Download - Lecture 9 - 10 Link Adaptive Packet Scheduling - Aalto · Lecture 9 - 10 Link Adaptive Packet Scheduling ... (cdma2000-1x) forward link ... – Modified frame structure:

1

S-72.3260 Radio Resource Management Methods 3 op TKK Comnet 1

Lecture 9 - 10Link Adaptive Packet Scheduling


Part I: Channel adaptive scheduling

2


Contents• Brief introduction to HDR and HSDPA• System model• Slow scheduling

– Benefits of one-by-one scheduling– Comparison of a class of slow schedulers

• Fast scheduling– Gain of using fast scheduling– Intercell interference– Limited bandwidth– Quantization of rates– Measurement delay and errors– Quality of service– Limits of fast scheduling

• Conclusions


High speed data in downlink• Performance of the downlink shared channels could be

improved by using– Higher order modulation such as 8PSK and 16QAM– Adaptive modulation and coding– Shorter frame size– Hybrid ARQ– Fast cell site selection (FCS), no soft handover– Fast scheduling– Advanced receiver structures (e.g. IC)– MIMO techniques

• Requirement: – Scheduling, transport format (coding etc.) selection and

retransmissions should be handled by base stations instead of radio network controllers in order to decrease the signalling delay.

3


HDR / 1xEV-DO• Qualcomm's HDR was accepted as phase I of 1xEV• Separate IS-95 (cdma2000-1x) forward link (downlink) RF

carrier for data and voice.• Transmissions are time multiplexed and transmitted with

full power• Channel SIR is estimated and data rate request (DRC) is

fed back once 1.67 ms.• QPSK, 8PSK, and 16QAM modulation at 1.2288 MHz symbol

rate. 16 orthogonal codes are allocated to the active user. => RF signal have the same characteristics as an IS-95 signal allowing reuse of all analog RF designs developed for IS-95 base stations

• Fast ARQ based on negative acknowledgements or HARQ • Peak data rate 2457.6 kbit/s

[BEN00, JOU00]


HDR / 1xEV-DO

• Link adaptation in CDMA2000 1xEV-DO

• A Data Rate Control (DRC) message is generated by the user, based on which scheduling decision is made and modulation and coding schemes are selected.

• Depending on the used coding scheme the number of slots per packet can vary between 1 to 16.

DRC

Forward link (downlink)

Reverse link (uplink)User 1User 2

Measurement delay ≤ 2*1.67 = 3,34 ms (due averaging)

DRC

User with best channel state can be selected

Pilot & Reverse link (uplink)Power control bits

4


High Speed Downlink Packet Access• WCDMA HSDPA (High Speed Downlink Packet Access)

– Max. data rate ~10 Mbit/s for best effort data transmission– Advanced signal processing:

• MIMO antennas• Interference cancellation

– Fast link adaptation: • Modulation and coding schemes are changed based on the channel

measurement: 1/2, 3/4 code rates (Convolution and Turbo coding)• High order modulation: QPSK, 16 QAM• No fast power control

– Fast cell selection: • Rapidly select the base station with best pilot SIR. (Selection

diversity)– Hybrid ARQ: Rather than discarding the erroneous packets,

they can be combined with subsequent transmissions to reduce the packet error rate.

– Modified frame structure: Shorter TTIs, minimum TTI = 3 slots– Fast scheduling: Channel state is taken into account in packet

scheduling– Downlink shared channels: Many users share the same

spreading code


High Speed Downlink Packet Access

• Intelligence is shifted from RNC to NodeBs– NodeB: MAC-HSDPA protocol

• Fast link adaptation• Fast scheduling• Hybrid ARQ

– RNC: RRM and RLC protocols• Ciphering• In-order delivery of data• Fast intra-Node B selection (select the best possible

base station out of the NodeBs controlled by the RNC.

• It could be difficult to support fast selection on cells if they are controlled by different RNCs

5



• Channel structure– New transport channel: HS-DSCH (High Speed

Downlink Shared Channel)– HS-DSCH is preferably allocated one user at the

time– Optionally code multiplexing could be used to share

the DSCH among several users at the time (Requires more control signaling)

– Short time slots for HS-DSCH (TTI 2 ms = three TPC time slots) in order to achieve high granularity in packet scheduling

– UE must have DCCH to transmit link measurements for the MAC-HSDPA



• Orthogonal variable spreading factor (OVSF)

– One HS-DSCH can use up to 12 codes– If a user scheduled for transmission has a small

packet, then the excess capacity (codes) can be allocated to other users using code division.

SF=1SF=2SF=4SF=8SF=16

1 10

1 1

, 1k kk

k k

H HH H

H H− −

− −

⎡ ⎤= =⎢ ⎥−⎣ ⎦

12 code channels reserved for HS-DSCHCode channels reserved for control channels and voice

6



• HSDPA Channel Structure

http://www.nokia.com/link?cid=PLAIN_TEXT_2655

CQI Channel Quality IndicatorDPCH Dedicated Physical Control CHannelHS-SCCH High Speed Shared Control CHannelHS-PDSCH High Speed Physical Downlink Shared CHannelHS-DPCCH Uplink High Speed-Dedicated Physical Control CHannel



• Higher order modulation methods require higher SIR to for the same FER

• Constant transmission power: SIR increases when mobile moves towards base station

• Use the best possible modulation scheme that gives tolerable FER

QPSK, 1/2QPSK, 3/416QAM, 1/216QAM, 3/4

7


1xEV-DV• Competitor to Qualcomm's HDR (1xTreme by Nokia and

Motorola)• Backwards compatible with IS-95, both data and voice

users• Adaptive modulation QPSK, 8PSK, and 16QAM• C/I feedback rate 800 Hz• Scheduling time granularity 1.25 ms• Variable packet duration 1,2,4,8 slots• At most two Forward Packet Data Channels (F-PDCH) both

of which can be scheduled for the same user• Peak data rate 3.09 Mbit/s• Incremental redundancy (IR) or chase combining (CH)

HARQ


High speed data in downlink

OVSH SF=16Walsh code length 32

Walsh code length 32

Spreading

10 Mbit/s3.09 Mbit/s2.4 Mbit/sPeak data rate

CH or IRAsynch. IRHybrid ARQ

QPSK16QAM

QPSK, 8PSK,16QAM

QPSK, 8PSK,16QAM

Modulation

500 Hz or 1500 Hz

800 Hz600 HzChannel feedback rate

Fixed2ms TTI(3 slots)

Variable frame size1.25,2.5,5,10 ms

Variable frame size1.67 ms up to 26.7 ms

Frame size

HSDPA1xEV-DV1xEV-DO

8


1xEV-DV and HSPDA• 1xEV-DV and HSPDA have many similarities• Harmonization process

– Ultimate objective: 1xEV-DV and HSDPA differ only in bandwidth

– 2007?

Real time servicePacket data

Dedicated channels withfast power control

Shared channels withfast link adaptation andscheduling


Packet scheduling– Slow scheduling

• Mean value of the channel state (received CIR) known to the scheduler

• Resources are divided among the user based on their average channel quality

• Snapshot analysis (constant channel gains) applicable

– Fast scheduling• Instant value of the channel state , possibly

with delay , is known to the scheduler.• Channel variations are exploited: resources are

allocated to the user when its channel is in good state.

iξ

( )i tξ τ−τ

9


System modelDownlink of a single in a cell DS-CDMA system• Consider cell k• users, -target of user is set to • No power control, transmission power is set to• Instantaneous channel state (CIR) is given by

( )( ) ik ki

i i

g t PtI

ξν

=+

N 0bE I iΓi

kP

( )ikg t time variant link gain betweenbase station k and user i

intercell interference + receiver noiseat receiver i

i iI ν+k

i

ikg


Channel model• We assume that can be accurately measured

and that it is wide sense stationary, ergodic, and mutually independent

• We assume that the channel fading follows the noncentral distribution (Rayleigh K=0 or Ricianfading)

( )i tξ

{ }( )i iE t tξ ξ= ∀

( ) ( )1

0

4 11 , 0i

i

KK

i i

K KKf e Iξ

ξξ

ξξ ξ

ξ ξ

+− − ⎛ ⎞++

⎜ ⎟= ≥⎜ ⎟⎝ ⎠

2χ

0 ( )KI x

Rice factor (linear scale)zeroth-order modified Bessel function

{ }( )

22

2 1var ( )1

i iKt t

Kξ ξ+

= ∀+

10


Rate - channel state relation• Rate - channel state relation

– Logarithmic relation: • Information theoretic bound (variable coding &

modulation)

– Linear relation:• Fixed modulation, variable coding

• Wideband channel

( )2log 1i ir W ξ= +

,i i i ii

W Wr r Wr

ξ ξΓ = ⇒ = ≤Γ

( )2 2log 1 log ,i i ir W W e Wξ ξ= + → → ∞Linear model can be usedeven if adaptive coding andmodulation schemes are used.

Variable processing gain

Shannon bound


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

ξi/Γi

r i/W

Rate - channel state relation• Relationship between rate and CIR

( )i i ii

Wr ξ ξ=Γ

1

1

0

( )

i

i i k k i ki

K i Ki

xWr x x x

W x x

ξ

ξ ξ

ξ

+

⎧⎪ ≤⎪⎪⎪= ≤ ≤⎨ Γ⎪⎪

≤⎪Γ⎪⎩

( )2( ) log 12i i i

Wr ξ ξ= +

max,( ) mini i ii

Wr rξ ξ⎧ ⎫

= ⎨ ⎬Γ⎩ ⎭i)

i)

ii)

ii)

iii) iii)

iv)

iv)

( )i tξ( )ir t

5i dBΓ =

11


One-by-one transmissions• Different transmission rates are provided by

varying the processing gain

– We assume linear relationship between SIR and bit rate.

– Time is assumed to be continuous variable without any restriction on scheduling instants or frame size granularity

• Different transmission rates are provided by varying both coding and modulation schemes

( )( )( )

1 1 ( )i i

ii i i i

tWr tt

ξθ ξ

Δ=

Γ + − Δ[ ]( ]

0,1

0,1i

iθ

Δ ∈

∈fraction of power allocated to user iorthogonality factor


One-by-one transmissions• Assume that a singe user is scheduled to transmit

at the time. Consequently,

• Asymptotical transmission rate is defined as a stochastic limit

0

1lim ( )Tdef

i i iTi

WR r t dtT

ξ→∞

= =Γ∫

( ) ( )i ii

Wr t tξ=Γ

1iΔ =

12


One-by-one transmissions• Assume that a fraction of the scheduling

interval is allocated to user .

• If the transmission intervals of the users are chosen without any knowledge on the instantaneous channel conditions, then

[ ]0,1iφ ∈

T i

1

1N

ii

φ=

=∑1Tφ 2Tφ

T

i i ii

WR ξ φ=Γ


One-by-one transmissionsProposition 1. The total throughput of one-by-one transmissions is greater than that of simultaneous transmission [BER03a].

Proof.

1

N

ii

R=

∑

{ } ( )

( ) ( ) ( )0 0

( )( )1 1 ( )

1 1 i i

i ii

i i i i

i ii i i i i i i i

i i i i i i

W tE r t Et

W W Wf d f dξ ξ

ξθ ξ

ξ ξ ξ ξ ξ ξ ξθ ξ

∞ ∞

⎧ ⎫Δ⎪ ⎪= ⎨ ⎬Γ + − Δ⎪ ⎪⎩ ⎭Δ

= < Δ = ΔΓ + − Δ Γ Γ∫ ∫

due to the fact that and . ( ) 0, 0i i ifξ ξ ξ≥ ≥ ( ) ( )

i i ifξ ξ δ ξ≠

Thus, we by using one-by-one transmissions, we can always reserve afraction of time to the user, so that the throughput of it is strictly greater than in the simultaneous transmission case.

i iφ = Δ

13


Slow scheduling• General Processor Sharing (GPS) principle:

– Resources, transmission time in our case, are divided according to the weights, so that a user i gets a fair share proportional to its weights.

0

0

1 ( )

1 ( )

T

ii i

Tj j

j

r t dtT R w

R wr t dt

T

= ≤∫

∫as T → ∞

1

ii

i i ii N

j jjj

j j

wR wR w

w

ξφ

ξ=

⎛ ⎞Γ⎜ ⎟⎝ ⎠= ⇒ =

⎛ ⎞Γ⎜ ⎟⎜ ⎟⎝ ⎠

∑


Slow scheduling• Round Robin (RR):

– Equal transmission times

• Equal Throughput (ET): – More time is allocated

to users with poor channel quality

• Fractionally Fair (FF): – More time to users

having favorable channel conditions

1i N

φ =

1

1

Ni i

ij i j

φξ ξ

−

=

⎛ ⎞Γ Γ= ⎜ ⎟

⎝ ⎠∑

1

1

Nj i

ij j i

ξ ξφ−

=

⎛ ⎞= ⎜ ⎟⎜ ⎟Γ Γ⎝ ⎠

∑

ET RR FF≤ ≤Proposition 2. The total throughput fulfills

[BER03a]

ii

i

w ξ=

Γ

1iw =

2

ii

i

w ξ⎛ ⎞= ⎜ ⎟Γ⎝ ⎠

14


Slow scheduling• In practice TTI is quantized• Slow scheduling can realized in practice using

Weighted Fair Queuing (WFQ) or some of its variants.

• If traffic shaping is used, slow scheduling techniques can guarantee QoS asymptotically.


Fast scheduling• Assume that the channel state information is

available.– Rapid estimation and feedback of the channel

states have been suggested for HDR and HSDPA for supporting fast adaptation.

• At time instant t schedule the user for transmission that has the best channel condition

• Fast scheduling rules can be divided into two classes:– Memoryless schedulers that utilize only the current

value ξi(t) in the scheduling decision.– Schedulers with memory that utilize also historical

values ξi(t-1),ξi(t-2),…

( )i tξ

15


Relative Best (RB) scheduling• A simple memoryless scheduling rule• User with relatively best channel state compared

to its mean channel is scheduled for transmission * ( )( ) arg max j j

j j

ti t

cξ ξ⎧ ⎫−⎪ ⎪= ⎨ ⎬

⎪ ⎪⎩ ⎭0ic > is a parameter that

controls the channel access

RB Scheduling rule


Fast scheduling

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

1.5

2

2.5

time

Dec

isio

n va

riabl

e

User 1User 2User 3

Schedule:

16


Channel access time• Asymptotic analysis• Time allocated to user by RB scheduler

• How to pick the weights ?– If for some users is large, then more time is

allocated to those users. However, it is not possible to achieve arbitrary time allocation by weighting the normalized link conditions.

– If , then the time allocation is proportionally fair

icic

1

( ) ( )Ei

Nj j i i

ij j ij i

t tc cξ

ξ ξ ξ ξφ χ=≠

⎧ ⎫⎧ ⎫− −⎪ ⎪ ⎪⎪= <⎨ ⎨ ⎬⎬⎪ ⎪⎪ ⎪⎩ ⎭⎩ ⎭

∏

iT → ∞

{ }1 if occurs0 otherwise

AAχ

⎧= ⎨

⎩Indication function ofevent A.

i ic ξ=1

i Nφ =


Channel access time• Time allocated to user by PF scheduler

• In case of Rayleigh and Rician channel, the decision variables of RF and PF have asymptotically the same statistics.

• From now, we will consider only RB as PF has the same characteristics.

1

1Ei

Nj i

ij j ij i

T T Nξ

ξ ξφ χξ ξ=

≠

⎧ ⎫⎧ ⎫⎪ ⎪ ⎪⎪= ≤ =⎨ ⎨ ⎬⎬⎪ ⎪⎪ ⎪⎩ ⎭⎩ ⎭

∏

i

{ }

{ } ( )( )

22

2

E 1 1

2 1var1

i i

ii i i i i

K NEK

ξ ξφ

ξ ξ ξ ξ ξ

=

⇒ =+⎧ ⎫= − =⎨ ⎬⎩ ⎭ +

For asymptotic analysis of PFscheme see [HOL01]

17


Channel access time• Liu et. al. [LIU01] have suggested Opportunistic

Transmission Scheduling (OTS), in which the channel access times can be controlled.

{ }( ) { }{ }

( )( )( )

1

*

*

*

max

. .

Pr ( )

E ( )

( ) arg max

N

v ii

i

i i i

i i i i

i i

U

s t

i t i

U u r i t i

i t u r v

u r

φ

χ

=

⎧ ⎫⎨ ⎬⎩ ⎭

= =

= =

= +

∑ Maximize expected utility

Channel access time constraint

Expected utility

Access policy

Instantaneous utility as a function of channelstate


Channel access time• Stochastic approximation algorithm (I-controller)

If the expected channel access time is not desirable, is increased.

• If channel access constraints cannot be met and the algorithm will fail.

• I-controller with antiwindup

– If the time allocations are not feasible, the algorithm will converge to greedy algorithm

( ) { }( ){ }{ } ( )*( 1) min ,max 0, ( ) ( ) , 0 1i max i iv t v v t t i t i tα χ φ α+ = − = − < <

iv

iv → ∞

{ } { } ( )( )E ( 1) E ( ) ( )i i i iv t v t t tα φ φ+ = − −

( )( ) ( )( )*( ) arg max arg maxi i i max i i ii t u r v u r= + =

( ) { }( ) ( )*( 1) ( ) ( ) , 0 1i i iv t v t t i t i tα χ φ α+ = − = − < <

18


Channel access time• Let the instantaneous utility be logarithm of the

bit rate

• Fairness constraint

• Optimal solution

Both RB and PF optimize utility and hence fulfill min-max fairness.

( ) ( )log logi i i ii

Wu r r ξ⎛ ⎞

= = ⎜ ⎟Γ⎝ ⎠

{ }*Pr ( ) ii t i φ= =

* *log ( ) arg max log arg maxj ji i j j

i j j

Wv i tξ ξ

ξξ ξ

⎧ ⎫ ⎧ ⎫⎛ ⎞ ⎪ ⎪ ⎪ ⎪= − ⇒ = =⎨ ⎬ ⎨ ⎬⎜ ⎟Γ ⎪ ⎪ ⎪ ⎪⎝ ⎠ ⎩ ⎭ ⎩ ⎭


Channel access time• Park et. al have suggested a simple memoryless

scheduling rule that can obtain desired channel access time φi if the cumulative probability density Fξj

(ξ)=Pr{ξj≤ ξ} is known:

– It can be shown that for given random variable X, the variable Y=FX(X) follows uniform U(0,1) distribution. Hence, the mapping Fξj

(ξ) makes the scheduling decision independent of the channel statistics.

( )1

*( ) arg max ( ) ij j

ji t F t φ

ξ ξ⎧ ⎫

= ⎨ ⎬⎩ ⎭

CDF Scheduling rule

19


Channel access time• Let Ui=Fξi

(ξi(t)) denote i.i.d. U(0,1) uniform random variables.

• We note that the CDF of U is simply Pr{U≤ u}=u• Let us first condition on ξi(t)

{ } ( )( )

( )( ) ( )( )

( )( ) ( )( ) ( )( )

1 1*

1 1

1 1

Pr ( ) ( ) Pr

Pr Pr

j ii

jj i i

i i

jj j i

i i ii i i

i j

j jj i j i

j i

i t i t U F j ì

U F U F

F F F

φ φξ

φφ φ φ

ξ ξ

φφφ φ φ

ξ ξ ξ

ξ ξ ξ

ξ ξ

ξ ξ ξ≠

≠ ≠

−

≠

⎧ ⎫⎪ ⎪= = = ≤ ∀ ≠⎨ ⎬⎪ ⎪⎩ ⎭

⎧ ⎫ ⎧ ⎫⎪ ⎪ ⎪ ⎪= ≤ = ≤⎨ ⎬ ⎨ ⎬⎪ ⎪⎪ ⎪ ⎩ ⎭⎩ ⎭

∑

= = =

∏ ∏

∏


Channel access time• Now taking the expected value over

• That is, the weight directly controls the channel access time.

( )( )ii iU F tξ ξ=

{ } { } ( )

( )( ) ( )1 1

* *

0

1 1

0

1

0

Pr ( ) Pr ( ) ( )i

ii i

i

i

i

i t i i t i t dF

F dF

u duφ

ξ

φξ ξ

ξ ξ ξ

ξ ξ

φ−

∞

∞−

= = = =

=

= =

∫

∫

∫( )

( )i

i

u F

du dFξ

ξ

ξ

ξ

=

=

20


Scheduling gain for RB scheduler• Asymptotical data rate of user is given by

• If (Rayleigh fading channel) , then

– Scheduling gain of RB compared to RR

Multiuser diversity gain = Selection diversity gain!

( )1

E Pri

Nj

i i j i i j iji ij i

cWRcξ ξ ξ ξ ξ ξ ξ

=≠

⎧ ⎫⎧ ⎫⎪ ⎪ ⎪⎪= ≤ − +⎨ ⎨ ⎬⎬Γ ⎪ ⎪⎩ ⎭⎪ ⎪⎩ ⎭∏

i

0K =1

10

11i i

i i

NN

i ii i

ki i i

W d WR e eN k

ξ ξξ ξ ξ ξξ

ξ

−∞ − −

=

⎛ ⎞⎜ ⎟= − =⎜ ⎟Γ Γ⎝ ⎠

∑∫

1

1 1ln2

N

k

G Nk N

γ=

= ≈ + +∑0.577γ ≈ Euler constant

i ic ξ=


Throughput as a function of load

[BER03a]

21


Scheduling gain

[BER03a]


Scheduling gain for CDF scheduler• Rayleigh fading channel

• Expected rate of the CDF scheduler

( ) 1 exp( )i

i i i

Fζ

ξ ξ ζζ ζ

=

= − −

{ } ( )( ) ( )

( )

( ) ( )

( ) ( )

1 1*

0

1 1

0

1

0 0

1

0 1

( ) ( )

1

1 11

1 11 1 11

ii i

i

i i i

i i

k kii i

k

k k

i ik k

E t i t i F dF

e e d

e dk

k kk k

φζ ζ

ζ ζφ

ζ

ξ ξ ζ ζ ζ

ξ ζ ζ

φξ ζ ζ

φ φξ ξ

∞−

∞− −

∞∞− +

=

+∞ ∞

= =

= =

= −

⎛ ⎞−⎜ ⎟= −⎜ ⎟⎜ ⎟⎝ ⎠⎛ ⎞ ⎛ ⎞− − −⎜ ⎟ ⎜ ⎟= =⎜ ⎟ ⎜ ⎟+⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∫

∫

∑ ∫

∑ ∑

( ) ( )0

1 1r k k

k

rx x

k

∞

=

⎛ ⎞− = −⎜ ⎟

⎝ ⎠∑

( 1) ( 1) 0( 1) 1 ,

0 0

r r r k krk k r

kk

− − +⎧ ≥⎛ ⎞ ⎪ −= ∈⎨⎜ ⎟⎝ ⎠ ⎪ <⎩

22


Scheduling gain for CDF scheduler• Corresponding generalized processor sharing

scheduler obtains rate proportional to • Scheduling gain

• If 1/φi=Ni is an integer, we have

That is, in CDF scheduler, a user with time fraction φi see the performance of a network with 1/φi users sharing the channel.

i iφ ξ

( ) 1

1

11 1 1 k

iki i

Gk

kφ

φ

∞+

=

⎛ ⎞⎜ ⎟= −⎜ ⎟⎜ ⎟⎝ ⎠

∑

( )1

1 1ln2

iN

ik i

G Nk N

γ=

= ≈ + +∑


Constrained bandwidth• Let us focus on Rayleigh fading channel.• Assume that the bandwidth of the channel is

limited. Consider the case, in which the rate is bounded above

• Asymptotic data rate of slow scheduling

max( ) min ( ),i ii

Wr t t Rξ⎧ ⎫

= ⎨ ⎬Γ⎩ ⎭

max

1iRW

i i ii

WR e ξφ ξΓ

−⎛ ⎞= −⎜ ⎟⎜ ⎟Γ ⎝ ⎠

ξi

ri

Rmax

23


Constrained bandwidth• Asymptotic data rate of RB-scheduling

• Scheduling gain

– As the scheduling gain approaches the unconstrained case.

– However, as the scheduling gain approaches 1.

( )max

1

1

11 1i

i

RN kk Wii

ki

NWR ekN k

ξξΓ

−+

=

⎛ ⎞⎛ ⎞= − −⎜ ⎟⎜ ⎟ ⎜ ⎟Γ ⎝ ⎠ ⎝ ⎠

∑

( )max max

11

1

11 1 1i iR RN kk W W

k

NG e e

k kξ ξ

−Γ Γ− −+

=

⎛ ⎞ ⎛ ⎞⎛ ⎞= − − −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

∑

maxi

i

RWξ

Γ→ ∞

max 0i

i

RWξ

Γ→


Constrained bandwidthmaxi

i

RS Wξ

Γ= [BER03a]

24


Discrete rates• In practice, the transmission rates are confined

to discrete set of values.• Let there be possible rates

assigned to the different channel states as follows

• Furthermore, let the relation between the rates be geometric:

M 1 2, ,..., Mx x x

1 , 1k kx xμ μ+ = >

( )1

1

0 ( )

( ) ( )

( )

i

i i k k i ki

M i Mi

t xWr t x x t x

W x t x

ξ

ξ ξ

ξ

+

⎧⎪ <⎪⎪⎪= ≤ <⎨ Γ⎪⎪

≥⎪Γ⎪⎩

( )i tξ

( )ir t


Discrete rates• The asymptotic data rate in the case of quantized

instantaneous rates becomes

( )

( ) ( )

1

11 1

1

1

1 21

1 1

1

1 1

i ik

i i

k

m

i i

NxMi

i iki ix

x xN Mk kk mi

k mi i

dWR r e e

NW x e ekN

ξ ξξ ξ

μξ ξ

ξξξ

ξ μ μξ

+

−

−− −

=

− −+ −

= =

⎛ ⎞= −⎜ ⎟⎜ ⎟Γ ⎝ ⎠

⎛ ⎞⎛ ⎞ ⎜ ⎟= − + −⎜ ⎟ ⎜ ⎟Γ ⎝ ⎠ ⎝ ⎠

∑ ∫

∑ ∑

1Mx + = ∞where

25


Discrete rates

1 ix ξ

2μ = [BER03a]


Discrete rates• For M=5, 70% (N=1) - 73% (N=20) of the ideal

throughput can be achieved.• Increasing the number of rates (M>5), increases

the throughput for small N a bit (71%, N=1, M=10), but the results seem to be quite insensitive to the number of rates.

• Conclusion, in case of quantized rates up to 70% - 73% of the ideal throughput can still be achieved.

26


Logarithmic rate relation• Rate model

• Scheduling gain in Rayleigh fading channel( )2log 1i ir W ξ= +

( ) ( ) ( )

( ) ( )

( )

1

1

1 12 1

0

1

1 1 ,,

1, log 1 exp 0,ln 2

,

Nk

iki

def

ii i

a t

x

NG kH k

kH k

d kH kk

a x t e dt

ξξ

ξ ξξ ξξ ξ ξ

+

=

∞

∞− −

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞⎛ ⎞= + − = Γ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

Γ =

∑

∫

∫ Incomplete Gamma Function


Logarithmic rate relation

0 dB

3 dB

10 dB

13 dB

[BER03a]

Number of users N

Sche

dulin

g ga

in G

Average SIR

27


Measurement delay• In practice, the link state information must be

transmitted from the mobile to the base station causing a delay of time units.

• Consider the following stochastic process for modeling the channel variations:

δ

( ) ( )( ) ( ) 2 ( )( ) ( ) 1 ( ), 1, 2k k ki i iZ t Z t N t kρ δ ρ δ= + − =

where are independent Gaussian random{ }( ) ( )kiN t

variables with zero mean and variance .2iξ

( ) 02 cvfJ

cπρ δ δ⎛ ⎞= ⎜ ⎟

⎝ ⎠Clarke's model (zeroth-order Bessel function)

( ) ( )2 2(1) (2)( ) ( ) ( )i i it Z t Z tξ = +


Channel correlation

1950cf MHz=Example

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

δ (ms)

ρ

v=5 km/hv=10 km/hv=20 km/hv=40 km/h

28


Measurement delay• The joint pdf of and can be written as

which could also be used to model estimation errors. In that case, would describe the correlation between the measurement and real channel state.

( ) ( )( )

( )2

( ) ( )2

1( ), ( ) 02 2 2

2 ( ) ( )1( ), ( )1 1

0 1

i i

i

i i

t t

i it t i i

i

t tf t t e I

ξ ξ δ

ρ ξξ ξ δ

ρ ξ ξ δξ ξ δ

ρ ξ ρ

ρ

+ +−

−

+

⎛ ⎞+⎜ ⎟+ =⎜ ⎟− −⎝ ⎠

≤ ≤

( )i tξ ( )i tξ δ+

ρ


Measurement delay• In the case of measurement delays, RB-scheduler

becomes

• and the asymptotic rate becomes

– If the measurement and channel state do not correlate, RB is reduced to RR, since the scheduling intervals becomes arbitrary and random.

• In [HÄM03], 11% performance loss for RR scheduling was observed for pedestrian mobiles (3 km/h).

* ( )( ) arg max j j

j j

ti t

cξ δ ξ⎧ ⎫− −⎪ ⎪= ⎨ ⎬

⎪ ⎪⎩ ⎭

2 2

1

1 1N

ii

ki

WRN kξ ρ ρ

=

⎛ ⎞= + −⎜ ⎟Γ ⎝ ⎠

∑

29


Measurement delay

[BER03a]


Limits of one-by-one scheduling• In practice TTI is quantized, but if it is small

compared to the rate at which the channel is changing and to the length of the scheduling interval T, the difference in throughput is small.

1 ( ) ( )t T

i it

r t dt r tT

+Δ

≈Δ ∫

TΔ

, 1,2,3,...iT k T kφ ≈ Δ =

30


Limits of one-by-one scheduling• Consider logarithmic rate relation

– Other simultaneously transmitting users are considered as noise

• At the given time k best users transmits simultaneously while the rest remain idle.

• Base station power is divided equally among the k active users.

• Position of the mobiles uniformly distributed around the service area of single cell. Pathloss is assumed to be proportional to the 4th power of the distance

( )2( ) ( )( ) log 1

1 1 ( ) ( )i i

ii i

t p tr t Wp t t

ξθ ξ

⎛ ⎞= +⎜ ⎟⎜ ⎟+ −⎝ ⎠

if user is active at the time instance ( )

0 otherwise i

P k i tp t

⎧= ⎨

⎩


Limits of one-by-one scheduling

Gai

n of

usi

ng o

ne-b

y-on

e co

mpa

red

to

L+1

sim

ulta

neou

s tra

nsm

issi

ons

Average SIR in a circular cell (dB)

Pseudorandom codes

Orthogonal codes

1θ =

0θ =

[BER03b]

31


Limits of one-by-one scheduling[BER03b]


One-by-one scheduling• Tse and Hanly [TSE98] considered the information theoretic

bound achievable by using successive decoding

– They showed that maximum throughput is obtained using one-by-one transmissions by scheduling only the best user at a given time instance. The same property has also been observed by Knopp and Humblet [KNO95]

{ }2

( )1: E log 1 1,2,2

i ii S

ii

g t PR R R S N

υ∈

⎧ ⎫⎧ ⎫⎛ ⎞⎪ ⎪⎪ ⎪⎜ ⎟⎪ ⎪ ⎪ ⎪⎜ ⎟∈ ≤ + ∀ ⊂⎨ ⎨ ⎬ ⎬

⎜ ⎟⎪ ⎪ ⎪ ⎪⎜ ⎟⎪ ⎪ ⎪ ⎪⎝ ⎠⎩ ⎭⎩ ⎭

∑

Mutual information bound

i maxi

E P P⎧ ⎫≤⎨ ⎬

⎩ ⎭∑

PossiblePowerallocation

32


One-by-one scheduling– In order to take QoS requirements into account,

Tse and Hanly [TSE98] suggested maximization of weighted sum of rates.• Example: Two groups of users; those being close to

the base station and those being on the edge. • The users on the edge are given higher weight.• Solution: Only the best user of each class should

transmit at the given time. • Successive interference cancellation is then used at

the receiver such that the user close by the receiver is decoded first.


One-by-one scheduling• One-by-one scheduling was shown to be optimal

if– There are no restrictions on frame size granularity– Transmission rates are linear functions of received

SIR (or logarithmic, but interference is canceled)

• It does not guarantee optimal throughput if– Transmission time intervals are quantized – Rate-SIR relationship is quantized

33


Conclusions• Downlink scheduling of non-real-time data in DS-CDMA

systems– Assuming linear relationship between rate and CIR, one-

by-one transmission over fading channels was shown to be superior to simultaneous transmission. However, for nonlinear relation this doesn't necessarily hold.

– For slow schedulers, it was shown that the throughput of ER is less than RR and that RR is inferior to FF. However, RR was found to be most fair from resource utilization point of view.

– PF and RB-schedulers were shown to yield considerable higher throughput than slow RR-scheduling.


Conclusions– An additional control variable can be added to provide

differentiate QoS.– Fast scheduling benefits from the randomness of the

channel, hence intercell interference actually increases its relative performance.

– In case the rates are quantized, up to 70% - 73% of the ideal throughput can still be achieved.

– In case of measurement delays, the performance deterioration is directly proportional to the square of the channel correlation.

– If chase combining is used, possible retransmissions must be made using the same coding and modulation as the original packet and thus they do not benefit from channel variations.

34


References[BEN00] P. Bender, P. Black, M. Grob, R. Padovani, N.

Sindhushayana, and A. Viterbi, "CDMA/HDR: A Bandwidth-Efficient High-Speed Wireless Data Service for Nomadic Users," IEEE Communications Magazine, July 2000.

[BER01] F. Berggren, S.-L. Kim, R. Jäntti, and J. Zander, "Joint power control and intra-cell scheduling of DS-CDMA non-real time data," IEEE Journal on Selected Areas in Communications, Vol. 19., No. 10, October 2001.

[BER03a] F. Berggren and R. Jäntti, "Asymptotically fair transmission scheduling over fading channels," IEEE Transactions on Wireless Communications, Vol. 3. No 1, January 2004.

[BER03b] F. Berggren and R. Jäntti, "Multiuser Scheduling overRayleigh Fading Channels," In Proc. IEEE Globecom 2003, 2003.

[ECK00] D. A. Eckhardt and P. Steenkiste, "Effort-limited Fair (ELF) Scheduling for Wireless Networks," In Proc. IEEE INFOCOMM 2000, 2000.

[GRI04] K. Gribanova and R. Jäntti, "On scheduling video streaming data in the HDR system," in Proc. IEEE VTC 2004 Fall, 2004.


References[HOL01] J. Holzman, "Asymtotic Analysis of Proportional Fair

Algorithm," In Proc. IEEE PIMRC 2001, 2001.[HÄM03] S. Hämäläinen, WCDMA Radio Network Performance, PhD

Thesis, University of Jyväskylä, Finland, 2003.[JOU00] Y. Jou, "Developments in Third Generation (3G) CDMA

Technology," In Proc. IEEE ISSSTA, 2000.[KAH97] N. Kahale and P. E. Wright, "Dynamic global packet routing

in wireless networks," In Proc. IEEE INFOCOM '97, 1997.[KEL97] F. Kelly, "Charging and Rate Control for Elastic Traffic,"

European Transactions on Communications, vol. 8, pp. 33-37, 1997.

[KNO95] R. Knopp and P. A. Humblet, "Information Capacity and Power Control in Single-cell Multiuser Communications," In Proc. IEEE ICC '95, 1995.

[KRU97] M. Krunz and S. K. Tripathi. "On the characterization of VBR MPEG streams." In Proc. ACM SIGMETRIC, 25(1), June 1997.

35


References[LIU01] X. Liu, E. K. P. Chong, N. B. Shroff, "Opportunistic

Transmission Scheduling with Resource-sharing Constraints in Wireless Networks," IEEE Journal on Selected Areas in Communications, October 2001.

[LIU02] X. Liu, E. K. P. Chong, and N. B. Shroff, "Joint Scheduling and Power-Allocation for Interference Management in Wireless Networks," In Proc. IEEE VTC 2002 Fall, 2002.

[MAI00] L. Mailaender, H. Huang, and H. Viswanathan, "Simple Inter-Cell Coordination Scheme fog High Speed CDMA Packet Downlink," In Proc. IEEE VTC 2000 Spring, 2000.

[PAR01] S. Parkvall, E. Dahlman, P. Frenger, and M. Persson, "The High Speed Packet Data Evolution of WCDMA", In Proc. IEEE PIMRC 2001, 2001.

[SHA01] S. Shakkottai and A. Stolyar. "Scheduling algorithms for a mixture of real-time and non-real-time data in HDR." In Proc. 17th International Teletraffic Congress (ITC-17), pages 793-804, 2001.

[TSE98] D. N. C. Tse and S. V. Hanly, "Multiaccess Fading Channels – Part I: Polymatroid structure, optimal resource allocation and throughput capacities ," IEEE Transactions on Information Theory, November 1998.


References[YUE02] J. Yuen, K.-Y. Lam, and E. Chan. A fair and adaptive

scheduling protocol for video stream transmission in mobile environment. In Proc. International Conference on Multimedia andExpo, 1:409412, August 2002.

36


Part II: QoS


Utility based scheduling• Throughput of flow (user) i is xi

• Aggregate utility with flow vector x is given by U(x)Type I

U(x) is some smooth (possibly non strictly) concave function with continuous and finite gradient ∇H(x) everywhere in x∈ N+

Type IIU(x)=∑i ui(xi) where ui(x) is strictly concave utility function with continuous derivative ui’(x) for x>0 and limx → 0ui(x) =-∞ u_i

x

37


Utility based scheduling• Time is slotted• The scheduler assigns users for the given slot t• The assignment k(t) defines the resource

allocation among the users. The resource pool Kis assumed to be quantized. – In TDMA system k(t) specifies which user is given

access to the channel at time slot t– In OFDMA system k(t) defines the allocation of

sub-carriers among the users at time slot t


Utility based scheduling• Data rate of user i at time slot t for assignment

k∈K is denoted by μi(t,k)– μi(t,k)=0 if it is not scheduled to transmit in

assignment k – in wireless systems μi(t,k) is assumed to be

random variable which depends on the channel state at time instant t

• Estimated throughput

– Exponentially smoothed estimate– Can be interpreted as fixed parameter Kalman filter

( ) ( )ˆ ˆ( 1) 1 ( ) , ( )ix t x t t k tβ βμ+ = − +

38


• Scheduling rule: Select the assignment k that maximizes the marginal utility

• Stoylar (2005): The gradient scheduler

is asymptotically optimal. That is, it maximizes the expected aggregate utility E{U(x)}

Utility based scheduling

( ) ( )( ) ( )ˆ ˆ1 ( ) , ( )iU x t t k U x tβ βμ− + −

( ) ( ){ }ˆ( ) arg max ( ) ,k K ik t U x t t kμ∈= ∇

( ) ( )ˆ ˆ( 1) 1 ( ) , ( )ix t x t t k tβ βμ+ = − +


FairnessDefinition (Mo and Walrand 2000)

A flow vector x* is said to be (p,α) proportionally fair if

for all any other feasible flow vectors x

– If pi=1 and α=0, then x* is called Proportional Fair(in sense of Kelly)

– If pi=1 and α → ∞ then x* approaches Max-Min Fair

( )*

*0i i

ii i

x xpx

α

−≤∑

39


Fairness• (p,α) proportionally fair schedulers maximize

utility function of the form

– Max C/I scheduler pi=1, α=0

– Proportional fair scheduler pi=1, α=1

( )( ) 1 1

log 1( )

1 1i

ii

p xu x

p x α

α

α α− −

⎧ =⎪= ⎨− ≠⎪⎩

( )( ) arg max ,k K ii

k t t kμ∈⎧ ⎫

= ⎨ ⎬⎩ ⎭∑

( ),( ) arg max

ˆ ( )i

k Ki i

t kk t

x tμ

∈

⎧ ⎫= ⎨ ⎬

⎩ ⎭∑


0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

α

Spe

ctra

l effi

cien

cy (b

it/s/

Hz)

SNRC=20 dB , SNRE=3 dB

Group C:α-PFGroup E:α-PFGroup C: RRGroup E: RR

Fairness vs coverage• Group C: Users close to base station (5 mobiles)• Group E: Users on the edge of the cell (5

mobiles)

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

α

Rel

ativ

e th

roug

hput

at t

he c

ell e

dge


α -PFRound robin

40


Fairness vs coverage• Proportional fair scheduler provides resource

fairness, but still heavily favors user close to base station

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

α

Spe

ctra

l effi

cien

cy (b

it/s/

Hz)


Group C:α -PFGroup E:α -PFGroup C: RRGroup E: RR


Fairness vs coverage

0 0.5 1 5 10 50 100 RR0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Proportional fair scheduling

α

Rel

ativ

e th

roug

hput

on

the

cell

edge

41


Fairness• (p,α) fairness considers asymptotic fairness, but does not

guarantee short term fairness in some time window of Wslots.

• The sort term fairness properties of Proportional-Fair scheduler can be controlled by tuning the parameter β. The larger β, the smaller the memory of the scheduler.

Limit case β=1: Combination of round-robin and max-C/I scheduling. User that was served in the previous time slot is excluded from the scheduling in the next slot.

( ) ( )ˆ ˆ( 1) 1 ( ) , ( )ix t x t t k tβ βμ+ = − +

( ),( ) arg max

ˆ ( )i

k Ki i

t kk t

x tμ

∈

⎧ ⎫= ⎨ ⎬

⎩ ⎭∑


Delay sensitive scheduling• Consider the case, in which the utility depends on

the queue length q(t) or head of line packet delay τ(t).

• Now the utility function U(.) is non decreasing function of the queue length or head-of-line packet delay.

• Asymptotically optimal scheduling rules are now given by the Generalized Longest Queue (GLQ)and Generalized Largest Delay (GLD) first scheduling policies (Mieghem, 2003)

42


Delay sensitive scheduling• Assume that packet length is s• Consider two flows• The utility if flow 1 is scheduled to transmit is

• For small packet size s, we have

• Comparing the utilities for transmission orders (1,2) and (2,1) yields

12 1 1 2 21 12 1 12 2 12

( , )( , ) ( , ) ( 1, )

s s sU k u ut k t k t k

τ τ τμ μ μ

⎛ ⎞ ⎛ ⎞= + + + +⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠

( ) ( ) ( ) ( )12 1 1 1 1 1 1 1 21 1 1 12 2 12

( , ) ' '( , ) ( , ) ( , )s s sU k u u u ut k t k t k

τ τ τ τ τμ μ μ

⎛ ⎞≈ + + + +⎜ ⎟

⎝ ⎠

( ) ( )12 21 1 1 1 12 2 2 2 21( , ) ( , ) ' ( , ) ' ( , )U k U k u t k u t kτ τ τ μ τ μ≥ ⇒ ≥


Delay sensitive scheduling• U’R-rule (Liu et. al. 2003):

– Modified largest weighted delay first (M-LWDF)

– EXP-rule

( )( ) arg max ' ( , )i i ii

k t u t kτ μ= ∑

1( )1

ii

pu ατ τα

−= −−

( )( ) expi iu pτ τ α= − +

43


Delay sensitive scheduling• In order to apply channel adaptive scheduling to services

that requite low latency and jitter, rules taking the head of line (HoL) packet delay into account when making the scheduling decision should be used.– Modified-Largest-Weighted-Delay-First (M-LWDF)

scheduling rule

– Exp-rule

Where the weight Wi(t) is selected to correspond to the HoLpacket delay τi(t) and the normalization parameter is γi=ai/E{Ri(t)}, ai is a tradeoff parameter between HoL delay and proportional fairness.

ai, β positive parameters


QoS aware scheduling rules• Comparison scheduling rules

PF best and worstMax-rateBest user EXP-rule best and worst

M-LWDF best and worst

(S. Shakkottai and A. Stolyar 2001)N=14Data rate per user 28.8 kbit/s

44


Packet scheduling for video streaming

• Quality of Service constraint: The frames should reach the play-out-buffer on time, i.e. before their playback deadline.

=> In order to improve the QoS, the scheduling decision should take the state of the play-out-buffer into account. (Cross-layer design).

• Play-out-buffer based scheduling has been suggested e.g. in [YUE02] for slow scheduling (bandwidth allocation)


Video streaming traffic• MPEG-4

– A picture is a complete frame. Its header indicates the resolution, the type and correct display time for the decoder.

– There are 3 types of frames • I frames, where only intra-frame coding, based on the

discrete cosine transform and entropy coding, is used.• P frames, inter-frame coded frames with motion-

compensated prediction from the previous I or P frame.• B frames, inter-frame coded frames with bi-directional

motion-compensated predication.

– MPEG coding arranges frames in a deterministic periodic sequence, e.g. “IBBPBBPBBPBB” which is called a group of pictures.

45


Video streaming traffic• We consider Variable Bit Rate

(VBR) encoded streams• It has been observed that

VBR video traffic has non-Gaussian marginal distribution, high variance, and complex correlation properties. It is shown to exhibit self-similar long range dependent characteristics.

• In order to simulate the video traffic we adopt the Auto-Regressive model suggested by Krunz and Tripathi[KRU97]

0 500 1000 1500 20000

2

4

6

8

10

12

14

16x 10

4

Frame number

Fra

me

size

(bi

ts)


Packet scheduling for video streaming

• [GRI04] proposes modification to the M-LWDF and EXP rules, in which weight W(t) is selected as follows

Di(t) HOL Packet delayLi(t) Level of the play out buffer (video frames)ρi(t) Video frame display rate

Channel feedbackPilot

Play-out-buffer feedbackBase station

Mobile

46


Simulation parameters• System parameters


Numerical results• Percentage of video frames, which do not meet

their playback deadlines for the worst user

0 5 10 15 20 250

20

40

60

80

100

Number of users in the system

Per

cent

age

of d

ropp

ed fr

ames

(%

)

M−LWDFEXPPB−M−LWDFPB−EXP

0 5 10 15 20 250

10

20

30

40

50

60


Per

cent

age

of d

ropp

ed fr

ames

(%

)


Dropped frames Dropped I-frames

47


Numerical results• Percentage of video frames, which do not meet

their playback deadlines for randomly selected user

10 15 20 25 3010

−6

10−5

10−4

10−3

10−2


Pro

babi

lity



Quality of service constraints• Equality constraint, E{xi}=xreq,i, E{τ

i}=τreq,i

– Equality constraint cannot be handled by designing proper utility-functions, since they only limit the proportional flow rates

– One solution is to control the access to the channel resources => OBES scheduler

• Minimum performance constraint E{xi}≥ xmin,i, E{τ

i}≤ τreq,i

– Performance of opportunistic scheduling is dependent on the number of users in the system => Use admission control

48


OBES SchedulerAl Rawi and Jäntti 2006• Activity of an user is controlled

– A user is included in the candidate set at time t with probability qi. That is, with probability 1-qi it chooses to remain idle during the next scheduling interval

• Activity factors are determined based on the required QoS-level

βi(n) is a step-size parameter

denotes the mean QoS-level during scheduling interval t


OBES Scheduler• Convergence analysis

49


OBES• Required mean rate • Required mean delay

0 2 4 6 8 1010

20

30

40

50

60

70

80

90

100

110Actual rates

Time (sec)

Ave

rage

Rat

e (k

bps)

−−−−− Actual Kalman estimate

0 2 4 6 8 100

10

20

30

40

50

60

70

80

90

Time (sec)

Ave

rage

Pac

ket D

elay

(m

sec)

−−−−− Actual Kalman estimate


Admission control• Admission control strategies:

– Limit the number of users• Works well if all the users have the same utility

function and channel statistics

– Estimate the actual impact of the new user on the active users• Probing schemes• Prediction schemes

50


Admission controlJäntti and Al Rawi 2005• Impact of adding new user is predicted using

recursive least squares estimator


Admission controlJäntti and Al Rawi 2005• Probing scheme – Active link protection (ALP-CAC)

– The impact of the new user is limited by controlling its access.

– A new user is excluded from the set of active users with probability p(t)

– The probability is decreased while the quality of the existing users is observed.

– If the quality of an new user drops below some threshold, new user is denied access; otherwise p(t)→ 0 and the user is admitted to the system

– If p(t) is decreased exponentially such that at slot t p(t)=pt-t0 we have E{xi(t+1)}>pE{xi(t)}. Hence, the impact of the new user on the old ones is bounded.

51


Admission control


Conclusions• Opportunistic scheduling rules can be derived

from the gradient scheduling method by properly selecting the utility functions

• For delay sensitive data U’R rule should be utilized rather than trying to tune the window length in PF.

• Strict quality of service constraints can be enforced by using admission control

52


References• M. Al Rawi and R. Jäntti, "Opportunistic Best-Effort Scheduling for QoS-

aware Flows," in Proc. IEEE PIMRC 2006, Helsinki, September 2006. • F. Berggren and R. Jäntti, "Asymptotically fair transmission scheduling over

fading channels," IEEE Transactions on Wireless Communications, Vol. 3. No 1., January 2004.

• R. Jäntti and M. Al Rawi, "An Admission Control Scheme for Opportunistic Scheduling" in Proc. IEEE ISWC 2005 , Siena, Italy, September 2005.

• P. Liu, R. Berry and M. L. Honig. Delay-sensitive Packet Scheduling in Wireless Networks, In Proc. IEEE WCNC 2003, 2003.

• J. A. Van Mieghem. Due-Date Scheduling: Asymptotic Optimality of Generalized Largest Delay Rules. Operations research. Vol. 51, No. 1, pp 113-122, 2003.

• J. Mo and J. Walrand. Fair End-to-End Window-Based Congestion Control. IEEE/ACM Transactions on Networking. Vol. 8, No. 5, 2000.

• S. Shakkottai and A. Stolyar. Scheduling algorithms for a mixture of real-time and non-real-time data in HDR. In Proc. 17th International TeletrafficCongress (ITC-17), pages 793-804, 2001.

• A. Stoylar. On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation. Operations Research. Vol. 53, No. 1, pp 12 – 25, 2005.

Download - Lecture 9 - 10 Link Adaptive Packet Scheduling - Aalto · Lecture 9 - 10 Link Adaptive Packet Scheduling ... (cdma2000-1x) forward link ... – Modified frame structure:

Top Related