1. Stratified Round Robin: A Low Complexity Packet Scheduler with Bandwidth Fairness and Bounded Delay Sriram Ramabhadran Joseph Pasquale
Presented by
Sailesh Kumar

2. Outline Packet fair queuing algorithms
Motivation for stratified round robin
Operation
Implementation
Analysis

3. Introduction
Recently a class of service discipline called Packet Fair Queuing (PFQ) has got much attention
PFQ Algorithms approximate the idealized Generalized Processor Sharing (GPS) policy which has two desirable properties
It can guarantee end-to-end delay for a flow in a packet switched network.
It can ensure instantaneous fair allocation of bandwidth among all the backlogged flows
While many PFQ algorithms has been proposed, few can achieve all of the following goals
Support lots of flows with diverse rates
Operate at high speeds (10 Gbps +)
Maintain both a) delay bound, and b) worst case fairness

4. Different classes of scheduling algorithms
Time stamp schedulers
Try to emulate GPS
WFQ
WF2Q
SCFQ …
Good delay bounds
Round robin schedulers
Assign time slots to flows
DRR
W-DRR
BSFQ …
Easy implementation

5. Time stamp schedulers There are three major associated costs
The computation of system virtual time
Normalized fair amount of service, each flow should receive
Management of priority queue to order the packet transmission
It involves sorting across all active flows
Management of another priority queue to regulate the packets
It can be thought of as the set of eligible flows
Computation of system virtual time may be complex
WFQ, WF2Q - O(N) complexity
SCFQ, WF2Q+ – O(1) complexity
Several other algorithms with O(logN), … complexities
Priority queues are almost always O(logN)

6. Round robin schedulers
Eliminates sorting/priority queues
DRR
Assigns a quantum to each queue and services the in a round robin fashion
W-DRR
Assigns different quantum to each flow but services them sequentially
Easy implementation
Poor delay bounds
Bursty output

7. Stratified round robin, Introduction
Uses best of both worlds
Round robin - Poor delay bound results from flows with high rate disparity
Deadline based – Hard to implement due to large number of flows, O(logN) can be prohibitive
SRR groups flows with similar rates into classes such that there are few classes, say n (<< N)
Use deadline based selection across groups, O(log n)
And round robin based selections within groups, O(1)
Total complexity O(log n)

8. Stratified round robin
Let there are N backlogged flows f1, f2, , fN that share an output link of bandwidth R.
Flow fi has a reserved bandwidth of ri such that
Sigma_ri (i = 1 to N) < R
Lets call the weight of ith flow as wi = ri/R
Thus, Sigma_wi (i = 1 to N) < 1
Flows are grouped into classes based on their weights
Flow class Fk is defined as
Fk = {fi : 1/2k ≤ wi < 1/2k-1}

9. SRR (cont) How many classes
Lets say that the minimum rate of a flow is r
Thus, there will be n = (log R/r) different classes
For R = 40 Gbps, and r = 1 bps,
n = 36
A priority queue with n = 36 can be implemented to run in O(1) complexity
We will come to it later

10. SRR (cont)

11. Inter-class scheduling
Time is measured in slots and only one flow can send packets in a slot
tC denotes the current time slot
tC is incremented after each slot
Thus virtual time concept over here is little bit similar to SCFQ
Slots may not be assigned to any flow, in which case tC is just incremented (zero real time)

12. Inter-class scheduling (cont)
Scheduling intervals
Fixed length and contiguous slots associated with a flow class
For class Fk, scheduling interval is always 2k slots
Thus, if a scheduling interval for a class begins at time t, the next will begin at time t+2k
Every flow fi ∈ Fk has a weight of approximately 2−k, Therefore, if slots represent fixed-size units of bandwidth allocation, fi is entitled to exactly one slot every 2k slots.
In fact, Stratified Round Robin does exactly this by trying to assign every flow fi ∈ Fk one slot in each scheduling interval of Fk.

13. Inter-class scheduling (cont)
A flow class Fk is called active if it contains at least one backlogged flow, i.e., Nk > 0.
Let A denote the set of active flow classes.
A backlogged flow fi ∈ Fk is called pending if fi has not been assigned a slot in Fk’s current scheduling interval.
A flow class is called pending if it contains at least one pending flow.
Let P denote the set of pending flow classes.

14. Inter-class scheduling (cont)
Assign every flow fi ∈ Fk exactly one slot in each scheduling interval of Fk.
The end of the current scheduling interval of a flow class is deadline for all backlogged flows belonging to that class.
Thus, the inter-class scheduler selects the flow class Fk with the earliest deadline.
The intra-class scheduler then assigns a flow fi ∈ Fk the current slot.
A flow class Fk ceases to be pending when all flows belonging to Fk is assigned a slot in its current scheduling interval.
Then Fk remains like that until the start of its next scheduling interval, when all flows belonging to Fk become pending again.

15. Inter-class scheduling (cont)
How to advance tC
After servicing a flow in the current time slot
If there are any pending flow classes, tC is incremented by 1
Otherwise, tC is advanced to the earliest time when some flow class becomes pending again

16. Inter-class scheduling (cont)
Weights
w1 = 1/2
w2 = 1/8
w3 = 3/16
w4 = 1/16
w5 = 1/16

17. Inter-class scheduling (cont)
Within a class flows are scheduled in a W-DRR fashion
Each flow is given a credit proportional to its weight
Output is not that bursty because maximum weight disparity within a class in 2

18. Implementation
A simple implementation aligns all the scheduling intervals
Although this may result a little bit unfair service, it makes the implementation extremely trivial
Deadline of class Fk will also be deadline of class Fk’, when k’ < k
Deadlines of various classes
Class Fk+2
Class Fk+1
Class Fk

19. Implementation (Selecting class)
Current tC
To select next class – choose the smallest k such that Fk is pending
Deadlines of various classes
Class FK+2
Class Fk+1
Class Fk
A simple priority encoder operating on the pending status bits of flow classes can be used to choose the class

20. Implementation (Advancing tC)
Current tC
Scheduling intervals starts here for various classes
Class FK+2
Class Fk+1 (First active class)
Class Fk
Advance tC such that at least one class becomes pending
If Fk+1 is the first class that is active then
Add 2k+1 and then reset k LSB bits
Can be implemented with a priority encoder and few gates

21. Analysis Golestani fairness
It essentially requires that the difference between the normalized service received by any two backlogged flows fi and fj, over any time period (t1, t2), be bounded by a small constant
(SRR results). In any time period (t1, t2) during which flows fi and fj are backlogged,
Si(t1, t2)/ri − Sj (t1, t2)/rj ≤ 5LM(1/ri + 1/rj)
Bennet-Zhang fairness
It compares the service received by a single flow fi to the service it would receive in the ideal case, i.e., when fi has exclusive access to an output link of bandwidth ri
(SRR results).
δi < qi/ri + 5LM/ri + 5(N − 1)LM/R

22. Analysis and simulation results
Single packet delay bound
(Single packet delay). For every flow fi, let ∆i be the maximum delay experienced by a packet at the head of fi’s queue. Then
∆i < 12*LM/ri
Independent of the the number of flows
Tighter bounds may be derived
A simple simulation demonstrates that SRR results in similar performance (in terms of avg. delay) as WFQ

23. If (doubts) Then
Ask;
Else
Thank you;
End if;