Multi-server Optimal Bandwidth Monitoring for QoS based Multimedia Delivery Anup Basu, Irene Cheng and Yinzhe Yu

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1 Multi-server Optimal Badwidth Moitorig for QoS based Multimedia Delivery Aup Basu, Iree Cheg ad Yizhe Yu Departmet of Computig Sciece U. of Alberta

2 Architecture Applicatio Layer Request receptio -coectio hadlig -request processig Adaptatio Layer Moitor Prepare Trasmit -moitor/poll badwidth -determie object size trasform requested object to target size deliver object To cliet Lower Layer feedback from etwork Object delivery across etwork A..Basu,I.Cheg ad Y.Yu, U. of Alberta 2

3 Assumptios ad otatios We eed to make a oe-time trasmissio of a multimedia object (servers to cliet. User specified a time limit T o cliet. It s epected that the trasmissio will fiish withi T by cofidece level. The first fractio t of T will be used for badwidth testig. Badwidth testig is performed by usig time slices of equal legth ts. Each time slice has badwidth sample i Ci / ts T / t s, badwidth populatio X, X 2,..., X t /, badwidth samples,..., t, s 2 A..Basu,I.Cheg ad Y.Yu, U. of Alberta 3

4 otatios s 2 i i X, is actual badwidth we try to estimate., is the average of badwidth samples. ( i i i i 2, is the variace of badwidth samples. Our Problem is: 2 s First, give,,,, give a estimatio of, so that P( <. est Secod, determie optimal value of, i order to maimize est ( ts. A..Basu,I.Cheg ad Y.Yu, U. of Alberta 4

5 Statistical Backgroud-Samplig ad Estimate Assume the paret populatio coforms to the ormal distributio: (, σ, σ is ukow is the mea of samples, the s / coforms to Studet s t-distributio (t-distributio. t If samplig without replacemet from a fiite populatio, we should have a fiite populatio correctio factor: t s A..Basu,I.Cheg ad Y.Yu, U. of Alberta 5

6 t-distributio As, the t-distributio is idetical as ormal distributio. Robust: t-distributio works well, eve if the paret populatio is ot eactly ormally distributed. A..Basu,I.Cheg ad Y.Yu, U. of Alberta 6

7 A..Basu,I.Cheg ad Y.Yu, U. of Alberta 7 Safe Badwidth Estimatio, ~,. (.., (,, (, (, ( > < > < s t The s t P t s P t s kow we As P e i P where fid to problem is Our est est est est

8 Safe Badwidth Estimatio Safe badwidth estimatio: t est (, s t-distributio table: values (v - t, ( Alpha0.75 Alpha0.90 Alpha0.95 v v v v v v A..Basu,I.Cheg ad Y.Yu, U. of Alberta 8

9 Epected Object Size Epect Object Size: V ( est ( ( ts t(, ( ts Importat property of V(: Statistically (if we view radom variable ad s as costat, V( has a sigle maimum value. (Proof omitted Ituitio of the property: Whe is too large, too much time is used for badwidth testig, leavig little time for real object trasmissio; whe is too small, t (, value is too large, leadig to great margi of uder-estimatio of badwidth. s A..Basu,I.Cheg ad Y.Yu, U. of Alberta 9

10 Multi-server Eviromet Cotet Storage Server Cliet Cotet Storage Server Iteret Cotet Storage Server From the perspective of the cliet, there are several server available to delivery the same cotet. Cliet ca request a strip of the object from each server. The size of the strips will be proportioed to relative badwidth of all the servers. A..Basu,I.Cheg ad Y.Yu, U. of Alberta 0

11 Multi-server Eviromet Suppose we have chaels available, the 2 We have 2 Vi ( est. i ( ts is the epected object strip size o ith chael. The total object size V ( V (. i i Theorem: The total object size has the same property as i sigle server eviromet. Statistically, it has a sigle maimum. A..Basu,I.Cheg ad Y.Yu, U. of Alberta

12 Multi-server Algorithm The multi-server algorithm: obtai samples V V ( V ( i i ( 2 V ( 2 2 i i ; while (V(>V(- { + ; ; ; obtai sample, 2, Calculate V V ; } i i retur ; est + 3 ( ( o each chael; o each chael; A..Basu,I.Cheg ad Y.Yu, U. of Alberta 2

13 Refiemet of the algorithm Actually, this simple etesio of the algorithm is ot always optimal. Whe icreases, 2 2 It s possible that V (, ( > V, + V2 (,. At this time, we d better drop chael #2. V( ( est, i V i Usig Usig 2 Y Y>Y2? Chael # < 2 2 Y2 Chael #2 O A..Basu,I.Cheg ad Y.Yu, U. of Alberta 3 t

14 Step 2 Refiemet of the algorithm V ( ( 2 V 2 ( V 3 ( V V ( 3 V ( V 2( 2 V 2( 3 V 2 ( V 3( 2 V 3( 3 V 3 ( V ( V ( ( Pick the largest k k: the umber of chaels for real trasmissio k 2 Sum the largest two V V ( 3 Sum the largest three Sum all values together Step Chael # Chael #2 Chael #3 Chael # Step 3 Pick the largest A..Basu,I.Cheg ad Y.Yu, U. of Alberta 4

15 Refied multi-server algorithm obtai samples o each chael; Calculate V, for ; ( GetMa( V ; while(true { } retur + i ; ;, 2 ( j i {,2,..., }, {,,..., } + obtai sample o each chael; CalculateVi (, j for i {,2,..., }, j {, 2,..., }; ; ( GetMa( V if (V(<V(- break; est j 2 o each chael that costitutes V(; A..Basu,I.Cheg ad Y.Yu, U. of Alberta 5

16 Simulatio Results 60 Time Limit Cofidece Level Result # of Overtime ru (out of % Our Algorithm Fi Sample Size Method # of Fi Samples Average badwidth: 00kbps ad 0kbps. Parameters: alpha0.95, 00 total slices. Two chaels. Stadard deviatios is {0.025, 0.05, 0., 0.5, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6} of the badwidth average. Results are average of all combiatio of the stadard deviatio parameter. A..Basu,I.Cheg ad Y.Yu, U. of Alberta 6

17 Simulatio Results Chael Usage (Drop 30%, SD: Ch#60.0, Ch#26.0 umber of rus use oly Chael # (out of %, SD: Ch#60.0, Ch#2 vary from 0.25 to 6.0. Average of all variace o Chael #2 Variace 0.6(mu o Chael # Variace of Chael # Two chaels -- 00kbps ad 0kbps. Stadard deviatios is {0.025, 0.05, 0., 0.5, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6} of the badwidth average. A..Basu,I.Cheg ad Y.Yu, U. of Alberta 7

18 Summary Itroduce a statistical model with cofidece level to multi-server badwidth moitorig Dyamically determie the umber of samplig Drop the ureliable chaels A..Basu,I.Cheg ad Y.Yu, U. of Alberta 8

19 The Ed Questios ad Commets? A..Basu,I.Cheg ad Y.Yu, U. of Alberta 9

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