analytic evaluation of quality of service for on-demand data delivery hongfei guo ([email protected])...
TRANSCRIPT
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
05/09/01 CS747 Project Presentation 3
Background
• Eager et al. reasoned minimum bandwidth requirements. But –
• How about Quality of Service ?
– Balking probability
– Waiting time
Given: – server bandwidth
– multicast protocol
05/09/01 CS747 Project Presentation 4
Two Multicast Protocols
• Grace Patching
– Shared multicast stream (current data)
– Unicast “patch” stream (missed data)
– Average required server bandwidth
112 ipatchingoptimuzed NR
05/09/01 CS747 Project Presentation 5
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
05/09/01 CS747 Project Presentation 6
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
05/09/01 CS747 Project Presentation 7
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
05/09/01 CS747 Project Presentation 8
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
05/09/01 CS747 Project Presentation 9
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
05/09/01 CS747 Project Presentation 10
(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
05/09/01 CS747 Project Presentation 11
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(
05/09/01 CS747 Project Presentation 12
(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
05/09/01 CS747 Project Presentation 13
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(
05/09/01 CS747 Project Presentation 14
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(
05/09/01 CS747 Project Presentation 15
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
05/09/01 CS747 Project Presentation 16
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
05/09/01 CS747 Project Presentation 17
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
05/09/01 CS747 Project Presentation 18
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!
05/09/01 CS747 Project Presentation 19
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
)()(
)(
05/09/01 CS747 Project Presentation 20
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
05/09/01 CS747 Project Presentation 21
Balk ing Model (Patching)
0.85
0.9
0.95
1
0 0.1 0.2 0.3 0.4 0.5 0.6
Available Server Bandw idth per Client
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
Available Server Bandw idth per Client
Ser
ver
Uti
lizat
ion 20 f iles
40 f iles
80 f iles
160 f iles
Avg. Total B/W
(2)
05/09/01 CS747 Project Presentation 22
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
Available Server Bandw idth per Client
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
Available Server Bandw idth per Client
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)
05/09/01 CS747 Project Presentation 23
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)
05/09/01 CS747 Project Presentation 24
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.
05/09/01 CS747 Project Presentation 25
Future Work
• Further investigate the discrepancy between model results and simulation results
• Use the models to evaluate QoS of stream servers with multiple categories
05/09/01 CS747 Project Presentation 26
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