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Analytical Models for Streaming
Media Server Performance
Evaluation
Qing Wang
Minyi Xu
May 11, 2001
Background
• Streaming media service:
Use streams to serve the client requests for large-size, longduration video-on-demand files
• Several protocols of such service let client receive data
from more than one streams, those streams can then merge
to decrease the server bandwidth (stream number).
What is merging?
Two streams deliver same file to a client, one of them
terminates in meantime, the other continues.
Patching and HMSM
• Patching:
client receives data from two streams at the
beginning and later two streams merge. The
mergee stream continue to finish the full duration.
• HMSM:
client also “listen to” two streams at first, and later
two streams also merge, BUT the mergee stream
can later merge with other stream (be a merger).
Performance of Patching and
HMSM
• Eager et al: calculate required server bandwidth
when patching or HMSM is used.
• Other system parameters are still needed to
analyze performance of patching or HMSM:
– waiting time (wait in the queue for service)
– balking probability (leave in case of no immediate
service)
– etc.
Measuring the waiting time and balking probability
is the goal of this project!
Balking model
• Simplest Machine Repair Model
Think node
FCFS center
Balking model
• Customer in the FCFS of that model: idle streams.
• Sthink = average duration of the active streams
– get the required stream number using equations from
Eager et al.
– use Little’s result to get average duration of active
streams
• SFCFS = 1 / (total arrival rate) = inter-arrival time of
client requests in stream media service system.
Waiting time
• Coalescing due to waiting in queue:
New-arrived client coalesces with client of
the same kind waiting in the queue
– coalescing probability
• AMVA
Note: number of one kind of clients waiting
in the queue is the same as coalescing
probability.
Zipf( ) function
• A random variable has a Zipf() distribution
if its possibility mass function is: P{X=k}
= C / (k 1- )
• The requesting frequency of a certain file is
a random variable which suits this
distribution.
Experiment – multi-group
Evening:
total  = 125/min
(p: probability for choosing this group)
•
•
•
•
Group1: 10 files, =0.2, T=30min, p=0.4
(CNN News)
Group2: 20 files, =0.3, T=60min, p=0.1
(Badger Herald News)
Group3: 25 files, =0.1, T=100min, p=0.2
(TNT Cable)
Group4: 30 files, =0.25, T=120min, p=0.3
(Starz Cable Movie)
Experiment – multi-group
Daytime:
total  = 125/min
(p: probability for choosing this group)
•
•
•
•
Group1: 10 files, =0.2, T=30min, p=0.6
(CNN News)
Group2: 20 files, =0.3, T=60min, p=0.25
(Badger Herald News)
Group3: 25 files, =0.1, T=100min, p=0.1
(TNT Cable)
Group4: 30 files, =0.25, T=120min, p=0.05
(Startz Cable Movie)
Comparison between evening service pattern and
daytime service pattern
• The long-duration files (movie) are less selected in
daytime, short-duration files (news) are more
selected in daytime.
Pro: longer-duration file less requested;
Con: shorter-duration file makes merging less
frequently to occur.
Balking Probability vs Server Bandwidth
(Optimal patching, multi-group files)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Evening
Daytime
800
900
1054
Balking Probability vs Server Bandwidth
(HMSM(2,1), multi-group files)
70.00%
60.00%
50.00%
40.00%
Evening
Daytime
30.00%
20.00%
10.00%
0.00%
530
550
600
Client Waiting Time vs Server Bandwidth
(Optimal patching, multi-group files)
3.50%
3.00%
2.50%
2.00%
Evening
Daytime
1.50%
1.00%
0.50%
0.00%
400
500
600
Client Waiting Time vs Server Bandwidth
(HMSM(2,1), multi-group files)
4.00%
3.50%
3.00%
2.50%
Evening
Daytime
2.00%
1.50%
1.00%
0.50%
0.00%
300
400
500