Design of Capacitated Survivable Networks With a Single Fac - PowerPoint Presentation

Slide1

Design of Capacitated Survivable Networks With a Single Facility

Author :

Hervé

Kerivin

,

Dritan

Nace

, and

Thi

-

Tuyet

-Loan Pham

R97725025

張耀元，

R97725036

李怡緯Slide2

IEEE

transactions on networking

Publication Date: April 2005Slide3

Hervé

Kerivin

received the Ph.D. degree in

combinatorial

optimization from the University Blaise Pascal, Clermont-Ferrand, France, in November 2000.Dritan Nace received the degree in mathematics from the University of Tirana, Albania, in 1991, and the M.Sc. (DEA) degree in computer science and the Ph.D. degree in computer science, both from University of Technology of Compiègne, Compiègne Cedex, France, in 1993 and 1997, respectively.Thi-Tuyet-Loan Pham received the B.Sc. Degree from the Technology University of Ho Chi Minh City, Vietnam, the M.Sc. degree from the Francophone Institut for Computer Science, and the Ph.D. degree from University of Technology of Compiègne, Compiègne Cedex, France.Slide4

Outline

Abstract

Introduction

Mathematical formulation

Solution methodComputational resultConclusion Slide5

AbstractSlide6

Abstract

Single-facility capacitated survivable network design problem SFCSND.

We optimize the network topology and the link dimensioning in order to rout all traffic commodities.

We also consider rerouting strategies to deal with link failure

We present a mix-integer linear programming model solved by combining several approaches.Slide7

IntroductionSlide8

Introduction

Given

a set of nodes

Link

Dimension a set of single type facilities with constant capacitya set of commodities (OD-pair and required bandwidth)We consider only the problem of designing survivable networks when a single link failure arisesSlide9

Introduction

The problem involves designing the

topology

and

dimensioning the linksThe installed capacities will be sufficient to route all traffic demands forNominal state: all network hardware is operational (without fail).Reroute interrupted traffic for failure stateThe problem determines the lowest cost resourceLink installation costA unit facility loading costSlide10

Introduction

In order to reduce cost, the spare capacity devoted to protection is usually shared among several rerouting paths: Shared reroute mode

local rerouting

: tries to reroute traffic locally between the extremities of the failed link

end-to-end rerouting: propagates failure information to the destination nodes of traffic demands, in order to set up rerouting paths between themSlide11

Mathematical Formulation

End-to-end rerouting

Local reroutingSlide12

Mathematical Formulation

We formulate both end-to-end rerouting and local

rerouting

Local

rerouting schemes have in theory a higher bandwidth overhead than end-to-end rerouting schemesSlide13

G(V,E)

Graph with vertex and edge

a

Installation cost associated with the edge of G

X

e={0,1}

Topology variable

K={1,2,…|K|}

Commodities for OD-pair

&

B

k

Traffic demand

(required bandwidth)

M

Maximum number of modularity

λ

Capacity of given facility

y

e

Dimension variable

C

e

A cost corresponds to the loading of a single facility onto edge e

L={1,2

,…|L|}

Link failure indexes where |L|

|E|p P(k)P(k) is the finite set of elementary paths of commodity kNominal flow variableq Q(l,k)Q(l,k) is the set of elementary paths of failed commodity k in fail index lEnd-to-end reroute flow variableSlide14

Mathematical FormulationSlide15

Mathematical Formulation

Local reroute

strategy:

interrupted traffic must be rerouted between the extremity nodes of the failed link

GelGraph composed of failed link elqQ(l)

Q(l) is the finite set of elementary paths of G

el

local rerouting flow variableSlide16

Mathematical Formulation

We rewrite some constrains:Slide17

Mathematical Formulation

The size of both mixed-integer linear programs may be very large because of the huge number of paths in P(k), Q(l,k), Q(l) .

The working paths P(k) and rerouting path Q(l,k), Q(l) are independent so decomposition method (such as

Benders’ decomposition

) can be used to obtain near optimal solution.Slide18

Solution method

A. Break down the problem

B. Capacity feasibility problem

C. Topology and dimensioning problem

D. Implementation detailSlide19

Solution method

We break down into 2 consecutive stages of optimization

Topology and link dimension

Capacity feasible

This breaking down of the problem has a drawback: there are some distance for optimal to our solutionThe higher is the basic capacity of the facility (λ) in relation to a single traffic demand (BK), the more critical this distance becomesSlide20

Solution methodSlide21

Implementation detailSlide22

Computational resultSlide23

Computational Results

A series of computational experiments were performed

to compare

and analyze the survivability cost based on

end-to-end and local rerouting strategiesCompare effectiveness of both restoration strategies (end-to-end and local rerouting):Total capacity installed in the networkTopologyGlobal cost with respect to the obtained networkSlide24

Computational Results (Cont.)

Algorithm implemented in C

CPLEX

7.1

Machine configuration:Sun Enterprise 450Solaris 2.6Quadri-UltraSparcII 400 MHz1 GB RAMSlide25

Problem Instances

Three

(undirected) network

instances considered to perform

the numerical experiments:net1 is generated randomlynet2, net3 are furnished by France Telecom R&DCorrespond to real telecommunication networksSlide26

Problem Instances (Cont.)

Main parameters of the network:

|V|: number of nodes

|E|: number of potential links

|K|: number of traffic demandsd(G): average nodal degreeT(k): average demand traffic Slide27

Problem Instances (Cont.)

Considered all possible traffic demands

The number of traffic demand:

|K| = ( |V| * (|V|-1) ) / 2

Run all of the tests with four different facility capacities 240018001200600All links are subject to failureL = E Slide28

Facility Capacity

Results obtained with four different facility capacities for the single-facility capacitated network design problem:

λ

: constant facility capacity

F: number of installed facilitiesCi: percentage of the whole capacity that is idle (unused)d: average nodal degree in the optimal network f: average link facility in the optimal networkSlide29

Facility Capacity (Cont.)Slide30

Facility Capacity (Cont.)

Facility capacity plays a significant role in the nature of the SFCSND problem

The major difference between

nonsurvivable

and survivable networks is the number of used linksSlide31

Obtained Network Topology

Average nodal degree for the obtained network depends on the value of facility capacity

λ

, regardless of the survivability requirementSlide32

Obtained Network Topology (Cont.)

Small values of

λ

are of the same magnitude order to some traffic demands

Often more cost-effective to create a link than to use long paths to carry this trafficObtained network is highly meshedSlide33

Obtained Network Topology (Cont.)

Sufficiently large values of

λ

may therefore enable us to obtain the minimal topology for both the

nonsurvivable case and for the survivable case problemsSlide34

Obtained Network Topology (Cont.)

If we stipulate survivability, the obtained network always has an average nodal degree strictly superior to that obtained in the

nonsurvivable

case (about 20% on average)Slide35

Obtained Network Topology (Cont.)

Survivable networks need spare links in order to meet the survivability requirements

Main difference between partial end-to-end rerouting without recovery and local rerouting:

Local rerouting tends to be slightly more meshed

Local rerouting generally uses longer rerouting paths than other rerouting strategiesMeshed network permits a better use of resources when addressing failure situationsSlide36

Obtained Network Topology (Cont.)

The obtained network topology is sometimes the same for both restoration strategiesSlide37

Network Cost

Consider link installation costs and the cost of capacity loading

Gaps between the global costs for the networks:

: end-to-end rerouting and

nonsurvivable case : local rerouting and nonsurvivable case : gap related to the global costs between two rerouting strategiesSlide38

Network Cost (Cont.)

The cost for a survivable network can be almost 70% more than the cost for a

nonsurvivable

network

We need to optimize simultaneously the dimensioning problem for the nominal state and the spare capacity computation, in order to reduce this gapSlide39

Network Cost (Cont.)

The cost of survivable networks based on a local rerouting strategy is slightly greater than the cost for an end-to-end rerouting strategy

Local rerouting may be used without bringing about a significant impact in terms of costSlide40

Computational Time

The computational time becomes generally greater as the facility capacity becomes smaller

Large combinatory of the problem with respect to the choice for installing links and assigning capacities

The case with large capacity facility where the number of links to be installed is obviously lower and the choice “easier.”Slide41

Computational Time (Cont.)

The computational time spent for solving the super master program takes often more than 50% of global time

The result justify our strategy to reduce the number of calls through introducing as much as possible valid inequalities in order to approach faster to the optimal solution before checking for the feasibility of assigned capacitiesSlide42

Conclusion Slide43

Conclusion

Survivable network design problem with single facility:

Survivability requirements are expressed in terms of the spare capacity required to address link failures

Various rerouting strategies:

Local and end-to-end reroutingPresented mixed-integer linear programming modelsProposed an appropriate decomposition approachAllows to accelerate the resolution timeSlide44

Conclusion (Cont.)

Reported some numerical results in terms of overall network cost for:

Restoration schemes

Nonsurvivable case

Main result is that survivable networks designed on basis of local restoration may be used without bringing about a significant impact in terms of costSlide45

Conclusion (Cont.)

Result could be very useful for telecommunication operators

Restoration strategy is already known to be quite simple and efficient in operational terms.Slide46

Thanks for your listening!