On Vt Design
Transcript of On Vt Design
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A. Genata
T, Dept. Computer Engineering2005
OPTICAL NETWORKS
Virtual Topology Design
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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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General Problem Statement
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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General Problem Statement
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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General Problem Statement
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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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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Formulation: Constraints
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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Formulation: Constraints
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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Formulation: Constraints
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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Experimental Results
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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Experimental Results
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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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.