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

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

A Potential Problem Scheduling resulting in blocking

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

… 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…

… the reservation vectors grow fuller.

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

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

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

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

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

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

Simulation Results

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

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

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