1. Multi-server Optimal Bandwidth Monitoring for QoS based Multimedia Delivery Anup Basu, Irene Cheng and Yinzhe Yu Department of Computing Science U. of Alberta

2. A..Basu,I.Cheng and Y.Yu, U. of Alberta 2 Architecture -connection handling -request processing Request reception Application Layer Adaptation Layer -monitor/poll bandwidth -determine object size transform requested object to target size deliver object To client MonitorPrepareTransmit Lower Layer Object delivery across network feedback from network

3. A..Basu,I.Cheng and Y.Yu, U. of Alberta 3 Assumptions and Notations  We need to make a one-time transmission of a multimedia object (servers to client).  User specified a time limit T on client. It’s expected that the transmission will finish within T by confidence level.  The first fraction t of T will be used for bandwidth testing.  Bandwidth testing is performed by using time slices of equal length. Each time slice has bandwidth sample , bandwidth population , bandwidth samples

4. A..Basu,I.Cheng and Y.Yu, U. of Alberta 4 , is actual bandwidth we try to estimate. , is the average of bandwidth samples. , is the variance of bandwidth samples. Notations Our Problem is:  First, given N, n,,, give an estimation of, so that.  Second, determine optimal value of n, in order to maximize.

5. A..Basu,I.Cheng and Y.Yu, U. of Alberta 5  Assume the parent population conforms to the normal distribution:, is unknown  is the mean of samples, then conforms to Student’s t-distribution (t-distribution).  If sampling without replacement from a finite population, we should have a finite population correction factor: Statistical Background-Sampling and Estimate

6. A..Basu,I.Cheng and Y.Yu, U. of Alberta 6  As, the t-distribution is identical as normal distribution.  Robust: t-distribution works well, even if the parent population is not exactly normally distributed. t-distribution

7. A..Basu,I.Cheng and Y.Yu, U. of Alberta 7 Safe Bandwidth Estimation

8. A..Basu,I.Cheng and Y.Yu, U. of Alberta 8  Safe bandwidth estimation:  t-distribution table: values ( v = n - 1 ) Safe Bandwidth Estimation Alpha=0.75Alpha=0.90Alpha=0.95 v=11.0003.0786.314 v=20.8161.8862.920 v=30.7651.6382.353 v=40.7411.5332.132 v=50.7271.4762.015 v=100.7001.3721.812

9. A..Basu,I.Cheng and Y.Yu, U. of Alberta 9  Expect Object Size:  Important property of V(n): Statistically (if we view random variable and s as constant), V(n) has a single maximum value. (Proof omitted)  Intuition of the property: When n is too large, too much time is used for bandwidth testing, leaving little time for real object transmission; when n is too small, value is too large, leading to great margin of under-estimation of bandwidth. Expected Object Size

10. A..Basu,I.Cheng and Y.Yu, U. of Alberta 10 Multi-server Environment  From the perspective of the client, there are several server available to delivery the same content.  Client can request a strip of the object from each server. The size of the strips will be proportioned to relative bandwidth of all the servers.

11. A..Basu,I.Cheng and Y.Yu, U. of Alberta 11  Suppose we have K channels available, then  We have  is the expected object strip size on ith channel.  The total object size.  Theorem: The total object size has the same property as in single server environment. Statistically, it has a single maximum. Multi-server Environment

12. A..Basu,I.Cheng and Y.Yu, U. of Alberta 12  The multi-server algorithm: obtain samples on each channel; ; while (V(n)>V(n-1)) { ; obtain sample on each channel; Calculate ; } return ;  Multi-server Algorithm

13. A..Basu,I.Cheng and Y.Yu, U. of Alberta 13 Refinement of the algorithm  Actually, this simple extension of the algorithm is not always optimal.  When K increases,  It’s possible that. At this time, we’d better drop channel #2. O V(n) t Channel #2 Channel #1 Using Y1 Y2 Y1>Y2?

14. A..Basu,I.Cheng and Y.Yu, U. of Alberta 14 Refinement of the algorithm … … … … … … … … … Channel #1 Channel #2 Channel #3 Channel #K Step 1 Sum all K values together Pick the largest Sum the largest two Sum the largest three Step 2 Pick the largest Step 3 k: the number of channels for real transmission

15. A..Basu,I.Cheng and Y.Yu, U. of Alberta 15 obtain samples on each channel; Calculate for ; ; while(TRUE) { ; obtain sample on each channel; Calculate for ; if (V(n)<V(n-1)) break; } return on each channel that constitutes V(n); Refined multi-server algorithm

16. A..Basu,I.Cheng and Y.Yu, U. of Alberta 16 Simulation Results  Average bandwidth: 100kbps and 10kbps.  Parameters: alpha=0.95, 100 total slices. Two channels.  Standard deviations is {0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6} of the bandwidth average.  Results are average of all combination of the standard deviation parameter. 4.5%

17. A..Basu,I.Cheng and Y.Yu, U. of Alberta 17 Simulation Results  Two channels -- 100kbps and 10kbps.  Standard deviations is {0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6} of the bandwidth average. 30%, SD: Ch#1=60.0, Ch#2=6.0 15%, SD: Ch#1=60.0, Ch#2 vary from 0.25 to 6.0.

18. A..Basu,I.Cheng and Y.Yu, U. of Alberta 18 Summary  Introduce a statistical model with confidence level to multi-server bandwidth monitoring  Dynamically determine the number of sampling  Drop the unreliable channels

19. A..Basu,I.Cheng and Y.Yu, U. of Alberta 19 The End Questions and Comments?