BSFQ: Bin Sort Fair Queueing

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BSFQ Bin Sort Fair Queueing

• Shun Y. Cheung and Corneliu S. Pencea
• IEEE INFOCOM 2002

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Abstract

• Existing packet schedulers that provide fair
  sharing of an output link can be divided into two
  classes
• Sorted priority methods excellent approximation
  for Weighted Fair Queueing (WFQ)
• Frame-based methods more computationally
  efficient.
• Bin Sort Fair Queueing (BSFQ) combines the
  strengths of both type of schedulers.

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I. Introduction

• Quality of service provisioning to flows is
  realized by insulating the flows from one
  another.
• Fluid Fair Queueing (FFQ)
• Ideal one to ensure fairness
• Data of active flows are transmitted one bit at a
  time in a round robin fashion.
• Not practical
• Packets must be transmitted in their entirety.
• WFQ (Weighted Fair Queueing) WF2Q (Worst-case
  Fair Weighted Fair Queueing)
• Most accurately approximation of FFQ.
• Computationally expensive

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• Other more efficient scheduling techniques
• (1) Priority-based schemes
• Packets are assigned a priority value (some
  function of their departure time).
• Packets are transmitted in increasing order of
  their priority values.
• ? Fairness guarantee
• ? Some sort procedure is used to maintain a
  priority queue and have non-constant per packet
  run time complexities.
• VC (Virtual Clock)
• LFVC (Leap Forward Virtual Clock)
• SCFQ (Self-Clocked Fair Queueing)

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• (2) Frame-based schemes
• Packets are transmitted in rounds.
• ? They do not use sort operations and have
  constant per packet processing time.
• ? The delay guarantee they provide have a larger
  bound than sorted-priority methods.
• DRR (Deficit Round Robin)
• URR (Uniform Round Robin)

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II. Related Work

• FFQ (Fluid Fair Queueing) GPS (General Processor
  Sharing)
• Ideal
• Bit-wise scheduling
• Not practical
• Packets must be transmitted as an atomic unit.
• PFQ (Packet-by-packet Fair Queueing)
• Practical
• Packet-wise scheduling
• To approximate FFQ
• Examples
• WFQ (Weighted Fair Queueing) and WF2Q
  (Worst-case Fair Weighted Fair Queueing)

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• A flow is backlogged if it has some packets in
  the output buffer.
• A packet scheduling method is fair if the
  difference in the normalized service provided to
  any two flows that are continuously backlogged
  over any interval is bounded by some constant
• The normalized service wf(t1,t2) received by flow
  f is defined as
• wf(t1, t2) is the amount of data of flow f
  transmitted in t1, t2
• rf is the reserved data rate of f.

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• If a scheduling discipline is fair then there is
  a constant e such that wf(t1,t2) wg(t1,t2)?
  e,for any two flows f and g that are backlogged
  during the interval t1,t2.
• For FFQ, wf(t1,t2) wg(t1,t2) 0.
• WFQ and WF2Q approximate FFQ

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• WFQ and WF2Q
• Compute the virtual finish time of a packet
• Transmit the packets in ascending order.
• WFQ does so for every packet.
• WF2Q only considers those packets that would have
  started receiving service. (Head-of-line)
• The most accurate approximation of FFQ
• Less computationally efficient

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• Virtual Clock (VC) method
• Assign the jth packet pjf of flow f with the
  virtual time stamp (vts)
• for j gt 0, where
• A(pjf) arrival time of packet pjf
• ljf length of packet pjf
• vtsVC(p0f) 0
• vtsVC(pjf) estimated finish time of packet pjf

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• VC provides delay guarantee.
• Xie and Lam showed that if the sum of the rate of
  all flows sharing a link does not exceed the link
  capacity, the departure time L(pjf) of packet pjf
  is bounded by where
• lfmax is the maximum packet length of flow f
• R is the data rate of the output link.
• vtsVC(pjf) estimated finish timeL(pjf) real
  finish time
• VC does not provide fairness guarantee.

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• Leap Forward Virtual Clock (LFVC)
• LFVC temporarily moves oversubscribed flows into
  a low priority holding area.
• Only flows in the high priority area will receive
  service.
• A flow is oversubscribed if the difference
  between the virtual time stamp of the current
  packet and the system time exceeds a certain
  threshold.
• When all flows are oversubscribed, the system
  clock is advanced forward to allow some flows to
  be moved into high priority area.

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• Self-Clocked Fair Queueing (SCFQ)
• A virtual system clock t(t) equals to the virtual
  time stamp of the packet that is being serviced
  at time t.
• The jth packet pjf of flow f is assigned with the
  virtual time stamp (vts)

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• Deficit Round Robin (DRR)
• Packets of different flows are placed in separate
  queues.
• Each flow is assigned a quantum size.
• Each flow has a deficit counter that measures the
  current unused portion of the allocated
  bandwidth.
• Packets are transmitted in rounds.
• In each round, each backlogged flow is
  transmitted up to the sum of its quantum and
  deficit counter.
• The unused portion of this amount is carried over
  to the next round as the deficit counter value.

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• Uniform Round Robin (URR)
• Cell-based method
• Space cell transmission uniformly over a round.
• Example
• Four flows A, B, C, and D, each with quantum
  value of qA 3, qB qC qD 1.
• Transmission order
• For DRR A, A, A, B, C, D
• For URR A, B, A, C, A, D

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III. Bin Sort Fair Queueing

• BSFQ is a frame-based method and uses virtual
  time stamps to determine the scheduling order.
• The virtual time space is divided into equal
  intervals or bins.
• Packets are assigned virtual time stamps and
  inserted into their corresponding bins.
• The queueing order within a bin is FIFO.

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• The output buffer is organized into N bins.
• Each bin is implicitly labeled with a virtual
  time interval and each interval has fixed length
  ?.
• BSFQ maintains a virtual system clock t(t) which
  is equal to the left end point of the virtual
  time interval of the current bin at time t.
• Whenever all packets in the current bin are
  transmitted, t(t) is incremented by ?.? The
  virtual time clock in BSFQ is a non-decreasing
  step function.

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djf ljf / rf ? 5 (Fig.3)
vts(p6)
d6f
bin3
A6ltvts5 ?
vts(p5)
d5f
vts(p4f)
bin2
d4
vts(p3f)
d3f
vts(p2f)
bin1
A5ltvts4 ?
d2f
A4ltvts3 ?
vts(p1f)
d1f
bin0
vts(p0f)
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• Virtual time stamp for pjf
• The index ijf of the bin used to store pjf
• If ijf 0 then pjf is stored in the current
  bin.
• If ijf lt N then pjf is stored in the ijf th
  bin.
• If ijf gt N then pjf is discarded.

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• For BSFQ
• t1A 0 9000/3000 3t2A 3 9000/3000 6t3A
  6 9000/3000 9
• t1B 0 9000/1000 9t2B 9 9000/1000
  18t3B 18 9000/1000 27

• Example
• Flow A and B
• rA 3000 bps and rB 1000 bps
• All packets are 9000 bits in length.
• A large number of packets from both flows arrive
  at the switch simultaneously at t 0.

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• For BSFQ
• t1A 0 9000/3000 3t2A 3 9000/3000 6t3A
  6 9000/3000 9
• t1B 0 9000/1000 9t2B 9 9000/1000
  18t3B 18 9000/1000 27

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• To accommodate non-conformant flows
• those do not make reservations
• Define the residual rate
• Packets from non-conformant flows are assigned a
  time stamp using rres and then scheduled in the
  same manner as other conformant flows

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• A. Delay Guarantee ?
• A packet scheduler is in class GR if the
  departure time L(pjf) of packet pjf is bounded
  byfor some constant ß.
• GRC(pjf) for j gt 0 is defined as
• GRC(p0f) 0.

(3)
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• The end-to-end delay dif of packet pjf that
  traverse a path of K nodes, each using GR
  scheduler, is bounded by
• where GRC1(pjf) GRC(pjf) at node 1,
  A1(pjf) the arrival time of pjf at the first
  node,
• ßn the constant of node n on the path
• dn,n1 propagation delay between nodes n and
  n1

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• If flow f is a leaky bucket compliant flow with
  parameters (sf, ?f), then

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• Lemma 1
• The number of bits of data Dk admitted into k
  consecutive bins is bounded by
• Proof
• ???

?
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• Corollary 1
• The number of bits of data D admitted into
  consecutive bins labeled from t1, t1?) to t2,
  t2?), t1 gt t2, is bounded by
• Proof
• ???

?
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• Theorem 1
• The departure time LBSFQ(pjf) of pjf in BSFQ is
  bounded by
• Proof
• ???

?
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• B. Fairness Guarantee
• Let L(pjf) departure time of packet pjf
• At time t L(pjf), BSFQ is servicing the bin
  with the label t(L(pjf)), t(L(pjf)) ?).
• ?t(L(pjf)) ? vts(pjf)lt t(L(pjf)) ? (8)

v
t
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• Lemma 2
• If flow f is backlogged at time t A(pjf),
  then (8a)
• Proof

?
?
?
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• Theorem 2
• If flows f and g are backlogged during the
  interval t1, t2, then
• (8b)
• Proof
• Let pk1f, pk11f, , pk2f denote the set of
  packets from flow f that depart in t1, t2.

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• ?Backlogged?A(pif) lt L(pi-1f) for i k1, k11,
  , k2, k21
• (9)

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• ?Non-decreasing step, ? (9a)

v
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t(L(pk2f))

• From (8) t(L(pjf)) ? vts(pjf)lt t(L(pjf)) ?
• we have
• vts(pk2f) ? lt t(L(pk2f))
• and
• t(L(pk1f)) ? vts(pk1f)
• Thus
• becomes

vts(pk2f) ?
vts(pk1f)
t(L(pk1f))
(9a)
(9b)
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• From Lemma 2
• Thus

• Summing all
• Thus (9b) becomes
• (9d)

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• From (9)
• From (9d)

To find upper bound
(9e)
(Move ? to the left)
(ReplaceSwith 9e)
? (10)
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• To find a lower bound, consider two cases
• (1)
• thus
• (2)
• thus
• Hint

(9x)
(9y)
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• (Case 1)
• Since no packet departure in t1, L(pk1f), thus
  L(pk1-1f) ?t1?

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vts(pk21f)

• From (8) t(L(pjf)) ? vts(pjf)lt t(L(pjf)) ?
• we have
• vts(pk1-1f) ? lt t(L(pk1-1f))
• and
• t(L(pk21f)) ? vts(pk21f)
• Thus
• becomes

t(L(pk21f))
(10x)
t(L(pk1-1f))
?
(10y)
vts(pk1-1f) ?
(10a)
(10b)
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• From Lemma 2
• Thus

• Summing all
• Thus (10b) becomes

?
(10z)
(10d)
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• From (9)
• From (10d)

To find lower bound
(10e)
(Move ? to the left)
(ReplaceSwith 10e)
? (11)
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• (Case 2)
• Since no packet departure in t1, L(pk1f), thus
  A(pk1f) ?t1?

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? (10x)
? (10z)
? (9y)
(11a)
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(11a)
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• From (9)
• From (11a)
• We have
• ?(11) lt (12) ?we take (11) as the lower bound

To find lower bound
(12)
? (11)
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• From (10) (11)
• we have

(13)
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• From (13), we have
• Thus

( subtracting)
? (13)
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IV. Numerical Examples

• Compare BSFQ with DDR
• DDR
• qf quantum size for flow f
• The reserved bandwidth for flow f
• The smaller quantum size, the better
  approximating of WFQ.
• Increased per packet processing cost (iteration
  without transmitting any packets deficit)
• BSFQ
• The smaller bin size, the better approximating of
  WFQ.
• Increased per packet processing cost
• Increased per packet processing cost (iteration
  without transmitting any packets t(t))
• For fair comparison, let ?bin qtot.

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• Simulation

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? Bursty ? Non-conformant
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• Fixed packet size of 53 bytes
• Packet arrivals are generated by Markovian of/off
  process
• On state constant rate at Rpeak
• Off state 0
• where Ton and Toff are the average length of
  the on and off periods, respectively.
• Average of Ton 1ms
• Packet shaper Leaky Bucket
• Bursty rate s
• Token generation rate ?
• Simulation time 5000 s

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• For DRR, take Q 1, 500, and 1000For BSFQ, ?bin
  45, 22500, 45000

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Flow 2 3 are similar to flow 1.
?
The DRR method using small quantum size and
the BSFQ method with small ?bin can effectively
approximate WFO.
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?
Flow 5 6 are similar.
4
The DRR method using small quantum size and
the BSFQ method with small ?bin can effectively
approximate WFO.
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?
Flow 8 9 are similar.
7
The DRR method using small quantum size and
the BSFQ method with small ?bin can effectively
approximate WFO.
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?
2
1
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?

1. BSFQ and DRR differ significantly from WFQ for
   small delays.
2. BSFQ converges to WFQ more quickly than DRR.

2
1
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?
2
1
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?
2
1
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?
2
1
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?
2
1
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? BSFQDDR
? BSFQ lt DDR
? BSFQ lt DDR
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BSFQ only drops packets from non-conformant flows.
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V. Conclusion

• BSFQ combines the strengths of frame-based and
  priority-based schedulers.
• Frame-based - bins
• Priority-based - virtual time stamps
• BSFQ is highly scalable
• Constant run time complexity for packet
  processing, as well as for connection
  establishment

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• Virtual time interval ? has a significant impact
  on BSFQ.
• For smaller ?, BSFQ is more akin SCFQ.
• The amount of state information is inversely
  proportional to ?.
• A small ? will increase the number of bins
  needed.
• The efficiency decreases as ? is decreased
  because it increases the likelihood of that some
  bins are empty.
• BSFQ with small bin size is similar to DRR for
  small quantum size.
• Determining an optimal value for ? is beyond the
  scope of this paper.

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• BSFQ provides end-to-end delay guarantee and
  fairness to flows.
• BSFQ had a built-in buffer management function
  that can insulate conformant flows from
  non-compliant traffic.
• BSFQ provides better approximation to WFQ than
  DRR.