Delay-Based Network Utility Maximization Michael J. Neely University of Southern California http://www-rcf.usc.edu/~mjneely IEEE INFOCOM, San Diego, March 2010 ored in part by the DARPA IT-MANET Program, NSF Career CCF-0747525 a 1 (t ) a 2 (t ) a K ( t) Utility Thruput x k S 1 (t ) S 2 (t ) S K (t )
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Delay-Based Network Utility Maximization Michael J. Neely University of Southern California mjneely IEEE INFOCOM, San Diego, March.
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Delay-Based Network Utility Maximization
Michael J. NeelyUniversity of Southern California
http://www-rcf.usc.edu/~mjneelyIEEE INFOCOM, San Diego, March 2010
*Sponsored in part by the DARPA IT-MANET Program, NSF Career CCF-0747525
Network Model: •1-Hop Network with K Queues --- (Q1(t), …, QK(t))•Slotted time, t in {0, 1, 2, … } •S(t) = (S1(t), …, SK(t)) = “Channel State Vector” (i.i.d. over slots)
Reliability is a Function of Transmission Decision: Observe S(t) every slot. Choose 0/1 transmission vector x(t).
Pr[Success on link k | x(t), S(t)] = Ψk(x(t), S(t))
ak(t) Ψk(x(t), S(t))
Packet Dropping: •We can decide to drop packets at any time.•Packets that fail in transmission can either be retransmitted or dropped.•Thruput on channel k = yk = λk – drop rate on channel k
ak(t) Ψk(x(t), S(t))
Delay-Based Control: •Stamp Head-of-Line (HOL) Packets with their Delays Hk(t).
Special case of “Infinitely Backlogged Sources”: •Agrawal, Subramanian [2002], Kushner, Whiting [2002]•Eryilmaz, Srikant [2005], Lin, Shroff [2004]
All of these references use queue backlog as weights!
Alternative “Delay-Based” Rules that use HOL Delaysas weights are known only for Network Stability:•Mekkittikul, McKeown [1996]•Shakkottai, Stolyar [2002]•Andrews, Kumaran, Ramanan, Stolyar, Vijaykumar, Whiting [2004]
Our work fills the gap by developing a Delay-BasedRule for Maximizing Network Utility Subject to Stability.
ak(t)Ψk(x(t), S(t))
Delay= 4
Delay= 2
Delay= 1
Dropsk(t)
Util
ityThruput xk
Challenges: •Prior “Drift-Plus-Penalty” Algorithm Admit/Drops Packets Immediately when New Packets Arrive: Δ(t) + V*Penalty(t).•This does not directly Affect the HOL Values!•Tricky Correlation Issues between HOL sizes and Decisions!Key Ideas for this paper:•Queue all packets. Admit/Drop only at HOL.•Use “Drift-Plus-Penalty” with a different queue structure•Use a “concavely extended utility function”
Advantages of Delay-Based Approach:•Provides “Delay-Fairness.” Queue-Based Rules canleave loner packets stranded.•Provides Worst Case Delay Guarantees.