1. COMP/ELEC 429/556 Introduction to Computer Networks
Weighted Fair Queuing
Some slides used with permissions from Edward W. Knightly, T. S. Eugene Ng, Ion Stoica, Hui Zhang
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

2. Critical Features of TCP
Increase rate until packet loss
What’s the problem?
Use loss as indication of congestion
Slow start to probe for initial rate
AIMD mechanism oscillates around proper rate
Relies on AIMD behavior of end hosts
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

3. Some Answers Increase rate until packet loss
Drives network into congestion
High queuing delay, inefficient
Use loss as indication of congestion
Cannot distinguish congestion from packet corruption
Slow start to probe for initial rate
Bad for short lived flows (e.g. most Web transfers, a lot of Internet traffic is web transfer)
AIMD mechanism oscillates around proper rate
Rate is not smooth
Bad for streaming applications (e.g. video)
Inefficient utilization
Relies on AIMD behavior of end hosts for fairness
People can cheat (not use AIMD)
People can open many parallel connections
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

4. Can Routers Provide Bandwidth Guarantee to a Traffic Flow?
If so, then sender can request for a bandwidth guarantee and knows exactly what rate to send at
No packet loss, no congestion
No need for probing bandwidth (slow start)
No AIMD oscillation
No cheating
The answer is yes, but it’ll add complexity to routers
???
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

5. Guaranteeing Performance Requires Flow Isolation
FIFO queue of packets in router memory buffer
flow 1
Classifier
flow 2
Scheduler 1 2
flow n
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

6. Classifier A “flow” is a sequence of packets that are related
Classifier takes a packet and matches it against flow definitions to decide which flow it belongs
Examples:
All TCP packets from Eugene’s web browser on machine A to web server on machine B
All packets from Rice
All packets between Rice and CMU
All UDP packets from Rice ECE department
A flow may be defined by bits in the packet
source/destination IP address (32 bits)
or address prefix
source/destination port number (16 bits)
protocol type (8 bits)
type of service (4 bits)
even bits beyond TCP and IP headers could be used
flow 1
flow 2
flow n
Classifier
Scheduler
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

7. Scheduler Decides how the output link capacity is shared by flows
A chance to be smart: Transmission of packets held in queues can be *scheduled*
Which stored packet goes out next? Which is more “important”?
Impacts quality of service
flow 1
flow 2
flow n
Classifier
Scheduler
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

8. What is Weighted Fair Queuing?
Packet queues w1 w2 R wn
A mathematical model for flow scheduling
Each flow i given a weight (importance) wi
WFQ guarantees a minimum service rate to flow i
ri = R * wi / (w1 + w wn)
Implies isolation among flows (one cannot mess up another)
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

9. What is the Intuition? Fluid Flow
water pipes w2 w3
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

10. Fluid Flow System: Example 1
Packet Size (bits)
Packet inter-arrival time (ms)
Arrival Rate (Kbps)
Flow 1
1000 10
100
Flow 2
500 50
Flow 1 (w1 = 1)
100 Kbps
Flow 2 (w2 = 1) 1 2 3 4 5
Flow 1
(arrival traffic)
time
Flow 2
(arrival traffic)
time 1 2 3 4 5 6
Service
in fluid flow
system
time (ms) 10 20 30 40 50 60 70 80 1 2 3 1 2 4 3 5 6
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

11. Fluid Flow System: Example 2
link
Red flow has packets backlogged between time 0 and 10
Backlogged flow  flow’s queue not empty
Other flows have packets continuously backlogged
All packets have the same size
flows
weights 5 1 1 1 1 1 2 4 6 8 10 15
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

12. Service Rate and Packet Delay in Fluid Flow System
WFQ guarantees a minimum service rate to flow i
ri = R * wi / (w1 + w wn)
What worst case delays are experienced by individual packets in the FFS?
Service curve
slope = ri
bits
Worst case
packet delay
Packet arrival curve
time (s)
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

13. Implementation in Packet System
Packet (Real) system: packet transmission cannot be preempted. Why?
Solution: serve packets in the order in which they would have finished being transmitted in the fluid flow system
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

14. Packet System: Example 1
Assume for this example all packets are waiting from time 0
Service
in fluid flow
system 2 4 6 8 10
Select the packet that is waiting and finishes first in the fluid flow system
Packet
system 2 4 6 8 10
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

15. Packet System: Example 21 2 3 4 5
Flow 1
(arrival traffic)
time
Flow 2
(arrival traffic)
time 1 2 3 4 5 6
Service
in fluid flow
system 1 2 3 1 2 4 3 1 4 3 5 4 3
 5 5 6 5
time (ms)
Select the packet that is waiting and finishes first in the fluid flow system
Packet
system 1 2 1 3 2 3 4 4 5 5 6
time
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

16. Implementation Challenge
Four flows, each with weight 1
Flow 1
time
Flow 2
time
Flow 3
time
Flow 4
time ε 1 2 3
Finish times computed at time 0
time
time
Finish times re-computed at time ε
Note that finishing order of packets
from flows 1, 2, and 3 unaffected 1 2 3 4
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

17. Implementation Challenge
Need to compute the finish time of a packet in the fluid flow system…
… but the finish time may change as new flows arrive!
Need to update the finish times of all packets that are in service in the fluid flow system when a new flow arrives
But this is very expensive; a high speed router may need to handle hundred of thousands of flows!
The new finish times don’t affect ordering of packets that are in service in the fluid flow system (a lot of work for nothing)
Can we capture ordering without using real world finish times??
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

18. Bit-by-Bit Round Robin Insight
If flows can be served one bit at a time, the fluid flow system can be approximated by bit-by-bit weighted round robin
During each round from each flow that has data to send, send a number of bits equal to the flow’s weight
Each packet therefore requires a fixed number of rounds to finish (depends only on weight and packet size); the finishing round number does not change even when new flows arrive
Packet queues
30 bits 3
100 bits/sec
How many seconds spent
in each round?
Note the answer depends on
the total weights 5
20 bits
34 bits 17
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

19. Solution: Virtual Time
Solution: instead of the packet finish time, maintain the round # when a packet finishes (virtual finishing time)
Virtual finishing time doesn’t change when a new flow arrives
Packet ordering based on virtual finishing time is the same as that based on real finishing time.
Need to compute system virtual time function V(t)
index of the round in the bit-by-bit round robin scheme at time t
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

20. Example All flow weight = 1
time
Flow 2
time
Flow 3
time
Flow 4
time ε
All flow weight = 1
Suppose each packet is 1000 bits, so takes 1000 rounds to finish. So, first packets of F1, F2, F3 finish at virtual time 1000
When packet F4 arrives at virtual time 1 (after one round), the virtual finish time of packet F4 is 1001
But the virtual finish time of packet F1,2,3 remains 1000
Finishing order is preserved
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

21. Computing System Virtual Time (Round #): V(t)
V(t) increases inversely proportionally to the sum of the weights of the backlogged flows
Since round # increases slower when there are more flows to visit each round.
Flow 1 (w1 = 1)
time
Flow 2 (w2 = 1)
time 3 4 5 1 2 1 2 3 4 5 6
V(t)
C/2 C
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

22. Weighted Fair Queuing Implementation
Define
virtual finishing time of packet k of flow i
arrival time of packet k of flow i
length of packet k of flow i
wi weight of flow i
The virtual finishing time of packet k+1 of flow i is
Smallest virtual finishing time first scheduling policy
/ wi
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

23. Recall in the Fluid Flow System
Service curve
slope = ri
bits
Worst case
packet delay
Packet arrival curve
time (s)
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

24. Properties of WFQ Implementation
Theorem: WFQ guarantees that any packet is finished within max_packet_length/link_rate of its finish time in the fluid flow system
Thus WFQ can guarantee bandwidth and delay
Weights assigned appropriately and admission control is performed
Packets paced by sender according to guaranteed bandwidth
Another way to use WFQ is to assign all flows the same weight and perform no admission control
Every flow gets a “max-min” fair share, provides performance isolation among flows
See proof at the end of the slide deck
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

25. Internet Today FIFO queues are used for most network traffic
No classifier, no scheduler, best-effort
Sophisticated mechanisms tend to be more common near the “edge” of the network
E.g. At campus routers
Use classifier to pick out BitTorrent packets
Use scheduler to limit bandwidth consumed by BitTorrent traffic
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

26. Remainder of this set of slides are for your reference only
Remainder of this set of slides are for your reference only. They will not be needed for assignments.
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

27. Proof (1) Packet pk with length Lk Subscript: index of pkt sent
in pkt system
Fluid Flow System
Behavior
uk: finish
ak: arrival
time
Packet System
Behavior
tk: finish
ak: arrival
time
Want to prove:
Lmax: largest allowed pkt
r: network link rate
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

28. Proof (2)
Let m be the largest packet index such that um > uk but tm < tk
More generally, we have um > uk ≥ ui and tm < ti < tk
Fluid Flow System
Behavior
... ui uk um
time
Packet System
Behavior
... ti tm tk
time
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

29. Proof (3) tm tk ti pm started transmission at Thus Q.E.D.
Packet System
Behavior
... ti tm tk
time
pm started transmission at
Thus
Q.E.D.
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University

30. Another Insight
Recall m is the largest packet index such that um > uk but tm < tk
If no such pm exists, then simply tk ≤ uk
That is, the packet system can be ahead of the fluid flow system by an unbounded amount 2 10 4 6 8
Service
in fluid flow
system
Packet
T. S. Eugene Ng eugeneng at cs.rice.edu Rice University