Packet Scheduling:
SCFQ, STFQ, WF2Q
Yongho Seok
Contents
• Review: GPS, PGPS
• SCFQ( Self-clocked fair queuing )
• STFQ( Start time fair queuing )
• WF2Q( Worst-case fair weighted fair queuing )
• Conclusion
GPS
• An idealized policy that can split bandwidth
among multiple sessions simultaneously
– Each session I has a queue and a weight  i
– At time t, GPS serves all non-empty queues
simultaneously in proportion to
ri (t ) 
i

jB ( t )
– Property
j
GPS(Cont’)
• Observation :
– Guaranteed service rate for session j whenever it
becomes backlogged
• Another View
– Weighted round robin with infinitely small service amount
PGPS
• Intuition
– Compute the time a packet would complete service had
we been serving packets with a GPS server, then serve
packets in order of these finishing times
– emulates GPS “on the side” and uses the results of this
simulation to determine service order
• Three virtual times
– Not real time, but time for representing the amount of
service
– Virtual Star time, Virtual Finish time : each flow
– Virtual System time : system-wide time
PGPS(Cont’)
Virtual Start Time
Si (t )  max{V (t ), Fi 1 (t )}
Virtual Finish Time
Fi (t )  Si (t ) 
Li
k
i
Virtual Time Implementation of WFQ
V (0)  0
V (t j 1   )  V (t j 1 ) 
C

iB j
i
  t j  t j 1 , j  2,3,...
PGPS(Cont’)
Si (t1 , t2 )
i
S k (t1 , t2 )
k
S j (t1 , t2 )
j



ri (t )  (t2  t1 )
i
k
k

jB ( t )
rk (t )  (t2  t1 )
S k (t1 , t2 )

j
jB ( t )
C


jB ( t )

i  C
ri (t ) 
 j
C
j
C

jB ( t )
j
If C=1 and Si (t1 , t 2 )  Lki , then
This packet finish service after virtual time
Lki
i
WFQ : Scheduling Example
• Situation
– Three sessions : A, B, and C
– Time 0 : packets of size 1(A), 2(B), and 2(C) arrives
– Time 4 : a packet of size 2(A) arrives
• Assumption
– Weight are all same
– Link Capacity C = 1
Result comparison(GPS, WFQ)
GPS
0
3
5.5 6
4
7
WFQ
0
1
3
5
7
A
B,C
V(t)
3.5
3
Virtual Time
2.5
2
1.5
1
F(0) = Max(0,0) + 2
=2
F(0) = Max(0,0) + 1
=1
0.5
0
Slope = C / weighted sum of backlogged flows = 1/3
1
2
3
4
5
6
Real Time(At time 0)
7
8
A
B,C
V(t)
3.5
3
Virtual Time
2.5
2
1.5
1
Flow A is unbacklogged in WFQ at time 1
Flow A is unbacklogged in GPS at time 3
0.5
0
1
2
3
4
5
6
Real Time(AT time 3)
7
8
2nd packet of size 2 arrives
3.5
A
B,C
V(t)
F(4) = Max(1.5,1) + 2
= 3.5
3
Virtual Time
2.5
2
1.5
Slope = 1/2
1
0.5
0
1
2
3
4
5
6
Real Time(At time 4)
7
8
A
B,C
V(t)
3.5
3
Virtual Time
2.5
Flow B or C
is unbacklogged in GPS at time 5.5
2
Slope = 1/3
1.5
1
0.5
0
1
2
3
4
5
6
Real Time(At time 5.5)
7
8
A
B,C
V(t)
3.5
3
Virtual Time
Slope = 1
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
Real Time(At time 7)
7
8
Fairness of WFQ
• The difference between GPS and WFQ
• Cannot fall behind GPS by one packet
• One Packet difference means
• Problem
– Cannot fall behind GPS by one packet, however, can fall
ahead GPS by infinite amount
– Motivation of WF2Q
Self-Clocked Fair Queuing (SCFQ)
• Same as WFQ except
Si (t )  max{CF, Fi 1 (t  )}
k
Li
Fi (t )  Si (t ) 
i
• CF : the virtual finish time of the packet currently
in service
• Easier to implement than WFQ
Relative Fairness & Absolute Fairness
• The service rate allocated to connection I at the
kth switch on its path from source to its
destination g (i, k )   (i, k )r (k )
 ( j, k )
• Relative Fairness
RFB |
S (i, , t ) S ( j,  , t )

|
g (i )
g ( j)
• Absolute Fairness
AFB |
S (i, , t ) G ( j,  , t )

|
g (i )
g (i )
Fairness of SCFQ
• The author has shown that the relative fairness
bound for SCFQ is
RFB 
Pmax (i ) Pmax ( j )

g (i )
g ( j)
• But, the absolute fairness bounded for SCFQ is
currently unknown
• Although the SCFQ round number update rule is
easy to implement, it can be unfair over short term
scales
Fairness of SCFQ(Cont’)
• Worst-case latency for SCFQ is
Pmax (i )
P
 ( N  1) max
g (i )
r
compared to
Pmax (i ) Pmax

g (i )
r
for WFQ
• STFQ improve a large worst case delay and shortterm unfairness
Start-time Fair Queuing (STFQ)

Same as WFQ except
Si (t )  max{SF, Fi 1 (t  )}
k
Li
Fi (t )  Si (t ) 
i




SF : the virtual start time of the packet currently in
service
Serves the packet having smallest virtual start time
Easier to implement than WFQ
Note
Worst-case Fair Weighted Fair Queuing
(WF2Q)
• Conceptually,
– S(t) : the total amount of service received by flow I
– V(t) : the total amount of service , which would be
received in GPS
• WF2Q algorithm
– WFQ scheduling + eligibility test
– eligible test
V (t )  Si (t )
• Among packets that have started service under GPS, pick
the packet having the smallest virtual finish time
WF2Q : Scheduling Example
Fairness of WF2Q
• Cannot fall behind GPS by one packet, however,
can not fall ahead GPS by one packet
• This means
Conclusion
• WFQ provides fairness and end-to-end delay
bound, but has a heavy implementation
complexity
• SCFQ, STFQ, WF2Q are easy to implement
• Issues
– Delay & bandwidth requirement is coupled
Di 
i
ri
K 1
Pmax,i
k 1
ri ,k

K
Pmax

m1 rm