ABSTRACT Comprehensive Statistical Admission Control for Streaming Media Servers

Comprehensive Statistical Admission Control forStreaming Media Servers∗Roger Zimmermann,Kun FuComputer Science DepartmentUniversity of Southern CaliforniaLos Angeles,California90089[rzimmerm,kfu]@ABSTRACTStreaming media servers and digital continuous media recordersrequire the scheduling of I/O requests to disk drives in real time.There are two accepted paradigms to achieve this:deterministic orstatistical.The deterministic approach must assume larger boundson such disk parameters as the seek time,the rotational latencyand the transfer rate,to guarantee the timely service of I/O re-quests.The statistical approach generally allows higher utilizationof resources,in exchange for a residual probability of missed I/Orequest deadlines.We propose a novel statistical admission con-trol algorithm called TRAC based on a comprehensive three ran-dom variable(3RV)model to support both reading and writing ofmultiple variable bit rate media streams on current generation diskdrives.Its major distinctions from previous work include(1)a veryrealistic disk model which considers multi-zoning of disks,seekand rotational latency profiles,and unequal reading and writingdata rate limits,(2)a dynamic bandwidth sharing mechanism be-tween reading and writing,and(3)support for random placementof data blocks.We evaluate the TRAC algorithm through an exten-sive numerical analysis and real device measurements.The resultsshow that it achieves a much more realistic resource utilization(upto38%higher)as compared with the best,previously proposed al-gorithm based on a single random variable(1RV)model.Mostimpressive,in all the experiments the difference between the re-sults generated by TRAC and the actual disk device measurementsmatch closely.Categories and Subject DescriptorsH.2.4[Information Systems]:Database Management—Multime-dia DatabasesGeneral TermsAlgorithms,PerformanceKeywordsAdmission control,statistical modeling,disk performance,stream-ing media2000004000006000008000001e+061.2e+061.4e+060200400600800100012001400C o n s u m p t i o n R a t e [B y t e s /s e c ]Time [second]102030405060051015202530T r a n s f e r R a t e (M B /s )Disk Capacity (GB)read avg.write avg.Fig.1a:The consumption rate of a movie encoded with a VBR MPEG-2algorithm (“Saving Private Ryan”).Fig.1b:The read and write transfer rate profile of a Seagate Cheetah X15disk drive.Figure 1:Important modeling parameters that must be considered by the admission control algorithm.the read/write mix.We propose a dynamic bandwidth shar-ing mechanism as part of the admission control.iii Support for multi-zoned disks.Fig.1b illustrates that the disk transfer rates of current generation drives is platter location dependent.The outermost zone provides up to 30%more bandwidth than the innermost one.iv Modeling of the variable seek time and variable rotational latency that is naturally part of every data block read and write operation.v Support for efficient random data placement [12].To the best of our knowledge,no prior work has investigated such a comprehensive set of parameters.We feel that an integrated approach is essential when building large-scale,high performance real time storage systems and the preliminary evaluation results of the TRAC algorithm show that an increase in throughput of up to 38%may be achieved in retrieval only experiments.The remainder of this paper is organized as follows.In Section 2we review some of the related work.Section 3describes our pro-posed TRAC algorithm and in Section 4we present the results of our extensive performance evaluation through numerical analysis and real measurements.Finally,Section 5concludes the paper and presents some future research directions of this work.2.RELATED WORKA number of studies have investigated admission control tech-niques in multimedia server designs.Fig.2classifies these tech-niques into two categories:measurement-based and parameter-based .The parameter-based approach can be further divided into deterministic and statistical algorithms.Figure 2:Taxonomy of different admission control algorithms.With measurement-based algorithms [8,1],the utilization of crit-ical system resources is measured continually and the results are used in the admission control module.Measurement-based algo-rithms can only work online and cannot be used to offline config-ure a system or estimate its capacity.Furthermore,it is difficult to obtain an accurate estimation of dynamically changing system re-sources.For example,the time window during which the load is measured influences the result.A long time window smooths out load fluctuations but may overlap with several streams being started and stopped,while a short measurement interval may over or un-derestimate the current load.Deterministic admission control [13,11,10,4]aims to provide guaranteed service,however it must as-sume the worst case for some of the system parameters and hence often under-utilizes available resources.Statistical admission control has been studied in a number of pa-pers [19,3,7,14].[19]exploits the variation in disk access times to media blocks as well as the VBR client load to provide statistical service guarantees for each client.Note that in [19],the distribution function for disk service time is obtained through exhaustive empir-ical measurements.[3]introduces three ways to estimate the disk overload probability while [7]proposes a probabilistic model that includes caching effects in the admission control.[14]introduces a stochastic model that considers VBR streams and the variable transfer rates of multi-zone disks.Recently,the effects of user interaction on admission control has been studied [9,5].[9]proposed an optimization for the disk and cache utilization while reserving disk bandwidth for streams that are evicted from cache.[5]introduced a Continuous Time Markov Chains (CTMCs)model to predict the varying resource demands within an interactive session and incorporated it into the admission control algorithm.Most of the previously proposed statistical admission control al-gorithms have adopted a very simple disk model.Only [14]con-siders the variable transfer rate of multi-zone disks.It differs from our TRAC algorithm in that (1)it assumes that all zones have the same number of tracks,(2)it did not consider the variance of the seek time,and (3)it is based on round-robin data placement and round-based disk scheduling.Additionally,no previous study has considered the difference in the disk transfer rate for reading and writing.3.THE TRAC ALGORITHMTo address the shortcomings of the previous approaches we in-troduce a novel statistical admission control algorithm called TRAC.Term Units Term Units B disk MBδT svr secondξnh ms n rsT seek(i)ms n wsR Dr MB/s D(i)MB R Dw MB/s p iodiskAverage disk read bandwidth during T svr The threshold of probability of missed deadline,(no bandwidth allocation for writing)it is the worse situation that client can endure.R Dw MB/sεW RBSεRRBSAverage combined disk bandwidth during a T svr Mean value of random variable D(i)Maximum disk read bandwidth during T svr Standard deviation of random variable D(i)(no bandwidth allocation for writing)The number of seeks during a T svrMaximum disk write bandwidth during T svr Seek time for disk access j,where j is an(no bandwidth allocation for reading)index for each disk access during a T svrDisk read bandwidth for disk access j Mean value of random variable t seek(j)(no bandwidth allocation for writing)Standard deviation of random variable t seek(j)where j is an index for each disk Seek distance for disk access j during a T svraccess during a T svr Rotational latency for disk access j during a T svrCurrent used disk read bandwidth Relationship factor between R Dr and R DwCurrent used disk write bandwidth t seek msβkµtseek t seekread bandwidth for zone k Standard deviation of random variable ms αa1,b1,a2,b2,rw,v i,k iTable1:List of terms used repeatedly in this study and their respective definitions.We start by describing the algorithm in a single disk environmentand then extend it to a multi-disk environment in Section3.3.Ta-ble1lists all the parameters and their definitions used in this paper.3.1Three Random Variable(3RV)ModelConsider the following scenario.The system is servicing n vari-able bit rate clients using deadline-driven scheduling and data blocksare allocated to a disk using a random placement policy.The server activity is observed periodically,during a time interval T svr.Hence, our model is characterized by three random variables:(1)D(i)de-notes the amount of data to be retrieved or recorded for client i dur-ing observation window T svr,(2)t seek denotes the average disk seek time during each observation time interval T svr.Let T seek(i)denote the disk seek time for client i during T svr1. Let n rs and n ws denote the number of retrieval and recording streams served respectively,i.e.,n=n rs+n ws.Also,R Dw represents the average disk bandwidth(in MB/s)allocated for writing dur-ing T svr,while R Dr represents the average bandwidth for reading. With such a mixed load of both retrieving and recording clients,the average combined disk bandwidth R Dio= R Dr+R Dw.Consequently,the maximum amount of data that can be read and written during each interval T svr can be expressed byR Dio×T svr−ni=1T seek(i)(1)Note that a missed deadline of a disk access does not necessarily cause a hiccup for the affected stream because data buffering mayt seek(2) where m denotes the number of seeks andB disk,where B disk is the block size.With the appropriate substitutions we arrive at ourfinal expression for the probability of over-committing the disk bandwidth,which may translate into missed I/O deadlines.p iodisk=Pni=1D(i)>1+R DioR Dio because of its interesting proper-ties.3.1.1Dynamic Disk Bandwidth SharingFig.1b shows the measured disk transfer rate for reading and writing with a modern multi-zone disk drive.Let R Dr denote the maximum disk read bandwidth without any bandwidth allocation for writing.Conversely,R Dw denotes the maximum disk write bandwidth.LetR Dw denotes the average disk write band-width.We observe that R Dr is much higher than R Dw and con-clude that1MB/s of read bandwidth is not interchangeable with1 MB/s of write bandwidth.Fig.3illustrates how the average com-bined bandwidthtition factor δthat defines the percentage of the disk bandwidth allocated for reading.x=Dr R x δy=Dw R x (1 − δ)z=Dw R + ( - )Dw R Dr R x δ=x+y Dio R =Dr R +Dw=DrR DwR ==DioR Figure 3:Relationships between the average read bandwidth R Dw ,the average combinedbandwidthD EFINITION 3.2.:The Reservation-based Bandwidth Sharing (RBS)policy is defined as:a fraction of the disk bandwidth is reserved for disk reading or writing.When disk bandwidth is re-served for writing,it is termed Write-Reservation-based Bandwidth Sharing policy (WRBS).When disk bandwidth is reserved for read-ing,it is termed Read-Reservation-based Bandwidth Sharing policy (RRBS).R Dio varies from R Dr .Thus,R Dio =δR Dw (4)As suggested in Fig.1b,R Dw are two random vari-ables.We model the relationship between the average read and the average write bandwidth with the parameter β=R Dw R Dr=µµR Dio =δR Dr (5)To satisfy DG1and DG2,the partition factor δmust be dynam-ically adjusted according to the system conditions,i.e.,the ratio between the read and write load.This behavior is modeled by the mixed-load factor αα=r Drβ(6)where r Dr and r Dw denote the current disk read and write band-width,respectively.For example,with α=1only reading clientsexist in the system.On the other hand,α=0implies only record-ing clients are in the system.Next,we must compute δunder disk read load r Dr and write load r Dw using different bandwidth shar-ing policies,assuming that r Dr +r Dw >0.We conjecture the following theorem.T HEOREM 3.3.:To satisfy the design goals DG1,DG2,andDG3,δ=α=r Drβ.We have omitted the proof here;for details see [20].Different bandwidth sharing policies might be adopted for dif-ferent applications.We first focus on NRBS to simplify the discus-sion.Based on Theorem 3.3and Eq.5,the disk bandwidth with a mixed-load factor αcan be expressed asR Dr +(1−α)βR Dio =R Dio =βR Dw .Based onEq.7,Eq.3can be further generalized to p iodisk=Pn i =1D (i )>(αR Dr )×T svrt seek ×(αR Dr )n rs i =1µi +n wsi =1µit seek andp iodisk in Eq.8can then be evaluated as followsp iodisk=P [(X,Y,Z )∈ ]=f XY Z (x,y,z )dxdydz(10)where =(X,Y,Z )|X >(αZ +(1−α)βZ )×T svrB disk(11)and f XY Z (x,y,z )is the joint probability density function (pdf)of X ,Y ,Z .Fig.5shows the integration region of Eq.11with10203040506070X (MB/s)0.0020.0040.0060.0080.010.0120.014Y (Second)010203040506070Z (MB/s)Figure 5:Example integration region for T svr =1second,B disk =1MB,α=0.5,and β=0.8.T svr =1second,B disk =1MB,α=0.5,and β=0.8.Note that this figure only shows a small portion of the 3D space,where 0<X <80MB/s,0<Y <14ms and 0<Z <70MB/s,which covers the operation parameters for most modern disk drives.Since the three random variables n i =1D (i ),R Dr are independent,we obtainf XY Z (x,y,z )=f X (x )f Y (y )f Z (z )(12)where f X (x ),f Y (y )and f Z (z )are the pdf of X ,Y and Z ,respec-tively.Next,we will present an overview of how to derive f X (x ),f Y (y ),and f Z (z ),and then continue with the actual admission control procedure.3.1.3Determination of f X (x ):pdf ofni =1D (i )Recall that D (i )denotes the amount of data that client i reads or writes during T svr .Since D (i )is only dependent on the stream bandwidth characteristics of each client,D (1)···D (n )are inde-pendent random variables.According to the central limit theo-rem ,n i =1D (i )approaches a normal distribution [15]with mean n i =1µi and variance n i =1σ2i ,where µi and σ2i denote the mean value and variance of D (i ),respectively 2.Therefore,we obtain the pdf of n i =1D (i )as:f X (x )=12πn i =1σ2ie−[x −ni =1µi ]22It is relatively easy to obtain µi and σ2i for a stream that is already stored on the server.For a new stream to be recorded–especially a live event–we have to rely on estimates.However,since such live streams usually use encoders or compressors at the source,itis often possible to obtain good estimates for µi and σ2i from the configuration parameters of the corresponding encoder and com-pressor.3.1.4Determination of f Y (y ):pdf of t seek =mj =1t seek(j )t seek is dependent on m random variables t seek (j ),withj ∈[1,m ].Due to the random data placement,these m random variables are independently and identically distributed with meanvalue µt seek (j )and variance σ2tseek(j ).Assuming m >30,by the central limit theoremm.Recall that m =ni =1D (i )B diskand vari-ance n i =1σ2it seekas:f Y (y )≈12πσ2t seek(j )e−ni =1µiσt seek(j )2(14)3.1.4.1Determination of µt seek (j )and σt seek (j ).Let U j denote the rotational latency for disk access j and let S j denote the percentage value (between 0and 100)of the total disk storage capacity.We consider the rotational latency part of the seek time t seek (j ).We express the relationship among t seek (j ),S j and U j through disk profiling and modeling [17]ast seek (j )=a 1+b 1100(s ∈[0,100])and f U j (u )=1R DrLet R Dr (j )denote the disk read bandwidth for disk access j during T svr .Then,the average read bandwidthR Dr =m j =1RDr (j )R Dr also approaches a normal distributionwith pdff Z (z )≈12πσ2R Dr(j )e −ni =1µiσRDr(j )2(16)Next,we will describe how to obtain µR Dr (j )and σR Dr (j ).3.1.5.1Determination of µR Dr (j )and σR Dr (j ).Most magnetic disk drives feature variable transfer rates due to a technique called zone-bit recording (ZBR),which increases the amount of data being stored on a track as a function of its distance from the disk spindle.We model the variable zone transfer rates with R Dr (j ).Let L denote the starting location of each disk access during T svr .L can be quantified using the percentage value of the100020003000400050006000700080000510********R e s p o n s e T i m e (u s )Disk Capacity (GB)Seek Timeavg0.050.10.150.20.25024681012R e l a t i v e F r e q u e n c y (f o r 20000 r a n d o m a c c e s s )Disk seek time (ms)Theoretical Computation Empirical measurementFig.6a:Seek time profileFig.6b:Probability density function(Note:rotational latency is not included)f t seek (j )(t )of t seek (j )Figure 6:Determination of µt seek (j )and σt seek (j )for a Seagate Cheetah X15disk drive.total disk capacity,i.e.,L ∈[0,100].From the disk transfer rate profile (see Fig.1b),the relationship between R Dr (j )and L is modeled asR Dr (j )=v 1if 0≤L ≤k 1(L ∈Zone 1)......v w if k w −1<L ≤k w (L ∈Zone w )(17)where w is the number of zones,and v i and k i model the multi-zone characteristics,where i ∈[1,w ],v 1>···>v w ,0<k 1<···<k w =100,and [0,k 1],[k 1,k 2],···,[k i −1,k i ],···,[k w −1,k w ]represent zones 1,2,···,i ,···,w ,respectively.These w ,v i and k i are termed disk transfer rate modeling parameters.Because of the random data placement,L is uniformly distributed with pdf f L (l )=1100δ(r −v i )(18)Using the pdf of R Dr (j ),we can obtain µR Dr (j )and σR Dr (j ).For example,for a Seagate Cheetah X15disk,µR Dr (j )=52.26MB/s and σR Dr (j )=5.33MB/s.The final step is to apply µR Dr (j )and σR Dr (j )to Eq.16resulting in the pdf forSize Write Transfer Start (MB)Rate (MB/s)(MB)12,00038.403,50037.612,2893,00036.815,8734,00036.218,9453,00035.323,0412,50034.526,1133,00033.128,6732,50032.231,7452,50031.734,305aRatio between write and read data transfer rate of a zone.Table 2:Zoning information of a Seagate Cheetah X15(model ST336752LC)disk.factor βbetweenR Dr in step 7.To illustrate,assume the disk transfer rate profile of a Seagate Cheetah X15disk as shown in Fig.1b.Table 2lists the βk value for each of the disk’s zones.For the Cheetah X15disk drive βk varies slightly between 0.668and 0.757(see Table 2).Recall that βis also bounded by the same range as βk .Follow a similar derivation in section 3.1.5,we can obtain µR Dw =µR Dw (j ),where µR Dw (j )is the disk write bandwidth for disk access j during T svr with no bandwidth allocation for reading.To simplify the model,we approximate βby its limit µµt seek ,n i =1D (i )andtotal read capacity ≈n rsi=1µitotal reading capacity ≈n wsi=1µi/βξon average for each individ-ual disk.As stated previously,ni=1D(i)denotes the total R/Wresource requirements during T svr.Thus,the average amount ofdata to be stored to or retrieved from each disk during T svr can becomputed asλavg=n i=1D(i)ξ,where i∈[1,ξ].Recall that ni=1D(i)follows a normal distribu-tion(see Section3.1.3)and sinceξis constant,λi also approachesa normal distribution with mean valueµλi=n i=1µiξ2.Consequently,following analogous reasoning asin the single disk case,the admission control criteria is modified to:p iodisk=P n i=1D(i)R Dr+(1−α)β1+R Dr+(1−α)βB disk≤p req(19)Note that the probability density functions need to be updatedto reflect the decreased mean and variance values for the load oneach disk.Furthermore,the number of seek operations will alsobe approximately evenly distributed across all disks.The detailedanalysis is contained in[20].4.PERFORMANCE EV ALUATIONTo evaluate the effectiveness of our TRAC algorithm we per-formed extensive comparisons between our analytical models andan actual system implementation.Additionally,we compared apreviously proposed,single random variable admission control al-gorithm[3,19]with our results.We termed this baseline algorithm1RV-AC since it only considers the disk workload variability.Thereexists an approach that considers both the variability of the diskservice time and the workload[19].However,since the distributionfunction for the service time is obtained through exhaustive empiri-cal measurements(and therefore difficult to reproduce),we felt thatthis method does not lend itself to a good analytical comparison.We expect that its performance would fall somewhere in betweenthe1RV-AC and TRAC algorithms.The performance measure usedwas the probability for missed deadlines p iodisk.This probabilitydirectly translates into how many streams can be supported with agiven miss-threshold.4.1Single Disk System Experiments4.1.1Experimental SetupnFigure8:Experimental system setup.The hardware platform used for our experiments was a Dell Pow-erEdge1650server with a Pentium III1GHz CPU,256MB of main memory and running RedHat Linux7.0.This configuration can at the present time be considered midrange.We wanted to en-sure that our measured results would be representative of a reason-able hardware configuration.Fig.8illustrates the structure of our experimental setup.Itsfive components are:a WorkLoad Genera-tor,a Movie Trace Library,a Disk Access Scheduler,a Measure& Report module and a Disk.Note that we did not run a fullfledged streaming server on our test system to reduce the number of param-eters that would influence the results.As such,the results represent the best case scenario and other system bottlenecks–if present–might reduce the performance.The WorkLoad Generator produces stream requests based on a Poisson process with mean inter-arrival time ofλ=5seconds.Each admitted stream produces data block requests with associated read/write deadlines according to movie bandwidth traces from the Movie Trace Library.The movie blocks are randomly placed onto disks and block requests are scheduled based on the deadline assigned to each block.Hence,the block with the earliest deadline is accessedfirst.The block requests are forward to the Disk by the Disk Access Scheduler at the set times. The Measure&Report module monitors the disk system perfor-mance and generates the result output.In this report,both the num-ber of missed deadline requests and the total number of disk block requests are collected.Furthermore,the ratio between these two numbers,which represents the fraction of the missed deadline re-quests,is interpreted as the probability of missed deadlines p iodisk. The WorkLoad Generator has several configurable parameters: the mean inter-arrival timeλ,the number of retrieval streams n rs and the number of recording streams n ws.We start with single media type experiments.Hence,the relationship between n rs,n wsand the mixed-load factorαcan be expressed asα=n rsβ.Table3summarizes the parameters used in the experiments and analysis and also lists the three movie traces:the DVD movie “Twister”,the DVD movie“Saving Private Ryan”and the VCD movie“Charlie’s Angels.”The rate profile of“Saving Private Ryan”is shown in Fig.1a as an example.The disk is a Seagate Cheetah X15(Model ST336752LC).Fig.6a shows the measured seek pro-file for the X15,while Fig.1b illustrates the data transfer rate pro-file for both reading and writing,with reading being significantly faster than writing.Recall thatβk denotes the ratio between the writing and reading rate for zone k and Table2shows that this ra-tio is not constant,but varies between0.668and0.757.We selected ParametersMPEG-2video,AC-3audio Average bandwidth50minutesThroughput std.dev.MPEG-2video,AC-3audio Average bandwidth50minutesThroughput std.dev.MPEG-1video,Stereo audio Average bandwidth70minutesThroughput std.dev.Disk Model(Model ST336752LC)1.0(retrieval only experiments)0.4094(retrieval and recording Relationship factorβ5secondsof streaming requestServer observation window T svrDisk block size B diskNumber of disks(ξ)Parameters MeasurementsMovie Name n maxtrue bMeasurements1.054 1.82%(Retrieving Only)49 3.92%20210.22%“Twister”40“Saving Private Ryan”38“Charlie’s Angels”1710.4094460%(Mix of Retrieving&42 4.55%Recording)17211.34%66 5.71%n max true×100%.Table4:Experimental results for different mixed-load factorsαand different movie types,assuming p req=1%.4.1.4Mix of Retrieval and RecordingA realistic workload for a large scale streaming media system isa mix of retrieval and recording load.As an example,we chosean equal number of retrieval and recording streams for our exper-iments(any other combination is also possible),i.e.,n rs=n wsand thus the mixed-load factorα=0.4094=n rsβ.Fig.11(a)shows an example graph for the movie“Twister”(the other media types produced analogous results).As expected,the 1%transition point at46streams lies between the pure retrieval (54)and recording(40)values.(See also Table4for summary information.)As afinal verification of the3RV model,we performed an ad-ditional mixed workload experiment.However,we not only mixed retrieval and recording streams(α=0.4094),but also two differ-ent media types(the DVD movie“Saving Private Ryan”and the VCD movie“Charlie’s Angels”).Fig.11(b)shows the experimen-tal results and once again,the miss probability computed by3RV model closely matches the measured results.4.2Missed Deadline Probability Analysis forMulti-Disk SystemWe evaluated the TRAC algorithm through numerical analysis for a multi-disk storage systems,with the number of disksξrang-ing from2to1024.We setαequal to1.0and chose the movie “Twister”as the candidate media type.The maximum number of supported streams for both the TRAC and1RV-AC algorithms were computed for a user acceptable missed deadline probability p req of 0.01.Table5summarizes the results.As expected,the benefits of the TRAC algorithm increase linearly with the number of disks. We have not included measurement results from disk arrays for the following reason.With only a few disks,the number of streams ad-mitted is expected to scale linearly.However,with current genera-tion,high-performance disks other parameters start to influence the results of disk arrays very quickly.For example,the Cheetah X15 disk used in our experiments has a read transfer rate in excess of55 MB/s.Hence,the device interconnect starts to become a bottleneck (e.g,SCSI buses top out at320MB/s,but more importantly a reg-ular PCI bus can only sustain133MB/s).Consequently,to obtain accurate results one needs to either test the disk array using ma-chines that have faster,but less common I/O interfaces(e.g.,PCI-X or PCI-Express[16]),or incorporate a complete system model into the admission control procedure.We are working on the latter ap-proach as part of our future research.Parametersnumber of disks1RV-AC algorithm1392814165832416660321337642694128546025610940512219051024438582)[6]. Consequently,let comp avg−det( )denote the minimum cost to compute the integration with domain as defined in Eq.11(and illustrated in Fig.5).Let D,T and R denote the range of the random variables ni=1D(i),R Dr respectively.Then comp avg−det( )can be derived as follows:comp avg−det( )=Θ(DT R−1[log −1]3。