On Vt Design

8/10/2019 On Vt Design

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A. Genata

T, Dept. Computer Engineering2005

OPTICAL NETWORKS

Virtual Topology Design


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Optical NetworksAyegl Genata,T, Dept. Computer Engineering

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Virtual Topology

A lightpath provides single-hop communication between anytwo nodes, which could be far apart in the physical topology.

However, having limited number of wavelengths, it may not be

possible to set up lightpaths between all user pairs. Multi-hopping between lightpaths may be necessary.

The virtual topology consists of a set of lightpaths.

packets of information are carried by the virtual topology as far

as possible in the optical domain using optical circuit switching packet forwarding from lightpath to lightpath is performed via

electronic packet switching, whenever required.

Lightpaths in the virtual topology is set up using RWA

techniques. The virtual topology is also referred to as Lambda Grid, or just

Grid.


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Problem

An optimization problem to optimally select a virtual

topology subject to

transceiver (transmitter and receiver)

wavelength constraints

with one of two possible objective functions:

1. for a given traffic matrix, minimize the network-wide average

packet delay.2. maximize the scale factor by which the traffic matrix can be

scaled up (to provide the maximum capacity upgrade for futuretraffic demands).

Since the objective functions are nonlinear and sincesimpler versions of the problem have been shown to be

NP-hard, we shall explore heuristic approaches.


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NSFNET Backbone


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General Problem Statement

Problem: Embedding a desired virtual topology on a given

physical topology (fiber network).

We are given: A physical topology Gp = (V ,Ep) consisting of a weighted

undirected graph, where

V is the set of network nodes,

Ep is the set of links connecting the nodes.

Undirected means that each link in the physical topology

is bidirectional.

A node i is equipped with a Dp(i) Dp(i) WRS,where Dp(i) is the number of physical fiber linksemanating out of (as well as terminating at) node i.


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Number of wavelengths carried by each fiber, M.

An N N traffic matrix, where N is the number of network nodes,

The (i, j)-th element is the average rate of packettraffic flow from node i to nodej.

The traffic flows may be asymmetric. The number of wavelength-tunable lasers

(transmitters) and wavelength-tunable filters

(receivers) at each node.


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The goal is to determine:

A virtual topology Gv= (V ,Ev) as another graph

where: the out-degree of a node is the number of transmitters at that

node

the in-degree of a node is the number of receivers at that node.

The nodes of the virtual topology correspond to the nodes in thephysical topology.

Each link in the virtual topology corresponds to a lightpath

between the corresponding nodes in the physical topology.

Each lightpath may be routed over one of several possible pathson the physical topology.


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A wavelength assignment for lightpaths.

If two lightpaths share a common physical link, they

must necessarily employ different wavelengths. The sizes and configurations of the WRSs at the

intermediate nodes.

Once the virtual topology is determined and thewavelength assignments have been performed, the

switch sizes and configurations follow directly.


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Packet Communication

Communication between any two nodes takes

place by following a path (a sequence of

lightpaths) from the source node to thedestination node on the virtual topology.

Each intermediate node in the path must

perform:1. an opto-electronic conversion,

2. electronic routing (or packet switching in the

electronic domain), and3. electro-optic forwarding onto the next lightpath.


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Illustrative Example

How WDM can be used to upgrade an existingfiber-based network.

Using the NSFNET as an example, a hypercubecan be embedded as a virtual topology over thisphysical topology.

We assume an undirected virtual topology. bidirectional lightpaths

In general, the virtual topology may be adirected graph.

The physical topology is enhanced by addingtwo fictitious nodes, AB and XY.


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Illustrative Example

The switching architecture of nodes consists of:

An optical component.

a wavelength-routing switch (WRS) can switch some lightpaths,

can locally terminate some other lightpaths by directing

them to nodes electronic component.

An electronic component.

an electronic packet router

(may be an IP router: IP-over-WDM)

serves as a store-and forward electronic overlay on topof the optical virtual topology.


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Example

The virtual topology chosen is a 16-node

hypercube.


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Example: A Possible Embedding


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Example

This solution requires 7 wavelengths.

Each link in the virtual topology is a lightpath with electronicterminations at its two ends only.

Example: The CA1-NE lightpath could be set up as an optical channel on one

of several possible wavelengths on one of several possible physicalpaths:

CA1-UT-CO-NE, or CA1-WA-IL-NE, or others.

According to the solution, the first path is chosen on wavelength 2for CA1-NE lightpath.

This means that the WRSs at the UT and CO nodes must beproperly configured to establish this CA1-NE lightpath.

The switch at UT must have wavelength 2 on its fiber to CA1connected to wavelength 2 on its fiber to CO.

Since connections are bidirectional, the CA1-NE connection impliestwo lightpaths, one from CA1 to NE and one from NE to CA1.


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UT Node


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UT Node

The switch UT has to support four incoming fibers plus

four outgoing fibers,

one each to nodes AB, CA1, CO, and MI, as dictated by the

physical topology.

In general, each switch interfaces with four lasers

(inputs) and four filters (outputs),

each laser-filter pair is dedicated to accommodate each of thefour virtual links on the virtual topology.

The labels 1l 2b 3d 5lon the output fiber to CO: The UT-CO fiber uses four wavelengths 1, 2, 3, and 5.

Wavelengths 2 and 3 are clear channels through the UT switchand directed to the physical neighbors CA1 and MI, respectively.

Wavelengths 1 and 5 connect to two local lasers.


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UT Node

The box labeled Routeris an electronic switch which

takes information from:

terminated lightpaths (1c 4b 5c)

a local source

and routes them via electronic packet switching to:

the local destination

the local lasers (lightpath originators)

The router can be any electronic switch.

e.g., an IP router.

The non-router portions of the node architecture are the

optical parts that may be incorporated to upgrade the

electronic switch to incorporate a WRS.


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Formulation of the Optimization

Problem

Notation:

s and d used as subscript or superscript todenote source and destination of a packet,

respectively.

i andj denote originating and terminating nodes,respectively, in a lightpath.

m and n denote endpoints of a physical link.


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Formulation: Given

Given:

Number of nodes in the network: N.

Maximum number of wavelengths per fiber: M Physical topology Pmn

Pmn = Pnm = 1 if there is a direct physical fiber link

between nodes m and n Pmn = Pnm = 0 otherwise

The problem can be generalized to accommodate

multi-fiber networks, where Pmn can take integervalues.


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Optical NetworksAyegl Genata,T, Dept. Computer Engineering20

Formulation: Given

Distance matrix whose elements are fiberdistance dmn from node m to node n.

For simplicity in expressing packet delays, dmn isexpressed as a propagation delay (in time units). dmn = dnm dmn = 0 if Pmn = 0.

Number of transmitters at node i = Ti (Ti 1). Number of receivers at node i = Ri(Ri 1). Capacity of each channel: C

normally expressed in bits per second, but convertedto units of packets per second by knowing the meanpacket length.


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Formulation: Given

Traffic matrixsd the average rate of traffic flow from node s to node d

ss = 0 Additional assumptions:

Packet inter-arrival durations at node s and packetlengths are exponentially distributed.

So standard M/M/1 queuing results can be applied toeach network link (or hop) by employing theindependence assumption on inter-arrivals and packetlengths due to traffic multiplexing at intermediate hops.

By knowing the mean packet length (in bits per packet),the sdcan be expressed in units of packets persecond.


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Formulation: Variables

Variables:

Virtual topology Vij: 1 if there is a lightpath from i toj in the virtual topology 0 otherwise.

The formulation is general since lightpaths are

not necessarily assumed to be bidirectional. Vij= 1 Vji= 1.

Further generalization of the problem can be

performed by allowing multiple lightpathsbetween node pairs, i.e., Vij > 1.


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Formulation: Variables

Traffic routing variable sdij denotes the traffic flowing from s to d and employing

Vijas an intermediate virtual link. traffic from s to d may be bifurcated with different

fractions taking different sets of lightpaths.

Physical-topology route variablep

ij

mn is: 1 if the fiber link Pmn is used in the lightpath Vij ;

0 otherwise.

Wavelength color variable cij

k is: 1 if a lightpath from i toj is assigned the color k

0 otherwise.


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Formulation: Constraints

Constraints:

On virtual-topology connection matrix Vij :

These equations ensure that: The number of lightpaths emanating out of and

terminating at a node

are at most equal to that nodes out-degree andin-degree, respectively.


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On physical route variablespijmn:

First two equations constrain the problem so thatpijmnexist only if there is a fiber (m,n) and a lightpath (i,j).

The remaining equations are the multi-commodityequations that account for the routing of a lightpath fromits origin to its termination.


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On virtual-topology traffic variables sdij :

Equations for the routing of packet traffic on the virtual topology.They take into account that the combined traffic flowing through a

channel cannot exceed the channel capacity.


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Optical NetworksAyegl Genata,T, Dept. Computer Engineering 27


On coloring of lightpaths cijk :

First equation requires that a lightpath be of one

color only.

Second equation ensures that the colors used indifferent lightpaths are mutually exclusive over a

physical link.


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Formulation: Objective 1

Delay Minimization:

The innermost brackets: the first component corresponds to the propagation delays on

the links mn which form the lightpath ij

the second component corresponds to delay due to queuing andpacket transmission on lightpath ij.

If we assume shortest-path routing of the lightpaths overthe physical topology, then thepijmn values becomedeterministic.

If, in addition, we neglect queuing delays, theoptimization problem reduces to minimizing the firstcomponent.


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Formulation: Objective 2

Maximizing Load (Minimizing Maximum Flow):

Also nonlinear

Minimizes the maximum amount of traffic thatflows through any lightpath.

Corresponds to obtaining a virtual topology

which can maximize the offered load to thenetwork if the traffic matrix is allowed to bescaled up.


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Algorithms for VT Design

The problem of optimal virtual-topology design

can be partitioned into the following four sub-

problems, which are not necessarilyindependent:

Determine a good virtual topology.

which transmitter should be directly connected to which

receiver?

Route the lightpaths over the physical topology.

Assign wavelengths optimally to the various

lightpaths. Route packet traffic on the virtual topology.


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Solutions

Several heuristic approaches have been employed tosolve these problems. Labourdette and Acampora, Logically rearrangeable multihop

lightwave networks, IEEE Transactions on Comm., Aug. 1991. I. Chlamtac, A. Ganz, and G. Karmi, Lightnets: Topologies for

high speed optical networks, IEEE/OSA Journal of LightwaveTechnology, May/June 1993.

B. Mukherjee, S. Ramamurthy, D. Banerjee, and A. Mukherjee,Some principles for designing a wide-area optical network,

Proceedings, IEEE INFOCOM 94, June 1994. R. Ramaswami and K. Sivarajan, Design of logical topologies

for wavelength-routed all-optical networks, Proceedings, IEEEINFOCOM 95, April 1995.

Z. Zhang and A. Acampora, A heuristic wavelength assignment

algorithm for multihop WDM networks with wavelength routingand wavelength reuse, IEEE/ACM Transactions on Networking,vol. 3, pp. 281288, June 1995.


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Solutions

Embedding of a packet-switched virtual topology

on a physical fiber plant in a switched network

was first introduced in the second reference, andthis network architecture was referred to as a

lightnet.

The work in ref. 4 proposes a virtual-topologydesign where the average hop distance is

minimized, which automatically increases the

network traffic supported. This work uses the

physical topology as a subset of the virtual

topology.


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Solution Approach

To obtain a thorough understanding of the problem, we

concentrate on Sub-problems 1 and 4 above.

the number of available wavelengths is not a constraint.

In the expanded problem, both the number of wavelengths and

their exact assignments are critical.

An iterative approach consisting of simulated annealing

to search for a good virtual topology (Sub-problem 1)

The flow-deviation algorithm for optimal (possibly

bifurcated) routing of packet traffic on the virtual

topology (Sub-problem 4).


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Solution Approach

We will consider lightpaths to be bidirectional in

our solution here

most (Internet) network protocols rely on bidirectionalpaths and links.

We consider Optimization Criterion (2)

(maximizing offered load) for our illustrativesolution.

mainly because we are interested in upgrading an

existing fiber-based network to a WDM solution.


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Simulated Annealing

Simulated annealing (along with genetic algorithms) has been foundto provide good solutions for complex optimization problems.

In the simulated annealing process, the algorithm starts with aninitial random configuration for the virtual topology.

Node-exchange operations are used to arrive at neighboringconfigurations.

In a node-exchange operation, adjacent nodes in the virtual topologyare examined for swapping.

Example: if node i is connected to nodesj, a, and b, while nodej is connected to nodesp, q, and i in the virtual topology,after the node-exchange operation between nodes i andj, node i will be connected to nodesp, q, andj, while nodej will be connected to nodes a, b, and i.


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Simulated Annealing

Neighboring configurations which give better results

(lower average packet delay) than the current solution

are accepted automatically.

Solutions which are worse than the current one are

accepted with a certain probability.

This probability is determined by a system control parameter.

The probability with which these failed configurations arechosen decreases as the algorithm progresses in time

so as to simulate the cooling process of annealing.

The probability of acceptance is based on a negative

exponential factor

inversely proportional to the difference between the current

solution and the best solution obtained so far.


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Flow Deviation

By properly adjusting link flows, the flow-deviation

algorithm provides an optimal algorithm for minimizing

the network-wide average packet delay.

Traffic from a given source to a destination may be

bifurcated.

different fractions of it may be routed along different paths to

minimize the packet delay.

Idea: If the flows are not balanced, then excessively

loading of a particular channel may lead to large delays

on that channel

and thus have a negative influence on the network-wide averagepacket delay.


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Flow Deviation

The algorithm is based on the notion of shortest-pathflows. First calculates the linear rate of increase in the delay with an

infinitesimal increase in the flow on any particular channel. These lengths or cost rates are used to pose a shortest-path

flow problem (can be solved using one of several well-knownalgorithms such as Dijkstras algorithm, Bellman-Ford algorithm,etc.)

The resulting paths represent the cheapest paths on whichsome of the flow may be deviated.

An iterative algorithm determines how much of theoriginal flow needs to be deviated.

The algorithm continues until a certain performancetolerance level is reached.


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Experimental Results

The traffic matrix employed is an actual measurement ofthe traffic on the NSFNET backbone for a 15-minuteperiod. 11:45 pm to midnight on January 12, 1992, EST.

The raw traffic matrix shows traffic flow in bytes per 15-minute intervals between network nodes.

Nodal distances used are the actual geographicaldistances.

Initially, each node can set up at most four bidirectionallightpath channels.

Later more experiments were conducted to study theeffect of having higher nodal degree.

The number of wavelengths per fiber was assumed to belarge enough. all possible virtual topologies could be embedded.


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Traffic Matrix


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For each experiment,

the maximum scale-up achieved

the corresponding individual delay components,

the maximum and minimum link loading the average hop distance

is tabulated.


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The aggregate capacity for the carried traffic is fixed bythe number of links in the network. reducing the average hop distance can lead to higher values of

load that the network can carry.

The queuing delay was calculated using a standardM/M/1 queuing system. mean packet length calculated from the measured traffic:

133.54 bytes per packet.

link speed is 45 Mbps. Infinite buffers at all nodes.

The cooling parameter for the simulated annealing isupdated after every 100 acceptances using a geometricparameter of value 0.9.

A state is considered frozen when there is noimprovement over 100 consecutive trials.


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Physical Topology as Virtual Topology

No WDM) Goal: to obtain a fair estimate of what optical hardwarecan provide in terms of extra capabilities.

Start off with just the existing hardware, comprising:

fiber and point-to-point connections a single bidirectional lightpath channel per fiber link

no WDM

The maximum scale-up achieved: 49

The load of the link with the maximum traffic: 98%

The load of the link with the minimum traffic: 32%.

These values serve as a basis for comparison as to whatcan be gained in terms of throughput by adding extraWDM optical hardware: tunable transceivers

wavelength routing switches.


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Multiple Point-to-Point Links No WRS)

Goal: to determine how much throughput we could

obtain from the network:

without adding any photonic switching capability at a node

by adding extra transceivers (up to four) at each node

The initial network had 21 bidirectional links in the

physical topology.

Using extra transceivers at the nodes, extra links are setup on the paths NE-CO, NE-IL, WA-CA2, CA1-UT, MI-

NJ, and NY-MD.

These lightpaths are chosen manually.

Different combinations were considered.

The channels providing the maximum scale-up was chosen.


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Arbitrary Virtual Topology Full WDM)

Full WDM with WRSs at all nodes.

It is possible to set up lightpathsbetween any two nodes.

All lightpaths are routed over theshortest path on the physicaltopology.

Starting off with a random initialtopology, simulated annealing is usedto get the best virtual topology.

shown in the table.

Provides a maximum scale-up of 106.

The increased scale-up demonstratesthe benefits of the WDM-basedvirtual-topology approach.


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O bl


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Open Problems

A significant amount of room exists for

developing improved approaches and

algorithms. An interesting avenue of research is to study

how routing and wavelength assignment of

lightpaths can be combined with the choice ofvirtual topology and its corresponding packet

routing in order to arrive at an optimum solution.

Dynamic establishment and reconfiguration oflightpaths is an important issue which needs to

be thoroughly studied.

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