1. Utility Optimization with “Super-Fast”
Delay Tradeoffs in Wireless Networks l l1 lL
Michael J. Neely
University of Southern California
Comm Theory Workshop, Sedona, AZ, 2007
*Sponsored by NSF OCE Grant

2. A1(t) AL(t) Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource Alloc.
A1(t)
S2(t)
AL(t)
SL(t)
-Slotted time t = {0, 1, 2, …} t …
-Traffic vector A(t) = (A1(t), …, AL(t)) i.i.d. over timeslots.
Rates E{A(t)} = (l1, …, lL)

3. R1(t) = New data admitted to link 1 on slot t
Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource Alloc.
A1(t)
S2(t)
AL(t)
SL(t)
Flow Control Decisions: Choose Ri(t) for each input i
U1(t) = Queue
Backlog
R1(t)
A1(t)
R1(t) = New data admitted to link 1 on slot t

4. A1(t) AL(t) Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource alloc.
A1(t)
S2(t)
AL(t)
SL(t)
-Channel State Vector S(t)=(S1(t), …, SL(t))
(Example: 2-state ON/OFF, state channel quality)
-Control Input I(t)=(I1(t), … , IL(t)) , I(t) W
(Example: Power Allocation, Server Scheduling,
Frequency Band Allocation, etc.)

5. A1(t) AL(t) m(t) = C(I(t), S(t))
Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource alloc.
A1(t)
S2(t)
AL(t)
SL(t)
-Channel State Vector S(t)=(S1(t), …, SL(t))
-Control Input I(t)=(I1(t), … , IL(t))
-Link Transmission Rate Function C(I(t), S(t))
“State a”
m(t) = C(I(t), S(t))
= Transmission rates on slot t

6. A1(t) AL(t) m(t) = C(I(t), S(t))
Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource alloc.
A1(t)
S2(t)
AL(t)
SL(t)
-Channel State Vector S(t)=(S1(t), …, SL(t))
-Control Input I(t)=(I1(t), … , IL(t))
-Link Transmission Rate Function C(I(t), S(t))
“State b”
m(t) = C(I(t), S(t))
= Transmission rates on slot t

7. A1(t) AL(t) m(t) = C(I(t), S(t))
Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource alloc.
A1(t)
S2(t)
AL(t)
SL(t)
-Channel State Vector S(t)=(S1(t), …, SL(t))
-Control Input I(t)=(I1(t), … , IL(t))
-Link Transmission Rate Function C(I(t), S(t))
“State c”
m(t) = C(I(t), S(t))
= Transmission rates on slot t

8. A1(t) AL(t) This determines m(t) = C(I(t), S(t))
Simple One-Hop Network with L Time Varying Links:
(example: Downlink, Uplink)
S1(t)
Cross-Layer Control:
Flow Control
Transmission
scheduling/MAC
resource alloc.
A1(t)
S2(t)
AL(t)
SL(t)
Transmission Scheduling/ MAC Resource Allocation
Decisions:
Every Slot, observe S(t), Choose I(t) W
This determines
m(t) = C(I(t), S(t))

9. Definition: The Network Capacity Region L is
the set of all long-term sustainable throughput
vectors, considering all possible scheduling algs.
(i.e., all ways to choose I(t) W ) l1 L lL
Thruput vector = (r1, r2, …, rL)
(Capacity region L is defined independently of arrivals)

10. Goal: Design a joint Flow-Control / Scheduling lL
Goal: Design a joint Flow-Control / Scheduling
Algorithm that maximizes utility and achieves
an optimal utility-delay tradeoff
general concave
utility functions
of thruput L
Maximize: gi(ri)
Subject to: r L
0 < ri < li
i=1

11. l1 l lL Maximize: gi(ri) Subject to: r L 0 < ri < li
Pop Quiz Question 1: How to design joint flow control
And scheduling in case when l is inside L? l1 l lL
Maximize: gi(ri)
Subject to: r L
0 < ri < li
i=1 L
Special Case Example:
Server Scheduling:
-1 server
-Time varying rates
-ON/OFF channels
(one packet when ON)

12. l1 l lL Maximize: gi(ri) Subject to: r L 0 < ri < li
Answer: Flow control should let everything in.
Resource Allocation: Max Ui(t) Ci(I(t), S(t)) i l1 l lL
Maximize: gi(ri)
Subject to: r L
0 < ri < li
i=1 L
Queue Lengths are
Important! Lyapunov Stability
Theory…

13. A brief history of Lyapunov Drift for Queueing Systems:
Lyapunov Stability:
Tassiulas, Ephremides [91, 92, 93]
P. R. Kumar, S. Meyn [95]
McKeown, Anantharam, Walrand [96, 99]
Kahale, P. E. Wright [97]
Andrews, Kumaran, Ramanan, Stolyar, Whiting [2001]
Leonardi, Mellia, Neri, Marsan [2001]
Neely, Modiano, Rohrs [2002, 2003, 2005]
Joint Stability with Utility Optimization was the Big Open
Question until:
Tsibonis, Georgiadis, Tassiulas [infocom 2003] (special structure net,
linear utils)
Neely, Modiano [thesis 2003, infocom 2005] (general nets and utils)
Eryilmaz, Srikant [infocom 2005] (downlink, general utils)
Stolyar [Queueing Systems 2005] (general nets and utils)

14. Comparison of previous algorithms:
Tassiulas Alg. MWM (max Uimi)
Borst Alg. [Borst Infocom 2003] (max mi/mi)
Tse Alg. [Tse 97, 99, Kush 2002] (max mi/ri)
Curves from [Neely, Modiano, Li, INFOCOM 2005]

15. Lyapunov drift for joint stability and performance
optimization:
Neely, Modiano [2003, 2005] (Fairness, Energy)
Georgiadis, Neely, Tassiulas [NOW Publishers, F&T, 2006]
Neely [Infocom 2006, JSAC 2006] (“Super-fast” delay tradeoffs)
Alternate Approaches to Stoch. Performance Optimization:
Tsibonis, Georgiadis, Tassiulas [2003] (special structure net,
linear utils)
Eryilmaz, Srikant [2005] (Fluid Model Transformations)
Stolyar [2005] (Fluid Model Transformations)
Lee, Mazumdar, Shroff [2005] (Stochastic Gradients)
Lin, Shroff [2004] (Scheduling for static channels)

16. Yields Explicit Delay Tradeoff Results!
Lyapunov drift for joint stability and performance
optimization:
Neely, Modiano [2003, 2005] (Fairness, Energy)
Georgiadis, Neely, Tassiulas [NOW Publishers, F&T, 2006]
Neely [Infocom 2006, JSAC 2006] (“Super-fast” delay tradeoffs)
Alternate Approaches to Stoch. Performance Optimization:
Tsibonis, Georgiadis, Tassiulas [2003] (special structure net,
linear utils)
Eryilmaz, Srikant [2005] (Fluid Model Transformations)
Stolyar [2005] (Fluid Model Transformations)
Lee, Mazumdar, Shroff [2005] (Stochastic Gradients)
Lin, Shroff [2004] (Scheduling for static channels)
Yields Explicit Delay Tradeoff Results!

17. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l2 l1

18. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l1
Av. Delay l2
shrinking radius

19. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l1
Av. Delay l2
shrinking radius

20. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l1
Av. Delay l2
shrinking radius

21. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l1
Av. Delay l2
shrinking radius

22. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l1
Av. Delay l2
shrinking radius

23. Pop Quiz Question 2: How to design joint flow control
and scheduling in case when l is outside L? 1 2 3 4 5 6 7 8 9
l93
l91
l48
l42
Un(c)(t)
Rn(c)(t)
ln(c)
sensor network
wired network
wireless
A general multi-hop
Heterogeneous network.
[O(1/V), O(V)] utility-delay
Tradeoffs from:
[Neely, Modiano, Li
INFOCOM 2005] l1
Av. Delay l2
shrinking radius

24. l V Question: Is [O(1/V), O(V)] the optimal utility-delay tradeoff?
Results: For a large class of overloaded networks, we
can do much better by achieving O(log(V)) average delay. l
O(log(V))
Avg. Delay e e V
[Neely Infocom 2006, JSAC 2006]

25. l V Question: Is [O(1/V), O(V)] the optimal utility-delay tradeoff?
Results: For a large class of overloaded networks, we
can do much better by achieving O(log(V)) average delay. l
O(log(V))
Avg. Delay e e V
[Neely Infocom 2006, JSAC 2006]

26. l V Question: Is [O(1/V), O(V)] the optimal utility-delay tradeoff?
Results: For a large class of overloaded networks, we
can do much better by achieving O(log(V)) average delay. l
O(log(V))
Avg. Delay e e V
[Neely Infocom 2006, JSAC 2006]

27. l V Question: Is [O(1/V), O(V)] the optimal utility-delay tradeoff?
Results: For a large class of overloaded networks, we
can do much better by achieving O(log(V)) average delay. l
O(log(V))
Avg. Delay e e V
[Neely Infocom 2006, JSAC 2006]

28. l V Question: Is [O(1/V), O(V)] the optimal utility-delay tradeoff?
Results: For a large class of overloaded networks, we
can do much better by achieving O(log(V)) average delay. l
O(log(V))
Avg. Delay e e V
[Neely Infocom 2006, JSAC 2006]

29. l V Question: Is [O(1/V), O(V)] the optimal utility-delay tradeoff?
Results: For a large class of overloaded networks, we
can do much better by achieving O(log(V)) average delay. l
O(log(V))
Avg. Delay e e V
[Neely Infocom 2006, JSAC 2006]

30. Theorem [Neely JSAC 2006]: For one-hop networks:
Under i.i.d. random traffic and immediate
admit/reject flow control decisions, no joint
flow-control and scheduling algorithm can do
better than a [O(1/V), O(log(V))] utility-delay tradeoff.
(b) Under overloaded assumptions, algorithm UDOA
(Utility-Delay Optimal Algorithm) achieves the
[O(1/V), O(log(V))] tradeoff! l2 l1
What is the
Algorithm UDOA?

31. What is the algorithm UDOA?
See slides and JSAC 2006 paper on following links:
Paper:
M. J. Neely, “Super-Fast Delay Tradeoffs for Utility Optimal Fair Scheduling in
Wireless Networks,” IEEE Journal on Selected Areas of Communications (JSAC),
Special Issue on Nonlinear Optimization of Communication Systems, vol. 24, no. 8,
pp , Aug
Slides: (from INFOCOM 2006)