1. Minimum Complexity Non-blocking Switching
Mario Baldi
Politecnico di Torino
staff.polito.it/mario.baldi
Yoram Ofek Università di Trento
Achille Pattavina Politecnico di Milano

2. Time-Driven Switching
Low routing complexity
No-header processing
Low buffer requirement
Low switching complexity
Architecture and control
Aligned switching
Pre-computed switching fabric configuration
Fabric
Banyan

3. A Potential Problem
Scheduling
resulting in
blocking

4. As connections/flows are set up
time frames are reserved on each link.
Reservation vectors
Scheduling
time cycle
As more connections/flows are setup …

5. … more time frames are reserved
Since nodes forward packets during the time frame following their reception …
… the time frames on a link follow the ones on the upstream link.
… more time frames are reserved
As more connections/flows are setup on different paths…

6. … the reservation vectors grow fuller.

7. … multiple possible schedules may exist.
Still, when setting up a new connection/flow...

8. … even though enough capacity is available on all the links.
However, scheduling may be impossible.
Not possible
Not possible
Blocking
Not possible

9. Simulation Results
1000 TFs
64 TFs
32 TFs
16 TFs
1 TF

10. Turning the Potential Problem into a Major Advantage
Banyan switching fabric N
a {
Minimum complexity: a•N •lgaN

11. Blocking 1 1 2 2 3 3 4 4
But only within the same time frame

12. Conflicts are minimized
The Intuition
Conflicts are minimized
across
multiple time frames

13. Simulation Results

14. Lia’s Theorem v
v: number of vertical replications that ensure the switch to be non-blocking

15. Time-space equivalence
Selecting one out of k TFs in a time-driven switch is equivalent to selecting one out of k vertically replicated switching fabrics
A time-driven switch with a single Banyan fabric is non-blocking up to a load (k-v)/k

16. Ongoing Work Formal Proof Simulation Network of switches
Basic time-space equivalence theorem
Effect of speed-up
Simulation
Validation of analysis
Behavior at higher loads
Network of switches
Analysis