1. Variations of Weighted Fair Queueing

2. Issues with WFQ
WFQ does not run behind GPS by more than Lmax/C . However, WFQ may run ahead of GPS by a lot
Improvement: Bound the time by which WFQ can run ahead of GPS
 WF2Q, WF2Q+
Implementation overhead of computing virtual time
Improvement: Avoid virtual time computation, while maintaining fairness properties
 SCFQ, SFQ, WF2Q+
Need to maintain a sorted queue (sorted in order of timestamps)
Improvement: Use a round-robin approach
 WRR, DRR (Stratified Round Robin)

3. Weighted Round Robin (WRR)
Parameters:
Li is the average packet size of flow i
ϕi : weight of flow i (ϕi > 0)
One FIFO queue for each flow
Operates in “rounds”, where each queue with a backlog is visited once in a round
Calculate the number of packets to be served in each round:
For each flow i: xi = ϕi / Li
x = mini { xi }
For each flow i: packets_per_roundi = xi / x

4. Weighted Round Robin (WRR)
If all flows are active and packets are equal to the average Li , then the rate allocated to flow i is
WRR is a good approximation of GPS if
All flows are active over long periods of time
Packet sizes are equal to the average size Li
Otherwise, WRR can deviate substantially from the desired fair allocation

5. Deficit Round Robin (DRR)
Can be viewed as
Improvement to WRR without need for average packet size
Approximation of WFQ without need for a sorted queue
One FIFO queue for each flow
Operates in “rounds”, where each queue with a backlog is visited once in a round
Qi : Quantum of flow Maximum number of bytes from flow i that are sent in one round
(Quantum is greater than max. size of flow i packets (Qi > Limax))
DCi : Deficit counter of flow i Credit of flows (in bytes) saved for the next round
Credits 50
100 75 50 50 50 75 50 50 50 75
150 75
Credits 50
100 75
Time 50 50 50 50 25 50 50 25
150 75
Credits 50
100
150 50 50
100 50 50
100
150
150
Drawing from:

6. Deficit Round Robin (DRR)
If queue is empty: Qi=0
Otherwise,
Add quantum Qi to flow i in each round:
DCi = DCi + Qi
Transmit packet with size L from head of queue i and set
DCi = DCi - L
Continue transmitting (and subtracting DCi) until packet size at head of queue i is larger than DCi
Credits 50
100 75 50 50 50 75 50 50 50 75
150 75
Credits 50
100 75
Time 50 50 50 50 25 50 50 25
150 75
Credits 50
100
150 50 50
100 50 50
100
150
150
Drawing from: 6

7. Deficit Round Robin (DRR)
The share of flow i:
The bandwidth guarantee of flow i:
Fairness metric for two backlogged flows i and j in [t1,t2]:

8. Worst-Case Fair Fair Queueing (WF2Q)

9. WFQ and WF2Q … … 12 flows, all packets have size 1, C = 1: Flow 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Flow 1
f1 = 0.5
time
Flow 2
f2 = 0.05
time … …
Flow 11
f11 = 0.05
time
fluid flow
system 20 2 6 4 21

10. WFQ and WF2Q … … … … 12 flows, all packets have size 1, C = 1: Flow 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Flow 1
f1 = 0.5
time
Flow 2
f2 = 0.05
time … …
Flow 11
f11 = 0.05
time
Flow 1
fluid flow
system
Flow 2 … …
Flow 11 20 2 6 4 21

11. WFQ transmission order
WFQ and WF2Q
12 flows, all packets have size 1, C = 1: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Flow 1
f1 = 0.5
time
Flow 2
f2 = 0.05
time … …
Flow 11
f11 = 0.05
time
WFQ transmission order
time 10 20 21

12. Worst-Case Fair Fair Queueing
Issue: While WFQ never falls behind the fluid-flow schedule by more than one packet size, it can run ahead of the fluid-flow schedule by an arbitrary amount.
WF2Q Scheduling:
Only considers packets for transmission that have already started transmission in the fluid-flow system
Of these, it selects the packet with the smallest finishing time (in the fluid-flow system)
WF2Q Properties:
Like WFQ, WF2Q never falls behind the fluid-flow schedule by more than one packet size ( same end-to-end delay bounds as WFQ)
Unlike WFQ, it never runs ahead of the fluid-flow schedule by more than one packet size

13. WFQ and WF2Q … … 12 flows, all packets have size 1, C = 1: Flow 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Flow 1
f1 = 0.5
time
Flow 2
f2 = 0.05
time … …
Flow 11
f11 = 0.05
time
WFQ transmission order
WF2Q transmission order
time 10 20 21

14. WFQ and WF2Q … … 12 flows, all packets have size 1, C = 1: Flow 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Flow 1
f1 = 0.5
time
Flow 2
f2 = 0.05
time … …
Flow 11
f11 = 0.05
time
WFQ transmission order
WF2Q transmission order
time 10 20 21