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, long- duration 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 FCFS center Think node

Balking model Customer in the FCFS of that model: idle streams. S think = 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 S FCFS = 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)

Balking Probability vs Server Bandwidth (HMSM(2,1), multi-group files)

Client Waiting Time vs Server Bandwidth (Optimal patching, multi-group files)

Client Waiting Time vs Server Bandwidth (HMSM(2,1), multi-group files)