Transcript Slide 1

CNP
On Location of POPs in FTTH Networks using
Center of Gravity
Rasmus H. Nielsen
Ph.D. Student
Center for Network Planning (CNP)
Department of Control Engineering
Aalborg University, Denmark
CNP
Overview
•
•
•
•
•
•
•
•
Motivation
• Evolution of broadband services
• Massive investments
Optimization
The facility location problem
• Different norms
Case study area
Results
Other methods
Comparison
Conclusion
CNP
Motivation – evolution of broadband services
•
ICT is becoming increasingly more important in society
•
Commercial companies and public institutions are becoming more and
more dependent on ICT for every day operations.
• Demand for higher bandwidth
• Video conferences, backup, remote storage etc.
• Demand for higher availability
• E-commerce, sensitive data (tele medicine, control applications),
communication with customers or other branches etc.
•
Increasing network usage and increasing expenses related to network
downtime
CNP
Motivation – evolution of broadband services
•
The real driver is the convergence of medias and services, which is already
increasing the demands to the network significantly
CNP
Motivation – massive investments
•
All over the world fiber is being deployed to fulfill the already existing or
expected requirements
•
The last years have given us plenty of new fiber-related acronyms and
terms to remember; FTTH, FTTC, VDSL, PON, Homerun, Triple Play etc.
•
In Asia and USA current telecommunication providers are taking part in
the deployment of new ICT infrastructure
•
In Europe, and in Denmark in particular, the old telephony monopolies are
hesitating to compete their own gold ore – the old copper networks
CNP
Motivation – massive investments
•
New players are entering the broadband market
• Power companies have announced huge investments in fiber networks
to a large part of the Danish households
• Covering 40 % of all households
• 1.3 billion Euros invested
• Medio 2005 – 13,500 homes passed
• Ultimo 2007 – 500,000 homes passed
• With the current expected investments,1 million homes will be passed
•
Large investments –> large possible savings
CNP
Optimization of network deployment
•
Until recently all research within telephony networks were taking place
within the telephony monopolies
• With the deregulation of the telephony markets, many research labs
were closed and the gathered knowledge became confidential
•
The knowledge of network deployment and optimization is limited
•
Many areas to consider:
• Economics
• Services
• Management
• Planning
CNP
Network planning
•
Considered in an application oriented scope – results should be put to
commercial use – the sooner – the better
•
Any demand point (customer) must be served at a service point (POP)
•
The demand points are fixed – unfortunately customers will not move
•
Location of the service point is essential for the cost of lines and to some
extent ducting
CNP
Facility location
•
Problem is well-considered within primarily operational research
•
•
Different variants:
P-median
• Minimize line cost for a fixed number of demand points
Uncapacitated
• Minimize the cost of lines and demand points – find the most optimal
combination
Capacitated
• As the uncapacitated but with an upper limit on the demand served at
each service point
Capacitated with Single Source
• As the capacitated but with each demand point served completely
from a service point
•
•
•
CNP
Facility location – p-median
•
Optimize the location of a number of facilities (service points) in relation
to a number of customers (demand points)
•
Brute force:
n

p 1
n!
p!n  p !
•
The amount of data makes this infeasible.
– n in the order of 10,000 – 100,000
•
Heuristics are needed
CNP
P-median – center of gravity
•
•
A simple first-try
The service point should be located at the center of gravity of the
demand points it services (here: that is closest to it)
•
Norms:
xSP  xDP 2   ySP  yDP 2
• 1. Euclidean distance –
• Cables will not be digged down as straight lines from service
point to demand point
• Computational fast
• 2. Road distance – shortest path (Dijkstra)
• More physical correct
• Computational heavy
CNP
P-median
•
Distance matrix
 d1,1


D


d n ,1

•
di, j
Cost
C  Yi , j  Di , j
j
i
• Connection matrix
d1,m 





d n ,m 
 y1,1


Y 


 yn ,1

yi , j
y1,m 





yn ,m 
Elements are 1 if the demand point
is connected to the service point
and 0 otherwise
CNP
Case Study Area
•
Municipality of Hals
• Area – 191 km2
• Population – 11,500
• Population density
• 60 citizens/km2
• Comparison [citizens/km2]:
• Denmark:
126
• Greece:
84
• Athens:
19,619
CNP
Results
CNP
Other methods for facility location
•
Tested so far:
• Center of gravity
• Very simple – Euclidean distance is very fast
• Space filling curves
• Another approach to density analysis
• Genetic algorithms
• Large potential and many possible extensions
• Lagrangean relaxation
• Well considered – guaranteed convergence
CNP
Lagrangean relaxation
•
Primary problem
m
n
 c x
i 1 j 1
ij ij
subject to
m
x
i 1
ij
1
•
Dual problem
m


cij xij   s j 1   xij 

i 1 j 1
j 1
 i 1 
m
n
n
subject to
m
y
i 1
i
p
m
xij  yi
i 1
yi , xij  (0,1)
 yi  p
xij  yi
yi , xij  (0,1)
CNP
Comparison
p
Center of Gravity
Lagrangean Relaxation with subgradient
optimization
4
2,477,938
2,136,171
-13.79
5
2,125,169
1,910,729
-10.09
6
1,824,115
1,822,845
-0.07
7
1,803,999
1,803,308
-0.04
8
1,840,690
1,823,764
-0.92
9
1,905,779
1,857,729
-1.52
10
1,970,287
1,894,557
-3.84
12
2,091,571
2,025,375
-3.16
14
2,191,479
2,170,971
-0.94
16
2,350,890
2,327,154
-1.01
18
2,523,818
2,487,093
-1.46
20
2,676,287
2,651,743
-0.92
CNP
Conclusion
•
Good potential for significant savings
•
Optimization is needed now – in 10 years it will be too late
• A 5% saving for the complete network is better than a 10% saving for
25% of the network
•
A method was tested and a better method has now been considered,
which verify the results
• Actually not that bad for a first try...
•
Even simple computer-aid easily beats the manual process when
considering larger data sets
CNP
Further Research
•
Best method in sense of optimality and processing time
•
Include more parameters;
• Cost – e.g. ducting
• Market – e.g. penetration rate, demographic groups
•
Test methods on already planned areas – it is more exciting to compare to
something “real”, than just comparing theoretical approaches
•
Integrate in a large framework of network planning optimizations
CNP
Thank you for your attention!