1. Routing mechanism and algorithm
Instructor: Davide Bertozzi

2. Acknowledgement
The theory about LBDR routing and OSR runtime reconfiguration has been conceived and mainly developed at Universidad Politecnica de Valencia
Prof. Josè Flich
The implementation effort of such ideas in an on-chip setting has been mainly led by University of Ferrara, within a many-year cooperation with Universidad Politecnica de Valencia
Prof. Davide Bertozzi

3. Key distinction Routing Mechanism Routing Algorithm
Source-based routing
Node-table routing
Algorithmic routing
Logic-based distributed routing (LBDR)
Routing Algorithm
xy routing
Segment-based routing
Up*/down*
…..

4. Source routing Source specifies output port for each switch in route
Table lookup of precomputed routes
Routing path field in packet header
Very simple switches
No routing decisions (zero routing delay)
just strip output port off header
Topology independent
Reuse of switches in arbitrary-sized networks
Cannot be made adaptive
Packet overhead
Length of routing path field accounts for worst case number of hops

5. Node-table routing
Routing tables distributed at each switch instead of at the network interface
Appropriate for adaptive routing
Multiple entries for each destination
Look-up table entries just consist of next hop information
Comes at the expense of performance penalty
routing delay at each switch
Scalability is also sacrificed
Tables contain next hop to all destinations in the largest possible network

6. Algorithmic routing
For given topology and routing algorithm, use simple algorithms to compute the route
usually implemented as combinational logic
may require info to process in packet header
specific for a network topology!
sx x sy y
E.g., 2D Torus
Packet header contains signed offset to destination (per dimension)
At each hop, switch +/- to reduce offset in a dimension
When x == 0 and y == 0, then at correct processor =0 =0
Productive direction vector
CAN WE MAKE THIS APPROACH MORE FLEXIBLE?

7. Routing Restrictions
A deterministic routing algorithm without cyclic dependencies among links or buffers can be represented by the set of routing restrictions it imposes
For irregular topologies as well
A routing restriction forbids any packets to use two consecutive channels

8. Configuration bits
With respect to algorithmic routing, let us introduce a few configuration bits (way less than a routing table) to add some flexibility to routing decision logic.
Connectivity bits Cx: port in direction x is connected
Routing bits Rxy: indicate whether taking the x port, it becomes then possible to turn y at the next hop
Important: a switch does not know its routing restrictions!

9. Logic-Based Distributed Routing (LBDR)
LBDR West wants to go north
INPUT WEST
OUTPUT NORTH
ARBITER
NORTH
INPUT EAST
OUTPUT SOUTH
SOUTH
LBDR EAST .
LBDR WEST
An LBDR routing module is placed at each input port
It consists of routing logic + few configuration bits

10. LOGIC-BASED DISTRIBUTED ROUTING (LBDR)
Destination
Switch
(Xcurr,Ycurr)
FORBIDDEN!
LBDR logic:
While (you are not at destination)
1- compute the target quadrant
NORTH-EAST
QUADRANT
2- Take North if at next hop I can turn east
3- Take East if at next hop I can turn north
4- Go East...provided the East port is connected!
Better scalability than routing tables

11. Logic-Based Distributed Routing
Shall I assert a request for the NORTH arbiter? ?
ARBITER
NORTH
Determine the
target quadrant
LBDR WEST
Am I going north (not east nor south)? NO
E.g., you should go north if you want to go to the north-east quadrant and at the next hop (if you choose to go north) it is possible to turn east
Works for shortest-path routing!

12. Logic-Based Distributed Routing
Shall I assert a request for the NORTH arbiter? ?
ARBITER
NORTH
Determine the
target quadrant
LBDR WEST NO NO
Going north-east, and at next hop it is possible to turn East?
E.g., you should go north if you want to go to the north-east quadrant and at the next hop (if you choose to go north) it is possible to turn east
Works for shortest-path routing!

13. Logic-Based Distributed Routing
Shall I assert a request for the NORTH arbiter? ?
ARBITER
NORTH
Determine the
target quadrant
LBDR WEST NO NO
Going north-west, and at the next hop it is possible to turn west? NO
E.g., you should go north if you want to go to the north-east quadrant and at the next hop (if you choose to go north) it is possible to turn east
Works for shortest-path routing!

14. Logic-Based Distributed Routing
Shall I assert a request for the NORTH arbiter? ?
ARBITER
NORTH
Determine the
target quadrant
LBDR WEST NO NO NO
YES NO
Is the North port connected?
Final decision: this packet will NOT go NORTH!
Works for shortest-path routing!

15. Deroute options
When non-minimal paths are required, LBDR does not return any solution (see example below)
Deroutes become necessary
Deroute bits can be hardwired for each input port, in compliance with routing restrictions
Packets entering A (destination: B):
- Coming from South: deroute to West
- Coming from West: deroute to South
Can route up to 80% of irregular (although still connected) topologies derived from a 2D mesh

16. Upper bound on coverage
In B (coming South):
Going to C: should go North
Going to A: should go West
In some cases, the target port would depend on the destination
Since LBDR works in quadrants, it cannot work even with deroutes in these cases!

17. Solution In B (coming South): Going to C: Fork! Going to A: Fork!
By replicating the packet to both directions,
one replica will certainly get to destination.
The other one will be discarded, since it will be requesting an output that does not make sense
Coverage: 100% of evaluated cases
4 more bits to the basic LBDR set indicate which direction to replicate
Subject to deadlock with wormhole switching (implicitely seen so far)
- Requires virtual cut-through to operate safely (deadlock-free)

18. Scalability ...with respect to routing tables
Network size
Network size
Routing area/delay does not increase with network size, but just with switch radix

19. Routing Algorithm What kind of routing algorithm
should we program on top of LBDR
(by setting the routing bits) ?
Routing algorithms can be:
Deterministic: The path is always the same
Ignore path diversity exposed by the topology
Poor load balancing
Easy to implement, easy to make deadlock-free
Adaptive: we can choose among different routing options at each node, based on congestion status of links and faults
Needs: historical link load information, buffer avg occupancy, status of nodes and links,..
Destroys the in-order-delivery property

20. Deadlock occurs due to a cyclic routing dependency
Main issue
Each packet holds a link, and is requesting for the next one, which it is not able to reserve!
Deadlock occurs due to a cyclic routing dependency

21. Routing in a regular topology
xy (or dimension-order) routing:
a deadlock-free shortest path routing which routes packets in the X-dimension first and then in the Y-dimension.
Used for tori and meshes
Destination address expressed as absolute coordinates 00 10 20 01 11 21 02 12 22 03 13 23 03 13 23
For torus, a preferred direction
may have to be selected.
For mesh, the preferred direction
is the only valid direction. 02 12 22 01 11 21 +y 00 10 -x 20

22. Adaptive routing
Multiple routing options available for a source-to-destination pair 03 13 23 03 13 23
Thick lines represent high-traffic links 02 12 22 02 12 22 01 11 21 01 11 21 00 10 20 00 10 20
RISK: To avoid slight congestion
in (01-02), packets then incur
more congested links
Minimal adaptive routing
is unable to avoid congested links
in the absence of minimal path diversity
A locally optimum decision may lead to a globally sub-optimal route
Minimal path diversity makes adaptive routing potentially effective

23. Adaptive routing
Additional path diversity can be provided by fully adaptive routing
Packets may be misrouted to avoid congestion 03 13 23 02 12 22 01 11 21 00 10 20
Pay attention to livelock!

24. Irregular Network Topologies
In general, non-symmetrical NxM switches
An irregular topology is custom-tailored to the communication pattern of the application domain at hand
Key issue: choice of a routing algorithm
xy routing does not work in this context!
Routing paths chosen to balance the load, and to avoid deadlock
Physical convergence is tough
Heterogeneous and asymmetric switches
Links of different lengths

25. Design Flow for application-specific NoCs
Typically, the design of an application-specific NoC starts
with the core graph representation of an application
with annotated average communication requirements vu au
sdr
sr1
sr2
mcp
rst
idct
dsp
ups
bab
risc
190
0.5 60 40
600
173
910 32
670
500