cs/ee 143 communication networks routing misc text: walrand & parakh, 2010 steven low cms, ee,...
TRANSCRIPT
cs/ee 143 Communication Networks
Routing Misc
Text: Walrand & Parakh, 2010
Steven LowCMS, EE, Caltech
Outline
Putting it all together Routing across Internet
LAN, intra-AS, inter-AS Routing across layers 2 and 3
Selfish routing: inefficiency
Dynamic routing: instability
Outline
Putting it all together Routing across Internet
LAN, intra-AS, inter-AS Routing across layers 2 and 3
Selfish routing: inefficiency
Dynamic routing: instability
Transportation network
Transportation Network
Which route to take?
10 f
10 f
f +50
f +50
Local alg: min my own delay xr
* with equal delay on all routes
All delays = 83 equilibrium: delays on all paths equalized
Transportation Network
Which route to take?
Local alg: min my own delay xr
* with equal delay on all routes
All delays = 83
10 f
10 f
f +50
f +50
f+10
Transportation Network
Which route to take?
10 f
10 f
f +50
f +50
f+10
“my delay (81) < 83!”
Local alg: min my own delay xr
* with equal delay on all routes
Transportation Network
Which route to take?
10 f
10 f
f +50
f +50
f+10
All delays = 82, 81,93
Local alg: min my own delay xr
* with equal delay on all routes
not an equilibrium !
Transportation Network
Which route to take?
10 f
10 f
f +50
f +50
f+10
All delays = 92>83!
Braess’s Paradox (1968)
Local alg: min my own delay xr
* with equal delay on all routes
new equilibrium: delays on all paths equalized, and worse!
Transportation Network
Dietrich Braess(German mathematician)
“Major road investments in thecity center [of Stuttgart] failed toyields the benefits expected. They were only obtained when a cross street… was withdrawn from traffic use.”
Murchlan, “Braess’s Paradox of trafficflow”, Transportation Research, 4:391-394, 1970
Transportation Network
Which route to take?
Global objective
onconservati flow s.t.
)( min)(
0
i
xf
ix
dzzDi
r
10 f
10 f
f +50
f +50
f+10
All delays = 92>83! Braess’s Paradox (1968)
not necessarily min!
Local alg: min my own delay xr
* with equal delay on all routes
Global objective
Transportation Network
onconservati flow s.t.
)( min)(
0
i
xf
ix
dzzDi
r
Local algorithm route to smaller delay xr
* with equal delay on all
routes
route to smaller cost xr
* with equal cost on all routes
cost = delay + toll
onconservati flow s.t.
))(()( min xfDxf ii
iixr
network delay
Outline
Putting it all together Routing across Internet
LAN, intra-AS, inter-AS Routing across layers 2 and 3
Selfish routing: inefficiency
Dynamic routing: instability