Post on 02-Oct-2015
description
Croatian Telecomm - TKC Rijeka
DESIGNING OPTICAL ACCESS NETWORKS
USING SIMULATED ANNEALING (SA)
ALGORITHM
Branko Luki
ConTEL 99, 5th International Conference on Telecommunications June 15-17, 1999, Zagreb, Croatia
Croatian Telecomm - TKC Rijeka
TIPICAL ACCESS NETWORK IN RESIDENTIAL AREA
AP 500-1000 subscribers
FP
DP 4-50 sunscribers
CORE NETWORK ACCESS NETWORK
AP:access point - OLT, ADM, XTC
FP: flexible point - first point of branching in double-star topology
DP: distribution point - ONU, or FTTx
Croatian Telecomm - TKC Rijeka
optical fiber
splitter
OLT or adequote node
meanhole
cable conduit
subscriber
PON NETWORK MAPPING ON
CONDUIT NETWORK
overlay PON structure
conduit network
OLT
Croatian Telecomm - TKC Rijeka
SIMULATED ANNEALING (SA)
Annealing the process in which a solid is heated up sufficiently to allow the atoms and molecules to rearange themselves into a stress-free state and then cooled gradually so as to lock the new configuration into place
Simulated annealing a probabilistic technique for solving combinatorial optimisation problems. In simulating annealing (SA), the value of the objective function being minimised is analogous to the energy of the solid; minimising is equivalent to finding the minimum value of the function
Croatian Telecomm - TKC Rijeka
SIMULATED ANNEALING (SA) - continued
SA begins with a random solution and then modifies that solution slightly to create a new potential solution. If the new solution satisfies the constraints and has a lower cost than the existing solution, it is accepted without question. However, if the new solution has a higher cost, than the decision as to whether it will be accepted is made on the basis of a probability that is governed by the current temperature of the system.
Occasionally accepting lower-valued solutions allows the process to break out of potentially sub-optimal local maxima.
SA method is a statistically based optimisation technique and can be presented as Boltzman distribution,
P EZ T
e
E
k TB{ }( )
E
1
Croatian Telecomm - TKC Rijeka
SIMULATED ANNEALING (SA) - continue Metropolis and his coauthors were still in 1953 discussed the problem of annealing simulate the evolution to thermal equilibrium of a solid for a fixed value of the temperature.
This is known as Metropolis algorithm. Kirckpatrick and his coauthors in 1982 i 1983 and Cerny in 1985 were undependently proposed and realized postupak of annealing of solid with Metropolis algorithm for solute combinatorial optimisation problems (TSP travel-salesman problem)
Croatian Telecomm - TKC Rijeka
METROPOLIS ALGORITHM
begin
initial configuration 0, set 0,
initial value of contol parameter T0, set TkT0,
while (stopping criterion is not satisfied) do
begin
while (not yet in equilibrium state) do
begin
new configuration is neighbours configuration of ;
let C() and C() be value of objective function of configurations and ,
if C() < C() then /* step to better solution accept */
accept new configuration ; set C()C(), else /* slowly step to worse solution: possible accept */
calculate probability Prob = e-C( ' )-C( )
T
for new configuration,
generate random number random(0,1),
if random(0,1) Prob then set C()C() endif
end begin
decrease value of control parameter Tk, Tk+1= Tk,
end while
end begin
end while
presents the best solution
end begin
Croatian Telecomm - TKC Rijeka
SIMULATED ANNEALING (SA) ALGORITHM
GENERATE INITIAL
SOLUTION
PERTURBATION
OF CURRENT SOLUTION
TO CREATE NEW SOLUTION
Does the new solution
have a lower cost
then the current one?
On the basis of probability
should the solution be
accepted?
NO
NO
YES YES
ACCEPT
NEW
SOLUTION
Have
the stoping criteria
been met?
YES
NO
ACCEPTED
SOLUTION
ITERATE
Croatian Telecomm - TKC Rijeka
SA - Implementation Considerations
Modelling of the Objective
Function
How can the objective function be represented efficiently, bearing in mind that minimising the generation of infeasible solutions can reduce the optimisation time significantly?
Initialisation What will be the starting point for the optimisation?
Starting value of Control
Parameter (Starting
Temperature)
If the starting value of control parameter is too low, optimisation process will converge too quickly and may produce suboptimal solution.
Cooling Schedule At what rate will the temperature be lowered? If the annealing process is cooled too quickly, potentially undesirable features may be locked into the solution and produce suboptimal result.
Perturbation How will the current solution modified to create the new solution?
Termination What criteria will be used to decide when to terminate the annealing process?
Croatian Telecomm - TKC Rijeka
OPTIMAL LENGTH OF OPTICAL FIBRES OF
PON STRUCTURE DOUBLE-STAR TREE
l = min l + min minopt kk=1
S2S2=1
N(S2)
S2S2=1
N(S2)
l l
OLT
1
2
3
4
.
.
.
K
l1
l2
l3
l4
.
.
.
lK
lKmin
k1
k2
.
.
.
kNs2
p1
.
.
.
pNs1
1
.
.
.
Ns2
1
.
.
Ns1
.
lNs2min lNs1min
lmin = lKmin + lNs2min +
lNs1min
Croatian Telecomm - TKC Rijeka
CIRCUMSTANCES FOR OPTIMISATION PROBLEM OF
PON DOUBLE-STAR TREE TOPOLOGY
the splitters locate in nodes with weigth equal zero (0),
ONUs locate in ending nodes (nodes with degree equal 1, and nodes with weigth
greater than zero,
each ONU links to splitters of second level,
each splitter of second level links to splitters of first level,
each splitter of first level links to root node (central office, head-end),
splitting ratio of solitters is 1:2i, i=1, 2, 3, 4, 5
Croatian Telecomm - TKC Rijeka
RESULTS OF OPTIMISATION PON DOUBLE-STAR TREE TOPOLOGY
Results for real problem with 19 nodes
starting value
of control
parameter
ending value of
control
parameter
decrement
factor
number of
iterations
optimal length of fibers (m)
splitting-ratio of
splitters of
1st level
splitting-ratio of
splitters of
2nd level
execute time
(s)
c0 cf a maxiter minlength s1 s2 t
500 100 0,75 10 1708 1:8 1:8 7 1000 100 0,75 10 1769 1:4 1:8 10
500 100 0,75 50 1729 1:4 1:4 32 1000 100 0,75 50 1675 1:8 1:8 50 3433 687 0,75 50 1410 1:4 1:4 15 4553 911 0,75 50 1649 1:8 1:8 18
60634 4042 0,75 50 1874 1:2 1:8 163 98376 6558 0,75 50 1604 1:4 1:8 165
500 100 0,75 100 1392 1:4 1:4 64 1000 100 0,75 100 1696 1:4 1:8 101 3939 788 0,75 100 1800 1:16 1:16 30 5657 1131 0,75 100 1901 1:4 1:4 34
14427 2885 0,75 100 1718 1:4 1:4 33 24212 4842 0,75 100 1754 1:16 1:16 34 57312 11462 0,75 100 1584 1:4 1:4 33 66864 13373 0,75 100 1719 1:8 1:8 34 12009 801 0,75 100 2107 1:2 1:16 55 3379 225 0,75 100 1677 1:8 1:8 55
42753 2850 0,75 100 1708 1:8 1:32 56 119305 7954 0,75 100 1558 1:4 1:4 57 182480 12165 0,75 100 1925 1:4 1:4 55 407026 21135 0,75 100 1787 1:32 1:32 55 944746 62983 0,75 100 1707 1:16 1:16 56
3240 648 0,75 500 1482 1:4 1:4 145
3926 785 0,75 1000 1601 1:2 1:8 332
Croatian Telecomm - TKC Rijeka
RESULTS OF OPTIMISATION PON DOUBLE-STAR TREE TOPOLOGY
Results for real problem with 119 nodes
starting value
of control
parameter
ending value
of control
parameter
decrement
factor
number of
iterations
optimal length
of fibers
(m)
splitting-ratio
of splitters of
1st level
splitting-ratio
of splitters of
2nd level
execute time
(s)
c0 cf a maxiter minlength s1 s2 t
32396 6479 0,75 5 15397 1:8 116 2181
27676 5537 0,75 5 16490 1:8 1:8 8131
1265 300 0,75 10 16169 1:8 1:8 3485
414285 27619 0,75 10 16732 1:8 1:16 5356
Croatian Telecomm - TKC Rijeka
RESULTS OF APLICATION SIMULATED ANNEALING OPTIMISATION METHOD
ON REAL AREA OF PON DOUBLE-STAR TREE TOPOLOGY
Podruje Podmurvice u Rijeci 119 vorova ukupno
1 vor smjetaj UPS-a 72 vora teine vee od nula (stambene zgrade i mali poslovni prostori) 46 vorova teine jednake nula (kabelski zdenci - mjesta predvidiva za smjetaj djelitelja)
Rijeka, 09.01.1998.
Broj ONU jedinica po objektu (zgradi)
Objekt 1 UPS 960 prikljuaka
Objekt korisnika ONU_256 ONU_128 ONU_64 ONU_32 ONU_12 ONU_4 ONU_2 ukupno ONU jedinica
2 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0
5 173 1 0 0 0 0 0 0 1
6 0 0 0 0 0 0 0 0 0
7 75 0 1 0 0 0 0 0 1
8 173 1 0 0 0 0 0 0 1
9 0 0 0 0 0 0 0 0 0
10 148 1 0 0 0 0 0 0 1
11 48 0 0 1 0 0 0 0 1
12 0 0 0 0 0 0 0 0 0
13 99 0 1 0 0 0 0 0 1 .
.
.
Ukupan broj ONU jedinica na promatranom podruju iznosi --> 72
Croatian Telecomm - TKC Rijeka
Broj djelitelja u ovisnosti o omjeru djeljenja i hijerarhiji djelitelja
Broj djelitelja 1_og reda 18 kom za omjer djeljenja 1: 2
Broj djelitelja 2_og reda 36 kom za omjer djeljenja 1: 2
Broj djelitelja 1_og reda 9 kom za omjer djeljenja 1: 2
Broj djelitelja 2_og reda 18 kom za omjer djeljenja 1: 4
Broj djelitelja 1_og reda 5 kom za omjer djeljenja 1: 2
Broj djelitelja 2_og reda 9 kom za omjer djeljenja 1: 8
Lokacije djelitelja 2_og reda
Djelitelji 2_og reda omjera djeljenja 1: 2
smjeteni su u vorovima 44 75 114 33 90 31 35 78 110 22 65 42 3 3 103 2
65 86 75 42 103 86 22 2 78 65 97 109 48 33 6 67
75 90 44 67
Djelitelji 2_og reda omjera djeljenja 1: 4
smjeteni su u vorovima 50 109 52 22 56 78 110 81 114 110 58 77 21 67 86 37
3 9
Lokacije djelitelja 1_og reda
Djelitelji 1_og reda omjera djeljenja 1: 2 na koje su vezani
djelitelji 2_og reda omjera djeljenja 1: 2
smjeteni su u vorovima 50 100 22 58 117 81 3 48 6 4 4 6 26 102 29 97
109 39
Djelitelji 1_og reda omjera djeljenja 1: 2 na koje su vezani
djelitelji 2_og reda omjera djeljenja 1: 4
smjeteni su u vorovima 97 22 90 25 60 4 114 58 70
Croatian Telecomm - TKC Rijeka
Djelitelji 1_og reda omjera djeljenja 1: 2 na koje su vezani
djelitelji 2_og reda omjera djeljenja 1: 8
smjeteni su u vorovima 60 21 42 65 21
Djelitelji 1_og reda omjera djeljenja 1: 2 na koje su vezani
djelitelji 2_og reda omjera djeljenja 1:16
smjeteni su u vorovima 110 25 63
Djelitelji 1_og reda omjera djeljenja 1: 2 na koje su vezani
djelitelji 2_og reda omjera djeljenja 1:32
smjeteni su u vorovima 114 110
Parametri primjene metode simulated annealing
tstart= 33705. tend= 2247. tfakt= .75 maxit= 50
Vrijeme izvrenja programa iznosi -62160 sekundi
Putevi od pojedine ONU jedinice do nadlenog djelitelja 2_og reda
Djelitelj 2_og reda omjera djeljenja 1: 4 smjeten je u voru 50
4 najkraa puta iz vora 50
28-ti put 51 50 duljina 28_og puta iznosi 15
29-ti put 53 52 50 duljina 29_og puta iznosi 39
30-ti put 54 52 50 duljina 30_og puta iznosi 52
31-ti put 55 52 50 duljina 31_og puta iznosi 60
Duljina odabranih putova iznosi 166 m
Djelitelj 2_og reda omjera djeljenja 1: 4 smjeten je u voru 109
Croatian Telecomm - TKC Rijeka
4 najkraa puta iz vora 109
69-ti put 115 114 109 duljina 69_og puta iznosi 36
70-ti put 116 114 109 duljina 70_og puta iznosi 36
71-ti put 118 117 114 109 duljina 71_og puta iznosi 73
72-ti put 119 117 114 109 duljina 72_og puta iznosi 90
Duljina odabranih putova iznosi 235 m
Putevi od pojedinog djelitelja 2_og reda do nadlenog djelitelja 1_og reda
Djelitelj 1-og reda omjera djeljenja 1: 4 smjeten je u voru 2
4 najkraa puta iz vora 2
14-ti put 67 2 duljina 14_og puta iznosi 15
11-ti put 58 60 63 65 67 2 duljina 11_og puta iznosi 153
12-ti put 77 75 72 70 2 duljina 12_og puta iznosi 158
5-ti put 56 58 60 63 65 67 2 duljina 5_og puta iznosi 178
Duljina odabranih putova iznosi 504 m
Djelitelj 1-og reda omjera djeljenja 1: 4 smjeten je u voru 16
4 najkraa puta iz vora 16
7-ti put 110 102 100 14 16 duljina 7_og puta iznosi 231
10-ti put 110 102 100 14 16 duljina 10_og puta iznosi 231
9-ti put 114 109 102 100 14 16 duljina 9_og puta iznosi 241
12-ti put 77 86 3 9 12 100 14 16 duljina 12_og puta iznosi 260
Duljina odabranih putova iznosi 963 m
Putevi od OLT_a do djelitelja 1_og reda smjetenih u 2 16 86 26 67
put 2 1 duljina puta 25
Croatian Telecomm - TKC Rijeka
put 16 14 100 12 9 3 86 77 75 72 70 2 1 duljina puta 444
put 86 77 75 72 70 2 1 duljina puta 230
put 26 25 22 21 56 58 60 63 65 67 2 1 duljina puta 359
put 67 2 1 duljina puta 40
Ukupna duljina odabranih putova iznosi 1098 m
Sveukupna duljina putova iznosi 17973 m
Pronaena optimalna sveukupna duljina PON strukture je za
omjer djeljenja ks1=1: 4 i ks2=1: 4
minlen(2,2)=17973 m
Croatian Telecomm - TKC Rijeka
Outline of calculated values of randomly choosed configurations
with application of simulated annealing method
Croatian Telecomm - TKC Rijeka
Shematic view
of optimal PON double-star tree in one real area in Rijeka
Croatian Telecomm - TKC Rijeka
Topographic view of
optimal PON double-star tree in some area in Rijeka
Croatian Telecomm - TKC Rijeka
CONCLUSION AND FUTURE WORK
We analyse a PON on double-star topology.
Cost function is full length of all optical fibres.
We use a SA method.
Optimal solution give us: i) a path-ways from root node to each 1-level splitters, from 1st level splitters
to 2nd level splitters, and from 2nd level splitters to end-users; ii) locations of all splitters; iii) splitting ratio for each splitter.
A practicaly result is:
posibility of use for connection plan of fibers between end-users and 2nd level splitters, then 2nd level splitters and 1st level splitters, and 1st level splitters and root node.
Croatian Telecomm - TKC Rijeka
CONCLUSION AND FUTURE WORK
The open problem is:
to make an efectively way to determine starting solution of PON.
We work on problem of influence between PON double-star topology and ring topology, i.e. rearrangement of PON double-star topology into ring topology. About this, is possible redesign of an part of PON, and conection with ring structure, or build a new ring structure on reconstruction of current buildings, build a new bussines buildings in residential area, on demand of great residential buildings for broadband or higher bitrate.
An interesting is discuss about deployment from current solutions based on cupper cable technology (xDSL), to new solutions based on optical fibres technology and architectures (FTTB, FTTH).
Croatian Telecomm - TKC Rijeka
THE END