1. Fair Queueing

2. Fair Queueing
Attempts to implement a scheduler that simultaneously serves all flows with a backlog at the same rate
Not easy to implement Fair Queuing in a packet network
FIFO
Fair Queueing

3. Discussion of Fair Rate Allocation
See class notes

4. Fair Scheduling Algorithms
Fair Queueing (FQ), a.k.a as Processor Sharing (PS)
 Objective: Achieve fair rate allocation
Weighted Fair Queueing (WFQ), a.k.a. Generalized Processor Sharing (GPS)
 Objective: Achieve weighted fair rate allocation
Problem: How to realize a fair rate allocation when
Traffic is transmitted in packet of variable size
Transmission of a packet cannot be interrupted

5. Fair Queuing in packet networks
Approach:
Take a fluid-flow view of traffic
View output link as a “pipe” with a given width
Transmitted traffic flows like a fluid through the pipe
 Scheduler can transmit traffic from multiple flows at the same time
Scheduler controls the “output rate” for each flow
 Output rates are set to satisfy “fairness”
Result is a fluid flow schedule
Approximate fluid-flow schedule by a packet-level scheduling algorithm

6. Fair Queuing (FQ): From fluid to packets
Packet Size (bits)
Packet inter-arrival time (ms)
Rate (Kbps)
Flow 1
1000 10
100
Flow 2
500 50
Flow 1 (f1 = 1)
100 Kbps
Flow 2 (f2 = 1)
Flow 1
(arrival traffic) 1 2 3 4 5
time
Flow 2
(arrival traffic) 1 2 3 4 5 6
time
Service
in fluid flow
system 10 20 30 40 50 60 70 80
time (ms)
Slide from Ion Stoica

7. Fair Queueing (FQ): From fluid to packets (complete)
Packet Size (bits)
Packet inter-arrival time (ms)
Rate (Kbps)
Flow 1
1000 10
100
Flow 2
500 50
Flow 1 (f1 = 1)
100 Kbps
Flow 2 (f2 = 1)
Flow 1
(arrival traffic) 1 2 3 4 5
time
Flow 2
(arrival traffic) 1 2 3 4 5 6
time 1 2 3 4 5 6
Service
in fluid flow
system
time (ms) 10 20 30 40 50 60 70 80

8. Fair Scheduling (fluid flow)
5000
5000
Flow 1
Flow 2
4000
4000
3000
3000
2000
2000
1000
1000 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80

9. Fair Scheduling (fluid flow)
5000
5000
Flow 1
Flow 2
4000
4000
3000
3000
2000
2000
1000
1000 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80

10. Fair Scheduling (FQ) (fluid flow view)
There are N flows
At any time t, all backlogged flows are served at the same rate of:
where B(t) is the set of backlogged flows at time t
C is the capacity of the link
The total rate guarantee to a flow j is:

11. Weighted Fair Scheduling (WFQ) (fluid flow view)
There are N flows with weights f1 , f2 , …,fN
The service given to two backlogged flows is proportional to their weights
At any time t , the rate allocated to a backlogged flow i is:
where B(t) is the set of backlogged flows at time t
C is the capacity of the link
The total rate guarantee to a flow is:

12. FQ/WFQ Scheduling for Packets (packet-level view)
Packet-level implementation of FQ and WFQ tries to emulate the fluid-flow version
Scheduling decision: Always select the packet that will finish next in the ideal fluid-flow FQ/WFQ system

13. WFQ scheduling (with place holder)
Packet Size (bits)
Packet inter-arrival time (ms)
Rate (Kbps)
Flow 1
1000 10
100
Flow 2
500 50
Flow 1 (f1 = 1)
100 Kbps
Flow 2 (f2 = 1)
Flow 1
(arrival traffic) 1 2 3 4 5
time
Flow 2
(arrival traffic) 1 2 3 4 5 6
time 1 2 3 4 5 6
Service
in fluid flow
system
time (ms) 10 20 30 40 50 60 70 80
Service
in packet
system 10 20 30 40 50 60 70 80
time (ms)

14. WFQ scheduling (complete)
Packet Size (bits)
Packet inter-arrival time (ms)
Rate (Kbps)
Flow 1
1000 10
100
Flow 2
500 50
Flow 1 (f1 = 1)
100 Kbps
Flow 2 (f2 = 1)
Flow 1
(arrival traffic) 1 2 3 4 5
time
Flow 2
(arrival traffic) 1 2 3 4 5 6
time 1 2 3 4 5 6
Service
in fluid flow
system
time (ms) 10 20 30 40 50 60 70 80
Service
in packet
system 1 2 1 3 2 3 4 4 5 5 6 10 20 30 40 50 60 70 80
time (ms)
Slide from Ion Stoica

15. Packet-level Implementation of WFQ
Problems to deal with:
The finishing time of a packet in the fluid-flow system may depend on arrivals after a packet has been selected packet-level version of WFQ cannot be 100% accurate
Once started, packet transmission cannot be preemtped
Implementation:
When a packet arrives, it is assigned a “virtual finishing time”
This is the finishing time in the fluid flow system if the set of backlogged flows does not change after packet arrival
Orders packets in increasing order of virtual finishing times
Compute virtual finishing time with the help of a system virtual time

16. Rate of system virtual time
B(t) : the set of backlogged flows at time t
The rate allocated to a backlogged flow i at time t is or
: service that a backlogged flow with weight 1 receives in GPS
Rate of
Rate of system virtual time

17. WFQ: System Virtual Time
WFQ uses a System Virtual Time which tracks the progress of GPS system
Suppose the times when the set B(t) changes are
Let Bl be the set of backlogged flows in time interval
Then we have
When fewer flows are active, virtual time moves faster

18. WFQ: Implementation Virtual finish time of k-th packet from flow j
ajk is the arrival time and Lkj is thesize of the k-th packet from flow j
Packets are sorted and transmitted in the order of virtual finishing times
Virtual time needs to be computed only at arrival time of packets
must keep track of the busy set Bl

19. WFQ Example (packet level)
Flow 1
(arrival traffic) 1 2 3 4 5
time
Flow 2
(arrival traffic) 1 2 3 4 5 6
time
5000
Virtual time V(t)
4000
Time t 10 20 30 40 50 60 70 80
V(t) (x 100)
Fn1 (x 100)
Fn2 (x 100)
3000
2000
actual transmission order 1 2 1 3 2 3 4 4 5 5 6
1000 10 20 30 40 50 60 70 80
time t
time (ms) 10 20 30 40 50 60 70 80

20. WFQ Example (packet level)
Flow 1
(arrival traffic) 1 2 3 4 5
time
Flow 2
(arrival traffic) 1 2 3 4 5 6
time
5000
Virtual time V(t)
4000
Time t 10 20 30 40 50 60 70 80
V(t) (x 100) 25 35 45
Fn1 (x 100)
Fn2 (x 100)
3000
2000
actual transmission order 1 2 1 3 2 3 4 4 5 5 6
1000 10 20 30 40 50 60 70 80
time t
time (ms) 10 20 30 40 50 60 70 80

21. Worst-Case Fair Fair Queueing (WF2Q)

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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