A SelfClocked Fair Queueing Scheme for Broadband Applications

1
A Self-Clocked Fair Queueing Scheme for Broadband
Applications

• S. Jamaloddin Golestoni

Presented by Cigdem Sengul
2
Outline

• Fair Queueing Systems
• FFQ, PFQ
• Virtual time implementation of PFQ
• Self-Clocked Fair Queueing
• Fairness Analysis
• Conclusion

3
Fair Queueing Systems

• Fair Queueing scheme by Parekh and Gallager is
  based on fluid-flow reference system.
• FFQ implies multiple sessions can be served
  simultaneously not feasible in real world.
• PFQ implementation uses virtual time high
  computational complexity.
• PFQ virtual time depends on FFQ work progress.

4
FFQ PFQ Definitions

• Ak(t) aggregated length of session k packets in
  0,t)
• Wk(t) aggregated length of traffic of session k
  served in (0,t)
• Qk(t) Total length of backlogged traffic at t.
• B(t1,t2) Set of sessions backlogged at (t1,t2).
• A(t1,t2) Set of sessions absent at (t1,t2).

5
FFQ PFQ Definitions

• wk(t) normalized service
• In FFQ wk(t1,t2) wj(t1,t2) k,j?B(t1,t2).
• In PFQ wk(t1,t2), wj(t1,t2) k,j?B(t1,t2) are
  close. So PFQ provides fairness.

6
Virtual Time Realization of PFQ

• Busy period A maximal interval of time during
  which a server is busy without interruption.
• Virtual time
• Packets are tagged with their virtual finishing
  times

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Complexity of Virtual Time (PFQ)

• v(t) is a piecewise linear function. It has
  breakpoints whenever a session becomes backlogged
  or absent in FFQ system.
• When the transitions in and out of the system
  becomes frequent, v(t) is not feasible.
• Worst-case complexity O( of connections)
• The reason for complexity PFQ is based on a
  hypothetical system.

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Self-Clocked Fair Queueing

• v(t) is based on queueing system.
• Rules
• Each arriving packet is tagged with a service tag
  before placed in to queue. The packets are served
  in increasing order of their service tag.
• v(t) is defined as the service tag of the packet
  receiving service at the time t.
• When the busy period is over v(t) and session
  packet counters are initialized to 0.

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Fairness Analysis Definitions

• SCFQ system is also work-conserving.
• To compare the fairness of queueing systems, the
  service opportunities missed must be included.
• The virtual time of a session k is the sum of its
  missed and received normalized services.
• Service lag

10
Fairness Analysis

• In FFQ, virtual times of all sessions are equal
  and service lag of each session is 0.
• The service lag of each session k in SCFQ is
  bounded
• Relative Fairness Difference in normalized
  service between two sessions.

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Fairness Analysis Proof

• During each busy period of the SCFQ v(t) is a
  non-decreasing function of time.
• Each time a packet finishes service in the SCFQ
  system the service lag of the corresponding
  system is 0.
• While a session is absent or each time it becomes
  backlogged, its service lag is 0.

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Worst-Case Delay in SCFQ

• Assume
• Connection 1 with r150.
• Connection i with ri1, i251
• Packets with size 1 arrive at time 0 from all
  sessions Connection 1 packet arrives just after
  time 0.
• SCFQ Connection 1 packet waits all other 50
  connections it is tagged 1.02 and others 1.
• PFQ Connection 1packet only waits 1 packet.
• Worst-case delay is O( of Connections)

13
Conclusion

• SCFQ provides good fairness and worst-case
  complexity O(1), but delay bounds are far above
  PGPS.
• Minimum-Delay Self-clocked Fair Queueing
  Algorithm for Packet-Switched Networks
• Fabio M. Chiussi and Andrea Francini
• High-Speed Networks Reasearch Department,Bell
  Laboratories, Lucent Technologies
• The same delay bounds as PGPS