Cross-layer Scheduling and Resource Allocation in Wireless ...skrishna/nitc-fdp11.pdf · Dynamic...

Cross-layer Scheduling and Resource Allocation inWireless Communication Systems

Srikrishna Bhashyam

Department of Electrical EngineeringIndian Institute of Technology Madras

21 June 2011

Srikrishna Bhashyam (IIT Madras) 21 June 2011 1 / 44

Cellular Systems

Time-varying channel

Resource sharing – Interference constraints


Downlink Resource Allocation Problem

Channel information

User 1

User 2

User K

TrafficBasestation

Physical resources: power and bandwidthTotal transmit power constraintMaximize system throughputFairness or Quality of Service (QoS) constraints


Dynamic Resource Allocation

User 1 User 2 User 3

Periodic

reallocation of

resources

Resources: Time, Bandwidth, Power

Adaptation to channel and traffic conditionsDynamic resource allocation

I Reallocation period of the order of a millisecond


Adapting to the Channel


Adapting to the Channel: Maximizing Capacity

User 1

User 2

User K

Basestation

Select theuser with

best channel

Channel K

Channel 2

Channel 1

Infinite backlog assumption

All power and bandwidth resources to one user

User with best achievable rate chosen:

i = arg maxk

Rk ,

where Rk is the rate that can be supported by user k .


Maximizing Capacity: Parallel Channels

User 1

User 2

User K

Basestation

For each

best channeluser with

Select the

parallelchannel

Parallel Channels to each user

Bandwidth resources split to achieve parallel channels

For each channel n, user with best channel conditions chosen:

in = arg maxk

Rk,n.

Water-filling power allocation


Fairness

Proportional Fairness

i = arg maxk

Rk

Rk,av,

where Rk,av is the average rate that can be supported by user k .

max∑

k log (Tk),

where Tk is the average long-term throughput of user k .


Parallel Channels: OFDM

Power

User 1

User 2

User 3Subc

arri

ers

Available resources:I SubcarriersI Transmit power

Channel is frequency-selective ⇒ subcarriers not identical.


Fairness: Joint Subchannel and Power Allocation

Proportional rate subcarrier allocation [Rhee]

Proportional rate subcarrier allocation + power optimization [Shen]

Joint subcarrier and power allocation


Fairness: Joint Subchannel and Power Allocation

power

Split power equally amongst subcarriers

Start

Checkif all subcarriers

are allocated

Allocate a subcarrier to a user

Start

Split power equally amongst subcarriers

Allocate all subcarriers to users

Update each user’squeue

No

Yes

End

Optimize powerallocation with

Update each user’squeue

End

Optimize power

allocation with

power


Gradient Algorithm

Stolyar (2005)

General utility functions

Multiuser scheduling at the same time

PF is a special case


Adapting to the Channel and Traffic


Adapting to the Channel and Traffic

Queues for each user

Servers

Users

Time-varying connectivity

Multi-Queue Multi-Server Model for each time slot

Server: Subcarrier/Group of subcarriers/Spreading code


Resource Allocation/Cross-layer Scheduling Goals

Scheduling GoalsI Stability and throughput optimality

F Stability: Average queue length finite

Arrival rate of user 1

Arr

ival

rat

e of

use

r 2

Stability region of policy 1

Stability region of policy 2

Stability region of throughput optimal policy

I Packet delay constraintsI Fairness


Stability in a general wireless network

[Tassiulas et al 1992, Georgiadis et al 2006]I Dynamic backpressure policy

Destination node

b1 r14

b2

b3r34

b1 b3

(b2 − b1)r21

(b1 − b3)r13

b2r24

Interference model: Only certain links can be activated simultaneously

Scheduling problem: Which links will you activate?

Solution: Activate those links such that the sum of their weights ismaximum.


Dynamic back-pressure policy for our settingMax-Weight Scheduling

Users Serversb1(t)

b2(t)

b1C11

b2C21

b1C

12

b2C22

Only one link per server to be activated. Which links to activate?

Solution:I Make the servers as destination nodes.I Assign the weights for each link as in back-pressure policy.I Activate those links such that the sum of their weights is maximum.

max∑

k

bnCnk

bn: Backlog of user n, Cnk : Capacity of user n on server k


Two Throughput Optimal Policies

Users Serversb1

b2

b3

b1C11

b1C12

b3C32

b2C21

b 3C 31

b2C22

Policy 1: Max-Weight Scheduling

Policy 2: Improving delay performanceI Update queue information after each server is scheduled


Joint Server and Power Allocation

Finite number of power levelsI Max-weight scheduling

Joint subcarrier and power allocationI Joint optimizationI Sub-optimal solutions


Results: Max. Arrival Rate vs. Transmit Power

4 4.5 5 5.5 6 6.5 7 7.5 82.5

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

Ptotal in dBW

Arriv

al ra

te (M

bps)

CAO+FPACAO+FPA+PAOCAO+JSPAMLWDFCAQA+FPACAQA+JSPAHomogenous rate users

Max. arrival rate for less than 0.5% packets droppedSrikrishna Bhashyam (IIT Madras) 21 June 2011 20 / 44

Results: Delay Performance

5 10 15 20 25 30 35 40

10−1

100

101

delay (time slots)

P(de

lay>

x)

CAO+FPACAO+FPA+PAOCAO+JSPAMLWDFCAQA+FPACAQA+JSPA

Ptotal = 8dBW Arrival rate = 3 MbpsHomogenous rate users

Best and worst delay performance among users plotted


Fairness and Utility Maximization

Arrival rate vector outside stability regionI Support a fraction of the trafficI Optimize utility based on long term throughputI Flow control to get stabilizable rates + stabilizing policyI Fairness based on choice of utility function

F Proportional fairness


Fairness and Utility Maximization

Flow control + stabilizing policy

Maximize utility subject to stability

max{rk}

∑k

[Vfk(rk)− bk rk ]


Adapting with Partial Information


Using Delayed Information

Second Interval Third IntervalFirst Interval

Slot

T

b(T − 1), C (T − 1) b(2T − 1), C (2T − 1)

T T

Time-slots are grouped into intervals

Channel and queue information available only once in T slots


Channel model

USER 1’s CHANNEL USER 2’s CHANNEL

1 2 3 4 5 6

0

1

2

3

654321

0

1

2

3

SERVERS SERVERS

PACKETS PACKETS

Cnk : channel capacity of user n on server k.

Cnk ∈ {0, 1, 2, 3}.


Loss model

0

Packets sent

Rate

Capacity

Rnk

Rnk <= Cnk Rnk > Cnk

Rnk : number of packets user n transmits on server k .

Cnk(lT − 1): channel information available at the start of l th interval.


Scheduling with infrequent measurements

Retain throughput optimality of dynamic backpressure policy

Two policies: Policy 1 and Policy 2

Comparison with KLS policy [Kar et al 2007]


Policy 1 & Policy 2Users Servers

b1

b2

b3

b1C11

b1 C12

b3C32

b 3C 31

b2C21

b2C22

Define Cnk = max E [Tnk(t)|Cnk(lT − 1)]

= maxr

r Pr{r ≤ Cnk | Cnk(lT − 1)}

Policy 1 is the dynamic back pressure policy for our setting

Assignment changes every slot

Policy 2: Update queue information after each server is scheduled


KLS Policy

Users Servers

b31C31

b11

b21

b31

b12

b22

b32

b32C32

b12 C

12

b11 C

11

b21C21

b22C22

Virtual queue for each user-server pair

Define Cnk(lT ) as

1

TE

(l+1)T−1∑t=lT

Cnk(t)∣∣∣Cnk(lT − 1)

Assignment changes once in T slots


Simulation setup

Truncated Poisson arrivals

128 users and 16 servers

Markov fading channel with probability transition matrix

Backlog and delay are used as metrics for comparison

Simulations for both symmetric and asymmetric arrivalsI Symmetric case shown here


Average backlog comparison: Slow fading, T = 8

5 10 15 20 25 30 35 40 45 500

100

200

300

400

500

600

700

Net arrival rate

Ave

rage

bac

klog

in p

acke

ts/ti

mes

lot/u

ser

KLS PolicyPolicy 1Policy 2

All the policies have similar stability region.


Average backlog comparison for low traffic

5 10 15 20 25 300

20

40

60

80

100

120

140

160

180

Net arrival rate

Ave

rage

bac

klog

in p

acke

ts/ti

me−

slot

/use

r


At low traffic, proposed policies outperform KLS policy.


Delay comparison

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.1810

−2

10−1

100

delay ’d’ in seconds

Pro

babi

lity

that

del

ay is

> ’d

’

min(delay) policy 2max(delay) policy 2min(delay) policy 1max(delay) policy 1min(delay) KLS policymax(delay) KLS policy

Net arrival rate = 25.6, T = 4


Average backlog comparison vs T for Policy 2

0 10 20 30 40 50 60 700

100

200

300

400

500

600

700

Net arrival rate

Ave

rage

bac

klog

in p

acke

ts/ti

mes

lot/u

ser

T=1T=2T=4T=8T=15


Average backlog comparison for different policies

5 10 15 20 25 30 35 40 450

100

200

300

400

500

600

700

Net arrival rate

Ave

rage

bac

klog

in p

acke

ts/ti

mes

lot/u

ser



Comparison of stability regions: Fast fading

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

100

200

300

400

500

600

700

Net arrival rate

Ave

rage

bac

klog

in p

acke

ts/ti

mes

lot/u

ser

Policy 1KLS PolicyPolicy 2

2 queues, 1 server, T = 2, states are {0, 1}

Probability transition matrix:

[δ 1− δ

1− δ δ

], δ = 0.1


Possible Extensions


More Physical Layer Options

Multiple antennas

Power allocation across resources (servers)

Interference processing vs. Interference avoidance

Multi-cell scenario: Centralized vs. Distributed methods


Approximate Solutions

Lower complexity/approximate solutions to optimization problem

Appropriate reduction search space of physical layer modes


Summary

Adapting to the channel

Adapting to the channel and trafficI Max-weight Scheduling

Adapting to partial informationI Conditional expected rate

Possible extensionsI Approximate lower complexity solutionsI Appropriate choice of physical layer modes


References

R. Knopp, P. Humblet, “Information Capacity and power control in single cell multiuser communications,” in Proc. IEEE

ICC, Seattle, WA, vol. 1, pp. 331-335, June 1995.

D. N. C. Tse, “Optimal power allocation over parallel Gaussian channels,” in Proc. IEEE ISIT, Ulm, Germany, pp. 27,

June 1997.

E. F. Chaponniere, P. Black, J. M. Holtzman, and D. Tse, “Transmitter directed multiple receiver system using path

diversity to equitably maximize throughput,” U. S. Patent No. 6449490, September 2002.

P. Viswanath, D. N. C. Tse, R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Transactions on

Information Theory, vol. 48, no. 6, pp. 1277-1294, June 2002.

C. Y. Wong, R. S. Cheng, K. B. Letaief, R. D. Murch, “Multiuser OFDM with Adaptive Subcarrier, Bit, and Power

Allocation”, IEEE Journal on Selected Areas in Communications, vol. 17, no. 10, pp. 1747-1758, October 1999.

J. Jang, K. B. Lee, “Transmit power adaptation for multiuser OFDM systems”, IEEE Journal on Selected Areas in

Communications, vol. 21, no. 2, pp. 171-178, February 2003.

W. Rhee, J. M. Cioffi, “Increase in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation”,

Proceedings of the 51st IEEE Vehicular Technology Conference, Tokyo, vol. 2, pp. 1085-1089, Spring 2000.

Z. Shen, J. G. Andrews, B. L. Evans, “Adaptive Resource Allocation in Multiuser OFDM Systems with Proportional Rate

Constraints”, IEEE Transactions on Wireless Communications, vol. 4, no. 6, pp. 2726-2737, November 2005.

C. Mohanram, S. Bhashyam, “A sub-optimal joint subcarrier and power allocation algorithm,” IEEE Communications

Letters, vol. 9, no. 8, pp. 685-687, August 2005.


References

L. Tassiulas, A. Ephremides, “Stability properties of constrained queueing systems and scheduling for maximum

throughput in multihop radio networks,”IEEE Transactions on Automatic Control, vol. 37, no. 12, pp. 1936-1949,December 1992.

L. Georgiadis, M. J. Neely, L. Tassiulas, “Resource allocation and cross-layer control in wireless networks,” Foundations

and Trends in Networking, vol. 1, no. 1, pp. 1-144, 2006.

M. Andrews, K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, P. Whiting, “Providing quality of service over a

shared wireless link,” IEEE Communications Magazine, vol. 39, no. 2, pp. 150-154, Feb 2001.

A. L. Stolyar, “On the asymptotic optimality of the gradient scheduling for multi-user throughput allocation,” Operations

Research, vol. 53, no. 1, pp. 12-25, 2005.

S. Kittipiyakul, T. Javidi, “Resource allocation in OFDMA with time-varying channel and bursty arrivals,” IEEE

Communication letters, vol. 11, no. 9, September 2007.

C. Mohanram, S. Bhashyam, “Joint subcarrier and power allocation in channel-aware queue-aware scheduling for

multiuser OFDM,” IEEE Transactions on Wireless Communications, vol. 6, no. 9, September 2007.

K. Kar, X. Luo, S. Sarkar, “Throughput-optimal scheduling in multichannel access point networks under infrequent

channel measurements,” IEEE Transactions on Wireless Communications, vol. 7, no. 7, pp. 2619-2629, July 2008.

C. Manikandan, S. Bhashyam, R. Sundaresan, “Cross-layer scheduling with infrequent channel and queue

measurements,” IEEE Transactions on Wireless Communications, vol. 8, no. 12, pp. 5737-5742, December 2009.

P. Chaporkar, K. Kar, X. Luo, S. Sarkar, “Throughput and Fairness Guarantees through maximal scheduling in wireless

networks,” IEEE Transactions on Information Theory, vol. 54, no. 2, pp. 572-594, February 2008.


Acknowledgements

Rajesh Sundaresan

Chandrashekar Mohanram

C. Manikandan

Parimal Parag

Department of Science and Technology


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