# Optimal Adaptive Bandwidth Monitoring for QoS Based Retrieval

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7 7 DEFIITIO 1: Basic otatio T is the time limit for the multimedia object trasmissio specified by a user. t is the time used for badwidth testig. t s is the legth of each time slice used for obtaiig badwidth samples. T =, is the umber of time slices i period T, which geerates our badwidth t s populatio, X 1, X,..., X. = t t s, is the umber of time slices i period t, which geerates our badwidth samples, x 1, x,..., x. X i µ =, µ is the average of badwidth populatio, the actual average badwidth we are tryig to calculate. ( ) xi µ σ =, σ is the variace of badwidth populatio. xi x =, x is the average of the badwidth samples x 1, x,..., x. s = ( x x) i 1, s is the variace of the badwidth samples. With the otatio defied above, our problem ca be stated as give,, x, s, estimate µ. I statistical practice, x is usually used as a estimate of µ. Actually, give,, x ad s, the

9 9 s x d ( α, ) µ (3) 1 s (3) tells us that the value of µ is greater or equal to x d ( α, ) with a probability of 1 100( 1 α)%. With this observatio we defie badwidth estimatio as follows. DEFIITIO : Safe Badwidth Estimatio s We defie µ est = x d( α, ) to be a safe estimatio of the future badwidth. 1 Accordig to the theory described above, we have a cofidece of 100( 1 α)% that the actual badwidth will ot be lower. We metioed that µ is a radom variable cetered at x. From Defiitio, we ca see that i order to provide a time limit guaratee we actually uder-estimate the badwidth. This uderestimatio has its cost; if we use µ est as future badwidth estimatio to determie the maximum size of the media object, the actual trasmissio will most likely uder-utilize the remaiig time T-t. It ca be show that the actual time uder-utilized is o the average ( t) µ est ~ T 1. So we defie the uder-utilized time T as follows: µ ( t ) ( T ) µ est t T, or µ

10 10 DEFIITIO 3: Uder-utilized Time ~ T s d( α, ) µ 1 = = x x est ( ) 1 ( T t). It determies the average uderutilizatio time with the safe estimatio. ( T t ) s Give all the defiitio ad aalysis above, we are ready to determie how much badwidth testig to perform i order to maximize the data delivered to a user while coformig to the time limit requiremet set by the user. From Defiitio 3, we assert T ~ is decreasig as grows ad the rate of decrease dimiishes (we provide a iformal proof i Theorem 1 below) whe is relatively small compared to. This meas as we take more badwidth samples, we ca estimate the future badwidth more accurately with the same cofidece α, thus reducig the cost of time uder-utilizatio. We ca ~ ~ ~ deote the beefit of each ew sample as T = T T 1. As we said, T ~ decreases as grows. O the other had, the cost of each ew sample is a costat, t s, which is a time slice. So we ca compare T ~ with t s each time a ew sample is obtaied, the process of badwidth testig cotiues util T ~ method. is less tha t s. The pseudocode i ALGORITHM 1 below illustrates the Theorem 1: T ~ Decrease as grows, ad the rate of decrease dimiishes whe is relatively small compared to.

11 11 Proof: Sice T ~ > 0, the statemet is equivalet to ( ) 0 ~ < T ad ( ) 0 ~ > T. We write ( ) T ~ as follows, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) h g f c t T d x s t T x s d T s s = = = ~,, α α (4) Sice s ad x are radom variables determied by the characteristics of the badwidth populatio, we view them as part of the costat c. We deote ( ) ( ) d f, α =, ( ) 1 = g, ( ) ( ) t s T h =. Thus, we have ( ) 1 = g, ad ( ) ( ) = g (5). We have ( ) 0 < g, ad ( ) 0 > g for 4 3 <. We also have ( ) 0 < = t s h, ad ( ) 0 = h (6). Thus, if we deote ( ) ( ) ( ) h g l =, the ( ) ( ) ( ) ( ) ( ) + = h g h g l, ( ) ( ) ( ) ( ) ( ) ( ) ( ) + + = h g h g h g l (7) Therefore, with (5)(6)(7), we have ( ) 0 < l, ad ( ) 0 > l for 4 3 <.

12 1 Fially, whe eed to show that for f ( ) = d ( α, ), we have similar results that f ( ) < 0 f ( ) > 0, ad. As f() is a very complex fuctio, a strict mathematical proof of the property is beyod the scope of this paper. To prove the property umerically, we calculated the values of α for α { 0.75,0.90,0.95} d (, ), ad = 1 500, ad verified that f( ) - f(-1) < 0 ad f()- f(-1)>f(-1)-f(-). We calculated the values of d ( α, ) usig the algorithm described i [15] ad compared these values with values provided i the t-distributio table i [16] for verificatio purpose. ~ T = + <, Therefore, ( ) f ( ) l( ) f ( ) l( ) 0 ~ T + ( ) = f ( ) l( ) + f ( ) l( ) f ( ) l( ) > 0 for 3 <. 4 ALGORITHM 1: Optimal Badwidth Testig Obtai samples x 1, x, x 3 ; ~ ~ ~ ~ ~ Calculate T, T 3, ad T3 = T3 T ; = 3; while ( T ~ > t ) { s = + 1; Obtai sample x ; Calculate T ~ ~ ~ ~ ad T = T T 1 ;

13 13 } retur µ est ; III. IMPLEMETATIO AD EXPERIMETS We aswer the followig questios through experimets: (a) How well does the model work i achievig our goal of performig optimal amout of badwidth testig i badwidth estimatio? (b) How well does the model deliver the fial QoS result to ed-users? For example, if a user specifies its target trasmissio time limit associated with a cofidece goal (say meet the time limit by 95% time ), ca the model really achieve this level of guaratee? Fially, we are iterested i the complexity of the model. Ca we implemet the model efficietly so that we ca make decisios based o them for retrieval applicatios while estimatig badwidth? I this sectio, we describe our implemetatio of the model i Java ad the preset the experimetatio results that aswer these questios. Our implemetatio cosists of two programs, a server ad a cliet. The server is a backgroud process o the server host. It listes to a kow port o the server machie ad waits for a coectio request from a cliet. The cliet is a Java Applet embedded i a HTML page. It icludes a GUI that allows a user to specify parameters for a object trasmissio. There are three parameters; Time Limit gives the time a user wats to use for object trasmissio, Cofidece Goal is the system s guaratee that with this probability the trasmissio will be fiished withi the time limit, Time Slice is the time used for each badwidth sample. Figure 1

16 16 Cofidece Goal 95% 75% Average o. Of Sample Sample Average (kbps) Sample Variace (kbps) Estimatio (kbps) Actual Average (kbps) Actual Trasfer Time (s) Actual Total Time (s) Total o. Of Exceptio i 100 rus 4 0 Table 1: Experimet results o campus etwork, with Time Limit of 10s, Time Slice of 0.0s. Results are for two differet cofidece goals. The results i Table 1 are based o experimets with parameters Time Limit = 10 secods, Time Slice = 0.0 secods. We give the results for Cofidece Goal = 95% ad 75% ( α = 5 adα = 5 ). For each parameter set, we perform the trasmissio 100 times ad report the averages. From the results i Table 1, we ca see that whe α = 5, it takes oly 14.6 samples out of 500 (=10/0.0=500) to achieve the optimal amout of badwidth testig. Oly 4% of the trasmissios exceed the time limit ad we still utilize 94.8% of the time limit for actual applicatio data trasfer. The results for α = 5 are similar, except that it takes fewer testig samples ad thus leads to a less accurate estimate of badwidth. This i tur produces more

17 17 trasmissio exceedig the time limit (0%) but utilizes a larger portio of time limit for actual applicatio data trasmissio (96.6%). I the secod experimet eviromet settig, we still use the server i Uiversity of Alberta, but use a host coected to a local broadbad ISP with cable modem as cliet. A traceroute result shows there are 11 hops betwee the cliet ad the host. The cliet rus Microsoft Widows 000 Professioal ad Iteret Explorer versio 5.0. We preset the same set of results i Table below. Cofidece Goal 95% 75% Average o. Of Sample Sample Average (kbps) Sample Variace (kbps) Estimatio (kbps) Actual Average (kbps) Actual Trasfer Time (s) Actual Total Time (s) Total o. Of Exceptio i 100 rus 7 Table : Experimet results o home etwork, with time Limit of 10s, Time Slice of 0.0. Results are for two differet cofidece goals. Comparig Table with Table 1, we ca see that the variace of the badwidth is sigificatly larger i the home etwork eviromet. Therefore, the badwidth testig part of the program is

18 18 forced to take more samples ad make more coservative estimatio o future badwidth, which i tur reduces the actual data trasfer time. evertheless, eve i this etwork eviromet, 87% of time limit is used i applicatio data trasmissio whe α = 5. We ow show the effectiveess of the method by comparig the results of our method with a o-adaptive badwidth testig method, which meas the cliet always takes the same umber of samples ad use the average of these as the estimate of future badwidth. Figure shows the results for the campus etwork eviromet described above. Figure : Actual trasmissio time with differet sample umber usig o-adaptive badwidth testig.

21 1 REFERECES [1] A. Vogel, B. Kerherv'e, G. vo Bochma, J. Gecsei, Distributed Multimedia ad QoS: a Survey, IEEE Multimedia, Vol. o., Summer [] P. Ferguso, G. Husto Quality of Service: Deliverig QoS o the Iteret ad i Corporate etworks, Wiley Computer Publishig, [3] I. Miloucheva, Quality of Service Research for Distributed Multimedia Applicatios ACM Pacific Workshop o Distributed Multimedia Systems, Hawaii, Hoululu, 1995 [4] G. Pacifici, R. Stadler, A Architecture for Performace Maagemet of Multimedia etworks. I Proceedig of IFIP/IEEE Iteratioal Symposium o Itegrated etwork Maagemet, Sata Barbara, Jue 1995 [5] G. Gopalakrisha, G.Parulkar, Efficiet Quality of Serverice i Multimedia Computer Operatig Systems, Departmet of Computer Sciece, Washigto Uiversity, Techical report, August [6] L. Zhag et al. RSVP: A ew resource reservatio protocol. IEEE etwork, 7(5):8-18, September [7] R. Brade, L. Zhag et al. Resource ReSerVatio Protocol - Versio 1 Fuctioal Specificatio (RFC 05), September [8] D. Ferrari, A. Gupta, ad G. Vetr, Distributed advace reservatio of real-time coectios. ACM/Spriger Verlag Joural o Multimedia Systems, 5(3), [9] J. Bolliger ad T. Gross. A Framework-based Approach to the Developmet of etworkaware Applicatios. IEEE Trasactios o Software Egieerig, 5(5): , May 1998.

22 [10] J. Bolliger, T. Gross et al. Badwidth modelig for etwork-aware applicatios. I Proceedigs of Ifocomm'99, March [11] X. Wag ad H. Schulzrie, Compariso of Adaptive Iteret multimedia applicatios, IEICE Tras. o Commuicatios, vol. E8-B, o. 6, pp , Jue [1] I. Cheg, A. Basu, Y. Zhag ad S. Tripathi, QoS Specificatio ad Adaptive Badwidth Moitorig for Multimedia Delivery. I Proc. Of EUROCO 001, page , Bratislava, Slovak Republic, July 001. [13] D. Harett. Statistical Methods, Third Editio. Addiso-Wesley Publishig Compay, Ic. 198 [14] R. Jai, The Air of Computer Systems Performace Aalysis. Joh Wiley & Sos, Ic., [15] William H. Press et al, umerical Recipes i C, secod Editio. Cambridge Uiversity Press, Jauary [16] Daiel Zwilliger, CRC Stadard Mathematical Tables, 30th Editio. CRC Press, Jauary 1996.

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