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A non-homogeneous QBD approach for the admission and GoS control in a multiserviceWCDMA system

13th International Workshop on Quality of Service (IWQoS 2005)June 21-23, 2005University of Passau, Germany

Ioannis Koukoutsidis¹, Eitan Altman¹, Jean-Marc Kelif²¹INRIA, Sophia Antipolis, France²France Telecom R&D, Issy-les-Moulineaux, France

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Traffic demand in a multiservice network

• Real-time traffic (RT)• Examples: conversational, streaming traffic (audio, video)• Strict QoS requirements (bit rate, duration)• Performance metric: blocking probability

• Non-real-time traffic (NRT)• Examples: web-browsing, e-mail, file transfers• No-guaranteed bit rate (elastic)• Performance metric: transfer time

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• Evaluation of capacity is more difficult than FDMA, TDMA or wireline networks

• Interference-limited capacity

• Coupling of traffic and transmission issues (mainly through power control)

• Different problem parameters in UL, DL (interference, power control, coding, channel structure, diversity, etc.)

Traffic analysis of CDMA networks

• Service differentiation• Different QoS requirements• Admission control policies

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Modeling Capacity and Throughput in a CDMA link

WR

IESIR b

0

=

0IEb : energy per bit to interference density, : processing gain

RW

Define a boundary of “capacity” based on the number of users the CDMA cell can theoretically sustain without the total output power (of a mobile, or BS) going to infinity

References

− H. Holma, A. Toskala, WCDMA for UMTS: Radio access for 3rd generation mobile communications. John Wiley & Sons, 3rd Ed (2004).

− Xu et al, Dynamic fair scheduling with QoS constraints in multimedia WCDMA cellular networks. IEEE Trans. Wireless Communications, Jan. 2004.

− K. Hiltunen, R. De Bernardi, WCDMA downlink capacity estimation. VTC 2000.

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Uplink

)( 1

where,ly Equivalent .,,1 , ~

~~

∗∗∆+

∆=∆′∆′=

++=∆=

−++s

sss

interintra

ss

sinterintra

s

IINPKs

PIINP

K

)( 0

~∗=∆

WR

IEs

s

ss

ss E

WIf

R 0

1⋅

∆−+∆

=

intrainter

K

s ssintra

IfI

PMI

⋅=

=∑ =,

1(K service classes)

The SIR target condition writes:

Solving for Ps :

∑ =∆′+−

∆′= K

s ss

ss

MfNP

1)1(1

Considering Ms∈ Ν, and physical power limitations we set

1)1(1

<Θ≤∆′+∑=

us

K

ss fM

Total resource capacity

Resource capacityof connection s, ∆s

Combining with (∗),(∗∗)

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Downlink

ss

ss E

WIaFa

R 0⋅∆−+

∆=

S base stations, M mobiles in cell l. Total output power of base station l :

)( 1k ,, ∗++=∑ =

MCCHSCHktot PPPP ll

SIR condition :

SCH: synchronization, CCH: control commonchannels

NIIgP

intrakinterk

kkk

++=∆

,,

,,~

ll( )

∑∑

≠=

≠

=

++=S

jj jkjtotinterk

kkj jCCHSCHkintrak

gPI

gPPPaI

l

ll

,1 ,,,

,,,

Define .,,

,1 ,,,

ll

l

l

ktot

S

jj jkjtotk gP

gPF

∑ ≠== Withkk

kk

a~

~

1 ∆+

∆=β it follows

NgPaFgP

ktotkk

kkk ++=

lll

ll

,,,

,,

)(β

Average approximation: Substitute Fk,l, gk,l, αk by averages F,G,α so that Ptot is the same(∗∗) (∗∗∗)

(∗), (∗∗), (∗∗∗) ⇒∑∑

+−

++=

s ss

s ssCCHSCHtot MFa

MNGPPP

ββ

)(1

Again we impose 1)(1

<Θ≤+∑=

ds

K

ss FaM β

Total resource capacityResource capacityof connection s, ∆s

Finally,

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Objectives of Analysis

• Solution of a multiservice model with RT and NRT traffic• Integration of RT and NRT with “shared resources”

– use of QBD process theory for numerical solution– control of shared resources, performance trade-offs,

admission and rate (GoS) control policies

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Admission and rate control

• RT traffic has priority over resources• GoS control: more RT calls with degraded transmission rates (e.g. AMR codec)

[ ] [ ]maxminmaxmin ,, ∆∆→RR

⎣ ⎦max∆= RTRT LN (number of calls with max rate)

⎣ ⎦minmax ∆= RTRT LM (max number of RT calls)

⎩⎨⎧

≤<≤∆

=∆ RTRTRTRTRT

RTRTRT MMNML

NMM

max

max

, ,

)(

NRTRT LL −Θ= ,

• NRT traffic shares resources• A portion of the total capacity, LNRT is reserved• Use of capacity left-over from RT traffic

⎩⎨⎧ ≤∆−Θ

=otherwiseL

NMifMMC

NRT

RTRTRTRT ,

,)( maxTotal NRT capacity:

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Models for NRT capacity usage

• Processor-sharing (standard CDMA)• Simultaneous transmissions

sRTNRT

RTNRTRTNRT

NRTtotal E

WIMCaFaM

MCMMMR 0

)()()(),( ⋅

⋅−+=

Total throughput (downlink)

• Time-multiplexed transmissions (high data rate schemes, e.g. HSDPA, HSUPA)

• Capacity assigned to a single mobile for a very short time

Total throughput (downlink)

sRT

RTRT

NRTtotal E

WIMCaFa

MCMR 0

)()()( ⋅

⋅−+=

Fair use of resources is considered in both models

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• Departure rate of NRT calls:

• QBD process with steady-state probability

• For level

Quasi-Birth-Death Analysis

),(),( RTNRTNRTtotalNRTRTNRT MMRMMv µ=

[ ]K),1(),0( πππ =

[ ]),(,),1,(),0,()( , maxRTMiiiii ππππ K= ( )phases 1max +

RTM

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

OOO

K

K

K

000

000

0)2(

1)2(

2

0)1(

1)1(

2

0

AAAAAA

AB

Q

)(0 NRTdiagA λ=

)0 );,(( max)(

2RTi MjjivdiagA ≤≤=

),(],[

]1,[

]1,[

)(1

)(1

)(1

jivjjjA

jjjA

jjA

NRTRTRTi

RTi

RTi

−−−−=

=−

=+

λµλ

µ

λ

Time-multiplexing: Homogeneous QBD processPS: Non-homogeneous QBD process (LDQBD)

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1. Compute stochastic matrices Si :

LDQBD algorithms

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

)(1

)(2

0)1(

1)1(

2

0

00

000

KK AA

AAAAB

Q

K

MOOMM

K

K

[Gaver, Jacobs, Latouche]: Finite birth-and-death models in randomly changing environments, Adv. Appl. Prob. 16 (1984) 715-731

Algorithm Finite LDQBD

.1 ,)(

,

011

)(2

)(1

0

KnASAAS

BS

nnn

n ≤≤−+=

=−−

2. Find stationary distribution of SK :

1,0

=⋅=⋅

eS

K

KK

ππ

3. Recursively compute Sn, 0≤ n≤ K-1 :

( )1121

−++ −⋅⋅= n

nnn SAππ

4. Renormalize :e⋅

=πππ

Extension to infinite system

endrun

while set

LDQBDFinitehKK

eKK

K

init

,

**

*

*

+=

>⋅=

επ

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Ergodicity of the LDQBD process

• For a homogeneous QBD process, a necessary and sufficient ergodicity condition is [Latouche, Ramaswami, 1999]:

• We observe that the total throughput reaches a limit in both the UL and DL cases, i.e. the sub-matrices of the LDQBD process converge to level-independent submatrices

Theorem: If the homogeneous QBD process is ergodic, the LDQBD process alsois. Conversely, if the homogeneous QBD is not ergodic with positive expected drift, d = πA0e- πA2e > 0, the LDQBD process is also not ergodic

e Aπe Aπ 02 >

NRTNRTtotalNRT RE λµ >⋅⇒ ][L

What is an ergodicity condition in the LDQBD case?

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Proof sketch

• Denote )( ),( tXtX ′ the LDQBD and QBD processes respectively

• It holds that ( ) ( )2

)(22

22

12 i.e. , AAAAA k ′↓′>>> L

•

( )finite. are times

recurrence mean both i.e.,that Provestate totimes recurrence consider ThenthatShow

],E[]E[ .0,0 , ).()(

ll

ll

l σσσσ

′≤=

′′≤ tXtX st

•

• Then )(tX L is not ergodic, from which we can establish that the

original LDQBD is not ergodic

Forward part :

Reverse part :

) levels for LDQBD truncated process QBD modified a exists therethatShow

LktXtXtXtX

LLst ≥≤′′

′′

:)(( )()( )(

holds whichfor andergodic not is which

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• Examine user-perceived QoS metrics• Blocking probability of RT traffic• Transfer (sojourn) time of NRT flows

Performance Evaluation

• Effect of NRT capacity reservation

• Compare time-multiplexing and standard CDMA schemes

• Impact of interference

• Admission control on NRT traffic

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Numerical parameters

0.2Fraction of power for SCH, CCH channels

W=3.84 McpsChip rate

5.0 dB (144 kbps, DL)

7.0 dB (12.2 kbps, DL)

α=0.64Non-orthogonality factor (DL)

λRT= λNRT=0.4Call arrival rates

1/µNRT=160 kbitsMean NRT session size

4.2 dB (12.2 kbps, UL)ERT/I0

(DL): F=0.55(UL): f=0.73Intercell interference factors

1/µRT=125 secMean RT call duration

2.2 dB (64 kbps, UL)ENRT/I0

Min 4.75 kbpsMax 12.2 kbpsRT transmission rate

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Uplink and Downlink performance

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

LNRT

threshold

Blo

ckin

g pr

obab

ility

of R

T c

alls

ULDL

• RT blocking increases with higher LNRT reservation• Trade-off with NRT performance

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0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

LNRT

threshold

NR

T s

ojou

rn ti

me

ULUL−HSUPADLDL−HSDPA

DL

UL

0.1 0.15 0.20

2

4

6

8

10

12

14

16

LNRT

threshold

NR

T s

ojou

rn ti

me

DLDL−HSDPA

• Time-multiplexing scheme outperforms standard approach under congestion conditions (high load, small LNRT capacity)• Choice of an operating region for both RT, NRT traffic is feasible

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• significant loss of performance due to interference (higher RT blocking, larger NRT transfer times (e.g., for F=1, LNRT=0, PB=0.05)

• more power to overcome interference, less available capacity

Impact of intercell interference

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

1

LNRT

threshold

Blo

ckin

g pr

obab

ility

of R

T c

alls

F=0.1F=0.4F=0.7F=1

0 0.2 0.4 0.6 0.80

5

10

15

LNRT

threshold

NR

T s

ojou

rn ti

me

F=0.1F=0.4F=0.7F=1

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• Admission control of data is even more necessary on a CDMA link• Ineffective traffic is also transmitted on the link (adding to interference)• Performance degradation: Large transfer times, user impatience phenomena

NRT admission control

0 0.1 0.210

−10

10−8

10−6

10−4

10−2

100

LNRT

threshold

NR

T b

lock

ing

prob

abili

ty

MNRT,max

=25M

NRT,max=50

MNRT,max

=100M

NRT,max=200

0 0.2 0.4 0.6 0.8

100

101

102

103

104

105

LNRT

threshold

NR

T s

ojou

rn ti

me

MNRT,max

=50M

NRT,max=100

MNRT,max

=200M

NRT,max=1000

MNRT,max

=infinite

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Modeling of admission and rate control scheme in CDMA with integrated multiservice traffic

• Adaptive-rate RT calls and elastic NRT traffic• “Shared” resources: NRT flows benefit from low RT traffic periods

Summary and Conclusions

QoS management: control of NRT capacity reservation• A small (e.g. 20%) reservation of resources vastly improves NRT sessions,

while not significantly harming RT connections

Time-multiplexing schemes (e.g. HSDPA, HDR) can improve performance, mainly under congestion conditions

admission control on data traffic is imperative to guarantee QoS, esp. under high loads

• Trade-off between number of transmissions allowed and rate offered to on-going flows

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Das Ende…Die Fragen?