1. scheduling for local-area networks”
CS244
Packet Switch Design
Tom Anderson et al.
“High-speed switch
scheduling for local-area networks”
Sachin Katti

2. Context Tom Anderson, Professor of CS, University of Washington
Susan Owicki,
Susan: Was on Stanford CS faculty. Went to DEC SRC (where this work was done). Now a Family Therapist in Palo Alto.

3. Throughput 1 1 l 1 1 Q: If l < 1 what happens to the queue? l/2 l/2
If the packets are all the same length, then at most one complete packet buffered at a time (plus one being drained).
If packets are of different length, then how much (max) data can be in the queue at a time? (Ans: 1 max packet being drained, plus 1 max packet waiting = 2 max packets)
The second queue shows that if two packets arrive at the same time, or if there is a collision of several packets for a while, then the queue will build up. In a switch, there are N such inputs. 1
l/2 1
l/2
Q: If l < 1 what happens to the queue?

4. Output Queued Packet Switch
Lookup
Address
Update
Header
Forwarding
Table
Data H
Queue
Packet
Buffer
Memory
Lookup
Address
Update
Header
Forwarding
Table
Data H
Lookup
Address
Update
Header
Forwarding
Table
Data H

5. Input Queued Packet Switch
Lookup
Address
Update
Header
Forwarding
Table
Queue
Packet
Buffer
Memory
Data H
Data H
Lookup
Address
Update
Header
Forwarding
Table
Queue
Packet
Buffer
Memory
Data H
Lookup
Address
Update
Header
Forwarding
Table
Queue
Packet
Buffer
Memory

6. Head of Line Blocking

7. Virtual Output Queues

8. Output Queued Packet Switch
The best that any queueing system can achieve. 8

9. Properties of OQ switches
They are “work conserving”.
Throughput is maximized.
Expected delay is minimized.
We can control packet delay.
Broadly speaking: When possible, use an OQ design.

10. Input Queued Packet Switch Head of Line Blocking
OQ Switch 10

11. Input Queued Packet Switch With Virtual Output Queues
VOQs
OQ Switch

12. Properties of OQ switches
They are “work conserving”.
Throughput is maximized.
Expected delay is minimized.
We can control packet delay.
Broadly speaking: When possible, use an OQ design.

13. Practical Goal Problem: Memory bandwidth
Therefore: Try to approximate OQ.
In this paper, we are just looking at those switches that attempt to match “Property 2: Maximize throughput”

14. Questions What is a virtual output queue (VOQ)? How does a VOQ help?
What does the scheduler/arbiter do?

15. Parallel Iterative Matching1 2 3 4 #1 #2
Iteration:
uar selection
uar selection 1 2 3 4 1 2 3 4
Grant 1 2 3 4
Accept
Request 1 2 3 4 1 2 3 4

16. PIM Properties
Guaranteed to find a maximal match in at most N iterations.
Inputs and outputs make decisions independently and in parallel.
In general, will converge to a maximal match in < N iterations.
How many iterations should we run?

17. Parallel Iterative Matching
FIFO
Maximum
Size
Output
Queued
Simulation
16-port switch
Uniform iid traffic

18. Parallel Iterative Matching
PIM with one iteration
FIFO
Maximum
Size
Output
Queued
Simulation
16-port switch
Uniform iid traffic

19. Parallel Iterative Matching
PIM with one iteration
PIM with four iterations
Simulation
16-port switch
Uniform iid traffic

20. Parallel Iterative Matching Number of iterations
Consider the n requests to output j k
Requesting inputs receiving no other grants j
n-k
Requesting inputs receiving other grants

21. Virtual Output Queues l 1

22. Throughput
“Maximize throughput” is equivalent to “queues don’t grow without bound for all non-oversubscribing traffic matrices” i.e. l ≤ 1 for every queue in the system.
Observations:
Burstiness of arrivals does not affect throughput
When traffic is uniform, solution is trivial

23. Uniform traffic
l = 1/3
1 1 1
1/3 1

24. Throughput for uniform traffic
100% throughput is easy for uniform traffic:
Serve every queue at rate 1/N in fixed round-robin schedule
Pick a permutation each time uniformly and at random from all possible N! permutations
Or, from among N round-robin permutations
Wait until all VOQs are non-empty, then pick any algorithm above.

25. With non-uniform traffic
100% throughput is now known to be theoretically possible with:
Input queued switch, with VOQs, and
An arbiter to pick a permutation to maximize the total matching weight (e.g. weight is VOQ occupancy or packet waiting time)
It is practically possible with:
IQ switch, VOQs, all running twice as fast
An arbiter running a maximal match (e.g. PIM)