the network: mesh
DESCRIPTION
Routing without Flow Control Costas Busch Rensselaer Polytechnic Institute Maurice Herlihy Brown University Roger Wattenhofer Microsoft Research. The network: mesh. Discrete time Bi-directional links At most one packet per link direction. Dynamic Routing:. - PowerPoint PPT PresentationTRANSCRIPT
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Routing without Flow Control
Costas BuschRensselaer Polytechnic Institute
Maurice HerlihyBrown University
Roger WattenhoferMicrosoft Research
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n
n
The network: meshnn
• Discrete time• Bi-directional links• At most one packet per link direction
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Dynamic Routing:Packets are injected continuously
destination
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A new packet can be injected whenthere is a free link:
A link direction is empty
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Most dynamic routing algorithmsuse flow control:
Don’t utilize all the free links
Disadvantage: Network is under-utilized
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Our Routing Algorithm:
•No flow control
•Utilizes all the free links
Advantage: Network is fully-utilized
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Features of our algorithm:• Dynamic
• Hot potato
• Optimal delivery time:
• Injection time guaranty: )(nO
)(nO
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Talk Outline The Algorithm
Time AnalysisStabilityFuture Work
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Hot-Potato Routing:
• Nodes are buffer-less
• Packets are immediately forwarded
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Conflicts
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Conflict
Conflicts
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Deflected
Conflicts
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Packet states:
Running
Excited
Active
Sleeping
Priorities:
high
low
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Sleeping packet
destination
Random destination
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Sleeping packet
Follows a path to destination
destination
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Sleeping packet
becomes Activewithprobability
n1
n
n
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Active packet
Follows a greedy path
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Active packet
Follows a greedy path
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Active packet
A conflict situation
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Conflict
Active packet
A conflict situation
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Deflected
Active packet
A conflict situation
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Deflected
Active packet
A conflict situation
becomes Excitedwithprobability
n
p 1
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Excited packet
Follows a one-bend path
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Excited packet
Follows a one-bend path
becomes Running
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Running packet
Follows a one-bend path
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Talk Outline The Algorithm
Time AnalysisStabilityFuture Work
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Good condition for a column: at most non-sleeping packets with destination in the column
n10
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Expected delivery time for one packet: n
(when the destination column is in good condition)
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Initially a packet is sleeping
In expected time stepsbecomes active
n
We will show: An active packet is delivered in expected time steps nO
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Interrupting a one-bend path
Excited
Time 1
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Interrupting a one-bend path
Running
Time 2
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Interrupting a one-bend path
Running
Excited
Time 2
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Interrupting a one-bend path
Running
Running
Time 3
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Interrupting a one-bend path
Running
Running
Time 4
conflict
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Interrupting a one-bend path
Active
Running
Time 5
deflected
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No interruption probability:
Number of non-sleeping packetswith destinations in same column
mp)1(
Excitement probability
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No interruption probability:
cp m )1(
n1
n
constant
(when the destination column is in good condition)
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Probability of success after a deflection:
n
cp 1
Expected number of deflections until success: n
Expected delivery timefor an active packet: nO
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Talk Outline The Algorithm
Time AnalysisStabilityFuture Work
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Divide time in time periods:
n6t
Examine the condition of a column
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Good condition Bad condition
ne1
ne
nm 10 nm 10
1 time period
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Good condition Bad condition
ne1
ne
nm 10 nne1
nne
nm 10
4n time periods
1 time period
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Good condition Bad condition
ne1
ne
nm 10 nm 10
1 time period
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Proof OutlineIn a time period:
•At most new non-sleeping packets are generated with destinations in the column
n2
•At least non-sleeping packets are delivered (if )
n2nm 8
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Good condition Bad conditionnm 10 nne1
nne
nm 10
4n time periods
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Proof OutlineIn a time period:
•At most new non-sleeping packets are generated with destinations in the column
n2
•At least non-sleeping packets are delivered
n3
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•Most of the time, the columns are in good condition
•Each packet is delivered in expected time
Consequences:
n
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Talk Outline The Algorithm
Time AnalysisStabilityFuture Work
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•Arbitrary network topologies
•De-randomization:Determistic destinationsNo randomized algorithm
• Small number of packets