Analytic Evaluation of Quality of Service for On-Demand Data Delivery Hongfei Guo ([email protected]) Haonan Tan ([email protected])

Analytic Evaluation of Quality of Service

for On-Demand Data Delivery

Hongfei Guo ([email protected])

Haonan Tan ([email protected])

05/09/01 CS747 Project Presentation 2

Outline

• Background

• Two Multicast Protocols

• Customized MVA Analysis

• Validation

• Model Improvement (Interpolation)

• Evaluation of Different Multicast Protocols

• Conclusion & Future Work


Background

• Eager et al. reasoned minimum bandwidth requirements. But –

• How about Quality of Service ?

– Balking probability

– Waiting time

Given: – server bandwidth

– multicast protocol


Two Multicast Protocols

• Grace Patching

– Shared multicast stream (current data)

– Unicast “patch” stream (missed data)

– Average required server bandwidth

112 ipatchingoptimuzed NR


Two Multicast Protocols (cont’d)

• Hierarchical Multicast Stream Merging

– Each data transmission stream is multicast

– Clients accumulate data faster than file play rate

– Clients merged into larger and larger groups

– Once merged, clients listen to the same streams

– Average required server bandwidth

)162.1ln(62.1)1,2( NiRHSMS


CMVA Analysis

• Customer Balking Model– Fixed number of streams in the server– An arriving customer leaves if no streams

available

• Customer Waiting Model– Fixed number of streams in the server– An arriving customer waits till it being served– Customers with same request coalesce in the

waiting queue


Input Parameters

• C server capacity external customer arrival rate

• M number of file categories

For i = 1, 2, …, M

• Ki the total number of distinct files in category i

• Ti mean duration of the entire file in category i

i zipfian parameter in category i

• Pi probability accessing category i files


Output Parameters (Balking)

• S1 average service time at center 1

• R0 mean residence time at center 0• X system throughput.

For i = 1, 2, … #files on the server • pi fraction of customer requests for file i• Ci’ average b/w for file i

• S1i mean service time of file i streams at center 1

• S0 mean service time at center 0

• Q0 mean queue length at center 0

• Xi throughput of streams serving file i

• PB mean incoming costumer balking probability


Output Parameters (Waiting)

• W mean waiting time for a request (not coalesced)• U system utilization• S overall mean stream duration estimate

For i = 1, 2, …, #files on the server • pi fraction of customer requests for file i

• Si mean stream duration for file i

• Qi mean number of waiting requests (not coalesced) for file i

• Xi mean throughput of requests (not coalesced) for file i

• Ri mean residence time of a request (not coalesced) for file i

• Ci’ average number of active streams for file i

• Ri’ mean residence time adjusted for coalescing

• Wi’ mean waiting time adjusted for coalescing


(1) Customer Balking Model

• Center 0

– SSFR center

– Represent the waiting state of a stream• Center 1

– Delay center

– Represent the active state of a stream

1

…Center 1

Center 0

C streams

X


CMVA Equations

),(')1( iii TXpRC

piX

CS i

i

')2( 1

(Protocol result)

)1

1()4( 000 C

CQSR

1

)3( 0 S (interarrival time)

00 )()5( RXCQ

ii

iSpR

CX

10

)6(

0)7( SXU

UPB 1)8(


(2) Waiting Model

• Center 0 – multi-channel server with C streams

• Two kinds of measurements (from two perspectives)

– Server only see non-coalesced customer requests

– Customers count in both coalesced and non-coalesced requests.

C streams

X

Center 0


CMVA Equations• Measurements for the server

CK

ijj

ji UC

SQ

C

SW

1

)5(

K

iiiK

ii

XSX

S1

1

1)3(

C

CU

K

ii

1

'

)4(

iii WXQ )6(

iii pQX )1()7( ii

iii Wp

WpQ

1)8(

),(')1( TXpRC ii piX

CS i

i

')2(


CMVA Equations (cont’d)

• Measurements for the customers

12')1(

i

ii

ii

i W

WW

WW

iii SWR '')3(

files

iii pWW

#

1

'')2(

files

iii pRR

#

1

'')4(


Validation (1)

Balking Probabilities

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 50 100 150 200 250 300

Capacity

Pro

bab

ilit

y Patching

HMSM(2,1)

Sim-P

Sim-H


Validation (2)Waiting Model

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 50 100 150 200 250 300

Capacity

Mea

n W

aiti

ng

Tim

e

Patching

HMSM(2,1)

Sim-P

Sim-H

Inter-P


Validation (3)Waiting Time Seen by Server

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 50 100 150 200 250 300

Capacity

Mea

n W

aiti

ng

Tim

e

Patching

HMSM(2,1)

Sim-P

Sim-H

Inter-P


Comparison of Patching Results

Capa-city

File1 File2 File3

Model Sim Model Sim Model Sim

100 0.249 0.957 0.253 0.947 0.258 0.846

125 0.195 0.56 0.201 0.498 0.208 0.455

150 0.152 0.327 0.161 0.283 0.170 0.265

175 0.117 0.175 0.13 0.168 0.141 0.171

200 0.089 0.096 0.106 0.112 0.12 0.126

Average Stream Durationa – Big error here!


Interpolation of Stream Duration

• g(Ni) – Threshold for patching

• Exact for two extreme cases:

Wi or Wi 0

• Exact for other cases ???

ii

ii

ii

ii T

NgWi

WS

NgW

NgS

)()(

)(


Evaluation of

Two Protocols(1)

Balk ing Model (Patching)

0

0.02

0.04

0.06

0.08

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6

Available Server Bandw idth per Client

Bal

kin

g P

rob

abili

ty

20 f iles

40 f iles

80 f iles

160 f iles

Avg. Total B/W

Balk ing Model (HMSM)

0

0.02

0.04

0.06

0.08

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6

Available S erver Bandwidth per C lient

Bal

kin

g P

rob

abili

ty

20 f iles

40 f iles

80 f iles

160 f iles

Avg. Total B/W


Balk ing Model (Patching)

0.85

0.9

0.95

1

0 0.1 0.2 0.3 0.4 0.5 0.6


Ser

ver

Uti

lizat

ion

20 f iles

40 f iles

80 f iles

160 f iles

Avg. Total B/W

Balk ing Model (HMSM)

0.85

0.9

0.95

1

0 0.1 0.2 0.3 0.4 0.5 0.6


Ser

ver

Uti

lizat

ion 20 f iles

40 f iles

80 f iles

160 f iles

Avg. Total B/W

(2)


Waiting Model (Patching)

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.1 0.2 0.3 0.4 0.5 0.6


Me

an

Cli

en

t W

ait

ing

Tim

e (

% o

f

pla

yb

ac

k d

ura

tio

n)

20 f iles

40 f iles

80 f iles

160 f iles

Avg. Total B/W

Waiting Model (HMSM)

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.1 0.2 0.3 0.4 0.5 0.6


Me

an

Cli

en

t W

ait

ing

Tim

e

(% o

f p

lay

ba

ck

du

rati

on

) 20 f iles

40 f iles

80 f iles

160 f iles

Avg. Total B/W

(3)


Tradeoff

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Balking Probability

Se

rve

r U

tiliz

ati

on

20 files

40 files

80 files

160 files

Avg. Total B/W

(4)


Conclusion

• Balking model – big relative error when utilization is low.

• Waiting model – good for HSMS, but

underestimates Patching when utilization is high.

• Interpolation helps !• C* is a good trade-off between QoS and server

utilization.• HSMS is always better than Patching.


Future Work

• Further investigate the discrepancy between model results and simulation results

• Use the models to evaluate QoS of stream servers with multiple categories


Comparison of Patching Results (1)

Capa-city

File1 File2 File3

Model Sim Model Sim Model Sim

100 0.956 0.983 0.916 0.967 0.88 0.952

125 0.923 0.962 0.858 0.928 0.802 0.896

150 0.868 0.916 0.769 0.847 0.691 0.79

175 0. 77 0.813 0.631 0.693 0.537 0.608

200 0.587 0.582 0.427 0.444 0.337 0.363

Coalesce Fraction

Documents

Analytic Evaluation of Quality of Service for On-Demand Data Delivery Hongfei Guo ([email protected]) Haonan Tan ([email protected])