Traffic Grooming in WDM Ring Networks

Traffic Grooming in WDM Ring Networks

Presented by:

Eshcar Hilel

236357 - Distributed Algorithms, Spring 2005

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Introduction

Optical Networks - A new generation of networks using optical fiber transmission– Excellent medium, high BW, low error…

SONET ring - synchronous optical network, currently the most widely deployed optical network infrastructure

WDM Technology – wavelength-division multiplexing


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Introduction – SONET Ring

SADM - SONET add/drop multiplexers can aggregate lower-rate signals into a single high-rate stream

SONET ring use one fiber pair (or two for protection) to connect SADMs in the source and destination nodes


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Introduction – WDM

Increases the transmission capacity of optical fibers

Allows simultaneously transmission of multiple wavelengths (channels) within a single fiber

One wavelength may carry Internet traffic; another may carry voice or video


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Introduction – SONET over WDM

Multiple SONET rings can be supported on a single fiber pair by using multiple wavelengths

The networks are limited by the processing capability of electronic switches, routers and multiplexers (not by transmission bandwidth)

New aim: overcoming the electronic bottleneck by providing optical bypass


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Introduction – Optical bypass

WADM - WDM Add/Drop Multiplexer allows to drop (or add) only the wavelength that carries the traffic destined to (or originated from) the node

The dropped wavelength is electronically processed at the node

All the other wavelengths optically bypass the node


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Introduction – WADM

More optical switches may be added to support more add-drop wavelengths


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Introduction – Traffic Grooming

Every wavelength needs a SADM only at nodes where it is ended

Traffic typically require only a small fraction of the wavelength

Traffic grooming can be used in such a way that all of the traffic to and from the node is carried on minimum number of wavelength


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Topics of Discussion

Traffic Grooming - Understanding the Problem Single Exit Node Network

– NP-complete problem– Special case: uniform traffic– Special case: minimum number of wavelengths

All-To-All Uniform Traffic Network

Traffic Grooming

Understanding the problem


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What’s the Problem?

Unidirectional (clockwise) WDM ring N nodes: 1,2,…,N c – grooming factor rij - number of low rate circuits from node i to

node j Objective: minimize total number of SADMs


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Illustration

Unidirectional ring network: N = 4 6 pairs of nodes rij = 8: 8 OC-3 circuits between each pair

c = 16: each wavelength supports an OC-48 ring

Total load: 6x8 OC-3 = 3 OC-48, requires 3 wavelengths


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Illustration

Traffic assignment: 1: 1↔2, 3↔4 2: 1↔3, 2↔4 3: 1↔4, 2↔3

Total: 12 SADMs


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Illustration

Traffic assignment: 1: 1↔2, 1↔3 2: 2↔3, 2↔4 3: 1↔4, 3↔4

Total: 9 SADMs


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Goal – Traffic Grooming

Tradeoff between efficient use of fibers and the cost of electronic equipment

When no limitation on wavelengths – dedicated wavelength per connection, no multiplexing

Else design traffic grooming algorithms to – Minimize number of electronics (SADMs)– Minimize number of wavelengths (efficient use of

wavelengths)

Single Exit Node Network

E. Modiano, A. Chio,

“Traffic Grooming Algorithms for Reducing Electronic Multiplexing Costs in WDM Ring Networks”


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Telephone company’s central office

Computational Complexity

Unidirectional ring All the traffic on the ring is destined to a single

exit node Denote the exit node 0 rij > 0, for j = 0 and i = 1,…,N

Note: maximum load Lmax = i=1..N ri0

and minimum wavelengths Wmin = Lmax / c


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Assume w.l.o.g. ri0<c for all i

Else fill ri0/c wavelengths with ri0/c *c low

rate circuits, and groom the remaining (<c) circuits

Theorem: The traffic grooming problem is NP-complete


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Bin packing problem: What is the least number of bins (containers of fixed volume) needed to hold a set of objects (of different volumes)?

The bin packing problem is an NP-complete problem.


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Claim: There exist an optimal solution such that no traffic from a node is split onto two rings

Proof: – Consider assignment where the traffic of some

nodes is split onto 2 or more rings– Each such node have at least 2 SADMs– Accommodate the traffic on a separate wavelength– Requires at most 2 SADMs


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Theorem Proof: – For any optimal solution with no split traffic: regular

nodes - N SADMs; exit node - k SADMs, where k is the number of SONET rings

– Problem reduced to minimizing total number of rings– Achieved by combining traffic from multiple nodes

onto single ring (wavelength)– This is basically the Bin Packing problem!

QED


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Special Case: Uniform Traffic

ri0 = r

Optimal solution does not require split traffic May groom traffic from at most c/r nodes on

one SONET ring Number of wavelengths: W = N/ c/r Hence, minimum SADMs Mmin = N + W

Not the minimum number of wavelengths!


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Special Case:Minimum Number of Wavelengths

Traffic from nodes may have to be split onto multiple rings, S - total number of traffic splits

Additional SADM per split Hence, #SADMs M = N + Wmin + S,

where Wmin = r*N /c

Objective: minimize the total number of splits


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Special Case:Minimum Number of Wavelengths

Maximum load for ring with no split Lns = c/r*r Wns Maximum number of rings with no split

Remaining rings contain at most c circuits:

Wns * Lns + (Wmin- Wns)*c >= Lmax

Wns = min{Wmin , (c* Wmin –Lmax) / (c-Lns)}


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Iterative Algorithm

Initialization: c0 = c, N0 = N, r0 = r, W0 = W0min

Steps of loop i:– If Wi

ns = Wimin then accommodate the remaining

traffic without splitting - terminate– Fill Wi rings with unsplit traffic from ci /ri nodes– Remaining capacity is ci+1 = ci - ci /ri*ri

– Ni+1 = Ni - ci /ri*Wi nodes needs to be assigned


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Steps of loop i (cont):– Ni+1 = Ni - ci /ri*Wi nodes needs to be assigned– Fill remaining capacity ci+1 by traffic from Ni+1

nodes

– Remaining traffic becomes ri+1 = ri – ci+1

– Wi+1 = Wi – N

i+1

– Continue to loop i+1

Ni+1 < Wi

Iterative Algorithm (cont)

All-To-All Uniform Traffic Network

J.C. Bermond, D. Coudert, “Traffic Grooming in Unidirectional WDM Ring Networks using Design Theory”


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All-To-All Uniform Traffic

We show the problem can be formulated in terms of graph partition into sub-graphs:– at most c edges and per sub-graph– minimize total number of vertices


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Traffic Grooming:Reformulating the Problem

N nodes of unidirectional ring CN

R = N(N-1)/2 circles c – grooming factor KN - Complete graph on N vertices

Bλ denote a sub-graph of KN

V(Bλ) (resp E(Bλ)) denote its vertex (resp edge)

set


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Bλ correspond to a wavelength

An edge of Bλ correspond to a circle in the ring

Bλ is viewed as a set of circles packed in a

wavelength |E(Bλ)| <= c

V(Bλ) correspond to the number of SADMs

A(c,N) denotes total number of SADMs


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Input:N and c Output: partition of KN into sub-graphs Bλ,

λ = 1,…,W, such that |E(Bλ)| <= c

Objective: minimize ∑1<=λ<=W|V(Bλ)|


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Lower Bound

ρ(Bλ) = |E(Bλ)|/|V(Bλ)| is the sub-graph ratio

ρ(m) maximum ratio of sub-graph with m edges ρmax(c) = maxm<=c ρ(m)


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Lower Bound

Theorem: any grooming of R circles with grooming factor c needs at least R/ρmax(c)

SADMs Proof: R = ∑W

λ=1|E(Bλ)| <= ρmax(c)* ∑Wλ=1|V(Bλ)|

Thus we have the lower bound:

A(c,N) >= N(N-1) / ρmax(c)*2


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Lower Bound

We compute ρmax(c) Theorem:

If k(k-1)/2<=c<=(k+1)(k-1)/2, then

ρmax(c)=(k-1)/2

If (k+1)(k-1)/2<=c<=(k+1)k/2, then ρmax(c)=c/k+1

Proof: on board


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Lower Bound

Note: these sub-graphs do not have necessarily exactly c edges and so the minimum is not necessarily attained for

W = Wmin

Example: N=13 and c=7


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Discussion

My opinion of the subject Your opinion of the subject (and

presentation…) That’s all folks!


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References

J.C. Bermond, D. Coudert, “Traffic Grooming in Unidirectional WDM Ring Networks using Design Theory”, IEEE International Conference on Communications, May, 2003

E. Modiano, A. Chio, “Traffic Grooming Algorithms for Reducing Electronic Multiplexing Costs in WDM Ring Networks”, IEEE J. Lightwave Tech., Jan. 2000 vol. 18(1)


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References

E. Modiano, P. Lin, “Traffic Grooming in WDM Networks”, IEEE Communication Magazine, July 2001.

Documents

Traffic Grooming in WDM Ring Networks