Multi-cost Routing and its use in Wireless Ad-Hoc Optical Burst Switched Max-Min Fair Share Networks Manos Varvarigos University of Patras, Greece

Multi-cost Routing and its use in

Wireless Ad-Hoc

Optical Burst Switched

Max-Min Fair Share

Networks

Manos VarvarigosUniversity of Patras Greece

Multi-cost Routing

Traditional algorithms use single-cost routing Limited types of cost criteria Inability to incorporate QoS Single path computed for each source-destination

The multi-cost routing approach Link costs are vectors Path costs are also vectors For each source-destination

pair a set of candidate paths is maintained For each packet (or session) a different cost function may be optimized The set of cost functions that can be used is substantially

enlarged

Multi-cost Routing

Each link is characterized by a k-dimensional cost vector

ul=(u1lu2l hellip ukl) For each path P a cost vector is produced based on its

constituent linksrsquo vectors

Vp=(v1p v2phellipvkp) The way the parameters are combined depends on their

type Each cost parameter is obtained using a (different)

associative operator ס

vip = ס uill on path P

Multi-cost Routing

additive

restrictive

maximum representative

Boolean operators (AND OR)

max1

ijlj

i uV

min1

ijlj

i uV

l

j

iji uV1

(eg path capacity node residual energy on the path)

(eg delay of hops dispersion of amplifiers total consumed energy on the path)

(eg node transmission power BER interference on the path)

(egall links or at least one link on the path must have a certain property)

d here is any additive cost parameter (eg delay hops energy consumed)c here is any restrictive parameter (eg capacity residual node energy)

Non-dominated paths

A path is said to dominate another path when all its cost components are superior to those of the other path

Set of non-dominated paths Pn-d for a given source - destination pair no path in the set dominates another path

Pn-d can be found using a multi-dimensional Dijkstra-like algorithm

Complexity can be polynomial or exponential depending on the type of the parameters

Multi-cost Routing

Calculation of non-dominated paths example (cont)

Multi-cost Routing

A multi-cost algorithm consists of two phases Enumeration of a set of non-dominated paths for a

given source-destination pair The optimum path from this set is chosen according

to some optimization function

f (h d c T R BER hellip)

of hopspath delay path capacity total consumed power

minimum node residual energy

The parameters and the choice of function f( ) may depend on the QoS of the user or the interests of the network

Energy-Aware Routing algorithmsWireless Ad-Hoc Networks

We propose multi-cost energy-aware routing algorithms that use the following parameters

The number of hops h (additive) The residual energy R at the transmitting nodes of the links on the path (restrictive) R=min Ri

The total consumed energy T of the transmitting nodes the links on the path (additive)

T= Σ Ti

The maximum consumed energy Trsquo on the path (maximum representative) Trsquo= max Ti

links i on path

links i on path

links i on path

Routing algorithms tested Wireless Ad-Hoc Networks

SUMMIN Energy

SUMMIN Energy-Hop

SUMMIN Energy-Half-Hop

Pii

Pii

R

T

min

max

Various optimization functions f (h R T Tprime) were tested and compared

Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop

MAXMIN Energy-Half-Hop

h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR

Note each optimization function corresponds to a different routing algorithm

The infinite time horizon modelWireless Ad-Hoc Networks

Packets and energy are generated at each node continuously over an infinite time horizon

The objective is to achieve the maximum throughput small average packet delay for a given throughput

packet generation rate p

energy generation rate X









The network evacuation modelWireless Ad-Hoc Networks The network starts with a certain number of packets to be

transmitted to their destination

Each node has a certain amount of energy The objective is

to serve the packets in the smallest number of steps or serve as many packets as possible before the energy at the nodes is depleted

Network Evacuation modelWireless Ad-Hoc Networks

Average residual energy

00

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of packets sent by each node

Avera

ge r

esid

ual en

erg

y

Minimum-Hop MAX MIN Energy MAX MIN Energy-Hop

hPi

i

Pii

R

Th

min

max

The Minimum-HopThe Minimum-Hop algorithm gives the best average node residual energy at the end of the evacuation problem buthellip

Minimum-Hop MAXMIN Energy MAXMIN Energy-Hop Pi

i

Pii

R

T

min

max

hellipbut the Minimum-HopMinimum-Hop algorithm also gives the worst variance of the residual energy σ2

Ε and the worst energy-depletion times DT

Variance of residual energy

000

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Minimum-Hop SUM MIN Energy SUM MIN Energy-Hop

Pii

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min

Pii

Pi

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T

minhMinimum-Hop SUMMIN Energy SUMMIN Energy-Hop



Current number of nodes with depleted energy

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min SUMMIN Energy SUMMIN Energy-Hop Minimum-Hop h

Node energy-depletion times

RS ReceivedSent ratioReceivedSent ratioReceived to sent packets ratio

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min SUMMIN Energy - SUMMIN Energy-Hop Minimum-Hop -

Evacuation problem

The average length of paths usedThe average length of paths usedAverage path length

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Ave

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minMinimum-Hop SUMMIN Energy SUMMIN Energy-Hop

Effect of the topology Update Interval

Capacity constraint

Limitations on an ad-hoc networkunder the infinite time horizon modelWireless Ad-Hoc Networks

Energy constraint1

1

aRLk

Xp

R is the transmission rangeL is the average physical source-destination distance ρ is the energy network densityX is the recharging rateK Krsquo are constants 2leαle4p = Bernoulli packet generation probability per node

X

Upper bound on p

Simulation Results ndash infinite time horizon

Pii

Pii

R

TTRf

min

)(Multicost algorithm with

Infinite time horizon modelWireless Ad-Hoc Networks

Optical Burst Switched Networks

Packets destined to the same egress node and with similar QoS requirements are aggregated into bursts A control packet is sent to reserve resources and is processed electronically the burst follows after an offset time and stays in the optical domain

Tell-and-wait protocolsTell-and-go protocols

OBS network

WDM linksLegacy networks

Controlchannels

Data channels

off set

OBS node

Burst size kB divide MB

Switching timesms divide s

Out- of- band signal

Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

Burst Routing and Scheduling Problem Given Network with links of known propagation delays dl and

link utilization profiles Source A wants to send a burst of size I bits and duration B=IC to some destination G

We want to find a feasible path and the time at which the burst should start transmission so as to optimize the burst reception time at its destination (or hop count orhellip)

A tell-and-go or a tell-and-wait reservation scheme is used to send the burst

r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1

Multicost Burst Routing and Scheduling

Each link l is assigned a vector Vl Vl =(dl Ĉl)=(dl c1lc2lhellipcdl)

A cost vector is defined for a path p based on the cost vectors of its links

p1 dominates p2 (notation p1 gtp2) iff

11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C

1) Calculate the set Pn-d of non-dominated paths

2) Apply an optimization function f(V(p)) to the path cost vectors to select the optimal one

Path Binary Capacity Availability Vector

Transmission of the CAV from node A to a source node C requires time equal to the propagation delay dAC

Assuming that the propagation delays are the same in both directions any data sent from A will incur to reach C dAC

Source A shifts the received CAV by 2dAC

The Capacity Availability Vector of a path is computed

AB ABAB BC AB BC AB BCd 2dABC amp (A) amp C C C C LSH (C C LSH (C) )

Polynomial Time Heuristic Algorithm

The number of non-dominated paths may be exponential Heuristic variations of the multicost algorithm define a

pseudo-domination relation gtps The pseudo-domination relation can be used to prune

paths yielding a set Pn-ps-d Pn-d

of non-pseudo-dominated paths of polynomial cardinality

Eg (Availability Weighted heuristic algorithm)

p1 pseudo-dominates p2 (p1 gtps p2) iff

1 21 2

and ( ) ( )l l l ll p l p

l p l p

d d weight weightC C

Delay vs traffic load ( =300kB)

The optimal multicost algorithm outperforms the Dijkstra and the DijkstraCA algorithms

Marginal difference between the optimal algo and the AW and CSA heuristic algorithms

I

0

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Arrival Rate λ ( burstssec)

End

-to-

end

dela

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sec)

Dijkstra

Optimal multicost

AW heuristic multicost

CSA heuristic multicost

DijkstraCA

The propagation delays in the network play a significant role on the link state information exchange mechanism

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End

-to-

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dela

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AW heuristic multicost - 200kmDijkstraCA - 200kmAW heuristic multicost- 100kmDijkstraCA - 100kmAW heuristic multicost - 50kmDijkstraCA - 50km

MaxndashMin Fair Share Networks

In a max min fair share network the connections using a particular link get a ldquofair sharerdquo of the link bandwidth

Cost Parameters

bullh number of links

bullr available capacity Usually the capacity of a link is taken to be the residual link bandwidth In the max min fair share networks however r is an estimate of the max min fair rate that would be obtained by the new connection if admitted

bulld path propagation delay

Routing algorithms tested MaxndashMin Fair Share Networks

Multicost cost functions (hrd) f(hr) = hr f(dbr) = d + br f1(dbrh) = (d + br)h f2(dbrh) = (d + br)hn

Widest-shortest path min(h)In case of a tie the one with maximum capacity is selected

Shortest-widest path max(r) In case of a tie the one with the minimum of hops is selected

bullb the amount of data to be transmitted

Simulation ResultsMaxndashMin Fair Share Networks

Metrics Average delay (when MCR = 0 ) Probability of success for a new connection (when MCR ne 0)

Topologies considered a random network and a 4x4 mesh network with varying capacities


MCR = 0 Random topology f(dbrh) = (d + br)h


MCR ne 0 Mesh topology f(dbrh) = (d + br)h05


Capacity availability definition

MCR = 0 Mesh and Random topology f(dbrh) = (d + br)h05


Link utilization information updates (P = 10 50 100)

MCR = 0 transmission time gtgt propagation time Mesh topology f(dbrh) = (d + br)h05

Conclusionsfor Wireless Ad-Hoc Networks

Multi-cost algorithms that take energy into account result in

Increased network lifetime More evenly spread energy consumption Higher throughput

The SUMMIN energy-hop algorithm where the cost function is

gives the most balanced results (in terms of node residual

energy energy variance packets dropped depletion times number of hops on paths taken)

The performance benefits diminish when the limitation posed by the network capacity is approached

Pii

Pi

i

R

Th

min

f (h T R) =

Conclusions for OBS networks

The proposed multicost burst routing and scheduling algorithm and its heuristic variations significantly outperform other simulated algorithms

The optimal multicost algorithm is not polynomial but the proposed AW multicost heuristic algorithm has polynomial complexity and performance that is very close to that of the optimal algorithm

The improvements obtained are more significant for small propagation delays

Conclusionsfor max-min fare share networks

Multi-cost algorithms can result in

Lower blocking probability Lower average delay

The algorithm that uses the cost function

f(dbrh) = (d + br)h05 gives the best results

The term r is an estimate of the max min fair rate that would be obtained by the new connection if admitted

Multi-cost Routing

Traditional algorithms use single-cost routing Limited types of cost criteria Inability to incorporate QoS Single path computed for each source-destination

The multi-cost routing approach Link costs are vectors Path costs are also vectors For each source-destination

pair a set of candidate paths is maintained For each packet (or session) a different cost function may be optimized The set of cost functions that can be used is substantially

enlarged

Multi-cost Routing








Multi-cost Routing

additive

restrictive



max1

ijlj

i uV

min1

ijlj

i uV

l

j

iji uV1






Non-dominated paths





Multi-cost Routing


Multi-cost Routing












T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















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Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

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6

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End

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dela

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Dijkstra

Optimal multicost



DijkstraCA


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End

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Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =











Multi-cost Routing








Multi-cost Routing

additive

restrictive



max1

ijlj

i uV

min1

ijlj

i uV

l

j

iji uV1






Non-dominated paths





Multi-cost Routing


Multi-cost Routing












T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















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Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

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8

0 20 40 60 80 100


End

-to-

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dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =











Multi-cost Routing

additive

restrictive



max1

ijlj

i uV

min1

ijlj

i uV

l

j

iji uV1






Non-dominated paths





Multi-cost Routing


Multi-cost Routing












T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

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Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















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Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

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End

-to-

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Dijkstra

Optimal multicost



DijkstraCA


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Cost Parameters





























Pii

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f (h T R) =












Non-dominated paths





Multi-cost Routing


Multi-cost Routing












T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =











Multi-cost Routing


Multi-cost Routing












T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =











Multi-cost Routing












T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =















T= Σ Ti


links i on path

links i on path

links i on path


SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =












SUMMIN Energy

SUMMIN Energy-Hop


Pii

Pii

R

T

min

max


Minimum-Hop

MAXMIN Energy

MAXMIN Energy-Hop


h

Pii

Pi

i

R

T

min

Pii

Pi

i

R

Th

min

Pii

Pi

i

R

Th

min

Pii

Pii

R

Th

min

max

Pii

Pii

R

Th

min

max

=radic h TR

=TprimeR

=hTprimeR

=radic h TprimeR

=TR

=hTR





















00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =






























00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =

















00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =













00

05

10

15

20

100 200 300 400 500 600 700 800 900 1000


Avera

ge r

esid

ual en

erg

y


hPi

i

Pii

R

Th

min

max



i

Pii

R

T

min

max




000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =














000

005010

015

020

025030

035

040

100 200 300 400 500 600 700 800 900 1000


Vari

an

ce o

f re

sid

ual

en

erg

y


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =













0

5

10

15

20

2200 3200 4200 5200 6200 7200 8200 9200

time (sec)

Cu

rre

nt

nu

mb

er

of

no

de

s

wit

h d

ep

lete

d e

ne

rgy


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T




00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =












00

0204

0608

1012

100 200 300 400 500 600 700 800 900 1000


Rec

eive

d to

sen

t pa

cket

s ra

tio


hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T


Evacuation problem


32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =












32

34

36

38

40

42

44

46

100 200 300 400 500 600 700 800 900 1000


Ave

rag

e p

ath

len

gth


Pii

Pi

i

R

Th

min

Pii

Pi

i

R

T





0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =













0

5

10

15

20

25

30

35

0 2000 4000 6000 8000 10000 12000

time (sec)

Cu

rren

t n

um

ber

of

no

des w

ith

dep

lete

d e

nerg

y

1 5 10 20 50 100

hPi

i

Pi

i

R

Th

min

Pii

Pi

i

R

T



Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =











Capacity constraint


Energy constraint1

1

aRLk

Xp


X

Upper bound on p


Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =












Pii

Pii

R

TTRf

min






OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =















OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =














OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager

OBS network


Controlchannels

Data channels

off set

OBS node




Reserv manager

Assemblymanager





r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =















r

r

r

0000011111111

0111111111111

1111111111111

r

0000011111111

r

1111111111111

A

B

C

G

dCB=1





11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =















11 1

( ) def kk k

ll l ll l

V p V d C

1 21 2

and l l l ll p l p

l p l p

d d C C
















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =
























1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =


















1 21 2


l p l p





I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =














I

0

2

4

6

8

0 20 40 60 80 100 120 140


End

-to-

end

dela

y (m

sec)

Dijkstra

Optimal multicost



DijkstraCA


0

2

4

6

8

0 20 40 60 80 100


End

-to-

end

dela

y (m

sec)




Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =













Cost Parameters





























Pii

Pi

i

R

Th

min

f (h T R) =




































Pii

Pi

i

R

Th

min

f (h T R) =































Pii

Pi

i

R

Th

min

f (h T R) =




























Pii

Pi

i

R

Th

min

f (h T R) =


























Pii

Pi

i

R

Th

min

f (h T R) =
























Pii

Pi

i

R

Th

min

f (h T R) =





















Pii

Pi

i

R

Th

min

f (h T R) =


















Pii

Pi

i

R

Th

min

f (h T R) =



























Documents

Multi-cost Routing and its use in Wireless Ad-Hoc Optical Burst Switched Max-Min Fair Share Networks Manos Varvarigos University of Patras, Greece