Optimal State Prediction for Feedback-Based QoS Adaptations

Transcription

1 Optmal State Predcton for Feedback-Based QoS Adaptatons Baochun L, Dongyan Xu, Klara Nahrstedt Department of Computer Scence Unversty of Illnos at Urbana-Champagn b-l, d-xu, Abstract In heterogeneous network envronments wth performance varatons present, complex dstrbuted applcatons, such as dstrbuted vsual trackng applcatons, are desred to adapt themselves and to adjust ther resource demands dynamcally, n response to fluctuatons n ether end system or network resources. By such adaptatons, they are able to preserve the user-perceptble crtcal QoS parameters, and trade off non-crtcal ones. However, correct decsons on adaptaton tmng and scale, such as determnng data rate transmtted from the server to clents n an applcaton, depend on accurate observatons of system states, such as quanttes of data n transt or arrved at the destnaton. Sgnfcant end-to-end delay may obstruct the desred accurate observaton. We present an optmal state predcton approach to estmate current states based on avalable state observatons. Once accurate predctons are made, the applcatons can be adjusted dynamcally based on a control-theoretcal model. Fnally, we show the effectveness of our approach wth expermental results n a clent-server based vsual trackng applcaton, where applcaton control and state estmatons are accomplshed by mddleware components. 1 Introducton When complex dstrbuted applcatons demand a partcular level of Qualty of Servce (QoS) from the underlyng system n a heterogeneous network envronment, only those systems that provde system-wde end-to-end QoS guarantees (va CPU and network resource reservaton and admsson control) are able to meet such demands. If ths s not the case, such as the Internet wth best-effort servces, applcatons may experence sgnf- Ths research was supported by the Ar Force Grant under contract number F , Natonal Scence Foundaton Grant under contract number NSF EIS , and Natonal Scence Foundaton Career Grant under contract number NSF CCR cant varatons n resource avalablty. These varatons are caused by ether physcal lmtatons, n the case of wreless lnks, or dynamc multplexng of multple compettve access to a lmted pool of resources. However, there exst flexble applcatons that present the followng characterstcs: Frst, they can accept and tolerate resource scarcty to a certan mnmum bound, and can mprove ts performance f gven a larger share of resources. Second, they are wllng to sacrfce the performance/qualty of some applcaton-level servces n order to preserve the performance/qualty of crtcal functons. For these flexble applcatons, t s possble to adapt to the avalablty varatons and stll manage to preserve QoS for crtcal parameters. Applcaton-level adaptaton support s also necessary when t s hard to specfy an upper bound of QoS demand for reservaton, e.g., for nteractve applcatons. The clent-server based vsual trackng applcaton s an example of flexble applcatons. A vsual trackng server grabs lve vdeo frames n real tme from a camera, and sends them over the network to the vsual trackng clent. The clent executes a computatonally ntensve trackng algorthm, whch tracks the coordnates of nterested objects. Our nterests focus on key applcaton QoS parameters such as the precson of trackng algorthms, whch depends on vdeo qualty, network bandwdth avalablty, jtter and other QoS parameters. As long as trackng precson s preserved, other parameters n the applcaton, such as vdeo qualty, can be dynamcally tuned, adjusted and reconfgured. In order to adjust the applcaton approprately, and to decde when, how and to what extent for the applcaton to adapt, accurate dentfcaton of current system states s needed, based on observable parameters. Ths observe and control process resembles a control system, where control sgnals are determned by a controller, based on the current state estmates. Our prevous work takes advantage of control theory to model ths process. As a consequence, a Control Model was developed and

2 theoretcal results were gven to prove stablty and farness propertes n the model [11]. The objectve of the approach was to optmally adjust the nternal parameters and semantcs of flexble applcatons, wth a centralzed control algorthm. The effectveness of a control algorthm depends on accurate observatons of system states. However, n a dstrbuted applcaton wth the presence of end-to-end delays, many system states are not drectly observable n the end system, thus need to be estmated. For example, n the vsual trackng applcaton, n order to control the applcaton and dynamcally adjust the data rate transmtted from server to clent, we need to obtan system states such as quanttes of data n transt or arrved at the clent. Sgnfcant end-to-end delay may obstruct the desred accurate observatons, when estmatons are used nstead. The key contrbutons of ths paper are the followng. (1) An extended Dstrbuted Control Model: The Control Model ntroduced n [11] s extended from a model focusng on local resources such as CPU, to a dstrbuted model focusng on bandwdth avalablty n Transmsson s. The tradeoff s that the farness property that was prevously proved can no longer be guaranteed. (2) A lnear model for Transmsson s: To characterze the Transmsson s n a dstrbuted applcaton, we develop a lnear model wth concrete coeffcents, on whch state estmaton technques are based. (3) Optmal state predcton mechansms: Accurate control sgnals are based on precse estmates of system states. Wth the presence of sgnfcant end-to-end delay that obstructs accurate state observatons, we present an optmal predcton approach to estmate current system states based on avalable observatons. We adopt optmal estmaton theores such as the Kalman Flter n our approach. Asssted by optmal state predcton technques, the applcaton can be optmally controlled to adapt to dynamc varatons. (4) Verfcaton wth vsual trackng: We show the valdty of our approach by experments wth a clent-server based vsual trackng applcaton, where trackng precson s the crucal QoS parameter consdered, and state predcton mechansms are mplemented as mddleware components. The rest of ths paper s organzed as follows. In Secton 2, we dscuss exstng related work. In Secton 3, we present an overvew of the mddleware control archtecture, n whch optmal estmaton algorthms contrbute a key functonalty. In Secton 4, we focus on modelng the Transmsson n a dstrbuted applcaton. In Secton 5, we present our optmal predcton approach to consder sgnfcant delays n the state estmaton process. In Secton 6, we show experments wth the clent-server based vsual trackng applcaton. Secton 7 concludes the paper and dscusses future work. 2 Related Work In recent research, control theores have been examned for QoS adaptaton. In [3], a control model s proposed for adaptve QoS specfcaton n an end-to-end scenaro. In [4], the tme varatons along the transmsson path of a telerobotcs system are modeled as dsturbances n the proposed perturbed plant model, n whch the moble robot s the target to be controlled. In our prevous work [11], theoretcal proofs are gven for varous propertes applyng control theory to model QoS adaptaton. The ssues related to applcaton-level QoS adaptaton has also been studed by varous prevous work. The work presented n [2] uses software feedback mechansms that enhance system adaptveness by adjustng vdeo sendng rate accordng to on-the-fly network varatons. In [5], the authors proposed applcaton adaptaton at the confguraton level, whch carres out transparent transton from prmary components to alternatve components, as well as at the component level, whch redstrbutes resources n dfferent components so that a QoS tradeoff can be made. In [1], a software framework was proposed for networkaware applcatons to adequately adapt to network varatons. Smlarly to the above, our approach models applcatons as a seres of tasks and asssted by the feedback loop. However, we dffer n the sense that we take the vew that mddleware components control the adaptaton behavor of applcatons, and we propose a separaton of control and estmaton algorthms. Wth respect to control, proper choces are made on adaptaton tmng, scale and methods used, whch balances between the frequency and responsveness of adaptaton actons wthn the applcaton; Wth respect to estmaton, optmal predctons are beng made to obtan the best possble estmate of actual states. Optmal control and estmaton theores, e.g., Kalman Flters, have been prevously appled to flow control n hgh-speed networks. In [9], a Kalman Flter was gven for state estmaton n a Packet-Par flow control mechansm. In [1], Kalman Flter was also used to shape traffc n a collecton of VC sources n one VP of an ATM network, n ths case the system state s the number of actve transmsson sources. Our work dstngushes tself from prevous work n the followng way: (1) Kalman Flter s used as a optmal predcton algorthm, nstead a flterng or smoothng algorthm; (2) We use a dffer-

3 ent and a macroscopc system model to nterpret the dynamcs of the Transmsson ; (3) Applcaton-specfc adaptaton are performed n a slower tme scale (n multples of round-trp delays) and (4) The mddleware components make control decsons n the applcaton level, and based on applcaton-specfc semantcs, rather than on the packet level va a traffc shaper. 3 The Mddleware Control Archtecture We have adopted a mddleware soluton n order to mplement a centralzed control of all actve applcatons. We present the general archtecture of the mddleware soluton n ths secton, followed by detaled dscusson of the model and algorthms proposed for optmal state predctons, whch partcpate n the desgn of the overall archtecture. A major objectve of the archtecture s to mplement the observe and control process,.e., to observe current system states n the dstrbuted envronment and produce control sgnals to the complex dstrbuted applcatons. These sgnals determne the actual adaptaton actons (reconfguratons or parameter tunng) wthn the applcatons. The archtecture conssts of two parts: the Adaptors and Confgurators. In an end system, each Adaptor corresponds to a sngle type of resource, such as CPU or transmsson bandwdth, and conssts of an Adaptaton and an Observaton. Each Confgurator corresponds to a sngle target applcaton, and makes control decsons based on the output of Adaptors correspondng to several types of resources. The nteracton among varous mddleware components and applcatons s made through avalable specfc servce enablng platform, such as CORBA or DCOM. Our mddleware archtecture uses actve components, n the sense that these components call external nterfaces n the applcatons n order to control them. Fgure 1 shows an overvew of the archtecture. Applcaton Mddleware A Applcaton 1 Applcaton 2 Applcaton 3 Applcaton 4 Control Actons State O Adaptor for CPU Confgurator Adaptaton System State Interactons va servce enablng platforms Observaton Adaptor for Bandwdth Operatng Systems and Transmsson Network Fgure 1: The Mddleware Control Archtecture The optmal predcton algorthms presented n ths paper are mplemented n the Observaton, a part of the Adaptor. The goal of the desgn s to accurately obtan system states at a specfc nstant n a dstrbuted envronment, wth the presence of sgnfcant end-to-end delays. The mechansms below show that the mddleware components can optmally estmate the states wthout solctng actons n underlyng layers, whch may lead to layerng volatons. Accurately estmated states lead to approprate control decsons made by the Adaptaton [11] n the Adaptor, whch are nterpreted by the Confgurator and delvered to the applcatons, where proper adaptaton actons are performed. 4 Modelng Transmsson s We vew each applcaton as a seres of connected tasks, wth each task as a concrete component that performs operatons on the nput, generates output and consumes resources. We represent the relatonshps among tasks wthn an applcaton usng a drected acyclc graph, wth each drected edge ndcatng the producer-consumer relatonshp between output of the upstream task and nput of the downstream task. The drected acyclc graph s referred to as the task flow graph [7]. Wth the above vew of an applcaton, a dstrbuted applcaton has one or more Transmsson s n ts task flow graph, whch transmts applcaton data between two end systems. Snce multple end systems are nvolved, the mddleware control archtecture shown n Fgure 1 resdes n all end systems. In the Observaton, we observe the current system states, such as avalable bandwdth n the Transmsson. These observatons are delvered to the Adaptaton, whch calculates control sgnals accordng to the control polcy [11]. The dstrbuted vew s shown n Fgure 2 n the example of a clent-server based applcaton. Applcaton 1 sgnals Adaptaton Confgurator System States Transmsson Observaton Operatng Systems mddleware end-to-end delay Transmsson mddleware Observaton Adaptaton System States Applcaton 2 Confgurator Operatng Systems sgnals Fgure 2: The Mddleware Control Archtecture wth a Dstrbuted Applcaton The control algorthms ntroduced n our prevous work

4 A [11] apply the control theory n the practce of calculatng control sgnals n the Adaptaton s. In the PID control algorthm ntroduced as an example, we were able to prove that, f prorty weghts are gven to each task, the system farly allocates resources among competng tasks accordng to the weghted max-mn farness property. We also proved that the system converges to equlbrum, and stablty of control s preserved around a local neghborhood. Wth an approprate model for the transmsson task, we can extend ths work to apply to a dstrbuted envronment, wth the presence of sgnfcant end-to-end delays. 4.1 State Observaton n the Transmsson The accuracy of control sgnals calculated by the Adaptaton reles on precse observatons of system states. However, n the dstrbuted envronment where observng system states n a Transmsson s necessary, endto-end propagaton delay poses serous dffcultes to observe and capture such nformaton. An mportant state to observe s avalable bandwdth wthn the Transmsson, wth beng an ndex n the set of tasks wthn the applcaton. We take a clentserver applcaton as an example, and assume that the Observaton located on the clent can observe the number of receved data unts 1 durng the tme ( beng dscrete tme nstants),. In realty, we assume that s the number of data unts actually receved durng. On the server, the actual number of data unts sent by durng, denoted by, s controlled by the the Adaptaton. Fnally, s the number of data unts n flght n the Transmsson. Note that the Transmsson tself s dstrbuted on both clent and server sde, therefore, both and are nternal states n, whle s also the output of. The above scenaro s llustrated n Fgure 3. data unts u Adaptaton Tranmsson T System States Observaton Server u In Flght Sent x end-to-end delay Network Transmsson T y Actually receved Observaton z Observed Clent Fgure 3: States n the Transmsson y The challenge s the followng. Snce the mddleware 1 Data unts are defned based on applcaton-specfc semantcs. For example, n a vdeo-on-demand applcaton, a data unt may be defned as a vdeo frame. control archtectures are stuated n dfferent end systems, f end-to-end delays are present, at any partcular tme nstant, the server Observaton can only obtan prevously observed states by the clent Observaton, wth the lag equvalent to the end-to-end delay. Ths calls for an estmaton algorthm n the server Observaton to compensate the observaton error, and to predct the states for the current tme nstant. 4.2 A Lnear Model for the Transmsson As a preparaton for later applcatons of analytcal technques n the optmal estmaton theory to estmate system states n the dstrbuted Transmsson, we present a precse analytcal model to characterze the nternal dynamcs of the Transmsson! Abstract Model for A Generc Applcaton In order to control any Applcaton, we dentfy several key parameters n ths task, referred to as States. If we use a vector denotes task states, denotes nput to the task, $ denotes task output, % denotes system nose wthn the task, & denotes observaton, and ' denotes observaton error, we examne a lnear and dscretetme model descrbed by the followng form: ( ()+*,-./ / 6%7./ (1) $8 8):9( (2) &; 8)<$8 2'8 (3) where =) to?>8@ba, and *, 1, and 9 are known transton matrces wthout an error. In later dscussons, we develop a concrete analytcal model based on the above generc lnear model, whch s frequently used wthn the state space approach n control systems A Concrete Model for the Transmsson In order to develop a concrete model for the dstrbuted Transmsson, we consder two types of noses n the system. Frst, the data unts n flght from server to clent, C, may suffer from random and unpredctable varatons and dsturbances D, caused ether by physcal unstable condtons (n the case of wreless lnks) or statstcal multplexng of network connectons. Consequently, the receved quantty of data unts durng EF,, may also suffer from random dsturbances DHG. These are obvously system noses caused by external dynamcs n the Transmsson. Second,

5 D A the Observaton tself s also subject to random errors, whch can be characterzed as the observaton nose. Assume that the observed value s, we have -)< (4) ) 9 In Equaton (1), 4 s actually a scalar B. Followng the analogy of Equaton (4) wth (2) and (3) combned, we have $8, and ( contans?. We thus can compute based on Equatons (2) and (3): &; 8): -) (5) and 9 ), ( -) and '8 () (6) In addton, from the defnton of,, D and D G, we have ;B -):;!.=..= CB!.= D -):. A A!.= (7)!6D G./ (8) It follows from Equatons (7), (8), (1) and (6) that DHG *), 1 ) and % ()., (9) Ths concludes the state space representaton of the lnear model for Transmsson!. 4.3 Extendng Control Algorthms to Dstrbuted Envronment In our prevous work [11], a PID 2 control algorthm was gven, and a weghted max-mn farness property was proved. A prerequste for the farness property to hold s that the Observaton has the ablty to observe complete global system states. For example, f the resource beng observed s CPU usage n the same end system, global states can be observed for all competng tasks. However, ths s normally not the case n a dstrbuted envronment, when observng task states wthn the Transmsson. Snce the Observaton s resde as mddleware components n the end system, t has no ablty to obtan states correspondng to all other connectons sharng the network. In such cases, the only observable states are the parameters used or allocated 2 PID control s a classc control algorthm where the control sgnal s a lnear combnaton of the error, the tme ntegral of the error, and the rate of change of the error. by the Transmsson tself, such as occuped bandwdth. Therefore, whle the control algorthm stll adapts to varatons n resource avalablty and shows stablty and convergence propertes, t lacks crucal observatons to guarantee any global farness propertes. In dstrbuted applcatons, the PID control algorthm adopted n the Adaptaton may be modfed as follows: ;B -):;./ 3. ;. ; C.<./. ;./ (1) where s the reference value expected at equlbrum, ; s the actual number of data unts sent by!, C s the number of data unts n transt from server to clent, and and are confgurable scalng factors. The stablty and convergence proofs stll hold as n the prevous work. However, wth the presence of end-to-end delays, t s nherently not trval to accurately estmate drectly at the server, snce the number of data unts n transt n s not drectly observable. 3, the number of data unts receved, s drectly observable, but only at the clent sde. Therefore, at the server sde, the avalable values for C computaton n the control algorthm (Equaton (1)) are mprecse, as the values (needed for computaton) prevously observed by the clent are receved by the server only after an end-to-end delay from the tme of observaton. Ths leads us to the followng approach. Instead of dervng? usng only the avalable observed values transmtted from the clent to the server wth an end-to-end delay, we wll adopt optmal state predcton technques to estmate at the current tme nstant, whch forms dscussons n the next secton. 5 Optmal Predcton of States In Transmsson s In ths secton, we present an optmal predcton approach to optmally predct the current task states n the Transmsson, based on observed task states n prevous tme nstants before the end-to-end delay. The optmal predcton algorthms are mplemented n the server Observaton, whle the actual observaton s made n the clent Observaton. Optmalty n the predcton algorthms guarantees that the relatve error between the predcton and actual values of task states s mnmzed, 3 Equaton (7) s part of the lnear model of the Transmsson, but t can not be easly utlzed for the estmaton of snce t s not observable drectly.

6 3.e., a best possble guess s obtaned. We adopt the optmal control and estmaton theory [12] to develop the proposed algorthms, and assocate the theoretcal solutons wth the practcal cases n complex dstrbuted applcatons, focusng the Transmsson. 5.1 The Need for Predcton It s obvous from Equaton (4) that the clent Observaton s able to observe as, wth an observaton nose. However, from the control algorthm expressed n Equaton (1), we note that s actually used n the Adaptaton. In order to derve C on the server from the observed values on the clent, we assume that the clent acknowledges all receved data unts to the server, and that the server Observaton has the knowledge of the total number of data unts unacknowledged at the server up to the tme nstant, denoted by. Then, we have )F - as the observed values of wth an observaton nose. Naturally, represents the total number of unacknowledged data unts whch are ether n flght from server to the clent, whch s C, or receved by the clent, but acknowledgments not yet receved by the server. We thus have C ()<. (11) where? s the end-to-end transmsson delay from clent to server, s the samplng tme nterval between., assumng?. Ideally, f.! $. s known, C can be computed and then used n the control algorthm of Equaton (1). However, the end-to-end delay, represented by, prevents the knowledge of B %&'/ =.(!.<. The last avalable observaton s B.)! $. The need of predctng these values of n the server Observaton before calculatng arses from ths lack of knowledge. Fgure 4 llustrates the above scenaro. Acks Tranmsson T Observaton z Server Last Avalable z Hstory k- d t c t c u d Data unts sent ys unacknowledged Data unts n flght end-to-end delay k-2 k-1 Transmsson T x y Actually receved z d Predcted y k (current tme nstant) Observaton Observed Clent Future Tme (t) Fgure 4: State Predcton n Transmsson s We use * to denote the predcted values of. Assumng that? * s already obtaned optmally, we can estmate C by the followng Equaton: C ():. + * B (12) The problem then shfts to the development of approprate mechansms to obtan *. 5.2 Mechansms for Optmal Predcton Defnton of Optmalty Based on the Separaton Prncple [12], for a lnear stochastc system where an observer s used to estmate the system state, the parameters for the observer and controller are determned separately. Informally, ths means that we can develop an optmal predcton algorthm for B &%.,.-. n the server Observaton, whle stll retanng complete freedom for adoptng alternatve control algorthms n the server Adaptaton. Wth regards to the predcton accuracy, we prefer to desgn an optmal predcton algorthm that mnmzes the sum of squared errors between the predctons and values beng estmated,.e., a least-squares estmate. More precsely, f / =) 3.*, where * s the predcted values of at tme, we try to mnmze the quadratc error cost functon 1( $ 8)21(? () 3 /. The optmal predcton approach, e.g., Kalman Flter, presented n ths secton s desgned to mnmze 1( $ Requrements of an Optmal Soluton The optmal predcton problem s generally hard f the lnear stochastc system s n ts generc form. However, t s proved n optmal control theory [13] that smplfed predcton algorthms can be adopted as an optmal soluton n a specal case, wth two prerequstes. Frst, the system random dsturbances % and observaton noses '8 are uncorrelated whte Gaussan-Markov sequences wth zero mean. Ths can be nterpreted that: (1) random vectors n the same stochastc sequence are ndependent of each other; (2) they can be unquely characterzed by a jont Gaussan probablty densty functon; (3) ths densty functon has zero mean expectaton, and (4) random vectors n dfferent stochastc sequences are uncorrelated wth each other. Second, the ntal system state vector ( s also a Gaussan random vector wth zero means. We assert that the system states and noses n the Transmsson observe such nature. Ths asserton s based on the followng characterstcs.

7 A A 3 (1) The states n the Observaton and the Transmsson are not correlated, snce the Observaton s are mplemented separately n the mddleware level, whle the Transmsson s part of the applcaton. Ths observaton guarantees that the observaton nose '4 and the system nose %7 are uncorrelated. (2) Wthn the transmsson path, when the number of smultaneous connectons sharng the same physcal communcaton channel (statstcal multplexng n ntermedate swtches) s large, we expect that n a tme nterval of length, the changes n s very small compared to tself. Ths leads to the fact that changes n due to actvtes of other connectons wll be small. Thus, when we model as a process gven by Equaton (7) ; -)<C... 7C. C7D., the term D.+, whch s the dynamc dsturbances caused by actvtes of other connectons, can be modeled as a zero-mean Gaussan whte nose [9]. Even though when C s small and the connecton s n a startng stage, the possblty of an ncrease s larger than a decrease, ths assumpton of zero mean s justfable when ; s suffcently far from. The same observaton also apples to and D G. Ths concludes that the random nose % s a whte Gaussan-Markov sequence wth zero mean. We conclude that random dsturbances of the Transmsson satsfy the requrements of applyng the smplfed predcton algorthms, such as the Kalman Flter predcton algorthm that follows Parameters n the Kalman Flter *. 1.. *. * We now apply the frequently used optmal estmaton algorthm, Kalman Flter, to solve the predcton problem of States n the Transmsson. Equaton (9) shows that both and. n Equaton (1) are constants wthout error. In addton, 4 are also known n the server Observaton wthout error n the nterval >4@BA. We ntroduce the defnton of the followng terms: (1) The expected values, or expectatons, of any random vector s defned as the mean vector of. Formally, 4) ;, where for a random varable s defned as (), f s the probablty densty functon of. (2) The error covarance matrx of n the Transmsson s defned as: () ( ( ( ( (13) (3) The dynamc system dsturbance % s a whte, zeromean Gaussan random sequence showng the followng propertes, where matrx: s the system nose covarance %7 ) (14) ) %7 % (15) % %7 ) ) (16) (4) Smlarly, n Equaton (2) and (3), 9 s a constant and the observaton nose s modeled as a whte, zeromean Gaussan random sequence that s uncorrelated wth the system dsturbance: '4 ) (17) 8) '4 '8 (18) '8 '8 ) ) (19) ) 8 %7 all and (2) where s the observaton nose covarance matrx. Accordng to Equaton (6), '8 s a scalar, t follows that s the varance of, (), when s a Gaussan dstrbuton!. In practce, t s necessary to determne and offlne. These covarance matrces ndcate the level of confdence n the system model and observatons, respectvely. If one were to ncrease, ths would ndcate that stronger noses are drvng the dynamcs. Consequently, the rate of growth of the elements of the error covarance matrx wll also ncrease, whch ncreases the flter gan (refer to Appendx for formal presentatons), thus weghng the measurements more heavly. Therefore, by ncreasng, we n effect put less confdence n the system model. Smlarly, ncreasng ndcates that the observatons are subject to a stronger corruptve nose, and therefore should be weghed less by Kalman Flter Operatons of Kalman Flter Based on these defntons, Kalman Flter operates recursvely n a predct-update manner as nformally descrbed n the followng phases. Refer to Appendx for the formal equatons. Observed Phase z (k-1) Update t c Propagaton z Update (k-1)- k-1 (k-1)+ - k + Tme Estmated x (k-1) x (k-1) - x + x Predct Update Predct Update Fgure 5: The Kalman Flter n operaton (1) Predcton Phase occurs at tme, that s, before observatons are made at tme. State predctons

8 are made for states, and error covarance predctons s also made. (2) Kalman Flter Gan Computaton Phase occurs between and, whch s the tme after. The Kalman Flter gan matrx s computed to be used later n the Update Phase. (3) Update Phase occurs at tme. The Kalman Flter gan matrx s used along wth the new observaton &;. The error covarance matrx 4 s also updated from prevously predcted n the Predcton Phase. These phases are executed repettvely tll the tme when the latest observaton s avalable from the clent Observaton. After ths tme nstant, we can deploy a lnear-optmal predctor to predct the state and ts error covarance on the bass of all the nformaton that s avalable wthout observaton. Denotng the tme of latest avalable observaton on the clent as 7. - for Transmsson, where s the present tme nstant on server, the lnear-optmal predctor starts wth the latest state estmate update phase usng Kalman Flter,.e.,..-, and then recursvely apples the state predcton phase to calculate (B ) B &..-.. Accordng to Equaton (6), we have the followng for Transmsson : * B ):9 (B.(. (21) Equaton (21) concludes our predcton mechansms utlzng the Kalman Flter. When the estmated values of are appled to Equaton (11), can be obtaned and thus appled to the control algorthm n the Adaptaton as presented n Equaton (1). 6 Experments wth Vsual Trackng Based on the algorthms developed n prevous sectons, we have mplemented a prelmnary mddleware control archtecture to control a clent-server based vsual trackng applcaton, adoptng Kalman Flter as a optmal predcton mechansm n the server Observaton, wth the presence of end-to-end delay. 6.1 Overvew of the Vsual Trackng Applcaton We use a clent-server based vsual trackng applcaton as an example of complex applcatons to evaluate our approach. Fgure 6 shows an overvew of ts archtecture. Based on the orgnal XVson [6] project n Unx, we have completed the mplementaton of the clent-server based vsual trackng applcaton on the Wndows NT 4. platform n Vsual C++ 5., usng Wndows Sockets 2 API for the network transmsson. Lve vdeo nput Vdeo Camera Frame Dgtzng Server Network Transmsson of Dgtal Lve Vdeo Vsual Trackng Feature Detecton Vsual Trackng Feature Detecton Vsual Trackng Feature Detecton State Update State Update State Update Identfcaton and dsplay Clent Fgure 6: The Clent-Server Vsual Trackng Applcaton We have mplemented the Adaptors shown n Fgure 1 n C++ and Java as mddleware components, ncludng both the Adaptaton, usng Equaton (1) as the control algorthm, and the Observaton, usng the Kalman Flter as the optmal state predctor. All mddleware components nteract among one another and wth the applcaton usng CORBA. We use ORBacus 2..4 [8] as our CORBA mplementaton. Fgure 7 shows the man trackng wndow of the applcaton wth three trackers (SSD, lne and corner) runnng smultaneously. By enablng adaptaton, the prmary QoS parameter that we focus on s the trackng precson. For qualty assurance of ths parameter, other QoS parameters such as the mage sze can be sacrfced as a tradeoff. We tested our system n a varyng network envronment, n order to experment applcaton-level adaptaton on transmsson bandwdth requrements. In order to smulate bandwdth fluctuatons n a typcal dstrbuted envronment over wde-area networks, we have also mplemented a smple network smulator, whch smulates packet delay through a transmsson path of multple network routers, each of them mplementng the FIFO schedulng algorthm. Because of the bursty nature of cross traffc, throughput fluctuatons may occur at varous tmes over the connecton. For the purpose of repeatng the same set of experments and for measurements of trackng precson, we use a computer generated mage sequence, n whch the object moves at fxed speed and path. For the expermental results shown n Fgure 8, the movng speed of the rectangle s set at a constant 3 screen pxels per second contnuously. In addton, we assume there are no other CPU ntensve process runnng n the background on the same platform. Ths s for the purpose of separatng the experments on bandwdth requrements from those on CPU requrements. In Fgure 8, the three graphs on the left are n the case wthout any adaptaton. The three graphs on the rght are n the case wth adaptaton support from the mddleware framework, wth ntegrated optmal predcton mechansms n acton n the server Observaton to

9 1.2e+6 1.4e+6 Observed Throughput (Bytes/s) Observed Throughput (Bytes/s) 1e+6 1.2e+6 1e+6 8 throughput (Bytes/s) 6 throughput (Bytes/s) tme (s) tme (s) (a) Observed Throughput (b) Observed Throughput Frame Sze (bytes) Frame Sze (Bytes) frame sze (bytes) 2 15 frame sze (bytes) Fgure 7: Vsual Trackng on Clent: The Man Trackng Wndow wth three trackers overcome end-to-end delay, as well as the PID control algorthm n the Adaptaton. We can observe that by changng the frame sze of the vsual trackng applcaton, the trackng precson wll be preserved wthout any trackng error at all tmes durng the connecton. In contrast, wthout any adaptaton, when the network throughput degrades to a certan degree, the trackng algorthm s not able to keep track of the object, the error accumulates rapdly verfyng that the trackng algorthm loses the object. Ths prove-of-concept system proves that the approach we have taken s effectve n preservng trackng precson n a dstrbuted envronment wth fluctuatng bandwdth and sgnfcant end-to-end delay between the clent and server. 7 Conclusons In ths work, we focus on the scenaro when flexble applcatons, such as clent-server based vsual trackng, need to adjust themselves to adapt to resource varatons and preserve crtcal QoS parameters, such as trackng precson. We have extended the Control Model n a dstrbuted envronment, modeled the Transmsson n a state-space representaton, presented an optmal state predcton mechansm to overcome end-to-end delay n dstrbuted state observatons, and presented prelmnary results wth our clent-server vsual trackng experments to verfy our approach. The optmal predcton mechansm proposed n ths paper s ntegrated n the server Observaton, as mddleware components and part of the mddleware control archtecture n a larger scale. On- Trackng Error (pxels) tme (s) (c) Applcaton-level Adaptaton: Orgnal Image Sze Trackng Precson: Error tme (s) (e) Trackng Precson Trackng Error (pxels) tme (s) (d) Applcaton-level Adaptaton: Chopped Image Sze Trackng Precson: Error tme (s) (f) Trackng Precson Fgure 8 (Left): Experments wthout adaptaton support Fgure 8 (Rght): Experments wth adaptaton support Fgure 8: Experments wth the Clent-Server Based Vsual Trackng Applcaton gong and future work nvolves applcaton-confgurable adaptaton and estmaton algorthms va a confguraton scrptng language, as well as QoS assurance and adaptaton n a multcastng envronment. Appendx: The Kalman Flter In the followng equatons, we dstngush between estmates made before and after the updates. s the state estmate that results from the predcton equaton (22) alone (.e. before the observatons are consdered), and s the corrected state estmate that accounts for the observaton made. and are defned smlarly. For completeness, the ntal condtons are 4 and.

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