STINs because they lack the joint
consideration of different movement patterns and fluctuating
loads. In this paper, we propose the time-varying resource
graph (TVRG) to model STINs from the resource perspective.
Firstly, we propose the STIN mobility model to uniformly model
different movement patterns in STINs. Then, we propose a
layered Resource Modeling and Abstraction (RMA) approach,
where evolutions of node resources are modeled as Markov
processes, by encoding predictable topologies and influences
of fluctuating loads as states. Besides, we propose the low-
complexity domain resource abstraction algorithm by defining
two mobility-based and load-aware partial orders on resource
abilities. Finally, we propose an efficient TVRG-based Resource
Scheduling (TRS) algorithm for time-sensitive and bandwidth-
intensive data flows, with the multi-level on-demand scheduling
ability. Comprehensive simulation results demonstrate that the
RMA-TRS outperforms related schemes in terms of throughput,
end-to-end delay and flow completion time.
I. INT ROD UC TI ON
The space-terrestrial integrated networks (STINs) have been
widely studied in recent years [1] [2]. By taking advantage of
software-defined networking such as flexible flow scheduling,
satellite networks (SNs) not only act as supplements to pro-
vide broadband multimedia broadcasting [3] [4], but also co-
operate with the terrestrial networks (TNs) to offer customized
applications [5] [6] and improve resource utilization [7] [8].
However, satellites move on separated orbits with multiple
time-dependent and constellation-related parameters, and they
handover frequently with stable earth stations and dynamic
satellites, resulting in continuous and complex connectivity
changes. Besides, the traffic is unevenly distributed temporally
and spatially, affecting the total amount of available resources.
Hence, modeling resources in STINs with joint considerations
of different movement patterns and fluctuating loads is a
critical but difficult problem [9].
Although related research has made great progress, most
of them lack the joint consideration of different movement
patterns and fluctuating loads. Specifically, the first category
of schemes used linear programming to formulate resource
usage and application demands as linear constraints, but
the effects of the dynamic topology on resource abilities
lack full considerations [10] [11]. The second category of
Feilong Tang is the corresponding author of this paper.
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Fig. 1: Different movement patterns and fluctuating loads
bring challenges to resource modeling
schemes modeled resource abilities under random loads based
on the stochastic control theory, however, resource usage
opportunities brought by predictable topologies were not fully
exploited [12] [13]. The third category of schemes used graph
to model resources and attracted much attention recently
such as the time-expanded graph model for remote sensing
networks [14], the time-evolving graph model for satellite
networks [15] and the unit ball graph model for mobile ad
hoc networks [16]. However, the movement pattern of their
target networks was usually restricted in one type such as the
random waypoint models [17], which cannot be applied in the
complex environment of STINs directly.
For example, as shown in Fig. 1(a), both satellites A and
B move in different movement patterns as indicated by blue
arrows and establish ground-satellite links (GSLs) with the
earth station C at t1. The available bandwidth of GSL from
A to C is 20 Mbps and the delay of the inter-satellite link
(ISL) between satellites A and B is 50 ms. At t2, the GSL
between satellite B and the earth station C is switched off as
shown in Fig. 1(b). The bandwidth of another GSL decreases
from 20 Mbps to 10 Mbps due to the increased load. Besides,
the delay of the ISL increases to 60 ms due to the relative
location changes of two satellites. Hence, to overcome chal-
lenges brought by different movement patterns and fluctuating
loads, we aim to propose a graph-based resource model to
capture heterogeneous topology dynamics and resource ability
variations. However, two key problems exist as
(1) How to uniformly model different movement patterns?
(2) How to jointly consider the effects of different movement
patterns and fluctuating loads on resource abilities?
In this paper, we propose the time-varying resource graph
(TVRG) to model resources for STINs. To the best of our
knowledge, it is the first work to model resources by jointly
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IEEE INFOCOM 2021 - IEEE Conference on Computer Communications | 978-1-6654-0325-2/21/$31.00 ©2021 IEEE | DOI: 10.1109/INFOCOM42981.2021.9488855

considering different movement patterns and fluctuating loads
in STINs. Main contributions are summarized as follows.
(1) We propose the time-varying resource graph (TVRG)
to model the STINs from the resource perspective. To
uniformly model different movement patterns, we propose
the STIN mobility model based on detailed handover
analyses of inter-plane ISLs and GSLs.
(2) We propose a layered Resource Modeling and Abstraction
approach, called RMA, based on the STIN mobility model.
In the node level, evolutions of resource are modeled as
Markov processes by encoding predictable topologies and
influences of fluctuating loads as states. In the domain
level, we propose a resource abstraction algorithm with a
low time complexity, where two mobility-based and load-
aware partial orders are defined to quantify abstracted
resource abilities.
(3) We propose a TVRG-based resource scheduling (TRS) al-
gorithm for time-sensitive and bandwidth-intensive flows.
Taking results of the RMA approach as inputs, TRS ef-
ficiently makes cross-domain and in-domain schedulings
according to flow demands. To evaluate RMA and TRS,
we build a simulation system where the TVRG is dy-
namically constructed in the two-sublayer control planes.
Comprehensive simulation results demonstrate that our
RMA-TRS under the layered but centralized resource
management architecture outperforms related schemes.
The rest of this paper is organized as follows. Section II
briefly reviews related work. Section III presents the system
model. In Section IV, we first introduce the definition of
TVRG; then we propose the STIN mobility model, the RMA
approach and the TRS algorithm. Section V introduces the
simulation system implementation and evaluates the perfor-
mance of RMA-TRS. We conclude this paper in Section VI.
II. RE LATE D WO RK
A. Linear Programming Based Resource Model
The linear programming based resource models include the
topology-based and topology-oblivious types. The first type
abstracted resource abilities of a set of nodes and links as
a star with a nucleus and several spokes [18] [19], or a full
mesh composed of all border nodes [20] [21]. The weights
of spokes and full mesh links were derived by solving the
linear programming problem with resource usage constraints
and application demands. An extension of this work drew
resource polylines to find representative nodes in terms of
bandwidth and delay [22]. The second type either abstracted a
set of nodes and links as a one-big-switch by equivalent policy
transformations [10] [23] or derived resource abilities through
algebraic-expression enumerations [11] [24]. However, these
models lacked full considerations of constant-changing but
predictable topologies. Besides, the effects of random arrival
loads on resource abilities were ignored.
B. Control Theory Based Resource Model
The control theory based resource models focus on scenar-
ios with random arrival traffic. In [12], Neely et al. modeled
the capacity regions for downlinks and uplinks based on the
Lyapunov drift. They further extended the stochastic network
optimization theory to model resource ability with arbitrary
arrival flows and channels [25], but the heterogeneous network
was assumed to be stable. In [26], resource abilities were
modeled as two queues by considering bandwidth and delays.
Authors in [13] considered both the randomness of base sta-
tions in space and dynamic user traffic session arrivals in time
to quantify the achievable throughput. In summary, resource
usage opportunities brought by the predictable mobility were
not well exploited by this type of resource models.
C. Graph Based Resource Model
The graph based resource models typically use graphs to
represent topologies or resource relations. The key is to quan-
tify weights of edges and vertexes, which represent resource
abilities [27]. In [28], the time-sharing graph and space-time
topology graph were proposed to model observation windows
and transmission resources of a single satellite. Authors in
[14] proposed the time-expanded graph to characterize the
variations of multi-dimensional heterogeneous resources in
small scale remote sensing networks. There exists a series of
work on modeling resources based on bipartite graphs [29],
time-evolving graphs [15], task merging graphs [30], weighted
multi-skill trees [31], temporal capacity graphs [32], determin-
istic finite automata [33] and track overlapping models [34].
However, effects of fluctuating loads were ignored.
In summary, our work differs from the aforementioned
schemes as we jointly consider different movement patterns
and fluctuating loads.
III. SYS TE M MOD EL
A. STIN Architecture
As shown in Fig. 2, the STINs consist of two layers. In
the SNs, satellites locate in the low-earth-orbit (LEO) con-
stellation and act as switches to communicate with neighbors
through inter-satellite links (ISLs). In TNs, a set of switches
located in the ground are connected by fiber-optic links.
They communicate with the SNs through the earth station by
ground-satellite links (GSLs). We use LEO to refer the LEO
satellite networks for brevity hereafter.
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Fig. 2: Space-terrestrial integrated networks
Both SNs and TNs have data planes and control planes. In
the data plane, we assume that nodes can transmit and process
data. We use a real number ranging from 0 to 1 to represent
the processing ability of a node, which is the ratio between
the amount of output data and input data in unit time.
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Definition 1. (Original topology): The topology of STINs is
modeled as a graph G= (V,E)such that V=VS∪ VG
and E=ES∪ EG∪ EGSL , where VS,VG,ES,EGand EGSL
represent the sets of satellites, terrestrial switches, ISLs, fiber-
optic links and GSLs, respectively.
In the control plane, we adopt the two-sublayer structure
in [35] to provide layered resource management. In the first
sublayer, controllers collect topology and resource informa-
tion within their domains to construct the node-level TVRG
and make intra-domain scheduling. Let Cbe the set of control
domains such that C={c}, where each domain consists of
a set of nodes and links. Formally, we have
c={{v|v∈ V} ∪ {e|e∈ E}},∀c∈C. (1)
In the second sublayer, the super-controller manages a set of
controllers, and collects the resource information to construct
the domain-level TVRG and make cross-domain scheduling.
In this paper, we assume that the numbers and locations of
controllers and super-controllers are known. As shown in Fig.
2, there are 4 controllers (green) and 2 super-controllers (red).
B. Satellite Constellation
We introduce key parameters about the LEO satellite con-
stellation throughout this paper. Let the constellation period
be T. The numbers of planes and satellites in each plane
are denoted as Nand M, respectively. Adjacent planes have
an angular distance of 2π
N. All nodes in the same plane are
separated from each other with an angular distance of 2π
M.
Let vi,j ∈ VSbe the jth node in the ith plane. Satellites
have the same angular speed ω. Each satellite has at most one
GSL, two intra-plane ISLs and two inter-plane ISLs. Three
time-independent and topology-related parameters are
(1) Inclination angle αis the angle between the equator and
the orbit plane.
(2) Polar area border βis the latitude threshold. Inter-plane
ISLs have to be switched off in polar areas, while intra-
plane ISLs exist during the whole period.
(3) Phasing factor Fcharacterizes the angle distance between
satellites in adjacent planes. As shown in Fig. 3, the angle
distance between vi,j and vi+1,j is ∆θ=2πF
NM [36].
Definition 2. (Elevation angle): Given v∈ VS, u ∈ VG, the
elevation angle φv,u(t)∈[0,π
2]is the angle of uwith respect
to the tangent plane of v, which is a function of time t.
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Fig. 4: Elevation angles at t
As shown in Fig. 4, the necessary condition for establishing
a GSL is that elevation angles of a pair of nodes are both no
smaller than the threshold, which is φLfor all satellites and
φGfor nodes in TNs. We define switch on/off behaviors of
inter-plane ISLs and GSLs as handovers. Thus, the connec-
tivity changes when a handover happens.
IV. TIME-VARY IN G RES OU RC E GRAPH
We first define the time-varying resource graph. Then, we
propose the STIN mobility model to uniformly model differ-
ent movement patterns. Next, we propose a layered resource
modeling and abstraction (RMA) approach. Finally, we design
a TVRG-based resource scheduling (TRS) algorithm.
A. Overview and Preliminaries
We model the time-varying resource graph (TVRG) as G=
(GN, GD,T)such that GN={GN
c(τ)|c∈C, τ ∈T}and
GD={GD
c(τ)|c∈C, τ ∈T}.Tis the set of intervals such
that T={τ}, where each interval τstarts from τsand ends
at τe. We assume the topology and the resource ability remain
stable during each interval. GNand GDare the node-level
and domain-level TVRG.
Definition 3. (Node-level TVRG) Given a domain c∈C,
the node-level TVRG during the interval τis modeled as
GN
c(τ) = {Vτ
c, Eτ
c, Dτ
c, Bτ
c, Qτ
c, Rτ
c}such that
Dτ
c={dτ
v|∀v∈c}, Bτ
c={bτ
v|∀v∈c},(2)
Qτ
c={qτ
e|∀e∈c}, Rτ
c={rτ
e|∀e∈c},(3)
where dτ
v, bτ
v, qτ
e, rτ
erepresent the propagation delay, available
bandwidth, queuing delay and processing ability, respectively.
Vτ
cand Eτ
care the sets of vertexes and edges, which are
defined by making line graph transformations from Gas
Vτ
c={v|∃e∈c},(4)
Eτ
c={e|∃v∈c, e1, e2∈ E, and
e1ends at vand e2orignates from v}.(5)
Assume that the first interval starts at 0. We put the node-
level TVRG into a coordinate system, which has three mutu-
ally orthogonal axes and takes (0,0,0) as the origin. B-axis,
D-axis and T-axis represent the available bandwidth, propa-
gation delay and time interval, respectively. Let (dτ
v, bτ
v, τs)
be the coordinate of v, where dτ
vcan be obtained based on
mobility features. Let (rτ
e, qτ
e, τs)be the edge weight, which
is assumed to remain stable during τ. The node-level TVRG
is independently updated by the controller at the beginning of
each interval.
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Fig. 5: Node-level TVRG
We give an intuitive example of the line-graph transforma-
tions and the node-level TVRG construction. The left half
of Fig. 5 is the original topology in domain c. For each
directed link in c, we add a vertex vinto Vτ
c. Since the brown
switch is the one where the black link ends and the green
link originates, we add an edge between the black and green
vertexes as shown in the right half of Fig. 5.
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In the original topology G, data is transmitted between
domains through cross-domain links. Let V∗
cbe the set of
vertexes representing cross-domain links. Formally, we have
V∗
c={v|v∈Vc,∃e1∈Eτ
c, e2∈Eτ
c0, c, c0∈C, and
vis the common end-point of e1and e2}.(6)
Definition 4. (Domain-level TVRG) Given a domain c∈C,
the domain-level TVRG during the interval τis modeled as
GD
c(τ) = {V∗
c, Dτ
c, Bτ
c}such that
Dτ
c={dτ
i j|∀vi, vj∈V∗
c}, Bτ
c={bτ
i j|∀vi, vj∈V∗
c},(7)
where dτ
i jand bτ
i jrepresent the time and bandwidth to
pass through domain cfrom vito vj.
As shown in Fig. 6, the dashed ellipse contains a set of ver-
texes and edges in the node-level TVRG where V∗
c={vi, vj}.
The domain-level TVRG is obtained by resource abstraction.
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Fig. 6: Domain-level TVRG
B. STIN Mobility Model
To uniformly model different movement patterns, we first
analyze handovers of inter-plane ISLs. Then, we formally
derive the time of GSL establishment and switching off.
We start from numbering nodes in the LEO. Assume that
the system begins at T0when there exists a satellite with
latitude equals to zero. We denote it by v1,1, meaning the
first satellite in the first plane. Then, other satellites in the
same plane are numbered increasingly along the direction of
movement. Other planes are numbered increasingly from 2 to
Nin the east direction. The numbering process in the LEO
is shown in Fig. 7, where the first plane is red.
o
1
o
X
Y
Z
direction
ploar area
border
1,1
v
i, j
v
2
o
i,1
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i,1
v
i
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1
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o
1
o
X
Y
Z
2
o
v,u
φ
v
u
d
ov
u
d
u
v
p
v
(t)
Fig. 8: GSL handover analysis
1) Handover analysis of inter-plane ISLs: When a satellite
moves into the polar area, the inter-plane ISLs associated with
it will be switched off. The reason is that the relative angular
speed between the two satellites keeps increasing when they
are approaching the polar area, and their antennas cannot
afford enough angular speed to maintain inter-plane ISLs. We
represent the ith plane by following key parameters.
(1) v0
i,1is a reference node with latitude equals to zero.
(2) θvi,j is the angle between ovi,j and ov0
i,1in the direction
of movement, which can be derived by
θvi,j = mod (i∆θ+2πj
M,2π),(8)
where mod(a, b)gives the remainder after adivides b.
Based on the geometric relations in Fig. 7, we have
βvi,j = arcsin(sin θvi,j ×sin α).(9)
On the one hand, for satellites not in the polar area (θvi,j ≤
θβor θvi,j ≤π+θβ), the one with maximum θvi,j will enter
the polar area first. On the other hand, for satellites in the
polar area (θvi,j ≤π−θβor θvi,j ≤2π−θβ), the first one to
leave the polar area has the minimum θvi,j . Hence, starting
from T0, the shortest duration τ0for handovers to happen is
τ0=¯
θ
ω,(10)
where ¯
θ= min{θ0−θvi,j |θvi,j ≤θ0,∃θ0∈Θ,∀vi,j ∈
VS},Θ = {θβ, π +θβ, π −θβ,2π−θβ}and θβcan be derived
by substituting βvi,j with βin Eq. (9).
Two key parameters are used to depict T:
(1) Starting point (T1) is the time when the first handover
happens. We have T1=T0+τ0based on Eq. (10);
(2) Basic interval (τ) is the time unit for describing durations
between two consecutive inter-plane ISL handovers.
Theorem 1. Given Ts=T
M,T∆θ=∆θT
2π=F T
NM , we have
τ= gcd(T, gcd(Ts, T∆θ)),(11)
where gcd() gives the greatest common divisor of two number.
Proof. The time interval for two nodes vi,j and vi,j+1 entering
or leaving polar areas is T
M. During this interval, satellites
in other planes may also arrive at or depart from polar area
borders, of which interval is calculated as ∆θT
2π=F T
NM .
Assume both Tsand T∆θare integers. There exist two cases
to discuss: if T∆θexactly divides Ts, the number of satellites
moving into polar areas during Tsis Ts
T∆θ. Otherwise, the
above two intervals are split into smaller pieces (their greatest
common divisor), during which handovers never happen.
2) Handover analysis of GSLs: Based on the definition of
elevation angle, necessary conditions to establish the GSL is
φv,u(t)≥φL,
φu,v(t)≥φG,(12)
where v∈ VSand u∈ VG. Considering the symmetry of Eq.
(12), we only discuss the first inequality. We aim to derive how
φv,u(t)changes with time by mobility features of the LEO.
Given a satellite v∈ VS, its Cartesian coordinate is denoted
as v(t) = (xv(t), yv(t), zv(t)). The intersection of the equator
plane and the v’s plane is vp(t) = (xp(t), yp(t),0).
As shown in Fig. 8, Let the node that satisfies vo1⊥oo1be
o1. The projection of von equator plane is o2. According to
the geometric relation, we can easily get

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
x2
v(t) + y2
v(t) + z2
v(t) = L2,
zv(t)
L= sin βv(t),
zv(t)
do2
o1
= tan α,
(13)
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where Land do2
o1are distances from the satellite to the
coordinate origin and from o1to o2, respectively.
By rewriting Eq. (9) as a function of time, we get
βv(t) = arcsin(sin α×sin(θv+ωt)).(14)
The line equation of oo1is x
xp=y
yp. We have
do2
o1=||ypxv−xpyv||
√x2
p+y2
p
=||ypxv−xpyv||
L,(15)
where ||x|| returns xif xis greater than 0 and −xotherwise.
By substituting Eq. (14) and Eq. (15) into Eq. (13), we can
get the trajectory equation of vas



x2
v(t) + y2
v(t) = L2(1 −sin2αsin2(θv+ωt)),
||yp(t)xv(t)−xp(t)yv(t)||=Lcos αsin(θv+ωt),
zv(t) = Lsin αsin(θv+ωt).
(16)
We now discuss the variation of φv,u(t)over time. The
equation of line ov is x
xv(t)=y
yv(t)=z
zv(t). Based on
geometric relations as shown in Fig. 8, we have
φv,u(t) = π
2−arcsin dov
u
dv
u,(17)
where dov
uand dv
uare distances from uto line ov and v,
respectively. Both of them can be obtained by simple algebra
operations. We can easily get φu,v(t)by symmetry.
There are two cases to consider for GSL handovers. Given
v∈ VSand u∈ VG, if the GSL is established (φv,u(t)> φL
and φu,v(t)> φG), the time twhen it will be switched off is
t= min{t|φv,u(t) = φL∨φu,v (t) = φG}.(18)
Otherwise, the time twhen the GSL can be established is
t= min{t|φv,u(t)≥φL∧φu,v (t)≥φG}.(19)
To sum up, the STIN mobility model takes parameters
representing different movement features; then it uniformly
models them and derives a set of stable intervals. The details
are summarized in Algorithm 1. We first calculate two key
parameters T1and τ0in lines 1-6. Then, starting from T1,
we consider whether handovers caused by inter-plane ISLs
happen. The basic time unit τis used to split Tinto a series
of intervals in lines 7-14. Finally, we construct the set TGSL
to record the time when handovers caused by GSLs happen
and split all time intervals of Tbased on TGSL in lines 15-23.
C. Resource Modeling and Abstraction
Since the TVRG is dynamically constructed in the layered
resource management architecture, one of the key points is
calculating weights of vertexes and edges to model resource
abilities on different levels, which depends not only on
uniform movement modeling and but also on fluctuating loads.
1) Node resource modeling: In essence, effects of random
traffic on resource abilities are reflected in the available
bandwidth and the queuing delay. Satellites move periodically
in orbits and their loads have spatial features, e.g., loads grow
when flying over big cities and decrease over the sea. Switches
in TNs remain stable but their loads show temporal features,
e.g., loads are high during the day and low at night. We model
the evolutions of bτ
vand qτ
eas Markov processes, by encoding
the dynamic features of topologies and the influences of loads.
Each controller independently maintains two Markov tran-
sition matrices Pband Pq, which are updated at the beginning
Algorithm 1 Uniform movement pattern modeling
Input: N, M , F, T, T0, α, β , VG,VS
Output: T
1: Ts=T
M, T∆θ=F T
NM , T S =∅
2: for vi,j ∈ VSdo
3: Get θvi,j and θβby Eq. (8)
4: Get τ0by Eq. (10)
5: end for
6: T1=T0+τ0
ω, τ = gcd(T, gcd(Ts, T∆θ))
7: τ= (τs, τe), τs=T1, τe=τs+τ
8: while τe6=Tdo
9: if ∃v∈ VS,vmoves into or leaves polar areas then
10: T=T∪τ, τs=τe, τe=τs+τ
11: else
12: τe=τe+τ
13: end if
14: end while
15: for v∈ VS, u ∈ VGdo
16: Get the set TGSL by Eq. (18) and Eq. (19)
17: end for
18: while TGSL 6=∅do
19: t←TGSL , TGSL =TGSL − {t}
20: if ∃τ∈T, τs< t < τethen
21: T=T− {τ},T=T∪(τs, t)∪(t, τe)
22: end if
23: end while
of each interval. We focus on the dynamic construction of Pb
since Pqcan be derived similarly.
Let Bcdenote the maximum bandwidth of links in the
domain c. Since bτ
vchanges continuously in time, we use
a configurable parameter to divide the available bandwidth
into mdiscrete states in each interval. Formally, given the ith
interval τof T, the bτ
vis in the ((i−1)m+j)th state if the
follow condition satisfies
(j−1)Bc
m< bτ
v≤jBc
m(20)
Considering the periodical movement of satellites, the
STINs return to the first interval when the last interval ends.
Hence, the total number of states is |T| × m.
Let pij ∈Pbbe the probability that v∈Vτ
ctransits from
the ith state to the jth state, from the current interval to the
next. Denote pτ−
ij as the transition ratio in the previous interval
τ−such that
pτ−
ij =Pv∈Vτ
cχτ−
ijv
Pv∈Vτ
cPm
j0=1 χτ−
ij0v
,(21)
where χτ−
ijv is an indicator to denote whether vtransits from
the ith state from the jth state (χτ−
ijv = 1) or not (χτ−
ijv = 0).
Then, we calculate pτ
ij as the weighted average of pτ−
ij and
pτ−
s
ij . The latter is the transition probability at the beginning
of τ−. To capture the spatial and temporal features of loads,
we take the forgotten factor η∈(0,1) as the weight such that
pτ
ij =ηpτ−
s
ij + (1 −η)pτ−
ij ,(22)
IEEE INFOCOM 2021 - IEEE Conference on Computer Communications

where i≤m(|T|−1) and di
mem<j≤ di+1
memor m(|T|−
1) < i ≤m|T|and 0< j ≤m, indicating the case from the
previous interval to current. Otherwise, we set pτ
ij to 0.
Finally, given a node in the ith state, the available band-
width during τis calculated as
bτ
v=Pm
j=1 pτ
ij ×jBc
m.(23)
2) Domain resource abstraction: At the beginning of each
interval, super-controller takes node-level resource informa-
tion from controllers to construct domain-level TVRG.
The main idea is to abstract a domain as a virtual node and
quantify resource abilities between each pair of cross-domain
links. In the node-level TVRG, there exists a set of logic paths
between two vertexes. Formally, ∀vi, vj∈Vc, denote the logic
path set from vito vjas Hτ
i j. The kth element contains a set
of vertexes and edges such that hτ
i j(k) = {vi, evi, . . . , vj},
where evis the edge starting from v.
To measure the resource ability of a logic path, we take the
minimum bandwidth of all vertexes as the bottleneck, where a
smaller rτ
eresults in a larger equivalent bandwidth. Besides,
we take the sum of queuing delays which are affected by
fluctuating loads, and propagation delays along the logic path
as the time for packets passing through a domain. So, we have
bτ
i j(k) = min{minv∈hτ
i j(k)−{vj}
bτ
v
rτ
ev, bτ
vj}(24)
dτ
i j(k) = Pv∈hτ
i j(k)dτ
v+Pe∈hτ
i j(k)qτ
e(25)
Since topologies and loads keep changing, we define two
mobility-based and load-aware partial orders to measure the
abilities of different logic paths.
Note that one objective to abstract a domain is to quantify
the maximum bandwidth to pass through it. Thus intuitively,
a logic path hτ
i j(k)dominates another path hτ
i j(k0)in
terms of bandwidth if (1) hτ
i j(k)has more bandwidth
than hτ
i j(k0)in the current interval, or (2) hτ
i j(k)has
the same bandwidth as hτ
i j(k0)for several intervals before
exceeding that of hτ
i j(k0). Formally, we say bτ
i j(k)b
bτ
i j(k0),∀hτ
i j(k), hτ
i j(k0)∈Hτ
i jif one of the following
two conditions satisfies
(1) bτ
i j(k)> bτ
i j(k0);
(2) ∃ξ∈N,∀ψ∈{0,1, . . . , ξ}, we have bτ+ψ
i j(k) = bτ+ψ
i j(k0)
and bτ+ξ+1
i j(k)> bτ+ξ+1
i j(k0), where τ+ψmeans the ψth
interval after τ.
Similarly, dτ
i j(k)≺ddτ
i j(k0)holds if one of the follow-
ing two conditions satisfies
(1) dτ
i j(k)< dτ
i j(k0);
(2) ∃ξ∈N,∀ψ∈{0,1, . . . , ξ}, we have bτ+ψ
i j(k) = dτ+ψ
i j(k0)
and bτ+ξ+1
i j(k)< dτ+ξ+1
i j(k0).
Given vi, vj∈V∗
c, resource abilities from vito vjare
bτ
i j={bτ
i j(k)|bτ
i j(k)bbτ
i j(k0),
∀hτ
i j(k0)∈Hτ
i j, k 6=k0},(26)
dτ
i j={dτ
i j(k)|dτ
i j(k)≺ddτ
i j(k0),
∀hτ
i j(k0)∈Hτ
i j, k 6=k0}(27)
As two important inputs for the cross-domain scheduling,
both Eq. (26) and (27) quantify abstracted resource abilities
Algorithm 2 Domain resource abstraction
Input: GN
c(τ)
Output: GD
c(τ)
1: for vi∈V∗
cdo
2: Uvisit =∅, Utotal =Vc, Ua←push(Adj(vi))
3: for vk∈Vcdo hτ,bmax
i k=∅, hτ,dmin
i k=∅end for
4: while Utotal 6=∅do
5: vj←pop(Ua), Hτ,bmax
i j=∅, Hτ,dmin
i j=∅
6: for vk∈Uvisit do
7: if ∃e∈Ecfrom vkto vjthen
8: Hτ,bmax
i j=Hτ,bmax
i j∪ {hτ,bmax
i k, e, vj}
9: Hτ,dmin
i j=Hτ,dmin
i j∪ {hτ,dmin
i k, e, vj}
10: end if
11: end for
12: if vj∈V∗
cthen
13: Get bτ
i jby Eq. (26) and dτ
i jby Eq. (27)
14: else
15: hτ,bmax
i j= arg maxhτ
i j(k)∈Hτ,bmax
i jbτ
i j(k)
16: hτ,dmin
i j= arg minhτ
i j(k)∈Hτ,dmin
i j
dτ
i j(k)
17: Uvisit =Uvisit +{vj}, Utotal =Utotal −{vj}
18: Ua←push({v|v∈Adj(vj)−Uvisit −Ua})
19: end if
20: for vl∈Uvisit do
21: if ∃e∈Ecfrom vjto vlthen
22: Hτ,bmax
i l=Hτ,bmax
i l∪ {hτ,bmax
i j, e, vl}
23: Hτ,dmin
i l=Hτ,dmin
i l∪ {hτ,dmin
i j, e, vl}
24: hτ,bmax
i l= arg maxhτ
i l(k)∈Hτ,bmax
i lbτ
i l(k)
25: hτ,dmin
i l= arg minhτ
i l(k)∈Hτ,dmin
i l
dτ
i l(k)
26: end if
27: end for
28: end while
29: end for
not only considering the mobilities reflected by τbut also the
loads reflected by queuing delays.
As shown in Algorithm 2, we start from vi∈V∗
cwhich
represents the cross-domain link, and use the first-in-first-out
queue Uato store adjacent vertexes, which are given by the
function Adj(). We initialize a set of paths to reduce the
searching overhead in line 3. In lines 6-11, we obtain all
candidate logic paths by concatenating the edge and the vertex
to recorded paths. Finally, if we reach vj∈V∗
c, we calculate
bτ
i jby Eq. (26) and dτ
i jby Eq. (27). Otherwise, we record
the two most representative logic paths from vito vj, update
key variables and push vj’s adjacent vertexes into Uain lines
15-18. We update the path set along with resource abilities in
lines 20-27. The above process is repeated until Uais empty.
Theorem 2. The time complexity of Algorithm 2 is
O(|V∗
c||Vc|(2degmax −1)), where degmax is the maximum
degree of the node-level TVRG.
Proof. Given a vertex vi∈V∗
c, we traverse all vertexes in
Vcto quantify the resource ability from vito other nodes
IEEE INFOCOM 2021 - IEEE Conference on Computer Communications

of V∗
c. In line 3, the initialization causes |Vc|iterations. In
line 5, we get a neighbor node vjand begin to consider the
edge from nodes in Uvisit to vj. Given a vertex v∈Vc
and one of its neighbor v0, denote the edge between them
as e. The number of edges that share the common endpoint
vwith eis upper bounded by degmax −1. Hence, the
total maximum number of edges in line 7 and line 21 is
2(degmax −1). Since numbers of cross-domain links and total
links are |V∗
c|and |Vc|, respectively, the time complexity of
Algorithm 2 is O(|V∗
c||Vc|) + O(|V∗
c||Vc|(2(degmax −1))) =
O(|V∗
c||Vc|(2degmax −1))
Algorithm 3 Cross-domain resource scheduling
Input: cs, cd, C, GD
c(τ) = {V∗
c, Dτ
c, Bτ
c}
Output: {v|v∈V∗
ci, ci∈C}
1: bmax =−1, dmin =M AX, hbmax =hdmin =∅
2: b=M AX, d = 0, h =∅, AD=∅, VD={cs}
3: AD←push({ci, vi, h, b, d|∃vi∈V∗
cs∩V∗
ci},∀ci∈C})
4: while AD6=∅do
5: {ci, vi, h, b, d} ← pop(AD)
6: AD=AD− {ci, vi, h, b, d}
7: if ci=cdthen
8: if bmax < b then hbmax =h, bmax =bend if
9: if dmin > d then hdmin =h, dmin =dend if
10: else
11: VD=VD∪ {ci}
12: for cj∈Cand cj/∈VDdo
13: if ∃vj∈V∗
ci∩V∗
cjthen
14: h=h∪{vi}, b = min{b, bτ
i j}, d =d+dτ
i j
15: AD←push({cj, vj, h, b, d})
16: end if
17: end for
18: end if
19: end while
20: Return hbmax or hdmin depending on the flow’s type
D. TVRG-Based Resource Scheduling
We design the TVRG-based Resource Scheduling (TRS)
algorithm for time-sensitive and bandwidth-intensive data
flows, where they prefer paths with the minimum end-to-end
delay and the maximum available bandwidth, respectively.
1) Multi-level on-demand resource scheduling framework:
In STINs with two-sublayer control planes, resource schedul-
ings are conducted based on flow demands hierarchically.
In the data plane, if a new-arrival flow matches a forwarding
rule, actions specified by the control plane will be taken.
Otherwise, the switch sends an OpenFlow Packet-In request
containing the flow type and destination to its controller.
In the control plane, if the destination is in the same do-
main, the controller makes in-domain scheduling and inserts
forwarding rules. Otherwise, the controller sends a cross-
domain scheduling request to its super-controller. Note that
when the destination locates in the domain whose controller
belonging to another super-controller, the top layer control
planes cooperate to make cross-domain scheduling.
Algorithm 4 In-domain resource scheduling
Input: vs, vd∈ V, GN
c(τ) = {Vτ
c, Eτ
c, Dτ
c, Bτ
c, Qτ
c, Rτ
c}
Output: {v|v∈Vc}
1: bmax =−1, dmin =M AX, hbmax =hdmin =∅
2: b=M AX, d = 0, h =∅, AN=∅, VN=∅
3: for v∈Vτ
cdo
4: Get the edge e∈Eτ
ccorresponding to vs
5: if vis one endpoint of ethen
6: d=qτ
e, h =h∪ {v}, VN=VN∪ {v}
7: AN←push({v, h, b, d})
8: end if
9: end for
10: while AN6=∅do
11: {v, h, b, d} ← pop(AN),AN=AN− {v, h, b, d}
12: for e∈Eτ
cdo
13: if ∃v0/∈VNand eis a edge from vto v0then
14: if ecorresponds to vdthen
15: if bmax< b then hbmax =h, bmax =bend if
16: if dmin> d then hdmin =h, dmin =dend if
17: else
18: VN=VN∪ {v0}, h =h∪ {v0}
19: b= min{b, bτ
v
rτ
e}, d =d+dτ
v0+qτ
e
20: QN←push({v0, h, b, d})
21: end if
22: end if
23: end for
24: end while
25: Return hbmax or hdmin depending on the flow’s type
2) Cross-domain resource scheduling: The main idea of
cross-domain resource scheduling is to calculate a set of
vertexes representing cross-domain links, from the source’s
domain csto the destination’s domain cd.
As shown in Algorithm 3, we initialize key variables in
lines 1-2, where VDis the set of visited domains. In line 3, we
first consider a set of cs’s neighbor domains {ci|∃v∈V∗
ci∩
V∗
cs},∀ci∈C}and push the 5-tuple with related resource
ability information into the first-in-first-out queue AD.
Then, when we find a candidate cross-domain path (ci=
cd), we store the path and update bmax or dmin if the available
bandwidth or end-to-end delay is better than the recorded
resource ability in lines 8-9. Otherwise, if there exists a
domain cj∈Cthat has never been visited, we record the
path along with its available bandwidth and propagation delay
before pushing a new 5-tuple into ADin lines 11-17. We
repeat the above process until ADis empty. Finally, the
algorithm returns the path depending on the type of flow.
3) In-domain resource scheduling: The controller takes the
node-level TVRG as inputs to calculate the path from the
source to the destination within a domain in Algorithm 4.
We first initialize key parameters in lines 1-2, where VNis
the set of visited nodes and ANis the first-in-first-out queue.
In lines 3-9, given any edge e∈Eτ
crepresenting vs, we
consider all vertexes that are one of the endpoint of e. For
each of them, we construct a 4-tuple including the vertex,
IEEE INFOCOM 2021 - IEEE Conference on Computer Communications

path, available bandwidth and delay into AN. Then, we use
pop() to get the first element {v, h, b, d}of ANand remove it
from AN. We consider all edges originate from v. When we
find the edge corresponding to the destination, we store the
path and update its resource ability if this path is better than
the recorded one in lines 15-16. Otherwise, we add another
endpoint v0into the path, update the available bandwidth and
the end-to-end delay, and push the 4-tuple {v0, h, b, d}into
ANin lines 18-20. We repeat the above process until ANis
empty and return the path depending on the flow’s type.
V. PE RF OR MA NC E EVALUATI ON S
A. Simulation System Design and Implementation
We designed and built the NS3-based simulation sys-
tem with layered resource management ability by extending
the OFSwitch13 module [37]. Specifically, taking the OF-
Switch13Controller as the base class, we developed two types
of controllers with layered resource modeling, abstraction
and scheduling functions, which we use to implement our
RMA approach and TRS algorithm. We integrated the STIN
mobility module into NS3, which shields effects of different
movement patterns and calculates Tgiven various topology
parameters. To simulate processing behaviors during transmis-
sion, we first implemented the random traffic generator to send
packets by batch, then extended the OFSwitch13Device mod-
ule that forwards only part of packets with higher sequence
numbers in the batch, based on the processing ability.
B. Simulation Setup
We use the CERNET topology from the Topology Zoo [38]
in TNs, which consists of 41 nodes and 53 links. We set the
height of the LEO as 785 km. The inclination angle, polar area
border and phasing factor are set as π
2,7π
18 and 1, respectively.
The LEO has 8 planes with 9 nodes in each plane. The
elevation angle threshold is 2π
9in SNs and π
9in TNs. Both
TNs and SNs have 4 controllers and 2 super-controllers.
All nodes are equipped with a modified NS3 built-in traffic
generator and a FIFO queue with a maximum size of 1000
packets. The processing capabilities of nodes range from 0.8
to 1. The capacities of ISLs are 1 Gbps. We use the gravity
model [39] to generate flows. The number of two types of
flows is the same. We repeat every experiment 5 times using
different random seeds and average the results.
C. Compared Algorithms
We compare the RMA-TRS against five related algorithms.
For MLS and SCA, the controller in TNs collects resource
information and distributes the scheduling results. To show
the performance of our RMA approach, we extend MLS and
SCA as RMA-MLS and RMA-BPS.
•MLS [26] selects the path with a minimum sum of end-
to-end delay and unit data transmission time.
•BPS [26] selects a path from the candidate path set with
probability equals to the ratio of the available bandwidth
of the path to all candidate paths.
•SCA [22] takes the resource abilities at the end of
the previous interval to make in-domain scheduling. In
domain level, SCA considers bandwidth and delays be-
tween border nodes and generates polylines with multiple
representative nodes. Both in-domain and cross-domain
schedulings extend the Dijkstra algorithm.
•RMA-MLS and RMA-BPS combine RMA to model re-
source abilities in node and domain level, and make
layered scheduling with criterion corresponding to MLS
and BPS, respectively.
D. Parameter Settings (mand η)
The number of discrete bandwidth states mand the forgot-
ten factor ηare two key parameters to reflect how well our
model captures the effects of mobilities and fluctuating loads.
Given mand η, we run a set of experiments for 120 intervals
and observe the average MSE (mean square error) between the
available bandwidth given by Eq. (23) and the actual value.
The Markov transition matrix is updated according to Eq.
(22) at the beginning of each interval. As shown in Fig. 9,
when the variance of the actual available bandwidth (σb) is
fixed, MSE decreases as mincreases and converges when m
approaches 100. The reason is that the larger the m, the finer
the division of the bandwidth discrete state and the higher the
accuracy. We need to make a trade-off in practical scenarios,
since increasing mheavies the processing load.
50 60 70 80 90 100
0
0.005
0.01
0.015
0.02
0.025
0.03
Value of m
Mean square error
σb= 0.6,η= 0.4
σb= 0.6,η= 0.6
σb= 0.3,η= 0.4
Fig. 9: MSE with the number of states m
Besides, when mis fixed, we can see from Fig. 9 that when
σbincreases, we need properly increase ηto get the smaller
MSE. This is due to fact that the larger the σbthe greater the
historical load fluctuation, and the greater the impact on the
current load. We set mand ηas 80 and 0.4 in the following
experiments. Similarly, we divide the queuing delay into 60
discrete states and set the forgotten factor as 0.45.
E. Results and Analysis
1) End-to-end (e2e) delay: As shown in Fig. 10, the aver-
age e2e delay increases with the increase of the ratio of cross-
domain requests, because of the growth in overall distances
between sources and destinations. However, we can see that
our RMA-TRS has the smallest e2e delay and both RMA-
MLS and RMA-BPS outperform SCA. The reasons are two-
fold. First, our RMA quantifies the domain resource abilities
based on two partial orders. The domain with greater resource
abilities in the long term will be chosen. Second, the SCA
algorithm abstracts a domain based on a set of representative
nodes in the staircase-liked polylines but ignores the mobility.
The available resources of the best domain in the current
interval may vary a lot in the next interval, causing the
scheduling to fall into a local optimum. The BPS has the worst
performance since it only considers the bandwidth. For MLS,
IEEE INFOCOM 2021 - IEEE Conference on Computer Communications

the resource states collected by the controller in TN may out
of date due to large propagation delay, degrading scheduling
performance and causing sharp growth in end-to-end delay.
0.1 0.2 0.3 0.4 0.5 0.6
50
100
150
200
250
Ratio of cross−domain requests
Average end−to−end delay (ms)
RMA−TRS
MLS
RMA−MLS BPS
RMA−BPS SCA
Fig. 10: E2e delay with the ratio
of cross-domain requests
200 400 600 800 1000 1200
20
40
60
80
100
120
Numbers of flows
Average end−to−end delay (ms)
RMA−TRS MLS
RMA−MLS BPS
RMA−BPS SCA
Fig. 11: E2e delay with the
number of flows
We further evaluate the performance by varying the number
of flows. As shown in Fig. 11, our RMA-TRS shows good
adaptation to the variation of number of flows. Note that SCA
simply takes the available resources at the end of the previous
interval. Instead, we use the Markov process to model node-
level resources by encoding different mobilities and influences
of fluctuating loads. So, RMA-TRS always has the smallest
e2e delay in different scenarios. Note that RMA greatly
improves MLS and BPS, because RMA precisely captures
effects of different movement patterns and fluctuating loads.
2) Aggregate throughput: To evaluate the throughput with
different ratio of cross-domain requests, we set the number
of flows as 1000. Fig. 12 demonstrates that the aggregate
throughput of RMA-TRS is significantly higher than other al-
gorithms under the same configuration. The overall aggregate
throughput of SCA decreases sharply with the increase of ratio
of cross-domain requests, because the polyline-based resource
abstraction method cannot precisely reflect resource abilities.
However, by combining RMA with MLS and BPS, available
resources are modeled and abstracted, indicating the RMA’s
good adaptation to different loads. The throughput decrease
of RMA-TRS remains stable, since TRS efficiently uses the
TVRG to make on-demand multi-level resource scheduling.
0.1 0.2 0.3 0.4 0.5 0.6
200
300
400
500
600
700
800
900
Ratio of cross−domain requests
Aggregate throughput (Mbps)
RMA−TRS MLS
RMA−MLS BPS
RMA−BPS SCA
Fig. 12: Throughput with the
ratio of cross-domain requests
200 400 600 800 1000 1200
0
100
200
300
400
Numbers of flows
Aggregate throughput (Mbps)
RMA−TRS MLS
RMA−MLS BPS
RMA−BPS SCA
Fig. 13: Throughput with the
number of flows
As shown in Fig. 13, the throughput of MRA-TRS grows
almost linearly with the increase of numbers of flows. MLS
has the worst performance since it only considers the end-to-
end delay and the unit data transmission time. SCA achieves
relatively better performance than BPS since the latter takes
the bandwidth of a path as the selection probability, which
may result in congestion as the load grows. On the one
hand, RMA-BPS outperforms SCA with different number of
flows, indicating the efficiency of our RMA approach. On the
other hand, there exists a performance gap between RMA-
TRS and RMA-BPS, because TRS selects paths based on the
TVRG, resulting in efficient adaptations among flow demands,
different mobilities and resources with different abilities.
3) Flow completion time: The flow completion time (FCT)
is defined as the duration from when a source begins trans-
mitting to when the destination receives the packet with the
largest sequence number of this flow.
0.1 0.2 0.3 0.4 0.5 0.6
0
20
40
60
80
100
120
Ratio of cross−domain requests
Flow completion time (s)
RMA−TRS MLS
RMA−MLS BPS
RMA−BPS SCA
Fig. 14: FCT with the the ratio
of cross-domain requests
200 400 600 800 1000 1200
0
10
20
30
40
50
Numbers of flows
Flow completion time (s)
RMA−TRS MLS
RMA−MLS BPS
RMA−BPS SCA
Fig. 15: FCT with the number
of flows
We can see that the flow completion time of RMA-TRS re-
mains almost unchanged under different scenarios, while those
of other four algorithms grow with different speed. Especially,
MLS has the worst performance because considering end-to-
end delay may get paths with small bandwidth. Although SCA
abstracts a domain with representative nodes, effects of mobil-
ity and random loads on the node level resource abilities are
ignored, resulting in sub-optimal scheduling. By combining
RMA with BPS and MLS, we obtain performance gains since
the process ability is converted as equivalent bandwidth in Eq.
(24) during the domain-level abstraction. However, RMA-BPS
and RMA-MLS lack efficient resource scheduling. Instead,
the TRS schedules hierarchically with good adaptations to
the complex environment and various application demands,
resulting in significant performance gains for RMA-TRS.
VI. CO NC LU SI ON
This paper presents how to model resources in STINs,
by jointly considering different movement patterns and fluc-
tuating loads. We first propose the time-varying resource
graph (TVRG); then we propose the STIN mobility model to
uniformly model different movement patterns. Based on the
model, we propose a layered resource modeling and abstrac-
tion (RMA) approach to construct TVRG in multi-levels. We
design a TVRG-based resource scheduling (TRS) algorithm for
time-sensitive and bandwidth-intensive data flows. We build
a simulation system providing layered resource management.
Comprehensive experimental results demonstrate that our
RMA-TRS outperforms other related schemes.
ACK NOW LE DG EM EN TS
This work was supported in part by the National Natu-
ral Science Foundation of China projects (Nos. 61832013
and 61672351), in part by STCSM (Science and Technol-
ogy Commission of Shanghai Municipality) AI project (No.
19511120300), in part by Aerospace Fund (No. 20GFC-JJ02-
012), in part by the National Key Research and Development
Program of China (No. 2019YFB2102204), in part by Alibaba
Innovative Research project (No. SCCT622019010803), and
in part by the Huawei Technologies Co., Ltd projects (Nos.
YBN2019105155 and YBN2020085026). Feilong Tang is the
corresponding author of this paper.
IEEE INFOCOM 2021 - IEEE Conference on Computer Communications

REF ER EN CE S
[1] T. Li, H. Zhou, H. Luo, and S. Yu, “Service: A software defined
framework for integrated space-terrestrial satellite communication,”
IEEE Transactions on Mobile Computing, vol. 17, no. 3, pp. 703–716,
2017.
[2] B. Feng, H. Zhou, H. Zhang, G. Li, H. Li, S. Yu, and H.-C. Chao,
“Hetnet: A flexible architecture for heterogeneous satellite-terrestrial
networks,” IEEE Network, vol. 31, no. 6, pp. 86–92, 2017.
[3] F. Tang, L. Chen, X. Li, L. T. Yang, and L. Fu, “Intelligent spectrum
assignment based on dynamical cooperation for 5g-satellite integrated
networks,” IEEE Transactions on Cognitive Communications and Net-
working, vol. 6, no. 2, pp. 523–533, 2020.
[4] J. Chen, F. Tang, H. Zhang, and L. T. Yang, “Lightweight retransmission
for random access in satellite networks,” in IEEE INFOCOM 2018, pp.
549–557.
[5] J. Liu, X. Hou, and F. Tang, “Fine-grained machine teaching with
attention modeling.” in AAAI 2020, pp. 2585–2592.
[6] F. Tang, “Bidirectional active learning with gold-instance-based human
training.” in IJCAI 2019, pp. 5989–5996.
[7] Y. Shi, Y. Cao, J. Liu, and N. Kato, “A cross-domain sdn architecture
for multi-layered space-terrestrial integrated networks,” IEEE Network,
vol. 33, no. 1, pp. 29–35, 2019.
[8] F. Tang, C. Tang, Y. Yang, L. T. Yang, T. Zhou, J. Li, and M. Guo,
“Delay-minimized routing in mobile cognitive networks for time-critical
applications,” IEEE Transactions on Industrial Informatics, vol. 13,
no. 3, pp. 1398–1409, 2016.
[9] H. Yao, L. Wang, X. Wang, Z. Lu, and Y. Liu, “The space-terrestrial
integrated network: An overview,” IEEE Communications Magazine,
vol. 56, no. 9, pp. 178–185, 2018.
[10] H. Xie, Y. R. Yang, A. Krishnamurthy, Y. G. Liu, and A. Silberschatz,
“P4p: Provider portal for applications,” SIGCOMM 2008, pp. 351–362.
[11] Q. Xiang, J. J. Zhang, X. T. Wang, Y. J. Liu, C. Guok, F. Le,
J. MacAuley, H. Newman, and Y. R. Yang, “Fine-grained, multi-domain
network resource abstraction as a fundamental primitive to enable
high-performance, collaborative data sciences,” in IEEE International
Conference for High Performance Computing, Networking, Storage and
Analysis, 2018, pp. 58–70.
[12] M. J. Neely, E. Modiano, and C.-P. Li, “Fairness and optimal stochas-
tic control for heterogeneous networks,” IEEE/ACM Transactions on
Networking, vol. 16, no. 2, pp. 396–409, 2008.
[13] W. Bao and B. Liang, “Radio resource allocation in heterogeneous
wireless networks: A spatial-temporal perspective,” in IEEE INFOCOM
2015, pp. 334–342.
[14] Y. Wang, M. Sheng, W. Zhuang, S. Zhang, N. Zhang, R. Liu, and
J. Li, “Multi-resource coordinate scheduling for earth observation
in space information networks,” IEEE Journal on Selected Areas in
Communications, vol. 36, no. 2, pp. 268–279, 2018.
[15] D. Zhou, M. Sheng, X. Wang, C. Xu, R. Liu, and J. Li, “Mission aware
contact plan design in resource-limited small satellite networks,” IEEE
Transactions on Communications, vol. 65, no. 6, pp. 2451–2466, 2017.
[16] H. Huang, H. Yin, Y. Luo, X. Zhang, G. Min, and Q. Fan, “Three-
dimensional geographic routing in wireless mobile ad hoc and sensor
networks,” IEEE Network, vol. 30, no. 2, pp. 82–90, 2016.
[17] F. Tang, M. Guo, S. Guo, and C.-Z. Xu, “Mobility prediction based
joint stable routing and channel assignment for mobile ad hoc cognitive
networks,” IEEE Transactions on Parallel and Distributed Systems,
vol. 27, no. 3, pp. 789–802, 2013.
[18] C. Liu and J. Wu, “Scalable routing in cyclic mobile networks,” IEEE
Transactions on Parallel and Distributed Systems, vol. 20, no. 9, pp.
1325–1338, 2009.
[19] L. Hu, F. Hu, and S. Kumar, “Moth-and ant-inspired routing in hierar-
chical airborne networks with multi-beam antennas,” IEEE Transactions
on Mobile Computing, 2018.
[20] S. Jain, A. Kumar, S. Mandal, J. Ong, L. Poutievski, A. Singh,
S. Venkata, J. Wanderer, J. Zhou, M. Zhu et al., “B4: Experience with
a globally-deployed software defined wan,” in ACM SIGCOMM 2013,
pp. 3–14.
[21] B. Awerbuch and Y. Shavitt, “Topology aggregation for directed
graphs,” IEEE/ACM Transactions on Networking, vol. 9, no. 1, pp. 82–
90, 2001.
[22] J. Hua, L. Zhao, S. Zhang, Y. Liu, X. Ge, and S. Zhong, “Topology-
preserving traffic engineering for hierarchical multi-domain sdn,” Com-
puter Networks, vol. 140, pp. 62–77, 2018.
[23] N. Kang, Z. Liu, J. Rexford, and D. Walker, “Optimizing the” one big
switch” abstraction in software-defined networks,” in ACM CoNEXT
2013, pp. 13–24.
[24] K. Gao, Q. Xiang, X. Wang, Y. R. Yang, and J. Bi, “An objective-driven
on-demand network abstraction for adaptive applications,” IEEE/ACM
Transactions on Networking, vol. 27, no. 2, pp. 805–818, 2019.
[25] M. J. Neely, “Universal scheduling for networks with arbitrary traffic,
channels, and mobility,” in IEEE Conference on Decision and Control
2010, pp. 1822–1829.
[26] E. Bouttier, R. Dhaou, F. Arnal, C. Baudoin, E. Dubois, and A.-L.
Beylot, “Analysis of content size based routing schemes in hybrid
satellite/terrestrial networks,” in IEEE GLOBECOM 2016, pp. 1–6.
[27] F. Tang, H. Zhang, L. Fu, and X. Li, “Distributed stable routing with
adaptive power control for multi-flow and multi-hop mobile cognitive
networks,” IEEE Transactions on Mobile Computing, vol. 18, no. 12,
pp. 2829–2841, 2018.
[28] X. Jia, T. Lv, F. He, and H. Huang, “Collaborative data downloading by
using inter-satellite links in leo satellite networks,” IEEE Transactions
on Wireless Communications, vol. 16, no. 3, pp. 1523–1532, 2017.
[29] Y. Wang, M. Sheng, J. Li, X. Wang, R. Liu, and D. Zhou, “Dynamic
contact plan design in broadband satellite networks with varying contact
capacity,” IEEE Communications Letters, vol. 20, no. 12, pp. 2410–
2413, 2016.
[30] J. Wang, X. Zhu, D. Qiu, and L. T. Yang, “Dynamic scheduling for
emergency tasks on distributed imaging satellites with task merging,”
IEEE Transactions on Parallel and Distributed Systems, vol. 25, no. 9,
pp. 2275–2285, 2014.
[31] F. Tang, “Optimal complex task assignment in service crowdsourcing,”
in IJCAI 2020.
[32] X. Zhu, Y. Li, D. Jin, and P. Hui, “Temporal capacity graphs for time-
varying mobile networks,” in Proceedings of the 23rd International
Conference on World Wide Web, 2014, pp. 723–726.
[33] F. Tang, H. Zhang, and L. T. Yang, “Multipath cooperative routing with
efficient acknowledgement for leo satellite networks,” IEEE Transac-
tions on Mobile Computing, vol. 18, no. 1, pp. 179–192, 2018.
[34] X. Zhu, J. Wang, X. Qin, J. Wang, Z. Liu, and E. Demeule-
meester, “Fault-tolerant scheduling for real-time tasks on multiple earth-
observation satellites,” IEEE Transactions on Parallel and Distributed
Systems, vol. 26, no. 11, pp. 3012–3026, 2015.
[35] F. Tang, “Dynamically adaptive cooperation transmission among
satellite-ground integrated networks,” in IEEE INFOCOM 2020, pp.
1559–1568.
[36] J. Wang, L. Li, and M. Zhou, “Topological dynamics characterization
for leo satellite networks,” Computer Networks, vol. 51, no. 1, pp. 43–
53, 2007.
[37] L. J. Chaves, I. C. Garcia, and E. R. M. Madeira, “Ofswitch13: En-
hancing ns-3 with openflow 1.3 support,” Proceedings of the Workshop
on ns-3, pp. 33–40, 2016.
[38] S. Knight, H. X. Nguyen, N. Falkner, R. Bowden, and M. Roughan,
“The internet topology zoo,” IEEE Journal on Selected Areas in
Communications, vol. 29, no. 9, pp. 1765–1775, 2011.
[39] M. M. Rahman, S. Saha, U. Chengan, and A. S. Alfa, “Ip traffic matrix
estimation methods: Comparisons and improvements,” in IEEE ICC
2006, pp. 90–96.
IEEE INFOCOM 2021 - IEEE Conference on Computer Communications