Integer Linear Programming Network Design and Planning (2016) - - PowerPoint PPT Presentation
Design of Optical WDM Networks using Integer Linear Programming Network Design and Planning (2016) Massimo Tornatore Dept. Electronics and Information Politecnico di Milano Piazza Leonardo da Vinci 32 - 20133 Milan, Italy
Politecnico di Milano
Piazza Leonardo da Vinci 32 - 20133 Milan, Italy tornator@elet.polimi.it
WDM Network Design 2
Introduction to WDM optical networks and network design WDM network design and optimization
– Integer Linear Programming approach – Physical Topology Design
– Notes on Traffic Grooming – Heuristics
WDM Network Design 3
Optical fiber advantages
– Huge bandwidth (WDM) – Long range transmission (EDFA optical amplifiers) – Strength – Use flexibility (transparency) – Low noise – Low cost – Interference immunity – ….
Optical components
– Rapid technological evolution – Increasing reliability (not for all…) – Decreasing costs (not for all…)
Ok, but from a network perspective?
– Convergence of services over a unique transport platform
WDM Network Design 4
Lunghezza d'onda [m] Frequenza [Hz] Doppino Cavo coassiale Fibra
Radio AM Radio FM TV 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 104 105 106 107 108 109 1010 1011 1012 1013 1014 1015 Satellite Microonde Luce visibile LF MF HF VHF UHF SHF EHF THF LF = Low Frequency MF = Medium Frequency HF = High Frequency VHF = Very High Frequency UHF = Ultra High Frequency SHF = Super High Frequency EHF = Extremely High Frequency THF = Tremendously High Frequency
s m c v f v / 10 3
8
Wavelength Frequency
WDM Network Design 5
WDM = wavelength- division multiplexing (wavelength = channel) (b) Traditional fiber (a) All-wave fiber (true wave, Leaf, etc.)
Check: http://www.thefoa.org/tech/ref/basic/SMbands.html
WDM Network Design 6
Check: ITU-T G.694.1 Spectral grids for WDM applications: DWDM frequency grid, Feb 2012.
WDM Network Design 7
WDM layer fundamentals – Wavelength Division Multiplexing: information is carried on high- capacity channels of different wavelengths on the same fiber – Switching: WDM systems transparently switch optical flows in the space (fiber) and wavelength domains WDM layer basic functions – Optical circuit (LIGTHPATH) provisioning for the electronic layers – Common transport platform for a multi-protocol electronic-switching environment
Optical transmission WDM Layer SDH ATM IP ... ... Electronic layers Optical layers Lightpath connection request Lightpath connection provisioning
WDM Network Design 8 EO Converter EO Converter Passive Optical Muliplexer
1300 nm 1310 nm
EO Converter
850 nm Ch 1 Ch 2 Ch n
WDM Network Design 9 EO Converter EO Converter EO Converter OE Converter OE Converter OE Converter 1 2 n
Mux & Demux Mux & Demux
1 2 n
WDM Network Design 10
1 2 1 2
WDM Network Design 11
Example: A European WDM Network
Helsinki Madrid
WDM Network Design 12
Introduction to WDM network design and optimization Integer Linear Programming approach Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path & link protection cases Heuristic approach
WDM Network Design 13
Logical topology (LT): each link represent a lightpath that could be (or has been) established to accommodate traffic
A lightpath is a “logical link” between two nodes
Full mesh Logical topology: a lightpath is established between any node pairs
LT Design (LTD): choose, minimizing a given cost function, the lightpaths to support a given traffic Optical network access point Electronic-layer connection request WDM network nodes Electronic switching node (DXC, IP router, ATM switch, etc.) WDM network CR1 CR2 CR4 CR3 WDM LOGICAL TOPOLOGY
WDM Network Design 14
Physical topology: set of WDM links and switching-nodes Some or all the nodes may be equipped with wavelength converters The capacity of each link is dimensioned in the design phase
Wavelength converter Optical path termination Optical Cross Connect (OXC) WDM optical-fiber link WDM PHYSICAL TOPOLOGY
WDM Network Design 15
*Jane Simmons, “Optical network design and planning”
WDM Network Design 16
1
2
Optical wavelength channels LP1 LP2 LP4 LP3 LP1 LP2 LP3 LP4 LP = LIGHTPATH
Solving the resource-allocation problem is equivalent to perform a
mapping of the logical over the physical topology
– Also called Routing Fiber and Wavelength Assignment (RFWA) Physical-network dimensioning is jointly carried out
3
Mapping is different according to the fact that the network is not (a) or is (b) provided with wavelength converters
(a) (b)
CR1 CR2 CR4 CR3
WDM Network Design 17
WA CA1 CA2 UT CO TX NE IL MI NY NJ PA MD GA UT IL CA1 TX WA CO PA NJ
WDM Network Design 18
Input parameters, given a priori – Physical topology (OXC nodes and WDM links) – Traffic requirement (logical topology)
the nodes
grooming)
Parameters which can be specified or can be part of the problem – Network resources: two cases
parameter (typically, in mono-fiber networks), while the number of wavelengths per fiber required to setup all the lightpaths is an output
preassigned global parameter (typically, in multi-fiber networks) and the number of fibers per link required to setup all the lightpaths is an output
WDM Network Design 19
Physical constraints – Wavelength conversion capability
– Propagation impairments
length constraint)
switching nodes
– Connectivity constraints
Links and/or nodes can be associated to weights – Typically, link physical length is considered
WDM Network Design 20
Routing can be – Constrained: only some possible paths between source and destination (e.g. the K shortest paths) are admissible
– Unconstrained: all the possible paths are admissible
Cost function to be optimized (optimization objectives) – Route all the lightpaths using the minimum number of wavelengths (physical-topology optimization) – Route all the lightpaths using the minimum number of fibers (physical- topology optimization) – Route all the lightpaths minimizing the total network cost, taking into account also switching systems (physical-topology optimization)
WDM Network Design 21
Routing and Wavelength Assignment (RWA) [OzBe03] – The capacity of each link is given – It has been proven to be a NP-complete problem [ChGaKa92] – Two possible approaches
Routing Fiber and Wavelength Assignment (RFWA) – The capacity of each link is a problem variable – Further term of complexity Capacitated network – The problem contains multicommodity flow (routing), graph coloring (wavelength) and localization (fiber) problems – It has been proven to be a NP-hard problem (contains RWA)
WDM Network Design 22
Optimization problem – optimization version
– Find the minimum-cost solution
Optimization problem – decision version (answer is yes or no)
– Given a specific bound k, tell me if a solution x exists such that x<k
Polynomial problem
– The problem in its optimization version is solvable in a polynomial time
NP problem
– Class of decision problems that, under reasonable encoding schemes, can be solved by polynomial time non-deterministic algorithms
NP-complete problem
– A NP problem such that any other NP problem can be transformed into it in a polynomial time – The problem is very likely not to be in P – In practice, the optimization-problem solution complexity is exponential
NP-hard problem
– The problem in its decision version is not solvable in a polynomial time (is NP- complete) the optimization problem is harder than an NP-problem – Contains an NP-complete problem as a subroutine
WDM Network Design 23
Routing Wavelength Fiber Time Physical layer Applications Mixed Rates Protection Grooming Energy Vendors Domains Cost
WDM Network Design 24
WDM network optimal design is a very complex problem. Various
approaches proposed
– Mathematical programming (MP)
– Heuristic methods
According to the cost function, the problem is – Linear – Non linear
WDM Network Design 25
Introduction to WDM network design and optimization Integer Linear Programming approach Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path & link protection cases Heuristic approach
WDM Network Design 26
WDM-network static-design problem can be solved with the mathematical programming techniques
– In most cases the cost function is linear linear programming – Variables can assume integer values integer linear programming
LP solution
– Variables defined in the real domain – The well-known computationally-efficient Simplex algorithm is employed
ILP solution
– Variables defined in the integer domain – The optimal integer solution is found by exploring all integer admissible solutions
search
WDM Network Design 27
A arduous challenge – NP-completeness/hardness coupled with a huge number of variables
virtual-topology mappings leading to the same cost-function value)
– Practically tractable for small networks Simplifications – RFWA problem decomposition: e.g., first routing and then f/w assignment – Constrained routing (route formulation, see in the following) – Relaxed solutions (randomized rounding) – Other methodologies:
ILP, when solved with approximate methods, loses one of its main
features: the possibility of finding a guaranteed minimum solution
– Still ILP can provide valuable solutions
WDM Network Design 28
Simplification can be achieved by removing the integer constraint – Connections are treated as fluid flows (multicommodity flow problem)
connection requests increases indefinitely, while their granularity becomes indefinitely small
imply bifurcation of lightpaths on many paths
– LP solution is found In some cases the closest upper integer to the LP cost function can
be taken as a lower bound to the optimal solution
Not always it works… See [BaMu96]
WDM Network Design 29
l,k: link identifiers (source and destination nodes) Fl,k: number of fibers on the link l,k l,k: number of wavelengths on the link l,k cl,k: weight of link l,k (es. length, administrative weight, etc.) – Usually equal to ck,l
WDM Network Design 30
RFWA – Minimum fiber number M
– VWP case
– Minimum fiber mileage (cost) MC
RWA – Minimum wavelength number – Minimum wavelength mileage
– Minimum maximal wavelength number on a link
k l k l
) , ( ,
C k l k l k l
) , ( , ,
) , ( , k l k l
C k l k l k l
) , ( , , MAX k l k l
, ,
WDM Network Design 31
Introduction to WDM network design and optimization Integer Linear Programming approach Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path & link protection cases References
WDM Network Design 32
Two basilar and well-known approaches [WaDe96],[Wi99] – FLOW FORMULATION (FF) – ROUTE FORMULATION (RF)
WDM Network Design 33
Flow variable
Flow on link (l,k) due to a request generated by to source-destination couple (s,d)
d s k l
x ,
,
s d 1 2 3 4
d s s d s s
x x
, 1 , , , 1 d s s d s s
x x
, , 3 , 3 , d s d s
x x
, 1 , 2 , 2 , 1 d s d s
x x
, 3 , 4 , 4 , 3 d s d d s d
x x
, , 4 , 4 , d s d d s d
x x
, 2 , , , 2 d s d s
x x
, 1 , 3 , 3 , 1 d s d s
x x
, 2 , 4 , 4 , 2
WDM Network Design 34
Variables represent the amount of traffic (flow) of a given traffic
relation (source-destination pair) that occupies a given channel (link, wavelength)
Lightpath-related constraints – Flow conservation at each node for each lightpath (solenoidal constraint) – Capacity constraint for each link – (Wavelength continuity constraint) – Integrity constraint for all the flow variables (lightpath granularity) Allows to solve the RFWA problems with unconstrained routing A very large number of variables and constraint equations
WDM Network Design 35
Solenoidality constraint
– Guarantees spatial continuity of the lightpaths (flow conservation) – For each connection request, the neat flow (tot. input flow – tot. output flow) must be:
appropriate sign) in s and d
Capacity constraint
– On each link, the total flow must not exceed available resources (# fibers x # wavelengths)
Wavelength continuity constraint
– Required for nodes without converters
1 2 3 4 5 6 s d
WDM Network Design 36
c: node pair (source sc and destination dc) having requested one or
more connections
xl,k,c: number of WDM channels carried by link (l,k) assigned to a
connection requested by the pair c
Al: set of all the nodes adjacent to node i vc: number of connection requests having sc as source node and dc
as destination node
W: number of wavelengths per fiber λ: wavelength index (λ={1, 2 … W})
WDM Network Design 37
k l c k l c k l c k l A k A k c c c c c k l c l k
l l
, , , , , , , , , ,
N.B. from now on, notation “l,k” implies l k
WDM Network Design 38
k l c k l c k l c k l c A k A k c c c k l c l k
l l
, , , , , , , , , ,
WDM Network Design 39
What happens in the bidirectional case? – i.e., Each transmission channel provides the same capacity λ in both directions.
WDM Network Design 40
In absence of wavelength converters, each lightpath has to preserve
its wavelength along its path
This constraint is referred to as wavelength continuity constraint In order to enforce it, let us introduce a new index in the flow
variable to analyze each wavelength plane
The structure of the formulation does not change. The problem is
simply split on different planes (one for each wavelength)
The vc traffic is split on distinct wavelengths vc,λ The same approach will be applied for no-flow based formulations
WDM Network Design 41
, , , , , , , , , , , , , , , , , ,
c k l c k l c k l c k l c c A k A k c c c c c k l c l k
l l
WDM Network Design 42
Variable xl,s,d: flow on link i associated to source-destination couple s-d
Variable rp,s,d: number of connections s,d routed on the admissible path p
r1,s,d r2,s,d r3,s,d
s d
s d 1 2 3 4
d s s d s s
x x
, 1 , , , 1 d s s d s s
x x
, , 3 , 3 , d s d s
x x
, 1 , 2 , 2 , 1 d s d s
x x
, 3 , 4 , 4 , 3 d s d d s d
x x
, , 4 , 4 , d s d d s d
x x
, 2 , , , 2 d s d s
x x
, 1 , 3 , 3 , 1 d s d s
x x
, 2 , 4 , 4 , 2
WDM Network Design 43
All the possible paths between each sd-pair are evaluated a priori Variables represent which path is used for a given connection – rpsd: path p is used by rpsd connections between s and d Path-related constraints – Routing can be easily constrained (e.g. using the K-shortest paths)
– Useful to represent path-interference
paths (e.g. ipr = 1 (0) if path p has a link in common with path r)
Number of variables and constraints – Very large in the unconstrained case, – Simpler than flow formulation when routing is constrained
WDM Network Design 44
k l n c R r k l n c n c n c
k l n c
, , , , ,
, ,
New symbols – rc,n: number of connections routed on the n-th admissible path between source
destination nodes of the node-couple c
– R(l,k): set of all admissible paths passing through link (l,k)
WDM Network Design 45
, , , , , , , , , , ,
, ,
c k l n c R r k l n c c c n c n c
k l n c
Analogous extension to FF case – rc,n,λ = number of connection routed on the n-th admissible path between node pair
c (source-destination) on wavelength λ
WDM Network Design 46
Reduced number of variables and constraints compared to the flow formulation Allows to evaluate the absolute optimal solution without any approximation and with unconstrained routing Can not be employed in case path protection is adopted as WDM protection technique
– Does not support link-disjoint routing
WDM Network Design 47
New flow variable – Flow carried by link l and having node s as source – Flow variables do not depend on destinations anymore Solenodality – Source node
equal to the total number of requests originating in the node
– Transit node
equal to the outgoing traffic plus the nr. of lightpaths terminated in the node
d d s k l s k l
, , , ,
WDM Network Design 48
2 connections requests – 1 to 4 – 1 to 3 Solution – X1,2,1,X1,6,1, X2,3,1, X6,5,1,X,5,3,1,X,3,41= 1 – Otherwise X,l,k,1= 0 1° admissible solution – LA 1-2-3-4 – LB 1-6-5-3 2° admissible solution – LA 1-2-3 – LB 1-6-5-3-4
Both routing solutions are compatible with the same SF solution
1 2 3 4 5 6
3
WDM Network Design 49
k l i k l i k l i k l A k A k l i i k l i l k A k j i j i i k i
l l i
, , , , , , , , , , , , , ,
New symbols – xl,k,i : number of WDM channels carried by link l, k assigned connections originating
at node i – Ci, j: number of connection requests from node i to node j
See [ToMaPa02]
WDM Network Design 50
) ( , , , integer , integer integer , , integer Integrity ) , , ( Capacity ) ( , , ) ( , , , , ity Solenoidal
, , , , , , , , , , , , , , , , , , , , , , , , , , , ,
l i j i c i s l,k F i l,k x k l F x l i l i C c l i l i c x x i C S s i s x
l i i k l i k l i k l i k l l i l i A k A k j i i k l i l k l l i i i A k i i k i
l l i
Analogous extension to FF case
WDM Network Design 51
The source formulation variables xl,k,s and Fl,k – Do not give a detailed description of RWFA of each single lightpath – Describe each tree connecting a source to all the connected destination nodes (a subset of the other nodes) – Define the optimal capacity assignment (dimensioning of each link in terms of fibers per link) to support the given traffic matrix
STEP 1: Optimal dimensioning computation by exploiting SF
(identification problem, high computational complexity)
STEP 2: RFWA computation after having assigned the number of
fibers of each link evaluated in step 1 (multicommodity flow problem, negligible computational complexity)
WDM Network Design 52
The second step has a negligible impact on the SF computational time – Fl,k are no longer variables but known terms Fully-connected virtual topology: C = N (N-1), S=N – Worst case (assuming L << N (N-1))
L W C W R C W L ) C(W L L) C( W C N C) L W( L C S L S W S C NS L W L R C C L C L N C L S L N S L 2 2 1 route WP 2 2 1 2 flow WP 2 ) 2 ( ) 2 ( source WP 2 2 route VWP ) 1 ( 2 2 flow VWP ) 1 ( 2 2 source VWP variab. # const. # n Formulatio
N N N N O O WP O O VWP variab. # FF/SF const. # FF/SF Case
Fully connected virtual topology
– Symbols
WDM Network Design 53
N = 14 nodes
L = 22 (bidir)links
C = 108 connected pairs
360 (unidir)conn. requests
NSFNET EON
Palo Alto CA San Diego CA Salt Lake City UT Boulder CO Houston TX Lincoln Champaign Pittsburgh Atlanta Ann Arbor Ithaca Princeton College Pk. Seattle WA
N = 19 nodes
L = 39 (bidir)links
C = 342 connected pairs
1380 (unidir)conn. requests
Static traffic matrices derived from real traffic measurements
Hardware: 1 GHz processor, 460 Mbyte RAM
Software: CPLEX 6.5
WDM Network Design 54
The number of constraints decreases by a factor – 9 for the NSFNet – 26 for the EON The number of variables decreases by a factor – 8.5 for the NSFNet – 34 for the EON These simplifications affect computation time and memory
Network/Formulation # const. # variab.
WDM Network Design 55
In the WP case – The number of variables and constraints linearly increases with W – The gaps in the number of variables and constraints between FF and SF increase with W The advantage of source formulation is even more relevant in the
WP case
1 1
5
2 1
5
3 1
5
4 1
5
5 1
5
2 4 6 8 1 1 2 1 4 1 6
E O N W P
s
r c e v a r i a b l e s f l
v a r i a b l e s s
r c e c
s t r a i n t s f l
c
s t r a i n t s Number of wavelengths, W Number of variables and constraints
WDM Network Design 56
The values of the cost function Msource obtained by SF are always equal
Coincident values are obtained if both the formulations converge to the
– Validation of SF by induction Memory exhaustion (Out-Of-Memory, O.O.M) prevents the
convergence to the optimal solution. This event happens more frequently with FF than with SF
W SF FF 2 27m 40m 4 28m 105m 8 36s 50m 16 6m 10h 32 19m 5h Computational time Memory occupation W SF FF 2 0.39MB 1.3MB 4 O.O.M O.O.M 8 5MB 42MB 16 47MB O.O.M 32 180MB O.O.M
WDM Network Design 57
Introduction to WDM network design and optimization Integer Linear Programming approach Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path & link protection cases Heuristic approach
WDM Network Design 58
Today WDM transmission systems allow the multiplexing on a single
fiber of up to 160 distinct optical channels
– recent experimental systems support up to 256 channels: A single WDM channel carries from 2.5 to 40 Gb/s (ITU-T G.709) The loss of a high-speed connection operating at such bit rates,
even for few seconds, means huge waste of data !!
The increase in WDM capacity associated with the tremendous
bandwidth carried by each fiber and the evolution from ring to mesh architectures brought the need for suitable protection strategies into foreground.
Example: 1ms outage for a 100G x 100Waves fiber [10Tbit/s] means
10Gbit=1.25Gbyte of data lost (n.b.: 1 cd-rom is 0.9 GByte)
WDM Network Design 59
Even though fiber are very resilient, the geographical dimension of a
backbone network lead to very high chances that the network is
Example: failure per 1000Km per year (2001 statistics) ≈ 2 (*)
What happens on a continental network?! Hundreds of failures….
1 3 2 6 10 4 5 7 8 9 12 13 14 11 1200 2100 4800 3000 1500 3600 1200 2400 3900 1200 2100 3600 1500 2700 1500 1500 600 600 1200 1500 600 300
(*) Source www.southern-telecom.com/AFL%20Reliability.pdf
WDM Network Design 60
Dig-ups 58.10% Other 9.70% Fallen Trees 1.30% Excavation 1.30% Flood 1.30% Firearm 1.30% Vehicle 7.50% Process Error 6.90% Power Line 4.40% Sabotage 2.50% Rodent 3.80% Fire 1.90% Source: D. E. Crawford, “Fiber Optic Cable Dig-ups – Causes and Cures,” A Report to The Nation – Compendium of Technical Papers, pp. 1-78, FCC NRC, June 1993
WDM Network Design 61
Customer’s concerns:
Bandwidth Availability Fee etc.
Operator’s concerns:
Resource Protection Penalty Network design decisions for protection are very important
WDM Network Design 62
Resource occupation (resource overbuild) Availability
– Probability to find the service up
Protection Switching Time Availability goes in tradeoff with the other two!!
WDM Network Design 63
1+1 or 1:1 dedicated protection (>50% capacity for protection) – Both solutions are possible – Each connection-request is satisfied by setting-up a lightpath pair of a working + a protection lightpaths – RFWA must be performed in such a way that working and protection lightpaths are link disjoint Additional constraints must be considered in network planning and
Transit OXCs must not be reconfigured in case of failure
The source model can not be applied to this scenario
WDM Network Design 64
This formulation does not need an upgrade of unprotected flow variable See [ToMaPa04]
k l c k l c k l c k l c c l k c k l k l k l c c c c c k l c k l
i i
, , , , , , , , , , ) , ( ) , ( , , , , I I
WDM Network Design 65
Same number of variables and constraints as the unprotected flow formulation Allows to evaluate the absolute optimal solution without any approximation and with unconstrained routing in almost all cases Requires an a posteriori control to verify the feasibility of obtained solution Problem: In conclusion, each unity of flow must be modelled independently, such that it can be protected independently
WDM Network Design 66
(l,k) F (l,k) c,t x k l F W x t c k l x x t c l s l d l x x
k l t c k l t c k l t c k l t c l k t c k l A k A k c c t c k l t c l k
l l
integer ), ( binary Integrity , Capacity , , , 1 disjoint
, ,
if 2 if 2 ity Solenoidal
, , , , ) , ( , , , , , , , , , , , , , , , ,
New symbols – xl,k,c,t = number of WDM channels carried by link (l,k) assigned to the t-th
connection between source-destination couple c
Rationale: for each connection request, route a link-disjoint connection route two connections and enforce link-disjointness between them.
WDM Network Design 67
k l n t c R r k l n t c R R r n t c n n t c
k l n t c l k k l n t c
, , , , , , , , , ,
, , , , , , ,
New symbols – rc,n,t = 1 if the t-th connection between source destination node couple c is routed
– R(l,k) = set of all admissible paths passing through link (l,k)
WDM Network Design 68
k l n c R r k l n c n c n c
k l n c
, , ' ' , , ,
, ,
Substitute the single path variable rc,n by a protected route variable
r’c,n (~ a cycle)
No need to explicitly enforce link disjointness Identical formulation to unprotected case How do we calculate the minimum-cost disjoint paths? Suurballe
WDM Network Design 69
c, v l,k F l,k c,t x k l F x t c k l x x c v t c l s l v d l v x x
t c k l t c k l t c k l t c k l t c l k t c k l t c A k A k c t c c t c t c k l t c l k
l l
bynary integer , , binary Integrity , , Capacity , , , 1 disjoint
2 ; , , ,
if if ity Solenoidal
, , , , , , , ) , ( , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
New symbols
– xl,k,c,t ,λ= number of WDM channels carried by wavelength λ on link l,k
assigned to the t-th connection between source-destination couple c – Vc,λ= traffic of connection c along wavelength λ
WDM Network Design 70
, , , , , , , , , , , , , , , , , , , ,
, , , , , , , , ,
t c k l n t c R r k l n t c R R r n t c t c n t c n t c
k l n t c l k k l n t c
WDM Network Design 71
k l n c R r k l R r n c n c c c n c n c
k l n c k l n c
, 2 , 1 , , , 1 ' ' , ' ' , , , , , , 2 , 1 , , ,
2 1 2 , 2 , 1 , , 2 , 1 , 2 , , 1 , 2 2 , 1 2 1 2 , 1 2 , 1 2 , 1
rc,n,λ = number of connections between source-destination couple c routed
wavelength λ1and the other over λ2
WDM Network Design 72
Nr of variables for rctnλ -> R x C x T x W – R x C number of single route variables Nr of variables for rcnλ’λ’’ -> R’ x C x W2 – R’ x C number of protected route variables – For R=R’, this is preferable if T>W
WDM Network Design 73
Introduction to WDM network design and optimization Integer Linear Programming approach Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path & link protection cases References
WDM Network Design 74
Protection-resources sharing
– Protection lightpaths of different channels share some wavelength channels – Based on the assumption of single point of failure – Working lightpaths must be link (node) disjoint
Very complex control issues
– Also transit OXCs must be reconfigured in case of failure
Sharing is a way to decrease the
capacity redundancy and the number
WDM Network Design 75
Given:
– Graph G(V,E) – Set of connections Li
(already routed) Link vector Specified in IETF (see, e.g., RSVP-TE Extensions For Shared-Mesh
Restoration in Transport Networks )
e' e ' * e e' e e' e e
e
WDM Network Design 76
e1 e2 e3 e4 e5 e6 e7 e8 A B C e2 e3 e4 e5 e6 e7
*
5
e
e1 e8 Connection A arrival: e5
( 0, 1, 1, 0, 0, 0, 0, 0 ) 1 ( 1, 2, 1, 0, 0, 0, 0, 0 ) 2
Initial state :e5
(a) Sample network and connections (a) Evolution of link vector for e5 ( 0, 0, 0, 0, 0, 0, 0, 0 ) 0 ( 1, 2, 1, 0, 0, 0, 1, 0 ) 2
Connection B arrival: e5 Connection C arrival: e5
WDM Network Design 77
Flow Formulation – Binary variables xl,k,c,t,p associated to the flow on each link l,k for each single connection request c,t (p=w working flow, p=s protection flow) Route Formulation – 1° approach: integer variables rc,n associated to each simple path n joining the node pair c (e.g. s,d). – 2° approach: integer variables r’c,n associated to the n-th possible working-spare route pair that joins each s-d node pair c
r1,s,d
s d
r2,s,d r3,s,d
s d
xs,a,c,1,w xa,d,c,1,w Connection request c,1
Explore Shared path protection by both classical approaches
xs,a,c,1,p xa,d,c,1,p Xs,b,c,1,w xs,b,c,1,p Xb,d,c,1,w xb,d,c,1,p
a b
WDM Network Design 78
l,k l,k,c c l,k l,k,c l,k,c A k A k c c c c l,k,c k,l,c l,k,c
l l
c c k) (l,
WDM Network Design 79
) , ( , ), ( binary integer ), ( binary Integrity ) , ( , ), ( , 1 Sharing ) , ( , , Capacity , , , 1 disjoint
; , ,
if 1 if 1 ; , ,
if 1 if 1 ity Solenoidal
, , , , , , , , , , , , , , , , , , , , ) , ( , ) , ( , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
j i (l,k) c,t z (l,k) F (l,k) c,t x j i (l,k) c,t y z x z y x z j i (l,k) z P k l F W x P t c k l y y x x t c l s l d l y y t c l s l d l x x
ij ct lk k l t c k l t c j i ij c lk t c j i ij ct lk t c k l t c j i ij ct lk t c ij ct lk lk t c k l t c k l lk t c l k t c l k t c l k t c k l A k A k c c t c k l t c l k A k A k c c t c k l t c l k
l l l l
WDM Network Design 80
k l n c k l n c k l n c n c n c n c n c
k l l
, , ) , ( ) , ( , ) , ( , , ,
) , ( '
New symbols
– Rl,k includes all the working-spare routes whose working path is routed on link l,k
– Rl’
(l,k) includes all the working-spare routes whose working path is routed on
bidirectional link l′ and whose spare path is routed on link (l, k)
Similar formulations can be found in [MiSa99], [RaMu99] , [BaBaGiKo99],
WDM Network Design 81
All the previous formulations and a additional one can be found in [CoToMaPaMa03].
k l n c k l n c k l n c n c n c n c n c
k l l
, 2 1 , , 1 ) , , ( ) , , ( , ) , ( , , , , , ,
2 , 1 2 2 ) 2 , , ( ' 2 , 1 2 , 1 2 , 1
New symbols
– Variable rc,n,λ1,λ2, where λ1 indicates the wavelength of the working path and λ2 indicates the wavelength of the spare path. – includes all the working-spare routes, whose working path is routed on bidirectional link l’ and whose spare path is routed on link (l, k).
) 2 , , ( ' k l l
R
WDM Network Design 82
Dedicated Link Protection (DLP)
– Each link is protected by providing an alternative routing for all the WDM channels in all the fibers – Protection switching can be performed by fiber switches (fiber cross-connects) or wavelength switches – Signaling is local; transit OXCs of the protection route can be pre-configured – Fast reaction to faults – Some network fibers are reserved for protection
Shared Link Protection (SLP)
– Protection fibers may be used for protection of more than one link (assuming single-point of failure) – The capacity reserved for protection is greatly reduced
C
n e c t i
N
m a l O M S p r
e c t i
( l i n k p r
e c t i
)
WDM Network Design 83
Different protected objects are switched
1) Fiber level 2) Wavelength level
FAULT EVENT (1) (2)
WDM Network Design 84
(l,k) F c,(l,k) q L (l,k) x Y k l F W x q L l q l F L l F Y Y c l s i v d i v x x
k l c k l q L k l c k l c k l q L k l A k q L k l A k q L q L q L l k q L k l A k A k c c c c c l k c k l
l l l l
integer ) , ( , integer Integrity ) , ( Capacity ) , ( ,
if if (spare) ity Solenoidal ,
if if (working) ity Solenoidal
, , , ) , ( , , , , , ) , , ( ) , , ( . , ) , ( , ) , ( , , , , , ,
New symbols – Y(l,k),(L,q) expresses the number of backup fibers needed on link (l,k) to protect link
(L,q) failure
WDM Network Design 85
Cost function (dedicated case)
Cost function (shared case)
– Relaxing the integer constraints on Y, each channel is independently protected protected (while not collecting all the channels owing to the same fiber)
See also [RaMu99]
k l q L q L k l k l k l
, , ) , ( , , , ,
) , ( , , , , , , ,
q L k l k l k l k l k l k l
WDM Network Design 86
Comparison between different protection technique on fiber needed to support the same amount of traffic
Switching protection objects at fiber or wavelength level does ot sensibly affects the amount of fibers.
– This difference increase with the number of wavelength per fiber
WDM Network Design 87
e.g., STM1 @ 155,52 Mbps e.g., OTN G.709 @ 2.5, 10, 40 Gbps
Optical transmission WDM Layer SDH ATM IP ... ... Electronic layers Optical layers Electronic connection request Lightpath connection provisioning
Definition
Optical WDM network
– multiprotocol transport platform – provides connectivity in the form of optical circuits (lightpaths)
WDM Network Design 88
WDM Network Design 89
Multi-layer routing
1 2 3 4 5 6 7 Lp1 Lp2 Lp3 Lp4
Physical Topology Logical Topology
ADM ADM ADM ADM ADM ADM ADM ADM ADM ADM ADM ADM ADM ADM
1 2 3 4 5 6 7
Suppose Lightpath Capacity: 10 Gbit/sec EXAMPLE CONNECTIONS ROUTING C1 (STM1 between 4 →2) on Lp1 C2 (STM1 between 4 →7) on Lp1 and Lp2 C3 (STM1 between 1 →5) on Lp3 C4 (STM1 between 4 →6) on Lp1 and Lp2 and Lp4
WDM Network Design 90
WDM Network Design 91
WDM Network Design 92
AND, OR, XOR etc can be expressed by using binary variables
AND OR XOR
XNOR
Robert G. Jeroslow, “Logic-based decision support: mixed integer model formulation”, North-Holland, 1989 ISBN 0444871195
OR AND
XOR
WDM Network Design 93
WDM Network Design 94
AND, OR, XOR etc can be expressed by using binary variables Negated operators (NAND, NOR, XNOR) are implemented with an
additional variable z = 1 - y, where y is the “direct” operation
AND OR XOR
2 1 2 1,
2 1 2 1
2 1 1 2 2 1 2 1
WDM Network Design 95
Also, they can be extended to a general N-variable case:
N i i N i i
1 1
N i i i
1
AND OR
N i i i
1
XOR
Arbitrarily large number (at least equal to N) Probably no simpler option exists
XOR XOR XOR XOR
3 2 1
WDM Network Design 96
Articles
– [WaDe96] N. Wauters and P. M. Deemester, Design of the optical path layer in multiwavelength cross- connected networks, Journal on selected areas on communications,1996, Vol. 14, pages 881-891, June – [CaPaTuDe98] B. V. Caenegem, W. V. Parys, F. D. Turck, and P. M. Deemester, Dimensioning of survivable WDM networks, IEEE Journal on Selected Areas in Communications, pp. 1146–1157, sept 1998. – [ToMaPa02] M. Tornatore, G. Maier, and A. Pattavina, WDM Network Optimization by ILP Based on Source Formulation, Proceedings, IEEE INFOCOM ’02, June 2002. – [CoMaPaTo03] A.Concaro, G. Maier, M.Martinelli, A. Pattavina, and M.Tornatore, “QoS Provision in Optical Networks by Shared Protection: An Exact Approach,” in Quality of service in multiservice IP Networks, ser. Lectures Notes on Computer Sciences, 2601, 2003, pp. 419–432. – [ZhOuMu03] H. Zang, C. Ou, and B. Mukherjee, “Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,” IEEE/ACM Transactions on Networking, vol. 11, no. 2, pp.248–258, april 2003. – [BaBaGiKo99] S. Baroni, P. Bayvel, R. J. Gibbens, and S. K. Korotky, “Analysis and design of resilient multifiber wavelength-routed optical transport networks,” Journal of Lightwave Technology, vol. 17, pp. 743– 758, may 1999. – [ChGaKa92] I. Chamtlac, A. Ganz, and G. Karmi, “Lightpath communications: an approach to high- bandwidth optical WAN’s,” IEEE/ACM Transactionson Networking, vol. 40, no. 7, pp. 1172–1182, july 1992. – [RaMu99] S. Ramamurthy and B. Mukherjee, “Survivable WDM mesh networks, part i - protection,” Proceedings, IEEE INFOCOM ’99, vol. 2, pp. 744–751, March 1999. – [MiSa99] Y. Miyao and H. Saito, “Optimal design and evaluation of survivable WDM transport networks,” IEEE Journal on Selected Areas in Communications, vol. 16, pp. 1190–1198, sept 1999.
WDM Network Design 97
– [BaMu00] D. Banerjee and B. Mukherjee, “Wavelength-routed optical networks: linear formulation, resource budgeting tradeoffs and a reconfiguration study,” IEEE/ACM Transactions on Networking, pp. 598–607, oct 2000. – [BiGu95] D. Bienstock and O. Gunluk, “Computational experience with a difficult mixed integer multicommodity flow problem,” Mathematical Programming, vol. 68, pp. 213–237, 1995. – [RaSi96] R. Ramaswami and K. N. Sivarajan, Design of logical topologies for wavelength-routed optical networks, IEEE Journal on Selected Areas in Communications, vol. 14, pp. 840{851, June 1996. – [BaMu96] D. Banerjee and B. Mukherjee, A practical approach for routing and wavelength assignment in large wavelength-routed optical networks, IEEE Journal on Selected Areas in Communications, pp. 903- 908,June 1996. – [OzBe03] A. E. Ozdaglar and D. P. Bertsekas, Routing and wavelength assignment in optical networks, IEEE/ACM Transactions on Networking, vol. 11, no. 2, pp. 259-272, Apr 2003. – [KrSi01] Rajesh M. Krishnaswamy and Kumar N. Sivarajan, Design of logical topologies: A linear formulation for wavelength-routed optical networks with no wavelength changers, IEEE/ACM Transactions on Networking, vol. 9, no. 2, pp. 186-198, Apr 2001. – [FuCeTaMaJa99] A. Fumagalli, I. Cerutti, M. Tacca, F. Masetti, R. Jagannathan, and S. Alagar, Survivable networks based on optimal routing and WDM self-heling rings, Proceedings, IEEE INFOCOM '99, vol. 2, pp. 726-733,1999. – [ToMaPa04] M. Tornatore and G. Maier and A. Pattavina, Variable Aggregation in the ILP Design of WDM Networks with dedicated Protection , TANGO project, Workshop di metà progetto , Jan, 2004, Madonna di Campiglio, Italy
WDM Network Design 98
Introduction to WDM network design and optimization Integer Linear Programming approach to the problem Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path protection case – Link protection Heuristic approach
WDM Network Design 99
Heuristic: method based on reasonable choices in RFWA that lead
to a sub-optimal solution
– Connections are routed one-by-one – In this case we will refer to an example, based on the concept of auxiliary graph Heuristic strategies can be: – Deterministic: greedy vs. local search
– Stochastic:
WDM Network Design 100
Framework
Greedy – Builds the solution step by step starting from scratch – Starts from an empty initial solution – At each iteration an element is added to the solution, such that
a feasible solution starting from the partial one
current partial solution (the greedy is a myopic algorithm)
Features – Once a decision is taken it is not discussed anymore – The number of iterations is known in advance (polynomial) – Optimality is usually not guaranteed.
WDM Network Design 101
We have to define – Structure of the solutions and the elements which belong to it – Criterion according to which the best element to be added is chosen – Partial solution feasibility check
WDM Network Design 102
Algorithm scheme
WDM Network Design 103
Framework
Given a feasible solution the Local Search tries to improve it. – Starts with an initial feasible solution: the current solution x∗ – Returns the best solution found xb – At each iteration a set of feasible solutions close to the current one, the neighborhood N(x∗), is generated – A solution x is selected among the neighbor solutions, according to a predefined policy, such that x improves upon x∗ – If no neighbor solution improves upon the current one, (or stopping conditions are verified,) the procedure stops, otherwise xb = x∗= x
WDM Network Design 104
Remarks
– Local search builds a set of solutions – The set of neighbor solutions is built by partially modifying the current solution applying an operator called move – Each neighbor solution can be reached from the current one by applying the move – Local search moves from feasible solution to feasible solution – Local search stops in a local optimum We have to define – The initial solution – The way on which the neighborhood is generated:
WDM Network Design 105
Algorithm scheme
WDM Network Design 106
Design problem
Routing, fiber and wavelength assignment for each lightpath Design variables
Number of fibers per link
Flow/routing variables
Wavelength variables Cost function: total number of fibers Scenarios: With or without wavelength conversion
WDM Network Design 107
Optimal design of WDM networks under static traffic A deterministic heuristic method based on one-by-one RFWA
is applied to multifiber mesh networks:
– RFWA for all the lightpaths is performed separately and in sequence (greedy phase) – Improvement by lightpath rerouting (consolidation phase) It allows to setup lightpaths so to minimize the amount of fiber
deployed in the network
WDM Network Design 108
Pre-assigned physical topology graph (OXCs and WDM links)
– WDM multifiber links
– OXCs
– In short, no block in the nodes
– No conversion: Wavelength Path (WP) – Full-capability conversion in all the OXCs: Virtual Wavelength Path (VWP)
Pre-assigned logical topology
– Set of requests for optical connections
WDM Network Design 109
(Some possible) Routing criteria – Shortest Path (SP) selects the shortest source- destination path (# of crossed links)
– Number of hops (mH) – Physical link length in km (mL)
– Least loaded routing (LLR) avoids the busiest links
– Least loaded node (LLN) avoids the busiest nodes
WDM Network Design 110
Wavelength assignment algorithms
– Pack the most used wavelength is chosen first – Spread the least used wavelength is chosen first – Random random choice – First Fit pick the first free wavelength
Similarly, for fiber assignment criteria – First fit, random, most used, least used
WDM Network Design 111
Physical topology
(3 wavelengths)
2 plane
I.Chlamtac, A Farago and T. Zhang: 1996
Equivalent wavelength
layer graph
1 plane 3 plane OXC with converters OXC without converters
WDM Network Design 112
Physical topology (2 fiber
links, 2 wavelengths)
Different OXC functions
displayed on the layered graph
– 1 - add/drop – 2 - fiber switching – 3 - wavelength conversion – 3 - fiber switching + wavelength conversion
WDM Network Design 113
Enables the joint solution of R,F and W in RFWA
Network topology is replicated W·F times and nodes are
layers
WDM Network Design 114
The layered graph is “monochromatic” Routing, fiber and wavelength assignment are solved together Links and nodes are weighted according to the routing, fiber and
wavelength assignment algorithms
The Dijkstra Algorithm is finally applied to the layered weighted
graph
Worst case complexity N = # of nodes F = # of fibers W = # of wavelengths
2
WDM Network Design 115
– Connection request sorting rules
first
– Processing of an individual lightpath
Wavelength Assignment (RFWA) criteria
performed on the multifiber layered graph Sort connection requests Idle network, unlimited fiber Setup the lightpaths sequentially Prune unused fibers Identify fibers with
Prune unused fibers Attempt an alternative RFWA for the identified lightpaths for k = 1 to W
WDM Network Design 116
National Science
Foundation Network (NSFNET): USA backbone
Physical Topology – 14 nodes – 44 unidirectional links Design options
– W: 2, 4, 8, 16, 32 – 8 RFWA criteria
WDM Network Design 117
WDM Network Design 118
Hop-metric minimization performs better
– Variations of M due to RFWAs and conversion in the mH case below 5%
100 200 300 400 500 100 200 300 400 500 2 4 8 16 32
404 207 109 59.7 36.2 410 213 114 64.5 39.4
VWP WP Total fiber number, M Number of wavelengths, W
.1 2 3 4 5 1 2 3 4 5 C 3 C 1 C 7 C 5 C 4 C 2 C 8 C 6 2 4 8 1 6 3 2 S P L L R S P L L R S P L L R S P L L R V W P W P V W P W P m H m L
The initial sorting rule resulted almost irrelevant for the final optimized result (differences between the sorting rules below 3%)
Total fiber number, M
WDM Network Design 119
– NSFNet with W = 16 wavelengths per fiber, mL SP RFWA criteria – The two numbers indicate the number of fibers in the VWP and WP network scenarios – Some links are idle
(3,4) (5,6) (2,2) (6,6) (2,2) (2,2) (6,5) (6,6) (6,5) (2,2) (0,1) (2,2) (2,2) (2,2) (2,3) (2,2) (2,2) (0,0) (4,4) (4,4) (4,4) (0,0)
WDM Network Design 120
Wavelength converters are more effective in reducing the
2 4 6 8 10 2 4 6 8 10 2 4 8 16 32
1.63 3.08 4.56 7.36 8.24
M gain factor, G
M
Number of wavelengths, W
VWP
WDM Network Design 121
0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 2 4 8 16 32 VWP WP
0.985 0.97 0.929 0.862 0.758 0.972 0.936 0.884 0.787 0.668
Number of wavelengths, W Saturation factor, r
. .L L R L L R L L R L L R V W P W P m L m H m L m H S P S P S P S P . 6 . 6 5 . 7 . 7 5 . 8 . 8 5 . 9 . 9 5 1 . 6 . 6 5 . 7 . 7 5 . 8 . 8 5 . 9 . 9 5 1 C 1 C 3 C 2 C 4 C 6 C 8 C 5 C 7 2 4 8 1 6 3 2 r
A coarser fiber granularity allows us to save fibers but implies a smaller saturation factor
VWP performs better than WP
– Variations of r due to RFWAs and metrics in the VWP case below 5%
C = number of used wavelength channels
Saturation factor,
WDM Network Design 122
Compared to the initial
routing (shortest path, which is also the capacity bound) the fiber
increases the total wavelength-channel
lightpath length in number of hops)
– C is increased of max 10% of CSP in the worst case
SP
CSP = number of used wavelength channels with SP routing and unconstrained resources (capacity bound)
2 4 6 8 10 12 2 4 8 16 32
2.18 2.37 3.86 4.62 9.61 2.23 1.93 3.39 3.6 6
VWP WP Capacity bound per cent deviation Number of wavelengths, W
mH cases
,
WDM Network Design 123
Compared to the initial
routing (shortest path) the fiber optimization algorithm decreases the total number
channels
– U is halved in the best case Notes – Initial SP routing curve: data obtained in the VWP scenario (best case) – Optimized solution curve: averaged data comprising the WP and VWP scenarios
10 20 30 40 50 5 10 15 20 25 30 35 initial SP routing
% Unused capacity, U Number of wavelengths, N
WDM Network Design 124
The algorithm appears to converge well before the last iteration
Improvements of the computation time are possible
Notes:
– Convergence is rather insensitive to the initial sorting rule and to the RFWA criteria
55 60 65 70 75 80 85 90 6 104 6.5 104 7 104 7.5 104 8 104 8.5 104 9 104 9.5 104 2 4 6 8 10 12 14 16
VWP W=16, mH, SP
M L Total fiber number, M Total fiber length, L (km)
WDM Network Design 125
ILP by SF is a useful benchmark to verify heuristic dimensioning
results
– Approximate methods do not share this property
.5 1 1 5 2 2 5 3 3 5 4 5 1 1 5 2 2 5 3 3 5
N S F N E T V W P
s
r c e f
m . h e u r i s t i c Number of wavelengths, W Total fiber number, M
2 4 6 8 1 1 2 1 4 1 6 1 2 3 4 5 6 7
E O N V W P
s
r c e f
m . h e u r i s t i c
Number of wavelengths, W Total fiber number, M
WDM Network Design 126
A heuristic method for multifiber WDM network optimization
under static traffic has been proposed and applied to various physical network scenarios
Good sub-optimal solutions in terms of total nr of fibers can be
achieved with a reasonable computation time
The method allows to inspect various aspects such as RFWA
performance comparison and wavelength conversion effectiveness
Future possible developments – Upgrade to include also lightpath protection in the WDM layer – Improvement of the computation time / memory occupancy
WDM Network Design 127 127 Politecnico di Milano
OTN design and simulation Semi-transparent OTN, physical impairments; ASON/GMPLS control plane
1996 year 2000 2003 2006 2007 2008
Resilience, protection, availability Multi-domain routing Multi-layer TE, learning algorithms SLA-aware routing; Submarine
WDM Network Design 128 128 Politecnico di Milano
OTN design and simulation Semi-transparent OTN, physical impairments; ASON/GMPLS control plane
1996 year 2000 2003 2006 2007 2008
Resilience, protection, availability Multi-domain routing Multi-layer TE, learning algorithms SLA-aware routing; Carrier-grade Ethernet
OPTCORE AGNES
WDM Network Design 129 129
Finds the best matching between the physical topology and the set of requests for lambda connections
Supports all the main WDM-layer protection techniques
Provides data for OXC and OADM configuration
Allows to inspect and try several network scenarios, including transparent,
Solves green-field design as well as network re-design under legacy element constraints
Is applicable to large systems with 128 and more wavelengths per fiber, multi-fiber links and high-dense connectivity
Performs dynamic-traffic simulation to assess the capability of a network to support unexpected lambda connection requests and traffic expansion
WDM Network Design 130 130
Network physical topology (links and nodes) Wavelength-conversion capability Number of wavelengths per fiber (W) Protection scheme (e.g. unprotected, dedicated, shared) Routing, fiber and wavelength assignment algorithms Processing tool Working and spare resources allocation OXC and converters configuration Cost-function minimization User interface (XML-based) OC-layer topology (OC request matrix) Initial conditions (e.g. initial # fibers) User interface (XML-based)
WDM Network Design 131 131
WDM Network Design 132 132
WDM Network Design 133 133
WDM Network Design 134 134
Integer Linear Programming (ILP) – The most general exact method – Exponential computational complexity not scalable – The number of variables and constraints is huge
formulation (e.g. constrained-route, source, etc.)
– Variables defined in the integer domain
Heuristic methods – Polynomial-complexity algorithms – No guarantee that the solution found is the optimum
– A very good alternative to ILP for realistic-dimension problems
Simplicity Precision
ILP Heuristics
WDM Network Design 135
Additional slides on Bhandary’s algorithm for link-disjoint paths Courtesy of Grotto Networking
WDM Network Design 136
WDM Network Design 137
NE 1 NE 3 NE 5 NE 2 NE 4 NE 6 8 4 2 1 1 1 NE 7 2 2 8 NE 8 2 2
Find the first shortest path, then prune those links
Primary path cost = 3
WDM Network Design 138
Find the second shortest path in the modified graph
NE 1 NE 3 NE 5 NE 2 NE 4 NE 6 8 4 2 NE 7 2 2 8 NE 8 2 2
Backup path cost = 12 Total for both paths= 15
WDM Network Design 139
Questions – Are these the lowest cost set of diverse paths?
– Are there situation where this approach will completely fail?
WDM Network Design 140
Step 1. Find the shortest path from source to destination Step 2. Prune out links from the path of step 1.
NE 1 NE 3 NE 5 NE 2 NE 4 NE 6 2 2 2 2 1 1 1
WDM Network Design 141
Step 3. Can’t find another path from 1 to 6 since we just separated the graph Hmm, maybe a solution doesn’t exist? Or maybe we need a new algorithm?
NE 1 NE 3 NE 5 NE 2 NE 4 NE 6 2 2 2 2
WDM Network Design 142
– Bhandari’s method utilizing a modified Dijkstra algorithm
– Suurballe’s algorithm: transforms the graph in a way that two regular Dijkstra computations can be performed. NE 1 NE 3 NE 5 NE 2 NE 4 NE 6 2 2 2 2 1 1 1 Answer: Find a better algorithm
WDM Network Design 143
1 1 1 4 3 A Z C B
Step1: Compute least cost primary path Primary path is A-B-C-Z, cost=3
WDM Network Design 144
Step2: Treat graph as directed. In all edges in the primary path: Set forward cost to . Set reverse cost to negative of original cost.
4 3 A Z C B 3 4
WDM Network Design 145
Step3: Find least cost back-up path
4 3 A Z C B 3 4
Back-up path is A-C-B-Z, cost=6
WDM Network Design 146
Step4: Merge paths. Remove edges where primary and back-up traverse in opposite directions
4
3 A Z C B 3 4
New primary is A-B-Z, back-up is A-C-Z, total cost = 9
WDM Network Design 147
WDM Network Design 148
Introduction to WDM network design and optimization Integer Linear Programming approach Physical Topology Design – Unprotected case – Dedicated path protection case – Shared path & link protection cases – p-Cycles Heuristic approach
WDM Network Design 149
A p-cycle (“preconfigured protection cycle”) is the most efficient
structure for preconfigured restoration in terms of capacity efficiency
p-cycles go beyond the behavior of a ring – Emulate the ring behavior for a class of failures (faults of the peripheral segments of the cycle) – Protect all its chord links like a mesh network, by providing two restoration paths – Recovery action is the same as in bidirectional-line switching rings (e.g., SONET/SDH 2-fiber SPRings) – No signaling is needed to activate restoration Optimal p-cycle selecting (NP-hard problem): a trade off between
minimizing path length and spare capacity
WDM Network Design 150
The failure of a peripheral link of
the p-cycle is bypassed using the
Like a self-healing ring peripheral link chord link P-cycle
WDM Network Design 151
For the failure of a chord link of
the p-cycle two restoration paths are available
K > 100% – In the example
% 33 % 100 2 9 9 9 K
WDM Network Design 152
(l,k) F c,(l,k) q L (l,k) x Y k l F W a x k l n a k l n y x c l s i v d i v x x
k l c k l q L k l c k l k l c k l p p p k l k l p p p k l c c k l A k A k c c c c c l k c k l
l l
integer ) , ( , integer Integrity ) , ( Capacity ) , ( ) , ( cycles
,
if if (working) ity Solenoidal
, , , ) , ( , , , , , , , , , , , , , , , , ,
New symbols
P : Set of p-cycles indexed by p
πp,l,k : equal to 1 if p-cycle p crosses link (l,k), otherwise it will be equal to 0
yplk : equal to 1 if the p-cycle p protects link (l,k) as on cycle span, equal to 2 if p- cycle p protects span (l,k) as straddling span and 0 otherwise.
WDM Network Design 153
How do you calculate good candidates for p-cycles?
WDM Network Design 154
Optimal design of WDM networks under static traffic with
dedicated path-protection (1+1 or 1:1)
– It allows to setup protected lightpaths so to minimize the amount of fibers deployed in the network (RFWA) – Each connection request is satisfied by setting up a working- protection (W-P) lightpath pair under the link-disjoint constraint
WDM Network Design 155
Lightpath Virtual topology Wavelength-continuity
constraint
Wavelength conversion