Multimedia Systems (1997) 5:271–281 Multimedia Systemsc© Springer-Verlag 1997

Disk placement for arbitrary-rate playbackin an interactive video serverTaeck-Geun Kwon1, Yanghee Choi2, Sukho Lee2

1 R&D Center, LG Information & Communications, Ltd., 533 Hogye-dong, Anyang 430-080, Korea2 Department of Computer Engineering, Seoul National University, San 56-1 Shinrim-dong, Seoul 151-742, Korea

Abstract. Multimedia data, especially continuous media in-cluding video and audio objects, represent a rich and naturalstimulus for humans, but require large amount of storagecapacity and real-time processing. In this paper, we describehow to organize video data efficiently on multiple disks inorder to support arbitrary-rate playback requested by differ-ent users independently. Our approach is to segment anddecluster video objects and to place the segments in multi-ple disks using a restricted round-robin scheme, calledprimeround-robin (PRR). Its placement scheme provides uniformload balance of disks for arbitrary retrieval rate as well asnormal playback, since it eliminates hot spots. Moreover, itdoes not require any additional disk bandwidth to supportVCR-like operations such as fast-forward and rewind. Wehave studied the various effects of placement and retrievalschemes in a storage server by simulation. The results showthat PRR offers even disk accesses, and the failure in read-ing segment by deadline occurs only at the beginning of newoperations. In addition, the number of users admitted is notdecreased, regardless of arbitrary-rate playback requests.

Key words: Video server – Interactive video-on-demand –Multimedia storage system – Disk placement

1 Introduction

With recent advances in storage and network technology,it is now possible to providevideo-on-demand(VOD) ser-vices, supporting the simultaneous transmission of indepen-dent video streams to thousands of viewers. Viewers sub-scribing to VOD services are expected to retrieve and ma-nipulate the stored video in the same way as users do todaywith VCRs [7, 8].

In VOD services, viewers are allowed to apply VCR-like operations, such as pause, resume, fast-forward (FF)and rewind the video. In addition, a viewer can request todisplay a particular set of videos at any time he/she wishesto do so. Although the transmission of video data is consid-ered feasible due to advances of today’s high-speed networks

Correspondence to: T.-G. Kwon

such as ATM and FDDI [10], the storage and retrieval ofdifferent portions of video simultaneously and interactivelyremain non-trivial problems, because disks are mechanicaldevices dominated by the non-negligible seek and rotationaldelays. The video server must access and retrieve video ob-jects under real-time constraints for the on-time display atthe clients’ sites. Moreover, in order to accommodate a largenumber of videos, a set of disks is employed in a videoserver.

The playback requests for video objects from differentclients are absolutely independent of each other and mayarrive at random time intervals. Thus, the performance of avideo server is critically dependent on hot spots (i.e., over-loaded disks) from the cluster of the resource requests toparticular disks. This becomes more complicated with VCR-like arbitrary-rate playback requests. The obvious remedy isto remove hot spots usingload-balancingmechanism on thedisks, which is usually achieved by efficient disk placementand retrieval schemes.

In video retrieval we are concerned with accessing thevideo segmentsfrom the disk for a request specified by di-rection, speed,quality-of-services(QOS), etc.; which maybe altered at any moment by the user within a session. Inthis paper, we consider that an interactive VOD session con-sists of a sequence of VCR-like operations such as play, FF,rewind, pause, random jump, etc. Figure 1 illustrates a basicstate diagram for an interactive VOD session and a typi-cal example of a session. From the users’ point of view, itis important that the state change is executed without anyservice degradation, regardless of the increased number ofsimultaneous sessions supported at the server.

Several disk placement and retrieval mechanisms havebeen proposed to support normal-rate real-time playback ofcontinuous media. To achieve the desired aggregated I/Operformance, disk arrays [3, 9] were introduced, using diskstriping [13] and declustering [5] techniques. In contrast withthe random, flexible block allocation on a disk for non-real-time data, continuous media storage systems usually employcontiguous block assignment to meet the real-time require-ments. This strategy is designed primarily to support onlynormal-rate playback. Rangan and Vin [12] proposed con-strained storage techniques for real-time continuous media

272

Fig. 1. State diagram and example of an interactive VOD session

retrieval in which the waste of disk space was reduced byallowing gaps between consecutive segments.

More elaborate disk placement and retrieval schemes areneeded in the presence of VCR-like requests that may pro-duce very skewed and unbalanced disk accesses in a diskarray environment, if a simple cyclic placement scheme isused. A simple approach to provide VCR-like functions isto store anFF replica for each object in the system andstarts displaying the replica instead of the normal speed ob-ject [1]. Chen et al. [2] proposed asegment selection schemeto support arbitrary-rate playback, which consists of two al-ternative methods; asegment sampling method(SSM), anda segment placement method(SPM). The SSM is based onthe simple round-robin (RR) placement, but shifts the datasegments retrieved in hot spot disks. The SPM, however,allocates segments across disks to minimize the variation onthe number of segments skipped while balancing the loadon the disk array for some pre-determined speeds.

In Berson’s approach [1], unnecessary overhead has beenpaid to provide arbitrary-rate playback. Moreover, in Chen’sscheme [2], the load to disks is not uniformly distributed forsome retrieval speeds, which may incur periodic failures inreading segments by deadlines from hot spots.

In this study, we present several new methods concern-ing the disk placement of video objects, in order to natu-rally provide arbitrary-rate playback during a session. First,we propose a new segment placement scheme, calledprimeround-robin(PRR). Unlike normal playbacks, FF and rewindoperations display skipped segments and clustered disk ac-cesses may occur in a simple RR. In order to remove the hotspots, we have modified the basic RR mechanism in such away that no hot-spot disk arises. By using a prime numberas a divisor in deriving the disk, uniform load balance ofdisks can be achieved for arbitrary-rate playback in PRR.This method has not been explored in existing work on datastriping, although the basic idea is well known in many ar-eas, e.g., random number generation. Second, to eliminateperiodic disruptions and frequent delays at a specific play-back speed, we apply a new retrieval strategy which pro-vides complete load balance for any desired playback rate.In addition, we present a bandwidth reservation algorithmto read segments by deadlines and to resolve the contentionof disk accesses by reservation basis scheduling. It can sup-

port a large number of simultaneous playbacks with desiredservice qualities. This is because video segments requestedreside on disks uniformly under the PRR, regardless of theplayback rate. Moreover, our placement scheme and reser-vation policy can prevent any disruption by displaying avideo object upon changing the mode of operations due tothe elimination of hot spots.

The remainder of this paper is organized as follows: Sec-tion 2 describes the system model for concurrent access toshared video data and the data model for storing compressedvideo data. Section 3 examines the existing segment place-ment schemes for variable-rate playback. In Sect. 4, a newstorage and placement mechanism for uniform load balanceat any playback rate is presented. The bandwidth reserva-tion algorithm for interactive real-time services is also intro-duced. By analysis and simulation study, the performanceof our placement scheme and its associated algorithms areinvestigated in Sect. 5. Section 6 presents an extension ofPRR over segment size variations. Finally, we conclude witha discussion of future work in Sect. 7.

2 System and data model

The objective of our video server is to provide simultaneousvideo streams to a large number of clients at any desired dataretrieval rate with minimum delay for changing the mode ofoperations during a session. We set the basic requirementsthat the system should satisfy as follows:

– The video server should provide concurrent accesses tothe same video object withtime lag. In addition, videostreams are transmitted independently to every user whosubscribes to a VOD service,

– The video server should adapt to non-uniformly dis-tributed disk accesses. In other words, load balanceshould be provided to reduce hot spots in the video servereven in the presence of random requests at various play-back rates.

– Since users may request any retrieval operation unpre-dictably during a session, the system should providesmooth transition of operations. Otherwise, the user mustwait for the video server to be prepared, and this delayis unacceptable for most interactive video applications.

– The client hardware should be simple and inexpensivewith a limited buffer.

In order to satisfy these requirements for the videoserver, a video object is generally segmented and stripedon multiple disk servers. The architecture of our system isbased on the disk server architecture [14]. The video serverconsists of multiple and identical disk servers which havetheir own local disks as shown in Fig. 2. A client’s requestis first assigned to a disk server, called the agent, that alignsthe retrieved video segments within its buffer to reduce fur-ther processing at the client. The name server manages allo-cation maps for all video objects and downloads the desiredallocation map to the agent when a session is established be-tween the server and the client which now sends requests tothe agent for presentation. After receiving the user’s request,the agent schedules the deadline for the requested operationsusing the allocation map of the target video data, and sends

273

Fig. 2. The overall architecture for VOD services

disk I/O requests to each disk server with deadlines. A diskserver accesses its local disk and transfers segments to theagent. To transmit segments, the agent first stores the pre-fetched segments into its local video buffer and then sendsthe composed stream when it is ready in the correct order tothe client. This is done to reduce the hardware complexityof client stations.

We assume that a video object consists of segments, andeach segment is composed ofindependently decodable datablocks (IDB), and that a number of frames constitute anIDB. In MPEG [6, 11], an IDB corresponds to agroup ofpictures(GOP) that contains one intraframe (I-frame), one ormore predicted frames (P-frame), and several bidirectionalframes (B-frame) coded with motion-compensated interpo-lation. Since most full-motion compression techniques arebased on the interframe compression, except for motion-JPEG, not all coded frames can be decompressed individ-ually without successive and/or past frames. For example,only I-frames in the MPEG standard are independent, i.e.,the starting point of I-frames is arandom access point(RAP)in a compressed video (Fig. 3). The video server accessesstored video whose frames are stored contiguously on a diskby segment to reduce the seek time.

Formally, a segment is defined as a sequence of codedframes containing at least one I-frame; i.e., the segment con-sists of more than one GOP in MPEG and more than onecoded frame in JPEG. It is easily observed that a small seg-ment provides a fine granularity level for concurrent resourcehandling at the expense of longer seek time. With MPEG-1, the compressed bit stream can be either variable bit rate(VBR) or constant bit rate (CBR). At first, we develop a ba-sic disk placement scheme to support CBR video, which iswidely used in practice. Then the basic scheme is extendedto support VBR video.

Fig. 3. Layers for compressed video

3 Existing schemesto support arbitrary-rate playback

3.1 Definitions

A video object is accessed by segments, and the duration fornormal playout of each segment is assumed to be identicalin this paper. Table 1 summarizes the symbols used in thispaper. Given a transactionT s

ij for the retrieval of a videoobjectSi, each VCR-like function can be defined as follows.

Normal play (Tij). Sji , Sj+1i , Sj+2

i , · · · should be playedout at t1, t2, t3, · · ·, respectively.

Fast retrievals (T |s|>1ij ). There are several possible ap-

proaches to implementing fast retrievals such as FF andrewind. To minimize additional resource requirements,stimes faster retrieval considered here is to be realized byretrieving only one segment for everys segments in thevideo server, so that the required disk and network band-width remains the same as that of normal play, andSji ,Sj+si , Sj+2s

i , · · · is to be played back att1, t2, t3, · · ·, re-spectively. For example, assuming that a segment consistsof two video frames, a client station displaysf0, f1, f6, f7,f12, f13, · · · (i.e.,S0, S3, S6, · · ·) for three times FF insteadof presentingf0, f3, f6, · · ·; where fi represents thei-thvideo frame,s > 0 for forward retrievals ands < 0 forbackward retrievals.Slow retrievals (T |s|<1

ij ). Sji , Sj±1i , Sj±2

i , · · · is to beplayed back att1, tb1+1/|s|c, tb1+2/|s|c, · · ·; i.e., a client sta-tion will display the same segment forb1/|s|c times, where0 < s < 1 for slow-forward and−1 < s < 0 for slow-backward. Unlike normal play or fast retrieval, lower trans-mission bandwidth by factorb1/|s|c is needed. For example,a client station displaysf0, f0, f1, f1, f2, f2, · · · for slow-forward withs = 1/2 (i.e., two times slower than the normalspeed).Pause. A client station presents the same frame until a fur-ther command is issued. It does not require any additionaldisk accesses; however, the server should be able to serveany operation immediately upon the user’s request.Random jump. This corresponds to a random segment ac-cess which is usually provided for faster browsing.

274

Table 1. Symbols used

Symbol DescriptionN number of disks in a video serverBdisk effective bandwidth of disks in a disk serverBrequest required bandwidth for presentationDi ith disk (0≤ i < N )Si ith video object (0≤ i < L) whereL is the number of video objectsSji jth segment of an objectSi (0 ≤ j < M ); whereM is the number of segments

T sij transaction to retrieve video object fromSj

i with speeds; Tij denotes normal play (s = 1)ti ith time unit to display segments

3.2 RR placement

In RR placement, video segments are stored onN disksaccording to the placement function of Eq. 1, i.e., a segmentSji is stored inDfRR(j).

fRR(j) = j modN (1)

Figure 4 illustrates an example of the RR placement andthe access sequence of the segment whens = 3 ands = 4,marked as superscripts. As illustrated, three times FF re-quires accessingD0, D3, andD6, repeatedly producing hotspots; however, four times FF as well as normal play re-quires balanced accesses to disks. Although the RR policyis simple to implement, it is not suitable for arbitrary-rateplayback because accesses are clustered on some specificdisks for specific retrieval speeds. Since segments of a videoobject are distributed to all disks, segments placed on hotspot disks may not be read by the deadline; this may causeperiodical read failures.

3.3 Segment sampling method

To achieve the segments sampled to be distributed as uni-formly as possible in Chen et al. [2], the segment samplingmethod (SSM) shifts to the right segments to be read forFF at some specific rate, in which segments are stored ba-sically in an RR manner. Figure 5 illustrates an example ofSSM and the sequence of disk accesses whens = 3 ands = 4. Although SSM is associated with RR in terms of seg-ment placement, it adopts the shift mechanism to achieveload balancing. As shown in Fig. 5, segments 0, 3, 6, 10†,13†, · · ·, are accessed instead of 0, 3, 6, 9, 12,· · ·, in ordernot to produce any hot spot; where† represents the shiftedsegments.

3.4 Segment placement method

The segment placement method (SPM) allocates segmentsto disks judiciously, so that the segment can be uniformlysampled in FF at some pre-determined speed. The placementfunction of a segmentSji is defined as follows:

fSPM (j) = (j + bj/Nc) modN . (2)

Although SPM does not require any special provision tosample segments, it can provide uniform load balance onlyfor pre-determined FF speeds, as shown in the example ofthree times FF in Fig. 6. However, for other playback speeds,

hot spots may be produced; e.g., in four times FF, the re-trievals of segments 0, 4, 8, 12, 16,· · ·, are restricted toD0,D4, andD8.

4 Proposed schemes

We now present new disk placement and retrieval schemesfor video data which achieve uniform load balance of disksfor arbitrary-rate playback. In addition, we describe a band-width reservation algorithm to schedule segment pre-fetchwithout violating the given transmission bandwidth.

4.1 PRR placement

In disk-array-based systems, the most important function isto provide uniform load balance of the disks achieving max-imum throughput. Thus, it needs to minimize the deviationfrom the uniform sampling sequence, so that better qualityin the retrieved video objects is achieved. In most RR-basedplacements such as RR, SSM, and SPM, the optimal loadbalance at any FF rate is achieved by settingN (the numberof disks) to a prime number.

Theorem 1 (PRR). In an RR-based placement, all fast re-trievals as well as normal play with speeds /= kN (k =1, 2, · · ·) require accesses toN distinct disks forN time unitsregardless of the value ofs, if and only ifN is a prime num-ber.

Proof. Let T sij be a transaction as described in Table

1. Sji , Sj+si , Sj+2s

i , · · · will be presented att1, t2, t3, · · ·and are stored onD(i+j) modN , D(i+j+s) modN , D(i+j+2s) modN

· · ·, respectively. IfSj+dsi (d = 0, 1, · · ·) is also stored on

disk D(i+j) modN storingSji , thends = kN (k = 1, 2, · · ·).Assuming thatN is a prime number, the minimum valueof d is equal to N , becauseN is not divisible by s(= 1, 2, · · · , N − 1). That is,T s

ij needs to access the samedisk only in everyN th time unit for s /= kN .

Example. Let N be 5. Assume video objectS0 is placedin an RR manner as follows:

P =

S0

0 S10 S2

0 S30 S4

0S5

0 S60 S7

0 S80 S9

0S10

0 S110 S12

0 S130 S14

0S15

0 S160 S17

0 S180 S19

0· · ·

For each time unitti, T 1

00, which is normal playback, presentsSj0 (j = 0, 1, 2, · · ·) stored onDj mod 5, i.e., D0, D1, D2,

275

Disk D0 D1 D2 D3 D4 D5 D6 D7 D8

Segment 03,4 1 2 33 44 5 63 7 84

number 93 10 11 123,4 13 14 153 164 17183 19 204 213 22 23 243,4 25 26273 284 29 303 31 324 333 34 35

363,4 37 38 393 404 41 423 43 444

Fig. 4. Example of segment access in RR (N = 9,M = 45)

Disk D0 D1 D2 D3 D4 D5 D6 D7 D8

Segment 03,4 1 2 33 44 5 63 7 84

number 9 103 11 124 133 14 15 163,4 1718 19 203,4 21 22 233 243,4 25 263

27 284 293 30 31 323,4 33 34 353

364 373 38 39 403,4 41 42 433 444

453 46 47 483,4 49 50 513 524 53

Fig. 5. Example of segment access with shifts in SSM (N = 9,M = 54)

D3, D4, andD0, · · ·. The same disk is accessed in everyfive time units.T 2

00 which is two times FF presentsS2j0

stored onD2j mod 5, i.e.,D0, D2, D4, D1, D3, andD0, · · ·.Furthermore,T 3

00 andT 400 need to accessD3j mod 5, D4j mod 5,

respectively; in which all five disks are accessed for five timeunits.T 5

00, however, presentsS5j0 stored onD0, so that the

server only accessesD0 in every time unit.

Now we extend the placement scheme for an arbitrarynumber of disks. The PRR scheme presents an evenly dis-tributed load on arbitraryN disks for arbitrary-rate playbackas well as normal play and slow retrievals, in which the samedisk is accessed in everyNp time units in the worst case.Here, we defineNp as the largest prime number, but notgreater thanN .

The PRR scheme works as follows:

1. FindNp on the value ofN .

2. Place segmentsSj/=kNpi (k = 0, 1, · · ·) into Np − 1 disksin an RR manner.

3. Place segmentsSj=kNpi into N −Np + 1 remaining disks

in the same way.

We present the placement function of PRR,fPRR(i, j);this means that video segmentSji is stored onDfPRR(i,j).

fPRR(i, j) ={[(N −Np + 1)i + [j]N−Np+1]N if j = kNp

[(N −Np + 1)i +N −Np + [j]Np ]N otherwise(3)

where [x]y means x mody. If N is a prime number,fPRR(i, j) is equivalent tofRR(i, j). Figure 7 illustrates anexample of PRR withN = 9 andNp = 7. As shown, atleast seven distinct disks are accessed for seven time unitsin all FF/rewind rates except for the multiples of seven timesfaster retrievals.

4.2 Speed adaptation

Since each disk stores every multiple ofNp-th segment inPRR, disk accesses are clustered only whens = kNp. Theclustering can be avoided for some specific FF/rewinds atan adapted (modified) speedkNp + 1 rather thankNp. Forexample, a server can deal with seven times FF as eight

times FF whenNp = 7. If N is large enough, the impactof shift is negligible for human perception. With this speedadaptation, PRR achieves complete load balance of disks forall arbitrary-rate playbacks.

4.3 Bandwidth reservation

In a large video server where thousands of different streamsare supported, the video server determines the actual pre-fetch time at each disk server to resolve the lack of diskbandwidth for reading segments due to contentions. One ap-proach to reserve disk usage is that a disk server managesthe timetable that represents the disk reservation status toavoid disk access contention. The timetable informs the diskserver when the server reads segments and whether the timeslot has been reserved to access disks or not. Let matrixRrepresent the timetable as follows:

RN×N = [R0R1 · · ·RN−1] . (4)

With considering the maximum seek time in a disk, the effec-tive disk bandwidth can be fully utilized to access segments.An element ofR, i.e., rij , represents the remaining effec-tive disk bandwidth onDj at ti. To provide real-time video,the disk usage must be scheduled not to exceed the capac-ity. Since the disk server explicitly reserves its own diskusage, each disk server managesRj (= [r1j r2j · · · rNj ]T )exclusively, and schedules the actual time to pre-fetch seg-ments independently. WithN being a prime number, onlyone segment is read forN time units and the time intervalfor re-accessing the same disk isN . Thus, the disk reserva-tion status atti and ti+kN are identical in general.

Suppose that there is a transaction which requires a seg-ment stored onDj to be read by deadlinetk with bandwidthBrequest. Then, the scheduler of the disk server determineswhether the remaining disk bandwidth is available or not.

The bandwidth reservation procedure can be formalizedas follows:{

If max1i=k{rij} ≥ Brequest guaranteed

Otherwise wounded(5)

where we assume thatt0 is the current time and the seg-ments must be read by deadlinetk but after t0. If one ofremaining bandwidths betweentk and t1 is available, the

276

Disk D0 D1 D2 D3 D4 D5 D6 D7 D8

Segment 03,4 1 2 33 44 5 63 7 84

number 17 93 10 11 123,4 13 14 153 164

25 26 183 19 204 213 22 23 243,4

333 34 35 273 284 29 303 31 324

Fig. 6. Example of segment access in SPM (N = 9,M = 36)

Segment\ Disk D0 D1 D2 D3 D4 D5 D6 D7 D8

03,4 1 2 33 44 5 63

S0 7 84 93 10 11 123,4 1314 153 164 17 183 19 204

213 22 23 243,4 25 26 273

44 5 63 03,4 1 2 33

S1 11 123,4 13 7 84 93 10183 19 204 14 153 164 1725 26 273 21 22 23 243,4

· · ·Fig. 7. Example of segment placement and retrieval sequence in PRR

Fig. 8. Example of disk reservation

disk server guarantees the reading of the segment. However,if the required bandwidth is not available by the deadline,the transaction iswounded, i.e., the storage server fails toread the real-time video segment by the deadline. The fail-ure occurs only when the deadline is close to the currenttime and many transactions are being served concurrently.Theoretically, the value ofk can be at mostM , which is thenumber of segments of a video object. Segments, however,are stored in an RR manner with prime numberN , and ev-eryN -th segment of a video object resides in the same disk.Thus, once a disk is reserved, everyN -th segment will beaccessed everyN -th time unit as long as a user does notchange the mode of operation.

Let N be 7 and the effective disk bandwidth be 1.5Mbits/s. Only one segment can be read at a time unit (i.e.,0.5 s) if a segment is an MPEG-1 GOP. Figure 8 representsan example of disk reservation when two times FF (T 2),normal playback (T 1), and four times FF (T 4) are requested,respectively. SinceD5 has no remaining bandwidth to reada segment forT 1, it will be accessed att6 instead oft7.If anotherT 1 starting fromD0 is requested, only the firstsegment cannot be read by deadlinet1, although successivesegments can be pre-fetched. In this case, the 8th segmenton D0 will be accessed att6 whose deadline ist8.

5 Performance evaluation

5.1 Rounding distance

We define the rounding distance, denoted byds, as the mini-mum time interval between consecutive accesses to the samedisk for retrievals at speeds. The average rounding distancefor FF and rewind is defined as follows:

1N − 1

N∑i=2

di . (6)

Note that the rounding distance ofs is equal to that ofs+kN(k = 1, 2, · · ·) in all placement schemes based on RR.

Figure 9 compares the average rounding distance of RR,SPM, and PRR for 1≤ N ≤ 100, where solid lines denotethe average rounding distances for each placement scheme.

The average distances are approximately 0.93N , 0.73N ,and 0.50N in PRR, RR, and SPM, respectively. Ideally,di/=N needs to beN , but actuallydi=N is 1; i.e., the optimalrounding distance is roughlyN whenN is large enough.As illustrated in Fig. 9, the average rounding distances ofboth RR and PRR are optimal, whenN is a prime number;however the distance of PRR is larger than those of RR andSPM for the arbitrary value ofN . Our assessment has beenthat PRR is always superior to any other placement schemesin terms of disk load balance.

Since each rounding distance is at leastNp in the PRRscheme, at leastNp distinct disks are accessed duringNp

time units due to thespeed adaptationdescribed earlier. WithRR and SPM, however, such uniform load balance cannotbe achieved for transactions requesting certain speeds, forexampleN/2 times FF. In this case, periodic read failurescan occur, severely affecting the quality of presentation.

5.2 Shifts

There exist two possible strategies to remove hot spots forarbitrary-rate playbacks: sampling with shift operation anddisk placement. In this subsection, the impact of shift oper-ation, which is introduced on SSM, is considered for three

277

9 10

11

Fig. 9. The average rounding distances for arbitrary-rate FF and rewind

Fig. 10. The average number of shifts to achieve uniform load balance

Fig. 11. The average miss-ratio after a new transaction

different placement schemes: RR, SPM, and PRR. Note thatSSM applies placement to a simple RR.

Shift operation is activated when the same disk is ac-cessed repeatedly, and it was proved that the placementpolicy with minimal shifts achieves the maximum through-put [2]. In addition, uniform segment selection is achievedonly at some pre-determined speeds in SPM, and shift is re-quired for other speeds to avoid access clustering. However,in PRR, according to Theorem 1, all segments are uniformlydistributed, except fors = kNp, and the number of shifts isalways zero whens /= kNp. Figure 10 represents the av-erage number of shifts to realize at leastNp distinct diskaccesses duringN time units (speed adaptation is neglectedfor all schemes). It is easy to see that PRR is superior toother schemes in the number of shifts for different numbersof disks. The number of shifts in SSM and PRR is equalonly whenN is a prime number. In addition, the numberof shifts in SPM increases withN because the portion ofpre-determined speeds decreases asN increases.

5.3 Number of admitted users

We will now consider the number of concurrent, admissible,interactive clients in a video server. We first assume that

a small portion of the users (20% in our experiment) aresending out new commands (i.e., FF or rewind at arbitraryspeeds) to the server. Clearly, the server may not process allthe commands by the deadlines when the server is alreadyloaded with access requests. We define themiss ratio asfollows:

number of segments failed to be read by the deadline

number of segments required to be read for presentation. (7)

Server load is defined by

K ′

NBdisk/Brequest, (8)

whereK ′ is the number of transactions present in the server.Figure 11 shows the change of miss ratio after starting

new transactions under various loads in which we considered20% of users request FF and rewind at arbitrary speeds. Weobserve that the miss ratio does not decrease sharply overtime after a new transaction in RR. This is because thereexist periodic access failures to hot spot disks. Besides, inthe RR scheme, a very low miss ratio (e.g., 10−4) is notattainable. We need not investigate SPM, since SPM is in-ferior to RR and PRR, because SPM is considered basicallyat some pre-determined speeds (see Fig. 9).

Figure 12 illustrates the waiting time until a given missratio is achieved for a new operation. Assuming that the

278

12a 12b

13 14

15

Fig. 12a,b.The waiting time to achieve the miss ratios 10−2, 10−3 (N =100)

Fig. 13. The waiting time in PRR (load = 0.6)

Fig. 14. Disk utilization with varyingN

Fig. 15. Example of variable frame size in an MPEG video

tolerable delay is 5 s and the miss ratio is 10−2 in VCR-like applications, about 50 users (50% load in Fig. 12a) canbe served simultaneously with the PRR placement scheme.However, from Fig. 12a, we can see that only 15 users areadmitted under the RR scheme. From Fig. 12b, note that fora low waiting time (less than 5 s), no single client is served

under the miss ratio of 10−3 with the RR scheme, even undervery low load such as 10%.

Figure 13 illustrates the average waiting time to achievethe miss ratio of 10−2, 10−3, and 10−4 under PRR withvaryingN . We see that under a given load, the waiting timeis not much dependent on the number of disks. This means

279

a b

c d

Fig. 16a–d.Size of data accessed (a: RR, b: PRR, c: RR with extension, d: PRR with extension)

Segment Size of fragment placed on disks (bytes)size D0 D1 D2 D3 D4 D5 D6

4727 1024 1024 1024 1024 6314760 1024 1024 1024 1024 6643769 1024 1024 1024 6974608 512 1024 1024 1024 10244710 1024 614 1024 1024 10243660 1024 588 1024 10245092 1024 1024 1024 996 10245248 1024 1024 1024 1024 1024 1283644 1024 1024 1024 5723587 1024 1024 1024 5153587 1024 1024 1024 5153595 523 1024 1024 10243680 1024 608 1024 10243599 1024 1024 527 1024· · · · · ·

Fig. 17. Example of fragment placement

that we can increase the number of admissible clients for avideo server in proportion toN . This scalable feature makesPRR a very practical candidate for a very large video server.

5.4 Disk utilization

Since PRR prefers the prime number as the number of disks,disk space is not fully utilized for other cases. The averagedisk utilization is defined as the ratio of the stored data sizeand the entire disk space. That is,

1N

×N∑L=1

number of segments in a system (=LM )N × max. number of segments in a disk

(9)

whereL is the number of video objects stored in the entiresystem. Figure 14 illustrates the average and minimum diskutilization for PRR in function of the number of disks.

Compared to simple RR and SPM, where 100% disk uti-lization is achieved, disk utilization can be as low as 70%in PRR. However, disk utilization in PRR improves asNgrows, and for largeN , average utilization of 98% is com-mon. We can conclude that with largeN disk space wastein PRR is negligible.

6 Extension to VBR video

Although the basic disk placement scheme has been devel-oped for CBR video because of its wide use in network and

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storage of limited capacity, the extended scheme to handleVBR video should be developed, since VBR compressiontechnique is theoretically common and it provides a constantpicture quality regardless of frame complexity and motionactivity in video objects. Now, we consider an extensionof PRR to apply VBR compression, such as Motion-JPEG.Figure 15 shows an example of frame size in a VBR MPEGvideo, where a GOP consists of an I-frame which is similarto the frame of Motion-JPEG video objects. Frames vary500 to 10000 bytes in size, and frame sizes depend on thecomplexity of a scene. If a segment consists of fixed numberof frames, segments vary in size, and uniform load balanceof disks is not achieved in PRR.

In practice, Fig. 16a and b show the size of data accessedfor two times, three times, and five times FF when disksstore the entire variable size frames as segments in RR andPRR, respectively. Although PRR is more efficient than RRin balancing disk load, data accessed from disks also varyin size, and there may exist hot spots in a video server.

In PRR, the maximum size of data stored in a disk fora segment can be determined if a segment is divided intoseveral fixed-length fragments distributed across disks. Thestarting fragment must be placed in a disk associated withthe Eq. 3 in Subsect. 4.1. Figure 16c and d show the size ofdata accessed in RR and PRR with extensions, respectively.Since the size of data accessed is strongly related to thenumber of disk accesses, the result shows the disk loads canbe balanced in a VBR compression.

Let N be 7 and the maximum length of a fragment be1024. Figure 17 shows the example of fragment placementin PRR with segment striping, where the segment size isobtained from an actual compressed video (see Fig. 15). Al-though the size of the segment is not fixed, the time forretrieving each fragment can be determined considering themaximum seek time in disks. In addition, disk space is rea-sonably utilized in VBR compression if a number of videoobjects is stored in the disks.

7 Conclusion

In this paper, we have presented a new data placementscheme to provide uniform load balance in a disk arrayfor any retrieval speed. The major idea is to introduce arounding distance based on a prime number to distributedisk accesses evenly at any retrieval speed. By the simpleRR scheme with the prime numberNp, the video serverhandles all speeds correctly except for onlykNp, which ismapped tokNp+1 for load balancing. If the number of disksin a video server is large enough, the user may not recognizethe effect of mapping. The proposed disk placement scheme,called PRR, does not require any additional disk bandwidthin a video server to support arbitrary-rate retrievals, com-pared to previous schemes, at least several times more userscan be admitted to a server due to the elimination of hotspots in the disk array.

In real-world applications, retrieval-only video serversare not likely to be dominant. Deletion, addition and re-arrangement of video objects in a video server are to besupported in order to satisfy the interactive users’ varying in-terests. In addition, dynamic and yet efficient data placementschemes are subjects for further research by the authors.

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Taeck-Geun Kwon received his BS,MS, and PhD degrees in Computer En-gineering from the Department of Com-puter Engineering, Seoul National Uni-versity, Seoul, Korea, in 1988, 1990,and 1996, respectively. Since 1992 hehas been with R&D Center in LG In-formation & Communications, Ltd., Ko-rea. His current research interests in-clude database management systems,multimedia systems, video-on-demandserver, high-speed networking, and ATMswitching systems.

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Yanghee Choi received BS in Elec-tronics Engineering from Seoul NationalUniversity in 1975, MS in ElectronicsEngineering from Korea Advanced In-stitute of Science in 1977, and Doc-tor of Engineering in computer sci-ence from Ecole Nationale Superieuredes Telecommunications, Paris in 1984.He worked at Centre National d’Etudesdes Telecommunications, France, IBMThomas J. Watson Research Center,New York, and Electronics and Telecom-munications Research Institute, Korea,in 1977–1991. He joined the Depart-ment of Computer Engineering, SeoulNational University, in 1991, where he

is now associate professor, director of the Computer Network ResearchCenter, and associate director of the University Computing Center. He ischairman of SIG-Information Networking in the Korea Information ScienceSociety, and has served in many domestic and international conferences asprogram chair.

Sukho Lee received his BA degree inPolitical Science and Diplomacy fromYonsei University, Seoul, Korea, in 1964and his MS and PhD in ComputerSciences from the University of Texasat Austin in 1975 and 1979, respec-tively. He is currently a professor ofthe Department of Computer Engineer-ing, Seoul National University, Seoul,Korea, where he has been leading theDatabase Research Laboratory. He hasserved as the president of Korea In-formation Science Society. His researchinterests include database managementsystems, multimedia database systems,and object-oriented database systems.