Download 40. optical networks- adms-basics.pps

1. Optical networks –
basic notions
Optical networks - 1st generation
the fiber serves as a transmission medium
Electronic
switch
Optic
fiber
Optical networks - 2nd generation
Routing in the optical domain
Two complementing technologies:
- Wavelength Division Multiplexing (WDM):
Transmission of data simultaneously at
multiple wavelengths over same fiber
- Optical switches: the output port is
determined according to the input port and
the wavelength
lightpaths
Data in
electronic form
ADM
OADM
Data in
electronic form
lightpaths
p1
Valid coloring
w( p1 )  w( p2 )
p2
OADM (optical add-drop multiplexer)
Optical
switch
lightpath
No two inputs with the same wavelength
should be routed on the same edge.
ADM (electronic add-drop multiplexer)
Electronic device at the endpoints of
lightpaths
Where can we save?
an ADM can be shared by two lightpaths
2 ADMs
1 ADM
1
2
3
1
2
3
Traffic grooming
• low capacity requests can be groomed
into high capacity wavelengths
(colors).
• colors can be assigned such that at
most g lightpaths with the same color
can share an edge
• g is the grooming factor
lightpaths - with grooming
g=2
Valid coloring
Optical networks
ADMs, OADMs, grooming
Graph theoretical model
Coloring and routing
2. Minimize number of ADMs
W=2, ADM=8
12
W=3, ADM=7
minADM
Input: a graph, a set of lightpaths, t>o.
Output: can the lightpath be colored such that
#ADMs ≤ t ?
The problem is easy on a path network
Reminder: coloring of an interval graph
k=4
Go from left to right …
2.1 minADM is NPC for a ring
minADM
Input: a graph, a set of lightpaths, t>o.
Output: can the lightpath be colored such that
#ADMs ≤ t ?
Coloring of a circular arc graph
Coloring of a circular arc graph
Not always possible with max load
Coloring of a circular arc graph
Input: circular arc graph G, k>o.
Output: can the arcs be colored by ≤ k colors?
Coloring of a circular arc graph
Input: circular arc graph G, k>o.
Output: can the arcs be colored with ≤ k colors?
G
minADM
Input: a graph, a set of lightpaths, t>o.
Output: can the lightpath be colored
such that #ADMs ≤ t ?
Given an instance of the circular arc graph
problem, construct an instance H of minADM:
Claim: can color G with ≤ k colors
iff can color H with ≤ k colors
iff can color H with #ADMs ≤ N.
G
H
Claim: can color H with ≤ 3 colors iff
can color H with #ADMs ≤ 13
Assume a
coloring with ≤ 3
colors …
Claim: can color with ≤ 3 colors iff
can color the lightpaths with ≤ 13 ADMs
Assume a
coloring with ≤
13 ADMs …
2.2 three basic observations
A. Structure of a solution
N lightpaths
cycles
chains
#ADMs = N + #chains
Cycles are good, chains are bad
#ADMs = N + #chains
In the approximation algorithms there are
two common techniques for saving ADMs:
Eliminate cycles of lightpaths
Find matchings of lightpaths
N lightpaths
N=13
cost(S) = N + chains=13+6=19
Every path costs 1 ADM –
cost(S) = 2N-savings=26-7=19
Every connection saves 1 ADM –
B. The competitive ratio
N: # of lightpaths
ALG: #ADMs used by algorithm
OPT: #ADMs used by an optimal solution
w/out grooming:
ALG  2N
N  OPT
ALG  2 OPT
w/ grooming:
ALG  2N
N/g  OPT
ALG  2g OPT
C. A basic lemma
Lemma: Assume that a solution ALG saves y ADMs,
and OPT saves x ADMs.
x
1
if y і
then cost(ALG) Ј (2 - )cost(S*).
k
k
x
for example : if y і
then
2
3
cost(S) Ј cost(S*)
2
Optimal solution OPT saves x ADMs
a solution ALG saves y ADMs
yі
x
k
Recall :
cost(ALG) = 2N - y
cost(OPT) = 2N - x
x Ј N Ј cost(OPT)
cost(ALG) - cost(OPT) = x - y Ј x 1
So : cost(ALG) Ј (2 - )cost(OPT)
k
x
1
1
= (1 - )x Ј (1 - )cost(OPT)
k
k
k