Optical Networks Routing and wavelength assignment in · 2014-01-08 · Optical Networks Routing...

Optical Networks Routing and wavelength assignment in

WDM wide area networks 3 September 2012, Belem, Para, Brazil

Dr. Cicek Cavdar, [email protected]

Optical Networks Lab (ONLab) Royal Institute of Technology, Stockholm, Sweden

Special thanks to Biswanath Mukherjee from UC-Davis, Aysegul Yayimli from ITU, Paolo Monti and Lena Wosinska from KTH for the class material.

Optical Networks, RWA, Cicek Cavdar, KTH 2

Outline n  Introduction to concepts: Lightpath, connection, virtual

topology, physical topology.. n  Static RWA

¨  ILP design to solve the routing problem ¨  Graph coloring to solve the wavelength assignment problem

n  Dynamic RWA: ¨ Routing:

n  Fixed routing, Fixed-alternate routing, Adaptive routing ¨  Wavelength assignment

n  Random, First-fit, Least-used, Most-used,...

n  Routing and flow assignment algorithms: ¨  Dijkstra, Ford-Fulkerson, Minimum spanning tree: Prim.


Wide-area Optical Networks n  Wide-area (long-haul) optical networks

¨  nodes employ optical cross-connects (OXCs) ¨  WDM channels called lightpaths are established between node

pairs. §  The terms lightpath

and connection are interchangeable.

§  To establish a “connection” between a source-destination pair, we need to set up a “lightpath” between them.


Lightpath n  A lightpath may span multiple fiber links. n  It provides a “circuit switched” interconnection between

two nodes that: ¨  have a traffic flow between them and ¨  are located “far” from each other in the physical fiber network

topology. n  Each intermediate node in the lightpath provides a

circuit-switched optical bypass facility to support the lightpath.

n  In an N-node network, ¨  if each node is equipped with N − 1 transceivers

(transmitters + receivers), and ¨  if there are enough wavelengths on all fiber links,

then every node pair could be connected by an optical lightpath, and there is no networking problem to solve.


Lightpath However: n  The network should be scalable. n  Transceivers are expensive so that each node

may be equipped with only a few of them. n  Number of wavelengths is limited (typically 64 to

160). n  Therefore, only a limited number of lightpaths

may be set up on the network. n  Some node pairs cannot have direct

connections, i.e., lightpaths.

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Logical/virtual topology

n  Logical topology: each link represents a lightpath that could be (or has been) established to accommodate the traffic demand

n  A lightpath is a “logical link” between two nodes n  Full mesh Logical topology: a lightpath is established between any

node pair n  LT Design (LTD): choose, minimizing a cost function, the lightpaths to

support a given traffic

WDM network nodes

Optical network access point

Electronic-layer connection request Electronic switching node (DXC, IP router, ATM switch, etc.)

WDM network

CR1

CR2 CR4

CR3

LOGICAL! TOPOLOGY

Optical Networks, RWA, Cicek Cavdar, KTH

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Physical topology

n  Physical topology: set of WDM links and switching-nodes n  Some or all the nodes may be equipped with wavelength

converters

n  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


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Split the Problem: VTD + RWA n  Hard to determine the lightpath

topology jointly with the routing and wavelength assignment

n  Split into two sub-problems: (1) Virtual Topology Design (VTD) and (2) Routing and Wavelength Assignment (RWA)

¨  Solve the VTD problem and then map the obtained VT within the physical layer (i.e., for the given lightpaths solve RWA problem)


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λ 1 λ 2

Optical wavelength"channels

LP1 LP2

LP4

LP3 LP1 LP2 LP3

LP4

LP = LIGHTPATH

Routing and Wavelength Assignment (RWA): Mapping the virtual topology over the physical topology

n  Solving the resource allocation problem is equivalent to mapping the virtual topology over the physical topology

λ 3

Mapping (a)  No wavelength

converters (b)  with

wavelength converters

(a) (b)

CR1

CR2 CR4

CR3



Routing and Wavelength Assignment (RWA) n  The offered traffic is “circuit-oriented”

¨  the offered traffic consists of a set of connections ¨ each connection requires the full bandwidth of a

lightpath to be routed between its corresponding source-destination pair.

n  Once a set of lightpaths has been chosen or determined, we need to: ¨  route each lightpath in the network, and ¨ assign a wavelength to it.

n  This is referred to as the routing and wavelength assignment (RWA) problem.

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RWA Constraints n  Resources (fiber and/or wavelength) n  Wavelength continuity n  Physical impairments n  Survivability n  ...



Wavelength Continuity n  Normally, a lightpath operates on the same

wavelength across all fiber links that it traverses. ¨  the lightpath is said to satisfy the wavelength-

continuity constraint. n  Thus, two lightpaths that share a common fiber

link should not be assigned the same wavelength.

n  If a switching/routing node is also equipped with a wavelength converter facility, then the wavelength-continuity constraint disappears. ¨ a lightpath may switch between different wavelengths

on its route from its origin to its termination.

Wavelength Conversion n  Three types of wavelength conversion capabilities: •  (1) C Full conversion: the node capable of FWC can

change the wavelength of an incoming lightpath to any of the outgoing wavelengths

•  (2) FC Fixed conversion: lightpath entering a node at a particular wavelength will always exit the node at another given wavelength. (determine in- and output wavelength channels when network is designed)

•  (3) LC Limited conversion: possible conversion from one wavelength to a limited subset of other wavelengths. Will become important when applying all-optical wavelength converters that won’t allow to convert to an arbitrary wavelength but just to a limited set of wavelengths.


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Physical Impairments Constraint n  Directly related to the nature of the optical

physical medium and transparent transmission n  Optical physical impairments affect the quality of

the lightpath signal n  Lightpaths have a reduced reach n  Physical impariments can be mitigated by

regenerating the signal ¨  3R regeneration: Reamplification, Reshaping and

Retiming n  Trade-off: cost vs. performance



Connection Requests n  Connection requests may be of three types:

¨ Static: n  The entire set of connections is known in advance. n  Set up lightpaths for the connections in a global fashion while

minimizing network resources n  Known as static RWA or static lightpath establishment (SLE)

problem ¨  Incremental:

n  Connection requests arrive sequentially and remains in the network indefinitely.

¨ Dynamic: n  A lightpath is set up for each connection request as it arrives,

and it is released after some amount of time. n  Known as dynamic RWA or dynamic lightpath establishment

(DLE).


RWA Problem Statement n  Formally, the static RWA problem can be stated as

follows. n  Given:

¨  a set of lightpaths that need to be established on the network, ¨  a constraint on the number of wavelengths and transceivers

n  Determine: ¨  the routes over which these lightpaths should be set up ¨  the wavelengths which should be assigned to these lightpaths

n  Minimize: number of wavelengths. n  In a dynamic traffic scenario, future arrivals are not known in

advance, therefore a new lightpath request may not be set up due to constraints on routes and wavelengths. Called BLOCKING. The corresponding network optimization problem is to minimize this blocking probability.

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n  Routing: ¨  Constrained: only some possible paths between source and

destination (e.g. the K shortest paths) are admissible n  Great problem simplification

¨  Unconstrained: all the possible paths are admissible n  Higher efficiency in network resource utilization

n  Cost function to be optimized (optimization objectives) ¨  Route all the lightpaths using the minimum number of

wavelengths ¨  Route all the lightpaths using the minimum number of fibers ¨  Route all the lightpaths minimizing the total network cost,

taking into account also switching systems

Static WDM network optimization


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Objective Realize the lightpath topology, meet all

constraints

¨ Minimize the number of wavelengths used per link

n  Offline: For all lightpaths determined by the LTD

¨ Minimize blocking and number of wavelengths used per link

n  Online: For demands coming during operation



Solving the Static RWA n  Physical topology and lightpath requests are

known. n  Offline RWA n  The objective is to minimize the number of

wavelengths. n  SLE can be formulated as an integer linear

program (ILP). ¨ Objective: minimize the flow in each link ¨ means minimizing the number of wavelengths used

on each link. n  The general problem is NP-complete.


Solution to SLE n  Approximation algorithms to solve the RWA problem for

large network sizes. n  The RWA problem can be decomposed into different

sub-problems, and each sub-problem can be solved independently with the results of one stage fed in as the input to the next stage. ¨  A linear program (LP) relaxation for routing (using the idea of

multi-commodity flow in a network) A general-purpose LP solver to derive solutions to this problem.

¨  Graph coloring algorithms to assign wavelengths to the lightpaths.

n  This method of subdividing the overall problem into smaller sub-problems, allows practical solutions to the RWA problem for networks with a large number of nodes.


Formulation n  The RWA problem, without the wavelength-continuity

constraint, can be formulated as a multi-commodity flow problem with integer flows in each link.

n  Let λsd denote the traffic (in terms of a lightpath) from any source s to any destination d. ¨  at most one lightpath from any source to any destination; ¨  λsd = 1 if there is a lightpath from s to d ¨  otherwise λsd = 0.

n  Let Fsdij denote the traffic (in terms of number of

lightpaths) that is flowing from source s to destination d on link ij.

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RWA: ILP formulation The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.Minimize:

Such that: maxF

# of lightpaths between s and d.

# of lightpaths on link i j that are following from s to d.

:

:0

,max

sdij

sd

sd

sd

i k

sdjk

sdij

ds

sdij

F

otherwisejdifjsif

FF

ijFF

λ

λ

λ

=

=

⎪⎩

⎪⎨

⎧

−=−

∀≥

∑ ∑

∑



Problem Size n  If we consider the general multi-commodity formulation,

the number of equations and the number of variables in the formulation grow rapidly with the size of the network.

n  For example, assume that there are: ¨  10 nodes ¨  30 physical links (ij pairs), ¨  an average of 4 connections per node, 40 connections (sd pairs)

n  In the general formulation, ¨  number of λsd variables: 10 × 9 = 90 ¨  number of Fsd

ij variables: 90 sd pairs × 30 ij pairs = 2,700. ¨  number of equations will be 3,721

n  Even for a small problem, the number of variables and equations are very large.

n  These numbers grow proportionally with the square of the number of nodes.


Problem Size Reduction n  A smarter solution can be obtained by only

considering the λsd variables that are 1, ¨  reduces the number of λsd variables from 90 to 40. ¨ eliminates all of the third set of equations. ¨  reduces the number of Fsd

ij variables to 40 × 30 = 1,200.

n  This approach is specific to the particular instance of lightpaths that need to be set up.

n  It only takes into account the lightpaths that need to be established.


Problem Size Reduction – Routing n  Assume that a particular lightpath will not pass through

all of the ij links. n  If we can determine the links which have a good

probability of being in the path through which a lightpath may pass, we can only consider those links as the Fsd

ij variables for that particular sd pair.

n  Thus, if on an average, a lightpath sd passes through seven links, there will be approximately 40 × 7 = 280 Fsd

ij variables.

n  We can find a set of alternate, shortest paths between a given source-destination pair.

n  The links constituting these alternate paths can then be used as part of the LP formulation.


Problem Size Reduction - Relaxation n  We can relax the integrality constraints, getting rid of all of

fourth set of equations. n  Using this approach, we will be left with a total of 351

equations. ¨  1 objective function ¨  30 instances of first set ¨  320 instances of second set.

n  Since there are on an average of seven links considered per connection, we need to enumerate equations in the second set for ¨  eight nodes (6 intermediate and 2 end nodes) per connection, ¨  for each of 40 connections.

n  Hence, using knowledge which is specific to a particular set of lightpaths, we can drastically reduce the size of the LP problem formulation and make it tractable for large networks.


Randomized Rounding n  Used to construct a good solution to the original ILP

using the information derived from the solution of the relaxed problem.

n  The randomized rounding technique is applicable to a class of 0-1 ILPs.

n  The technique is probabilistic. ¨  With high probability, the algorithm will provide an integer

solution in which the objective function takes on a value close to the optimum of the relaxation.

n  The optimal value of the objective function in the relaxed version is better than the optimal value of the objective function in the original 0-1 integer program.

n  This technique has been effectively used in multi-commodity flow problems.


Multi-commodity Flow n  In a general multi-commodity flow problem, we are given:

¨  an undirected graph G(V,E) ¨  k commodities that need to be routed.

n  In an instance of the problem, various vertices are the sites of source and sink for a particular commodity.

n  One unit of flow is to be conveyed from each source s to each destination d through the edges in E.

n  Each edge e has a capacity c(e) ¨  it is an upper limit on the total amount of flow in E.

n  The flow of each commodity in each edge must be 0 or 1. n  The objective is to minimize the common capacity in each link. n  The general integral problem is known to be NP-complete. n  The non-integral version can be solved using linear programming

methods in polynomial time.


Multi-commodity Flow n  In the formulation of the problem:

¨  Each commodity corresponds to a lightpath from a source node to a destination node.

¨  The capacity is the number of wavelengths supported in each fiber.

¨  The objective function is to minimize the number of wavelengths needed to accommodate all of the requests.

n  The algorithm consists of the following three phases: ¨  solving a non-integral multi-commodity flow problem ¨  path stripping ¨  randomized path selection


Non-integral Multi-commodity Flow n  We relax the requirement of the 0-1 flows to allow

fractional flows in the interval [0,1]. n  The relaxed capacity minimization problem can be

solved by a linear programming method. n  If the flow for each commodity i on edge e is fi(e),

¨  a capacity constraint of the form:

is satisfied for each edge in the network. ¨  C is the optimal solution to the non-integral optimization problem.

n  The value of C is a lower bound on the best possible integral solution.

fi (e)i=1

k

∑ ≤C


Path Stripping n  The main idea is to convert the edge flows for

each commodity i into a set τi of possible paths which could be used to route the flow of that commodity.

n  Initially, τi is empty. n  For each commodity i do:

A.  Discover a loop-free, depth-first, directed path e1, e2, . . . , ep from the source to the destination.

B.  Let fm = min fi(ej ), where 1 ≤ j ≤ p. n  For 1 ≤ j ≤ p, replace fi (ej) by fi(ej) − fm. n  Add the path e1, e2, . . . , ep to τi along with its weight fm.


Path Stripping C. Remove any edges with zero flow from the set of

edges that carry any flow for commodity i. n  If there is nonzero flow leaving si, repeat Step B. n  Otherwise, continue for next commodity i.

n  Upon termination, the sum of the weights of all the paths in τi is 1.

n  Path stripping gives us a set of paths τi that may carry the flow for commodity i in the optimal case.


Randomized Path Selection n  For each i, cast a |τi| die with face probabilities

equal to the weights of the paths in τi. n  Assign the path whose face comes up, to

commodity i. n  As a summary:

¨ The formulation of the problem allows the Fsdij

variables to take on fractional values. ¨ These values are used to find the fractional flow

through each of a set of alternate paths. ¨ A coin-tossing experiment is used to select the path

over which to route the lightpath λsd based on the probability of the individual paths.


Assigning Wavelengths n  Once a path has been chosen for each connection, we

need to assign wavelengths to each lightpath. ¨  any two lightpaths that pass through the same physical link are

assigned different wavelengths.

n  If the intermediate switches do not have the capability to perform wavelength conversion, a lightpath is constrained to operate on the same wavelength throughout its path.

n  Assigning wavelength colors to different lightpaths, to minimize the number of wavelengths under the wavelength-continuity constraint, reduces to the graph coloring problem.


Graph Coloring n  Construct a graph G(V,E)

¨  Each lightpath in the system is represented by a node in graph G.

¨  There is an undirected edge between two nodes if: corresponding lightpaths pass through a common physical fiber link.

n  Color the nodes of the graph G such that no two adjacent nodes have the same color.

n  This problem has been shown to be NP-complete n  The minimum number of colors needed to color a graph

G is difficult to determine. n  However, there are efficient sequential graph coloring

algorithms.


Physical Topology for Simulations n  A randomly-generated physical topology:

¨ 100 nodes ¨ Each node having a physical nodal degree uniformly

distributed between two and five. ¨ All links are unidirectional ¨ 357 directed links ¨ There are enough transceivers at the access nodes to

accommodate all of the lightpath requests that need to be established.

n  No lightpath request will be blocked due to lack of transceivers at the access nodes.


Traffic Model n  A set of lightpaths to be established between

randomly-chosen source-destination (sd) pairs ¨ An sd pair can have zero or one lightpath, and all sd

pairs are treated equally. n  Associated with each node, we identify d:

¨  the average number of lightpath connections the nodes will source.

n  Thus, in an N-node network, the probability that a node will have a lightpath with each of the remaining (N − 1) nodes equals d/(N − 1).

n  d is the average “logical degree” of a node.


Solving LP n  To reduce the size of the LP formulation, consider a set

of K alternate, shortest paths between a given sd pair. n  Only the links which constitute these alternate paths are

used as the Fsdij variables.

n  The LP formulation result (Fsdij values) is used as input

for the randomized rounding algorithm. n  The value of the objective function denotes the lower

bound on congestion that can be achieved by any RWA algorithm.

n  The individual flow variables are used in the path-stripping technique and the randomization technique to assign physical routes for the different lightpaths.

n  Once this procedure is completed, the congestion on the different links in the network is obtained.


Results


Results n  The maximum network congestion gives the

number of wavelengths we would need, if the intermediate switching nodes were equipped with wavelength converters.

n  The time taken to solve the LP increases rapidly as the number of connections increase (corresponding to larger problem formulations).

n  The table entries which are nil correspond to the case when the LP solver failed to give a solution.


Routing Algorithms for dynamic RWA

n  In case of dynamic traffic, LP is not an option. n  Heuristic methods are used to solve the dynamic

RWA problem. n  The general RWA is divided into:

¨ Routing sub-problem ¨ Wavelength assignment sub-problem

n  Basic routing heuristics are: ¨ Fixed routing ¨ Fixed-alternate routing ¨ Adaptive routing


Fixed Routing n  The most straightforward approach n  Always choose the same fixed route for a given

s,d pair. n  Example: Fixed shortest path routing

¨ The shortest paths are calculated in advance for each source-destination pair.

¨ Any connection between a specified node pair is established using the pre-determined route.

n  Disadvantage: ¨  If the wavelengths along the fixed path are busy, the

connection is blocked.


Fixed Alternate Routing n  Each node maintain a routing table that contains

a list of fixed routes to each destination. ¨ Example: shortest path, second shortest path, third

shortest path n  Alternate routes are link disjoint. n  When a connection request arrives:

¨ The source node attempts to establish the lightpath on alternate path 1.

¨  If no wavelength on the route is available, then the second alternate path is tried.

¨ Connection is blocked if a lightpath cannot be established on any of the alternate paths.


Adaptive Routing n  The route between two nodes are calculated

dynamically. n  Ongoing connections are taken into account. n  Network state must be represented in some

form. n  Each time a connection request arrives, the

route must be determined according to free wavelengths on the physical links.

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Algorithmic solutions n  They are mostly based on the notion of

shortest path routing n  Fixed routing -> shortest path

¨ Dijkstra Algorithm ¨ Bellman-Ford

n  Fixed alternate routing-> k-shortest path ¨ Yen’s algorithm

n  Adaptive -> shortest path ¨ Dijkstra Algorithm



Wavelength Assignment for DLE n  Several heuristics are used:

¨ Random ¨ First-fit ¨ Least used / SPREAD ¨ Most used / PACK ¨ Min product ¨ Least loaded ¨ Max-Sum ¨ RCL ¨ etc.


Random Wavelength Assignment n  Determine the set of all available wavelengths

on the required path. n  Choose one randomly (with uniform probability).


First-fit WA n  All wavelengths are numbered. n  A lower-numbered wavelength is considered

before a higher-numbered one. n  That is, the first available wavelength is selected. n  Compared to random WA lower computation

cost. n  Main idea: Pack all of the in-use wavelengths

toward the lower end of wavelength space. ¨ Continuous longer paths toward the higher-numbered

end will have a good chance of being available.


Least Used (SPREAD) n  Select the wavelength that is least used in the

network. n  Attempts to balance the load, among all the

wavelengths. n  Breaks the long wavelength paths quickly. n  The performance is worst than random WA.


Most Used (PACK) n  Attempts to select the most used wavelength in

the network. n  Outperforms LU significantly, and slightly better

than FF. n  Packs connections into fewer wavelengths.


Min Product n  Used in multi-fiber networks. n  The goal is to pack wavelengths into fibers,

thereby minimizing the number of fibers. n  It computes:

π(p) is the set of links of path p Dlj is number of fibers on link l and wavelength j

n  Chooses the lowest numbered wavelength that minimizes the above value.

n  In a single-fiber network, becomes FF.

( )lj

l p

Dπ∈∏


Least Loaded n  Designed for multi-fiber networks. n  Selects the wavelength that has the largest

residual capacity on the most loaded link along the route.

n  In single-fiber networks it reduces to FF. n  Outperforms LU and FF in multi-fiber networks.

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Dijkstra Algorithm

n  Greedy procedure to compute a set of paths at minimum cost originating at a given node

n  Assumption: cost associated to the each link have to be positive

n  Given ¨ a graph G(N,V) and a source (root) node s

n  Output ¨ Minimum cost tree from s node to all the

other nodes in the network


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Dijkstra Algorithm in a nutshell n  Starting from the one closest to the

root each node is visited once n  Once node is visited, algorithm

guarantees that cost to reach that node is the minimum

n  While visiting a node, algorithm checks all unvisited neighbors to see if cheaper routes are available

n  Algorithm stops when all nodes are visited


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Dijkstra Pseudo Code Algorithm Dijkstra (G (V,E), s){

for (each vertex v in V) do { // initialization

dist[v] = infinity ; // distance vector from the source node

previous[v] = NULL ; // pointer to the previous node in sh-path

endfor}

dist[s] = 0 ; // distance from root to itself

U = V ; // all nodes are set to not visited

while (U is not empty) do {

u = vertex in U with min dist[] ; // node with min dist from the root

if (dist[u] = infinity) do{ // the root is disconnected

break ;

endif}

remove u from U // mark node u as visited

for (each neighbor v in U of u) do { // where v belongs to U,

temp = dist[u] + distance(u, v) ;

if (temp < dist[v]) do { //update the distances

dist[v] = temp ;

previous[v] = u ;

endif}

endfor}

end while}

endDijkstra}

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Dijkstra Example

n  One Dijkstra interactive example available at: ¨ http://www-b2.is.tokushima-u.ac.jp/

~ikeda/suuri/dijkstra/DijkstraApp.shtml?demo1


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Dijkstra Algorithm Applications n  Link weights in Dijkstra algorithm can

be assigned according to the parameter that needs to be optimized. ¨ Distance (for shortest path) ¨ Delay (for minimum delay) ¨ Power consumption (for minimum power) ¨ Reliability (for maximum reliable path) ¨ Load (for load balancing)


Minimum spanning tree n  There are two solutions:

¨ Prim ¨ Kruskal

n  See following for an example and the pseudo-code: ¨ http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/

dijkstra/Prim.shtml ¨ http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/

kruskal/Kruskal.shtml


Max Flow n  Ford-Fulkerson n  See following animation and pseudo-code: n  http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/

maxflow/Maxflow.shtml


？

For questions, please send e-mail: [email protected]

Note: In the presentation, most material are cited from related sources. Since some material cited here may be confidential, or not be allowed to be circulated, please directly contact their own sources if you will use them.


Optical Networks Routing and wavelength assignment in · 2014-01-08 · Optical Networks Routing...

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