Connectivity and Coverage Problems in Emerging Networks Arun Sen - - PowerPoint PPT Presentation

Connectivity and Coverage Problems in Emerging Networks

Arun Sen Computer Science & Engineering Program School of Computing, Informatics and Decision Systems Engineering Arizona State University

Joint Aerial Layer Network

Efforts are currently underway in the U.S. Air Force to utilize a heterogeneous set of physical links (RF, Optical/Laser and SATCOM) to interconnect a set of terrestrial, space and highly mobile airborne platforms (satellites, aircrafts and Unmanned Aerial Vehicles (UAVs)) to form an Airborne Network (AN)

Region-based faults – p. 2/2

Joint Aerial Layer Network

Region-based faults – p. 2/4

Joint Aerial Layer Network

JALN Integrated with space and surface networks enables Leader Centric Command and Control, and Battlespace Awareness in a net-enabled environment, enabling advanced warfighter information exchange capabilities across the range of military operations JALN Capability GAPS

• Connectivity
• Capacity
• Aerial Layer Network Management
• Share Information and Data

Region-based faults – p. 3/4

Joint Aerial Layer Network

Region-based faults – p. 4/4

!"##$%&'()*+,#-+!"'$.,/$+0."12$34

+

Slide from the presentation of

• Dr. Robert Bonneau, AFOSR, at

IEEE Infocom 2008 in Phoenix, AZ. Efforts are currently underway in the U.S. Air Force to utilize a heterogeneous set of physical links (RF, Optical/Laser and SATCOM) to interconnect a set of terrestrial, space and highly mobile airborne platforms (satellites, aircrafts and Unmanned Aerial Vehicles (UAVs)) to form an Airborne Network (AN) Conceptual View of an Airborne Network

!"##$%&'()*+,#-+!"'$.,/$+0."12$34

+

Completely Mobile Ad-hoc Network Infrastructure-less Network Conceptual View of an Airborne Network Workshop on Cognitive Networking for Air and Space Networks Organizer – Dr. John Matyjas, AFRL, Utica, N.Y in June 2008 and September 2010. Solicitation of input for architecture of an Airborne Network

Architecture and Algorithms for an Airborne Network !

Perils of Completely Mobile Ad-hoc Networks – Our Experience

Shared-Vision: Embedded Technology for Military Operations in Urban Terrain Army Research Office (ARO) and Defense University Research Instrumentation Program (DURIP) supported research project on real time video transmission over Mobile Ad-Hoc Network. A 25 node Mobile Ad-hoc Network test-bed for evaluation

• f real time video transmission over mobile ad-hoc networks.

Architecture and Algorithms for an Airborne Network

Perils of Completely Mobile Ad-hoc Networks – Our Experience

Completely Mobile Ad-hoc Networks are not as stable as we would like them to be. If video transmission stops due to path breakage, it takes considerable time to restart transmission Our suggestion – Hybrid network comprising of static and mobile routers Low cost disposable routers camouflaged as street objects (stones, bricks etc.) can be placed on the paths

• f the soldiers

Noticeable improvement in performance – Take the idea to Airborne Network Scenario

Architecture and Algorithms for an Airborne Network ! Architecture of an Airborne Network

Architecture and Algorithms for an Airborne Network ! Architecture of an Airborne Network

Airborne Warning and Control Systems (AWACS) like aircrafts (Boeing 707/767) forming the backbone of the Airborne Networks (Mobile Base Stations) Tactical aircrafts on a Mission can be conceived of as Mobile Clients

Architecture and Algorithms for an Airborne Network

!

Relay Node Relay Node Relay Node Relay Node

(From the presentation slides of Dr. John Matyjas, AFRL, at the AFOSR organized Complex Networks Workshop in Arlington, VA, February 2009)

Architecture and Algorithms for an Airborne Network Coverage Area of Airborne Networking Platforms

Architecture and Algorithms for an Airborne Network

!

Ground Footprints of an Airborne Networks

!"#$%&##"'&#$(&#$)*+$ $ !"#,-./+0$12"00"-+03

$

Robust Network Design – Connectivity and Beyond (AFOSR supported research project at ASU (Sen) and UC Berkeley (Ramchandran)

Design of mobility pattern of Airborne Networking Platforms to provide a stable operating environment Design of networks that enables graceful performance degradation Protocol design for networks with partial and uncertain information Information transfer capacity of dynamic heterogeneous airborne network Security measures against a diverse set of attacks Routing performance in diverse networking conditions

Objectives of our study

Architecture and Algorithms for an Airborne Network !

Design of mobility pattern of Airborne Networking Platforms to provide a stable operating environment Design of networks that enables graceful performance degradation Protocol design for networks with partial and uncertain information Information transfer capacity of dynamic heterogeneous airborne network Security measures against a diverse set of attacks Routing performance in diverse networking conditions

Objectives of our study

Architecture and Algorithms for an Airborne Network !

What do we mean by “stable operating environment” ? The (backbone) network formed by the (mobile) ANPs should have the following two properties: 1.The backbone network should remain connected at all times. 2.The air corridor should have radio coverage at all times.

Objectives of our design

Architecture and Algorithms for an Airborne Network !

The (backbone) network formed by the (mobile) ANPs should have the following two properties: The backbone network should remain connected at all times. The air corridor should have radio coverage at all times. Connected Coverage with Mobile Nodes (ANPs) Problem How to solve the “connected coverage” problems with ANPs?

Objectives of our design

Architecture and Algorithms for an Airborne Network !

How to solve the Connected Coverage Problem?

A two phase approach Phase 1: Find out the minimum number of ANPs required to provide radio coverage in the air corridor at all times. Find out the minimum transmission range required by the ANPs to form a backbone network that remains connected at all times.

Architecture and Algorithms for an Airborne Network !

How to solve the Connected Coverage Problem?

A two phase approach Phase 1: Find out the minimum number of ANPs required to provide radio coverage in the air corridor at all times. Phase 2: Find out the minimum transmission range required by the ANPs to form a backbone network that remains connected at all times.

Coverage Problem Definition

Given:

• The dimensions of the rectangular parallelopiped section of air

corridor: Lac, Wac, Hac

• The radius of coverage sphere associated with each ANP: rs

Find:

• The radius of orbit of the ANPs: ro
• Number of ANPs in each orbit: n and number of orbits required: m
• Placement of the m orbits and the placement of the ANPs.

Such that:

• Entire volume of air-corridor is covered at all times.
• Number of ANPs (mn) is minimized.

Region-based faults – p. 2/2

Architecture and Algorithms for an Airborne Network

!

Large orbit of the ANPs – holes in the coverage area (Time invariant coverage area is empty)

ANPs in Circular Orbit Top View of the Coverage Spheres Side View of the Coverage Spheres

Architecture and Algorithms for an Airborne Network

!

Large enough orbit of the ANPs to have non-empty time invariant coverage area (time invariant coverage area is a point)

ANPs in Circular Orbit Top View of the Coverage Spheres Side View of the Coverage Spheres

Architecture and Algorithms for an Airborne Network

!

Small enough orbit of the ANPs to have non-empty time invariant coverage area (football shaped time invariant coverage area)

ANPs in Circular Orbit Top View of the Coverage Spheres Side View of the Coverage Spheres

Architecture and Algorithms for an Airborne Network

!

Small enough orbit of the ANPs to have non-empty time invariant coverage area (doughnut shaped time invariant coverage area)

Cylindrical region extracted from time invariant coverage area Top View of the Coverage Spheres Side View of the Coverage Spheres

Relation between rs, ro and n

!"

#$"

rc = 2rocosπ n hc =

• r2

s − r2

• Region-based faults – p. 2/2

Architecture and Algorithms for an Airborne Network

!

Parallelopiped Coverage with Cylinders Problem What is the fewest number of cylinders needed to cover a parallelopiped? Rectangle Coverage with Circles Problem What is the fewest number of circles needed to cover a rectangle?

Rectangle Coverage with Circles - Strategy 1

!"# $"#

• Largest Square inscribed in

the disc of radius rc.

• Use squares to cover the

rectangular region Lac × Wac.

• m = Lac

√ 2rc × Wac √ 2rc

minimize mn = Lac 2 √ 2rocos π

n

× Wac 2 √ 2rocos π

n

× n subject to : hc =

• r2

s − r2

• ≥ Hac

Region-based faults – p. 2/3

Rectangle Coverage with Circles - Strategy 2

!"# $"#

• Largest rectangle (a × b) with

aspect ratio Lac

Wac from the disc

• f radius rc ( a

b = Lac Wac )

• Use rectangles to cover the

rectangular region Lac × Wac.

• m

=

• √

L2

ac+W 2 ac

4rocos π

n

• ×
• √

L2

ac+W 2 ac

4rocos π

n

• minimize mn =
• L2

ac + W 2 ac

4rocos π

n

2 × n

(1)

subject to : hc =

• r2

s − r2

• ≥ Hac

(2)

Region-based faults – p. 3/3

Effect of variation of rs on ro and n

!" #$ #" %$ %" &$ $ !$ #$ %$ &$ "$ '$ () !"#$%$&''($)

"#$%$*'($+"#$%$&'

*+(,+-./0#0123-4+56- *+(,+-./0!0123-4+56- (7 8 !" #$ #" %$ %" &$ $ "$ !$$ !"$ #$$ '( !"#$%$&''($)"#$%$&*'($+"#$%$&' )*'+*,-./!/012,3*45, )*'+*,-./#/012,3*45, '6 7 !" #$ #" %$ %" &$ $ #$ &$ '$ ($ )* !"#$%$&''($)"#$%$&''($*"#$%$&' +,-./012. )3 4

Region-based faults – p. 6/19

Effect of variation of Hac on ro and n

! "# "! $# $! %# %! # $# &# '# (# )*+ ,*+-.-"##/-0*+-.-1#/-23-.-$# 452*5678-$-9:;6+5<=6 452*5678-"-9:;6+5<=6 2> ? ! "# "! $# $! %# %! # !# "## "!# $## $!# &'( )'(*+*"##,*-'(*+*".#,*/0*+*$# 12/'2345*$*6783(29:3 12/'2345*"*6783(29:3 /; < ! "# "! $# $! %# %! # $# &# '# (# "## "$# )*+ ,*+-.-"##/-0*+-.-"##/-12-.-$# 13 4

• 5678+9:;8

Region-based faults – p. 7/19

Observation 1

• Increase in rs results in increase in ro and decrease in mn for

both the strategies.

• Intuitive - as the radius of the coverage sphere increases, the

radius of the circular orbit of the ANPs will increase and the total number of ANPs needed to cover the entire air corridor will decrease.

• When rs is too small compared to Hac, there may not be a

feasible solution.

Region-based faults – p. 2/5

Observation 2

• Increase in Hac results in decrease in ro and increase in mn for

both the strategies.

• Intuitive - as the height of the air corridor increases, the radius of

the circular orbit of the ANPs has to decrease.

• Consequently, the total number of ANPs needed to cover the

entire air corridor must increase.

Region-based faults – p. 3/5

Observation 3

• Number of ANPs in an orbit remains a constant (n = 5)

irrespective of changes in Lac, Wac, Hac and rs.

• This is because the factor n/cos2( π

n), present in the objective

function, reaches its minimum at n = 5.

! " # $ %& %! %" %# %$ !& ' %& %' !& !' ( ()*+,-!.!*(/

Region-based faults – p. 4/5

Observation 4

• The cost of the solution (i.e., the number of ANPs needed to

provide complete coverage of the air corridor) using strategy 1 is less than that of strategy 2

• Explanation - by comparison of the objective functions of the

strategies.

Region-based faults – p. 5/5

Architecture and Algorithms for an Airborne Network !

How to solve the Connected Coverage Problem?

A two phase approach Phase 1: Find out the minimum number of ANPs required to provide radio coverage in the air corridor at all times. Phase 2: Find out the minimum transmission range required by the ANPs to form a backbone network that remains connected at all times.

Robust Network Design - Connectivity and Beyond

Consider n nodes (SSying platforms) in an m-dimensional space m (for AN scenario m = 3) xi(t) ∈ m denotes the coordinates of the node i at time t, where by convention xi is considered an m × 1 column vector, and by x(t) = [xT

1 (t), . . . , xT n(t)]T , the mn vector resulting from stacking the

coordinates of the nodes in a single vector The dynamics of node i (for all i ∈ {1, 2, . . . , n}), is given by ˙ xi(t) = ui(t), where ui(t) is the control vector taking values in some set U ⊆ m

Region-based faults – p. 2/5

Robust Network Design - Connectivity and Beyond

In vector notation, the system dynamics become ˙ x(t) = u(t) where ˙ x(t) = [ ˙ xT

1 (t), . . . , ˙

xT

n(t)]T , u(t) = [uT 1 (t), . . . , uT nu(t)]T are

mn × 1 vectors, respectively. The network of flying platforms described by the system dynamics, gives rise to a dynamic graph G(x(t)) G(x(t)) = (V, E(x(t))) is a dynamic graph consisting of

• a set of nodes V = {1, . . . , n} indexed by the set of flying

platforms, and

• a set of edges E(x(t)) = {(i, j) | dij(x(t)) < δ} with

dij(x(t)) = xi(t) − xj(t) as the Euclidean distance between the platforms i and j and δ > 0 is a constant.

Region-based faults – p. 3/5

Robust Network Design - Connectivity and Beyond

Can we control the motion of the ANPs so that G(x(t)) retains graph-theoretic properties of interest P for all time t > 0? Often times the property P will correspond to the requirement that the graph G remains connected at all times. Formally the problem can be stated as follows: Given Cn,P , the set of all graphs on n nodes with property P, is it possible to nd a control law u(t) such that if G(x(0)) ∈ Cn,P then G(x(t)) ∈ Cn,P for all t ≥ 0? Alternately, given the movement pattern of the platforms (location, SSight path, velocity), we may want to know the minimum transmission range of the on-board transceivers so that the resulting network is always connected.

Region-based faults – p. 4/5

Robust Network Design - Connectivity and Beyond

Mobility Pattern for Connected Dynamic Graph (MPCDG): This problem has five controlling parameters: (i) a set of points {p1, p2, . . . , pn} on a two dimensional space (representing the centers of circular flight paths of the platforms), (ii) a set of radii {r1, r2, . . . , rn} representing the radii of circular flight paths, (iii) a set of points {l1, l2, . . . , ln} representing the initial locations (i.e., locations at time t = 0) of the platforms on the circular flight paths, (iv) a set of velocities {v1, v2, . . . , vn} representing the speeds of the platforms, and (v) transmission range Tr of the transceivers on the airborne platforms.

Region-based faults – p. 5/5

Robust Network Design - Connectivity and Beyond

O x y

• rci
• rcj
• Ri(t)
• Rj(t)
• sij(t)
• ri(t)
• rj(t)

θi(t) θj(t) αci αcj ci

• cj
• i
• j
• Region-based faults – p. 2/2

O x y

• rci
• rcj
• Ri(t)
• Rj(t)
• sij(t)
• ri(t)
• rj(t)

θi(t) θj(t) αci αcj ci

• cj
• i
• j
• s2

ij(t) = (

Ri(t) − Rj(t))2 = R2

i (t) + R2 j(t) − 2

Ri(t) · Rj(t)

Region-based faults – p. 16/19

O x y

• rci
• Ri(0)

αci θi(0) βi ci• i(0)

• tan βi =

Ri(0)cos θi(0)−rcicos αci Ri(0)sin θi(0)−rcisin αci

Region-based faults – p. 17/19

• Condition for having a link between nodes i

and j sij(t) ≤ D

Region-based faults – p. 18/19

• Condition for having a link between nodes i

and j sij(t) ≤ D

• Expression for sij(t)

s2

ij(t) = r2 ci + r2 i + 2rciri cos(βi + ωit)

+ r2

cj + r2 j + 2rcjrj cos(βj + ωjt)

+ rcircj cos αcicj + rirj cos(βij + (ωi − ωj)t) + rcirj cos(αci − βj − ωjt) + rcjri cos(αcj − βi − ωit)

(4)

Region-based faults – p. 18/19

Distance between i and j as a function of time - links being active and inactive

50 100 150 200 250 300 350 400 450 500 5 10 15 20 25 Time Distance Between Nodes i and j 50 100 150 200 250 300 350 400 450 500 5 10 15 20 25 Time Distance between nodes i and j Edge exists between i and j No edge between i and j

D = 4 D = 24 D = 18

• For D = 4: the link i − j never exists
• For D = 24: the link i − j always existss

Region-based faults – p. 19/19

!"#$%&'#&("')*+,)!-./"%&$01)2/")*+)!%"3/"+')4'&5/"6 ) ))7$'#6%+.)2/")#/++'#89%&:)/2)&$'),:+*0%#)

))))))."*;$)2/"0',)3:)&$')!%"3/"+')4'&5/"6%+.) ))))))<-*=/"01>)5$'+)&$':)*"')0/9%+.)*&)*)1;'#%?',) ))))))1;'',@) ))A%2'80')/2)*)-%+6)#*+)3');"'#%1'-:)#/0;(&',)) ))))))(1%+.)&$')&'#$+%B(')1;'#%?',)'*"-%'"@) ))C"/0)-%2'80')/2)'*#$)-%+6>)#/++'#89%&:)/2)&$') )))))),:+*0%#)."*;$)#*+)3')#/0;(&',@)

!"#$%&'#&("')*+,)!-./"%&$01)2/")*+)!%"3/"+')4'&5/"6 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Link 1: Link 2: Link 3: Timeline Links Alive Links Dead

Architecture and Algorithms for an Airborne Netw!"#

$

Visualization of Flight Paths of Airborne Networking Platforms and its relationship with Topology Change

• f the Dynamic Graph formed by an Airborne Network

Mobile Network of Airborne Platforms

Mobility Models

Predictable Well-structured Flight Paths Predictable Ill-structured Flight Paths Unpredictable Flight Paths

Airline Route Maps

Transatlantic Route Map Route Map – Continental United States Route Map – North and South Americas

Airline Route Maps

Route Map – North and South Americas

Airborne Network

Route Map – North and South Americas

A Day in the Life of Air Traffic over the United States

Predictable Ill Structured Flight Path

Unpredictable Flight Path

Network without Infrastructure - Unpredictable Flight Path

Initial Distribution: The ANPs are distributed uniformly over the deployment region. Relationship between transmission range (cn) and number of nodes (n) can be calculated using theoretical results in the literature. Let us consider a random graph Gn(x), which is constructed on independent random points U1, . . . , Un distributed uniformly on [0, 1]d, d ≥ 1, in which two distinct such points are joined by an edge if the l∞ distance between them is at most some prescribed value 0 < x < 1.

Region-based faults – p. 1/5

Appel and Russo’s Result

Proposition: For each n and x, {cn ≤ x} = {Gn(x) is connected} Theorem: lim

n→∞

• cd

n

n log n

• =

1, if d = 1 = 1 2d, if d ≥ 2

Region-based faults – p. 2/5

Unpredictable Flight Path - Mo- bility Model

Mobility Model:

• Modified Random Way Point model.
• Time domain is divided into equal intervals.
• Select randomly a value within a specified range for

displacement along x-axis and y-axis.

• For each node randomly select the directions for both

dimensions, i.e. East/West for x dimension and North/South for y dimension.

• If the corresponding destination falls outside the deployment

region for either dimension, bounce back with the excess amount.

• Reach destination at the end of the time interval.

Region-based faults – p. 3/5

Unpredictable Flight Path - Dis- tribution after Movements

How does the mobility of the nodes effect the distribution? X1, X2 - random variables representing the x and y co-ordinates of a point over a unit square before movement (uniform distribution). Y1, Y2 - random variables representing the x and y co-ordinates of a point over a unit square after movement. It can be derived that: FY1Y2(y1, y2) = y1y2 fY1Y2(y1, y2) = ∂2 ∂y1∂y2

• FY1Y2(y1, y2)
• = 1

Therefore, distribution of nodes remain uniform and results derived for uniformly distributed static nodes can be used for the mobile airborne networks as well.

Region-based faults – p. 4/5

Architecture and Algorithms for an Airborne Network ! Path Switching and Routing Problem

Flying ANPs result in change in the backbone network topology

A path established between a source-destination node pair may not last for the entire duration of communication In order to complete communication, paths may have to be switched

Architecture and Algorithms for an Airborne Network ! Path Switching and Routing Problem

Path switching has associated overhead and is undesirable

Communication has to complete with as few path switching as possible Minimum Path Switch Routing Algorithm

Architecture and Algorithms for an Airborne Network ! Path (Channel) Diversity Quality of links may depend on various factors

(mobility, atmospheric condition, jamming) Multi-channel communication

Two channel (high and low) communication model

Possibilities High and Low quality channels exists on a link Low quality channel exists on a link No

Architecture and Algorithms for an Airborne Network ! Routing performance in diverse networking conditions

Architecture and Algorithms for an Airborne Network ! Routing performance in diverse networking conditions Option 1: P2 P1 P2 P3 P4 P5 Option 2: P5 P6 P4 P5 P6

5"164)+7$)8".9+:$4(/#+;+!"##$%&'()*+,#-+<$*"#-!

• =$).(%+>".+?,62)@)"2$.,#%$+;+!"##$%&'()*+">+)A$+/.,BA+(4+

646,22*+),9$#+,4+)A$+3$).(%+">+>,62)@)"2$.,#%$C+D>+)A$+ %"##$%&'()*+">+)A$+/.,BA+(4+9EFG+)A$#+()+%,#+)"2$.,)$+9+ >,62)4C+

• H(3(),&"#+">+!"##$%&'()*+,4+,+3$).(%+>".+>,62)+)"2$.,#%$+

– ?,(24+)"+%,B)6.$+,#*+#"&"#+">+2"%,2()*+">+>,62)4+ – 0,.&%62,.2*+(3B".),#)+(#+4"3$+4%$#,.("4+8A$.$+>,62)4+ ,.$+9#"8#+)"+1$+2"%,2(I$-+J1,K2$L$2-G+'(.64+ B."B,/,&"#G+4"%(,2+%"A$4('$#$44M+

5"164)+7$)8".9+:$4(/#+;+!"##$%&'()*+,#-+<$*"#-+

N(#/2$+5$/("#+?,62)+="-$2+J45?=M+ =62&B2$+5$/("#+?,62)+="-$2+35?=M+ 0."1,1(2(4&%+?,62)+="-$2O+0."1,1(2()*+ ">+>,(26.$+(4+(#'$.4$2*+B."B".&"#,2+ )"+)A$+-(4),#%$+>."3+)A$+$B(%$#)$.++ ,K,%9C+

5$/("#@1,4$-+!"##$%&'()*+(#+45?=!

• PA,)+(4+,+5$/("#Q+
• =,#*+B"44(12$+-$L#(&"#4+">+,+5$/("#+

– R"B"2"/(%,2+-$L#(&"#+

• S+461@/.,BA+">+-(,3$)$.+-+

– T$"3$).(%,2+-$L#(&"#+

• S+%(.%2$+">+-(,3$)$.+-+
• 5$/("#@1,4$-+%"##$%&'()*+!"J#M+J8()A+

.$4B$%)+)"+)A$+2,*"6)+">+,+/.,BA+TM+

– U$%&'&$(V+(4+)A$+4$)+">+,22+B"44(12$+%(.%62,.+.$/("#4+ – )W*X+(#-(%,)$4+)A$+3(#(363+#631$.+">+#"-$4+(#+ 5$/("#+$*G+8A"4$+>,(26.$+8(22+-(4%"##$%)+T+ –

:(Y$.$#%$+1$)8$$#+!"##$%&'()*+,#-++ 5$/("#@1,4$-+!"##$%&'()*!

0"8$.+N,'(#/+8()A+5$/("#@1,4$-+!"##$%&'()*!

@+:$4(/#+.$Z6(.$3$#)O++R"2$.,)$+>,(26.$+">+6B+)"+[+#"-$4+++++++++++++++++++++++++++++ @+\#"82$-/$O++?,62)4+,.$+%"#L#$-+)"+,+%(.%62,.+.$/("#+8()A+-(,3$)$.+]3++++++ @+N"26&"#O++N$)+)A$+).,#43(44("#+.,#/$+)"+F^3C+S2)A"6/A+)A(4+.$462)4+(#+,+ #$)8".9+8()A+%"##$%&'()*+[+J>,(26.$+">+6+,#-+'+%,#+-(4%"##$%)+)A$+ #$)8".9MG+()+(4+46_%($#)+)"+.$,2(I$+)A$+-$4(/#+/",24+,4+)A$+-(4)J6G'M+`+]3G+ )A$*+%,##")+>,(2+4(362),#$"642*C+

6+ '+

0"8$.+N,'(#/+8()A+5$/("#@1,4$-+!"##$%&'()*!

@0"8$.+N,'(#/O++RA$+%"#'$#&"#,2+4"26&"#+)"+)"2$.,)$+[+>,62)4G+(4+)"+-$4(/#+ ,+#$)8".9+8()A+%"##$%&'()*+aC++?".+)A$+#$)8".9+)"+A,'$+%"##$%&'()*+aG+ ).,#43(44("#+>."3+)A$+#"-$+1+364)+.$,%A+)A$+#"-$+AC+D#+)A(4+%,4$G+)A$+ ).,#43(44("#+.,#/$+364)+1$+FbCa+3$)$.4+(#4)$,-+">+F^+3$)$.4C++N(#%$+ B"8$.+%"#463B&"#+(4+,BB."c(3,)$2*+B."B".&"#,2+)"+)A$+4Z6,.$+">+)A$+ ).,#43(44("#+.,#/$G+)A$+B"8$.+%"#463B&"#+8(22+(#%.$,4$+1*+#$,.2*+[^^dC+ @+RA$+(#%.$,4$-+B"8$.+%"#463B&"#+-"$4+#")+$#A,#%$+)A$+>,62)@)"2$.,#%$+ %,B,1(2()*+">+)A$+#$)8".9C++

6+ '+

0"8$.+N,'(#/+8()A+5$/("#@1,4$-+!"##$%&'()*!

• e6$4&"#O+D4+4614),#&,2+B"8$.+4,'(#/+B"44(12$+"#2*+(#+

B,)A"2"/(%,2+%,4$4G+,4+)A$+"#$+4A"8#+$,.2($.G+".+()+(4+).6$+(#+ 3".$+/$#$.,2+%,4$4Q+

• S#48$.O+P$+6#-$.)""9+$c)$#4('$+4(362,&"#+)"+L#-+,#+

,#48$.+)"+)A,)+Z6$4&"#C+N(362,&"#+.$462)4+4A"8$-+)A,)+(#+ ,22+%,4$4G+-$4(/#+8()A+)A$+.$/("#@1,4$-+%"##$%&'()*+3$).(%+ (4+,28,*4+1$K$.+)A,#+".+,)+2$,4)+,4+/""-+,4+)A$+-$4(/#+8()A+ )A$+%"##$%&'()*+3$).(%+6#-$.+)A$+.$/("#@1,4$-+>,62)+ 3"-$2C+

• f14$.',&"#O+S2)A"6/A+)A$+%"4)+$Y$%&'$#$44+">+>,62)@

)"2$.,#)++#$)8".9+-$4(/#+8()A+.$/("#@1,4$-+%"##$%&'()*+(4+ 4A"8#+(#+,+8(.$2$44+#$)8".9G+4(3(2,.+,./63$#)4+A"2-+>".+ 8(.$-+#$)8".94+,4+8$22C++

N(362,&"#+gcB$.(3$#)4!

• !"3B,.$+)A$+).,#43(44("#+.,#/$+.$Z6(.$-+)"+

$#46.$+)A$+-$4(.$-+%"##$%&'()*+8()A+)A$+ ).,#43(44("#+.,#/$+.$Z6(.$-+)"+$#46.$+)A$+

• $4(.$-+.$/("#@1,4$-+%"##$%&'()*+(#+
• (Y$.$#)+$cB$.(3$#),2+4$h#/+

–i,.*(#/+)A$+#631$.+">+#"-$4+#+ –i,.*(#/+)A$+.$/("#+-(,3$)$.+-+ –i,.*(#/+)A$+-$4(.$-+%"##$%&'()*+".+.$/("#@1,4$-+ %"##$%&'()*+9+

N(362,&"#+5$462)4+;+',.*(#/+9!

#+j+F^^G+-+j+F^^+ #+j+F^^G+-+j+Fk^+

5$/("#@1,4$-+!"##$%&'()*+(#+35?=++!

• 5$/("#@1,4$-+%"##$%&'()*+(4+)A$+3(#(363+#631$.+">+

.$/("#4+8A"4$+.$3"',2+-(4%"##$%)4+)A$+/.,BAC++

• 5$/("#@!6)+1$)8$$#+#"-$4+4+,#-+)O+=(#(363+#631$.+

">+.$/("#4+8A"4$+.$3"',2+-(4%"##$%)4+)A$+#"-$4+4+ ,#-+)C+

• 5$/("#@-(4l"(#)+0,)A4O+R8"+B,)A4+0F+,#-+0[+%"##$%&#/+

#"-$4+4+,#-+)+,.$+4,(-+)"+1$+.$/("#@-(4l"(#)+(>+)A$+ .$/("#4+,44"%(,)$-+8()A+)A$+(#)$.3$-(,)$+#"-$4+">+0F+ ,#-+)A$+.$/("#4+,44"%(,)$-+8()A+)A$+(#)$.3$-(,)$+ #"-$4+">+0[++,.$+-(4&#%)C+

5$/("#@1,4$-+!"##$%&'()*+(#+35?=+!

=$#/$.m4+RA$".$3+JFn[bMO++RA$++ 3(#(363+#631$.+">+#"-$4+ 8A"4$+.$3"',2+-(4%"##$%)4++ )A$+#"-$4+4+,#-+)+(4+$Z6,2+)"++ )A$+3,c(363+#631$.+">++ #"-$@-(4l"(#)+B,)A4+1$)8$$#++ )A$+#"-$4+4+,#-+)C+ D3B".),#)oD#)$.$4&#/+e6$4&"#O+:"$4+=$#/$.m4+RA$".$3+ +A"2-+>".+.$/("#@-(4l"(#)+B,)A4Q+ D#+")A$.+8".-4O++D4+)A$+3(#(363+#631$.+">+.$/("#4+8A"4$+ +.$3"',2+-(4%"##$%)4++)A$+#"-$4+4+,#-+)G+$Z6,2+)"+)A$++ 3,c(363+#631$.+">+.$/("#@-(4l"(#)+B,)A4+1$)8$$#+)A$++ #"-$4+4+,#-+)Q+

5$/("#@1,4$-+!"##$%&'()*+(#+35?=+!

S#48$.+8()A+R"B"2"/(%,2+:$L#(&"#O+7"+ gc,3B2$O+5$/("#+(4+,+461/.,BA+">++ :(,3$)$.+FC+ 5$/("#+!6)+1$)8$$#+)A$+#"-$4+4+,#-+)+j+[+ 5$/("#@-(4l"(#)+B,)A4+1$)8$$#+4+,#-+)+j+F+ S#48$.+8()A+T$"3$).(%+:$L#(&"#O+7"+ gc,3B2$O+5$/("#+(4+,+%(.%62,.+,.$,+">++

• (,3$)$.++k+3(2$4C+

5$/("#+!6)+1$)8$$#+)A$+#"-$4+4+,#-+)+j+[+ 5$/("#@-(4l"(#)+B,)A4+1$)8$$#+4+,#-+)+j+F+

5"164)+7$)8".9+:$4(/#+;+!"##$%&'()*+,#-+<$*"#-

+

Further limitations of Connectivity as the metric of fault-tolerance It does not capture the number or the size of the connected components in which the network disintegrates when the number of failed nodes exceeds the connectivity of the network.

Connectivity is 1 for both the graphs. However, in one case, after failure of one node, one large connected component is guaranteed to exist. No such guarantee can be given in the other case.

Our solution: Region-based Component Decomposition

Number

5"164)+7$)8".9+:$4(/#+;+!"##$%&'()*+,#-+<$*"#-

+

How to design a network that will be k region-based fault tolerant under single/multi-region fault model? How to design a network whose RBCDN is at most k? How to design a network whose RBSCS (or RBLCS) is at least k? How to design a network that ensures that the key nodes retains a specified structural property (large connectivity, small diameter) under single/multi-region fault model? How to design a multi-layer network so that impact of failures in one layer i (say, layer 1) can be mitigated by resources in layer j?

Objectives of our study

Visualization of Airborne Networks

Visualization of Airborne Networks ANPs in Reality

Region-based faults – p. 2/2

Specification of ANPs

• The STS-111 is an unmanned Mid Altitude Long

Endurance UAV and is designed to carry crucial communications technology, provide persistent surveillance capabilities and work in tandem with

• ther UAVs.
• Multi-layered communications software package that

enables multi-vehicle IP-based messaging (TCP/IP , UDP) over line-of-sight (LOS) or beyond-line-of-sight (BLOS*) communication channels.

!"#$%&'( !"#$%&'()*+,- !."&$./0 1&2$3)4.05$) 5&6' 7/86'#/9-) :6/'-%6-"-8; <-#'"+)&,-'#$./0)9&2$)%&') &/-)#.'9'#%$)#$)=>3?)9&@-'0-

!"!#$ %&'!(& )*+#,-./0121 3456.4,-./0 7819.:58 ;+<=,'!(& !>8$?>@AB1@@14>CD E51>CF,G<G,.>8H8.I: E51>CF,G<G,.>8H8.I: J.K.4,.>8H8.I: L!M,.>8H8.I: L!M,.>8H8.I: '1:?1819,.185$:.: N5/,!4:>:O91,E4>P@ Q.CC19 Q.CC19 Q.CC19 Q.CC19 LCP.CC19 LCP.CC19 LCP.CC19 R+<S<<< R+<S<<< RTUSG<< R+VSW<< RWS<<< RX<<*,W<< RTSU<< TT,?5O8$ TT,?5O8$ ;YG,?5O8$ XW,?5O8$ ;<,?5O8$ TW*X<,9.2$ +*X,9.2$ RTGW,Q RTGW,Q RTVX,Q R+X+,Q R;;,Q RXYW,Q RTWYU,Q Region-based faults – p. 2/2

Backbone Network Design in Presence of Faults

• Earlier, we presented algorithms to compute the minimum

transmission range of the airborne transceivers so that the backbone network remains connected at all times.

• This transmission range ensures a time-invariant property

(connectivity) of a time-varying network topology.

• Our earlier results did not consider impact of an attack on an

airborne network.

• Our current results provide an algorithm to compute the minimum

transmission range of the airborne transceivers so that the backbone network remains connected at all times in spite of failure of several airborne nodes due to an attack.

Region-based faults – p. 2/2

Visualization of Airborne Network with Fault

Region-based faults – p. 2/2

Previous Result

• We considered a similar scenario in an Infocom 2006 paper

where the nodes are stationary

• We extended these results to fit in a Airborne Network

scenario where nodes are mobile

• Mobility of the nodes increases the complexity of the

problem significantly.

Region-based faults – p. 2/16

Previous Result (cont’d)

• Infinite number of points can potentially be centers of fault regions.
• However, it is sufficient to consider only O(n2) points as centers of

fault regions (Sen et al. - Infocom 2006).

!"# !"$ # $ %#$ & %#$ '

(

Vulnerability Zone (V Zi): Circular area of radius R centered at node i I-points: The intersections of two vulnerability zones of two different

• nodes. If VZ of one node does not intersect with any other VZ, then the

location of the node is considered as an I-point.

Region-based faults – p. 3/16

Previous Result (cont’d)

Computation of Region-Based Connectivity

!"#$%&'()

*%&&"*+",'*%-)%&"&+'. *%&&"*+",'*%-)%&"&+'/ *%&&"*+",'*%-)%&"&+'0

• Algorithm computes, for each region, the minimum number of

nodes inside the region whose removal will disconnect the graph

• The objective is to find the minimum transmission range so that

graph remains connected even after the failure of all the nodes in any of the regions.

• Required information:
• 1. Time-varying network topology without faults in every time slot

(interval)

• 2. Nodes within each fault region in every time slot (interval)

Region-based faults – p. 4/16

Computation of time-varying network topology without faults in every time slot (interval)

Region-based faults – p. 5/16

Time-varying Distance Between a Pair of Nodes

O x y

• rci
• rcj
• Ri(t)
• Rj(t)
• sij(t)
• ri(t)
• rj(t)

θi(t) θj(t) αci αcj ci

• cj
• i
• j
• s2

ij(t) = (

Ri(t) − Rj(t))2 = R2

i (t) + R2 j(t) − 2

Ri(t) · Rj(t) Condition for having a link between nodes i and j: sij(t) ≤ D

Region-based faults – p. 6/16

Link Lifetime

Distance between i and j as a function of time - links being active and inactive

50 100 150 200 250 300 350 400 450 500 5 10 15 20 25 Time Distance Between Nodes i and j 50 100 150 200 250 300 350 400 450 500 5 10 15 20 25 Time Distance between nodes i and j Edge exists between i and j No edge between i and j

D = 4 D = 24 D = 18

• For D = 4: the link i − j never exists
• For D = 24: the link i − j always exists

Region-based faults – p. 7/16

Link Active/Inactive Time Intervals

!"#$%&' !"#$%(' !"#$%)' *"+,-"#, & ( ) . / 1 2 3 &4 && &( &) &. &/ &0 &1 !"#$5%678"9, !"#$5%:,;<

• Check for the graph-connectivity in each of these intervals

between time t = t1 and t = t2 (time of operation)

• Binary search over the range [0, Tmax] to find the minimum

transmission range to make the graph connected

Region-based faults – p. 8/16

Computation of nodes within each fault region in every time slot (interval)

Region-based faults – p. 9/16

Vulnerability Zone for an ANP

• Vulnerability Zone of an ANP moves along with the ANP
• At time t, it is denoted by V Zi(t)
• For a pair of ANPs, ANPi and ANPj, the I-points are denoted as

I1

ij(t) and I2 ij(t)

!"# !"$ # $ %#$ & %#$ '

( )# )$ *+,#- )./-.+0*10*+,#-

I-points when VZs intersect

!"# !"$ # $

%# %$

&'()#*+,-.,#*%/-!"#-0*1-!"$- 1)-*)+-#*+/2,/%+3

I-points when VZs do not intersect

Region-based faults – p. 10/16

Lifetime of I-points

• Distance sij between ANPi and ANPj at time t is given as:

s2

ij(t) = (

Ri(t) − Rj(t))2 = R2

i (t) + R2 j(t) − 2

Ri(t) · Rj(t)

• The existence of the I-points (I1

ij(t) and I2 ij(t)) at time t, is denoted

by indicator variables II1

ij(t) and II2 ij(t) defined as follows:

II1

ij(t) =

   1,

if sij < 2R

0,

• therwise

!"# !"$ # $ %#$ & %#$ '

!"#$%$&'

II1

ij = II2 ij = 1

!"# !"$ # $

%# %$ !"#$%$&'

II1

ij = II2 ij = 0

!"# $%&' !"# (%&' &")* !!"# $%&'+,+!!"# (%&'+,- !!"# $%&'+,+!!"# (%&'+,$

vvehvuberviue

Region-based faults – p. 11/16

Nodes within Fault Region

• F = {f1, f2, . . . , fl}: the set of regions centered at I-points, where

l = n(n − 1) + n

• Dpk(t) = distance between center of region fp and ANPk at time t
• For every region fp and every node ANPk, if at time t the

distance Dpk(t) ≤ R, then ANPk is within the fault region fp

!"#$ %& '&()!*+,-. '&/ '&0 1 1 1 2345+6"!7"0+%&+-+8(9/90: 2345+6"!7"0+%&+-+8(9/: )!*+,-. )!*+,-.

Region-based faults – p. 12/16

Putting it Altogether

• Step 1: Computation of time-varying network topology

without faults in every time slot (interval)

• Step 2: Computation of nodes within each fault region in

every time slot (interval) Combining Step 1 and Step 2:

• Step 3: Division of the time intervals computed in step 1 into

sub-intervals, to identify the set of vulnerable nodes in each

• ne of them, due to occurrence of an attack (fault)

Region-based faults – p. 13/16

Computation of the Minimum Transmission Range to keep the Residual Graph Connected when Some or All Nodes in a Fault Region fp have Failed

!"#$ %"&'( %"&') %"&'* %"&'+ %"&', ( ) * + ,

• .

/ !"#$ 12 32( 4!56789 32) 32+ 4!56789 4!56789

:( :)

;6;6;

:0

) + * %"&'( %"&') %"&'* 32* 4!56789 (

!( !) !*

:(6<

=!6!(6>6126&?!6@A@"%@B%$

:(4!)56<6

) + * %"&'( %"&') %"&'* (

:(4!*56<6

) + * %"&'( %"&') %"&'* (

• From link lifetime information, the graph Gi corresponding to time

interval i is computed

• From the fault region (fp) information, we compute the

subintervals, during which a subset of nodes of Gi is vulnerable due to fault fp

Region-based faults – p. 14/16

Computation of Minimum Transmission Range to keep the Dynamic Backbone Network Connected at All Times Even in Presence of an Attack

• Step 1: After identification of a set of vulnerable nodes due to a

fault fp in one sub-interval, we compute the minimum transmission range necessary to keep the residual graph connected

• Step 2: Step 1 is repeated for every sub-interval corresponding to

a fault fp and every fault in the fault set F = {f1, f2, . . . , fl}

• Step 3: The maximum of the minimum transmission ranges

required to keep the residual graph connected over every sub-interval and every fault in F, gives the minimum transmission range necessary to maintain graph connectivity at all times

• Computational Complexity: O(n6log n)×(the number of sub-intervals)

Region-based faults – p. 2/2

Conclusion

• We proposed an architecture for an airborne network for stable
• perating environment
• We introduced the notion of region-based (spatially-corelated)

faults that captures fault scenario in a combat environment more accurately

• We introduced a few new metrics to evaluate the network state,

when the number of faults exceeds the connectivity (or, region-based connectivity) of the network

• We developed algorithms to compute minimum transmission

range to keep the backbone of the airborne network connected, even when some nodes fail after an attack

• We developed polynomial time algorithms to design static

networks with targeted values of RBCDN, RBLCS or RBSCS, and working on extending these solutions for mobile networks

Region-based faults – p. 2/2

On Sparse Placement of Regenerator Nodes in Translucent Optical Network

Facility Location Problem in Emergent Optical-bypass-enabled (translucent) Optical Networks

Globecom 2008

Classification of Optical Networks

Optical Networks: Regeneration

Transparent (all-optical) Opaque Networks Optical Networks Translucent Optical Networks

(TON)

– Transparent Networks

• Signal is carried purely in the optical domain

– Opaque Networks

• All nodes have electronic switching technology

– Translucent Optical Networks (TON)

• Hybrid network with subset of nodes having electronic switching

technology

Optical Networks: Regeneration

What is Regeneration in TONs ?

• Optical signal loses strength as it goes through an optical fiber
• Optical signal needs to be regenerated (re-amplify, reshape, re-time – 3R)
• Optical reach: a distance that approximates the extent to which an optical

signal can travel before its signal strength drops below a threshold

• Actual factors that cause signal degradation: chromatic dispersion,

polarization mode dispersion, crosstalk, etc.

Optical Networks: Regeneration

Regenerator Placement & Routing Problems

• Regenerator Placement Problem

– Given a network with link distances, find the minimum number of regenerators and their locations so that a communication path can be established between every pair of nodes in the network.

• Regenerator Routing Problem

– Given a network with link distances, a subset of nodes which are regenerators, source s & destination t nodes, find a path from s to t that goes through the fewest number of regenerators

• Why minimize number of regenerators ?

– For routing problems: more regenerators = more delay – For placement problems: save money – Importance of the problem underscored by recent US Patents

Regenerator Placement Problem

Long haul network Long haul network with Regenerators

Optical Networks: Regeneration

Related Work

• B. Ramamurthy, et al.

– Solved placement, routing problems individually and jointly – Intra-domain and Inter-domain routing – Main idea of the algorithms: Compute shortest paths between all source-destination pairs, place regenerators on these paths – this may end up being far from minimum!

• G. Shen, et al.

– Placement problem = K-center problem ? K-center solution = {B, D} (Every node is within 1500 miles of the centers) Minimum # Regenerators = 3 (B, C, D) (Optical reach 1500 miles)

Optical Networks: Regeneration

Related Work

• J. Simmons

– Routing: enumerate large number of paths – Does not guarantee finding a path even if it exists

• Telecordia Technologies Inc.

– Compute Connected Dominating Set on ‘Rechability’ graph (patent issued in October 2007)

• Limitations of earlier research work

– Do not consider need for edge-disjointness between path segments

Optical Networks: Regeneration

Need for edge-disjointness among path segments

• Path-segment

– Given a network graph Gn=(Vn,En), a subset V'n  Vn, s-t path P, path segment PS is a subpath of P whose endpoints are in V'n U {s,t} and no intermediate node of PS is in V'n – Unrestricted Regenerator Placement Problem (URPP)

• Given Gn = (Vn, En) and optical reach R, find smallest subset V'n of

Vn such that

1. there is a path between every pair of nodes s, t in Vn 2. no path segment of the s-t path has length more than R

Path Segment

1 3 4 5 6 2

NOT a Path Segment

V'n= {4}

Optical Networks: Regeneration

Need for edge-disjointness among path segments

• Example:

– Optical Reach = 3250, Min. Regenerator for URPP = {D}, – Consider source A, destination H – If only 1 wavelength is available on link (B,C), this solution is not acceptable

• New Problem Formulation: Regenerator Placement Problem (RPP)
• Given Gn = (Vn, En) and optical reach R, find smallest subset V'n  Vn such

that

1. there is a path between every pair of nodes s, t in Vn 2. no path segment of the s-t path has length more than R 3. the path segments of the s-t path are mutually edge-disjoint

Regenerator Placement Problem

Solution Approach: Step 1: Compute Reachability Graph of the network

Network Reachability graph of the network

Step 2: Compute Connected Dominating Set of the Reachability Graph.

Regenerator Placement Problem

Question: Does it work?

Connected Dominating Set of RG Reachability Graph (RG)

• Works for the unrestricted version (no disjoint-ness )
• Does not work for the restricted version

Reason: composite edges in the reachability graph does not carry information about atomic edges of the network that constitute a composite edge. Solution: Composite edges must carry information about atomic edges that constitute a composite edge. Enter Labeled Graph.

Optical Networks: Regeneration

Definitions

• Labeled Graph

– Each edge in the graph has a label drawn from an alphabet set of symbols

• (Labeled) Reachability Graph

– For a given weighted network graph Gn=(Vn,En) and distance R, reachability graph has an edge (u,v) if there is a u-v path in Gn of length  R – Label of edge (u,v) = edges in the u-v path in Gn – Reachability graph is a multigraph

Optical Networks: Regeneration

Defintions: Reachability Graph

• Example:

Network Graph with Optical Reach R = 2000 Reachability Graph

Regenerator Placement Problem

Connected Dominating Set of RG

Reachability Graph

(RG)

• Connected Dominating Set

Lemma 1: A feasible solution of for MCDS problem of G’ , is a feasible solution for RPP of G.

Regenerator Placement Problem

Connected Dominating Set of RG

Reachability Graph

(RG)

• Connected Dominating Set

S1 s2 si u v si+1 sk sj u v sj+1

sp Dist (u, Sj) ≥ Dist (u, Si+1) Dist (u, Sj) > Dist (v, Si+1)

Lemma 2: A feasible solution of for RPP problem of G, is a feasible solution for MCDS of G’.

• (Proof Sketch)
• Construct an instance of G of RPP from an instance of G’ of MCDS
• Set G = G’ and R =1
• Set weight of each edge in G to be 1
• Then any feasible solution of for RPP problem of G, is a feasible solution for

MCDS of G’. But both Lemma 1 and 2 holds except the trivial case when reachability graph G’ is clique. Lemma 3: There is a O(ln n)-approximation algorithm of RPP problem. Lemma 4: There is a O(ln δ)-approximation algorithm of RPP problem, where δ, is the maximum degree of the graph.

Conclusions

Regenerator placement problem taking into account disjoint path segment requirement studied A solution technique, utilizing the concept of Connected Dominating Set is used to find the solution Approximation algorithm with guaranteed performance bound is available.