1
Examination Committee:
Dr. Poompat Saengudomlert (Chairperson)
Assoc. Prof. Tapio Erke
Dr. R.M.A.P. Rajatheva
Telecommunications FoS
Asian Institute of Technology

WDM networks and the problem of capacity expansion

Motivation

Proposed Model

Optimal Capacity Expansion with Budgetary Constraint

Aknowledgements
2
3
WDM networks..>
Video
Conferencing
Multimedia
on the
Internet
Video on
demand
P2P
Huge
Bandwidth
Requirement


Predicted in 2007 : Present traffic
could quadruple by 2011
Youtube : Feb, 2005
4
WDM networks..>


Analogy: Different modes of transport on the
road
Optical transport technologies:
 SDH
 PDH
 Metro Ethernet
 WDM/DWDM
5
WDM networks..>

Preferred choice for the future
▪ Multiply the capacity of a single fiber
▪ Easy to expand
▪ Cost: Scale linearly with capacity

Full wavelength conversion at nodes
 Any input to any output
6
WDM networks..>
Known: Network topology, source-destination
pairs, Planning horizon (T)
 Constraints to be satisfied:

 Traffic demand prediction

Need to find the best possible capacity allocation
 Objective: Save the budget
Source
Destination
Less cost
7
WDM networks..>

Similar to dimensioning

Differences:
 Existing capacity in the network
 Existing connections
 Existing connections must be preserved
8
9
Motivation>

WDM networks vs. Traditional Telephone Networks


(Assuming Poisson arrivals and Exponential Holding times)
Telephony
WDM
Traffic
Telephone calls
Lightpaths
Arrival rates
1 – 10 calls per hour
1-10 lightpaths per year
Holding times
Few minutes
Few months or years
Due to slowness of WDM traffic:


Significant traffic growth: Arrival rates change during network
operation
 t     01  t /  
 Linear growth
 Exponential growth
WDM Networks may not operate in steady state (Nayak and
Sivarajan, 2002)
10
Motivation>



Nayak and Sivarajan (2002)
Continuous time Markov Chain model of a WDM link
Absorption probability instead of blocking probability:
 An imaginary state
 Time dependant

Existing Method to compute absorption probabilities
 Complex
 Only for networks at initially zero state
11
A technique of dimensioning and expansion of WDM, under
traffic growth with minimum cost
1.

2.

Based on absorption probabilities
Solve dimensioning & expansion of WDM with budgetary
constraint and traffic uncertainty
Contribution
 For dimensioning and expansion with a minimum cost:
▪ Simple algorithm instead of Non-linear optimization that exists
 For dimensioning and expansion with budgetary constraint:
▪ A linear optimization technique
▪ A heuristic algorithm that gives optimal solution (Maximum lifetime)
▪ Consider all possible demand scenarios
12
13
Proposed Model >
Consider a WDM network
 Approximate link arrival rate using a
method similar to Erlang Fixed Point
method (consider bi-directional,
symmetric traffic)
 Disctrete-time Markov Chain of the
link
 Arrival rate, termination rate, growth > Absorption probability

 At each small time interval δt,

Iterative computations required to
get final link absorption probabilities
and then path absorption probabilities
P(k 1) t  A k t Pk t
PK t  AK 1 t ...A t A0P0
Pk t : State probabilities at time k t
A k t : State transition matrix at time k t
K δt = T
14
Proposed Model >


Existing method is a non linear optimization
Link Criticality based Capacity Expansion






Proposed algorithm
gives results close to optimal
Can be used for networks at any initial state
Can incorporate any traffic growth model
The First time multi-period capacity expansion is performed for WDM
networks based on transient state analysis
Published at the International Conference on Electrical
Engineering/Electronics, Computer, Telecommunications, and
Information Technology -2009
Gunawardena B. and Saengudomlert P.,“Dimensioning and
Expansion Algorithm for WDM Networks Under Traffic Growth”,
ECTI-CON’09
15
16
Optimal Capacity Expansion with Budgetary Constraint >

To make full use of the budget
 Network have to last longer without further expansion
 a relationship between capacity allocation and life

Can consider an s-d as an isolated logical link
 λ(0), μ and τ  Absorption prob. of s-d

99%-guarantee lifetime:
 L99= Time at which Absorption probability exceed 0.01 for a
single s-d pair
17
Optimal Capacity Expansion with Budgetary Constraint >

Need to Maximize the guaranteed lifetime, for the given
budget
Variation of L99 with
capacity for a single s-d pair
Convex
log10(L99) with capacity
Concave
18
Optimal Capacity Expansion with Budgetary Constraint >

Simple modification: make the problem linear:
 Non-linear function to Piecewise linear function
Log10(Life Expectancy)
Utility Function ( Usd)
gx+1(xsd)
gx(xsd)
gx-1(xsd)
x–1
x

g1  x sd  ;0  x  1

sd

g
x
;1  x  2



2
sd
sd
U sd  0 , ,  x   


sd
g
x

 ; xmax  1  x  
x
 max
x + 1 Capacity allocated (xsd)
19
Optimal Capacity Expansion with Budgetary Constraint >

Objective: Maximize the utility
 
maximize min Usdsd  0, ,  x sd 
sdD


E
Constraints:
 Total cost must be below budget
Q w
e 1
e
e
B
 At least the demand prediction at time T must be satisfied
xsd  dsd ,
 Conservation of existing traffic
 Other constraints


wp  vp ,
Multiple paths are considered for an s-d pair
Tools used: CPLEX, Matlab, C# Express Edition, Excel
B : Available Budget
v p : Existing lightpaths on path p
d sd : Demand for s-d pair sd
we : Lightpath allocation for link e
Qe : Cost for an additional lightpath on link e
w p : Lightpath allocation for path p
sd
U sd  0 , , : Utility function for s-d pair sd
x sd : Lightpath allocation for s-d pair sd
 s, d   D
p  P
20
Optimal Capacity Expansion with Budgetary Constraint >
Used to compare with the results of optimization
Only shortest paths are considered
Demand based Capacity Allocation (DeCA)


1.



An instinctive solution to the problem
Excess capacities are allocated to s-d pairs based on demand
Until budget is fully used
Minimum Utility based Capacity Allocation (MUCA)
2.


Step by step allocation
Each step, capacity allocated to s-d pair with minimum utility
21
Optimal Capacity Expansion with Budgetary Constraint >
To validate and compare optimization and heuristic
algorithms
1. 99%-guarantee lifetime of resulting network



Optimization: Objective function gives the lifetime
Heuristics: Explicitly calculated
Simulation
2.


Simulate the arrival and termination process for all s-d
pairs
Find out lifetimes of all s-d pairs in every trial
Omean 
sd
mean  number of times LTrial
isbelow L
sdS
NTrials

 100%
22
Optimal Capacity Expansion with Budgetary Constraint >
(s,d)
Source Node
1
2
3
4
5
6
7
8
9
10
1
1
4
4
5
8
10
11
14
15
Destination
Node
9
17
17
18
11
19
14
15
18
20
Initial Arrival
Rate
3
4
4
2
2
4
1
3
3
4
Paths
(2-shortest link disjoint paths)
1-11-9, 1-2-4-6-8-9
1-11-13-14-17, 1-3-5-7-10-19-17
4-5-7-10-19-17, 4-6-8-12-18-17
4-6-8-12-18, 4-5-7-10-19-17-18
5-3-1-11, 5-7-10-9-11
8-10-19, 8-12-18-17-19
10-19-17-14, 10-8-12-15-14
11-13-14-15, 11-9-8-12-15
14-17-18, 14-15-18
15-20,15-18-17-19-20
Table of Parameters
20
16
ARPANET
1
Planning Horizon, T
2 year
Pth
0.01
Termination rate, μ
1 per year
Traffic Growth param. , τ
2 year
Cost of 1 wavelength
1 unit
19
2
3
13
11
9
4
14
5
7
17
10
15
18
12
6
8
Min Budget = 287
23
Optimal Capacity Expansion with Budgetary Constraint >

99%-Guarantee Lifetime


because most cases use only
the shortest paths
 Other path uses too much
resources


Extra guaranteed lifetime gained by using MiLECA instead of DeCA
Best Solution: Optimal with
2 paths
Not too different from 1
path case.
MUCA is as best as optimal
with 1 path
Instinctive solution, not
suitable (DeCA)
24
Optimal Capacity Expansion with Budgetary Constraint >


Within 1% at all values of budget
Approach is accurate
25
Optimal Capacity Expansion with Budgetary Constraint >
99% Guaranteed lifetime: A direct representation of
the objective
 No significant advantage of using multiple linkdisjoint paths
 MUCA can replace optimization for 1 path case
 Opens up a lot of possibilities..

26

Spin-off Project:
 With the Electricity Generating Authority of
Thailand (EGAT) :
 “Development of Optimization Algorithm and
Program for Dimensioning and Expansion of
WDM Optical Fiber Networks”
27

My advisor
 Dr. Poompat Saengudomlert

Examination committee members
 Assoc. Prof. Tapio Erke
 Dr. R.M.A.P.Rajatheva
Scholarship donors
 My friends at AIT
 My family back home

28