A Methodology for Evaluating Storage Systems in Distributed and Hierarchical Video Servers

Transcription

1 A Mehodology for Evaluaing Sorage Sysems in Disribued and Hierarchical Video Servers William Tezlaff, Marin Kienzle, Dinkar Siaram BM T. J. Wason Research Cener Yorkown Heighs, NY Absrac Large scale mulimedia sysems combine echnologies from audio and video sysems, communicaions sysems, and compuer sysems. Mulimedia sysems sore compressed video files digially on a server ha is shared by a large number of users. A video server is characerized by he number of simulaneous video sreams i can suppor and he size of he video library. Sorage coss are a significan aspec of a video server because of he very large size of he objecs. n seing up a video service here is a choice beween having one very large cenral server, muliple decenralized servers, or a hierarchical senw srucure. This paper discusses he scaling and cos issues in he server in order o provide informaion on how o balance server coss agains communicaions coss. nroducion Video servers [l-51 are used o sore compressed digial video. One of he uses of video servers is o provide new services and enerainmen o he home. A large number of cliens and a wide dispersion of he cliens leads o many poenial ways o place video servers. This paper will primarily explore he rade-offs ha relae o he cos of he video sorage. A movies on demand scenario will be used o as a basis for he workload. A video server is composed of wo primary componens ha conribue o he cos. One par of he sysem sores he compressed video daa. he oher par of he sysem manages he sreams. Thr. cos of he sorage componen is a funcion of l..: size of he library and he number of sreams o he suppored. The cos of he sream managemen is a funcion of he number of sreams. The sorage sysem is composed of he disks and appropriae aachmen o he sream managemen funcion. This is ypically he disks, conrol unis, SCS cards and a swiching fabric. The size of he sorage sysem depends upon boh he size of he video library and he number of sreams ha are acive. The sreams ha are acive may reference much of he same video maerial. The endency oward a small amoun of video maerial is called skew. This creaes conenion for arms, conrol funcions and pahs. As differen maerial is referenced lrmugh differen viewing periods of he day, and from day o day, here will be a change in he frequency of access o maerial. Thus he skew oward paricular maerial changes. A cerain amoun of over capaciy mus be planned o cope wih he changing skew. The high aciviy daa mus be spread across muliple disk arms in order o preven overload. Since here is a pracical limi o spreading he load, here comes a ime ha he video daa mus be replicaed. Thus cerain overcapaciy, in he form of replicaed daa, mus be planned for. The size of he sorage sysem is mos easily measured in erms of he number of disk arms ha are needed. The number of disk arms is deermined by boh library size and hroughpu in sreams. For a paricular library size i is simple o compue he number of disk arms ha are needed o sore he conen. Simply divide he number of movies by he number of movies ha can be sored under one disk arm. The number of disk arms ha are needed for sream capaciy purposes is somewha more complicaed. )sing MPJG 1 compression raes, disks can suppor from 5 o 20 simulaneous video sreams. owever maximum use of all disk arms canno be planned because he load varies. The number of arms needed for sream capaciy is he number of sreams divided by p sreams ha an individual disk arm can suppor. A key consideraion in server design is he amoun of daa read each ime a disk is accessed. For each /94 $ EEE 430

2 access he disk arm mus move o a new posiion. Since we are assuming ha many users are using he daa under one arm, every access mus be assumed o have a seek. The normal assumpion is ha he seek will cover one hird he maximum seek disance. Nex he disk mus roae o he correc posiion. The normal assumpion is one half of a roaion. Having used approximaely one roaion o ge o he daa i is imporan o read a significan amoun of daa. f he read is for wo roaions worh of daa hen he drive will suppor wo hirds of he maximum hroughpu. Beyond his poin very large buffers are required and he increases in hroughpu become relaively small. For disks ha have fas seek imes a reasonable approximaion of maximum device hroughpu is wo hirds of he maximum daa rae. n mos video applicaions i will probably be necessary o organize he video daa so ha cerain maerial is accessible hrough more han one disk arm. For example very shor segmens of a movie migh alernae beween wo disk arms. This would average he aciviy across wo arms and increase he number of users ha could see he same movie. The remaining space could be used o sore a very lighly used movie. This echnique is called inerleaving or sriping. The use of sriping and careful placemen of movies makes all he bandwidh of he arms available. Once he number of sreams per arms is esablished i is possible o calculae he number of arms by dividing he number of sreams by he number of sreams per arm. The number of arms ha are required is he maximum of he number needed for sorage and he number ha are needed for sream hroughpu. RAD devices fall ino his model, bu require some exra consideraion. Some of he RAD algorihms cause muliple disk arms o move in andem and read in andem which means he number of arms is smaller han i appears. is as if he device has a single arm. For example RAD3 moves all of he arms o a paricular poin and hen reads from all of he disks in parallel, resuling in a high hroughpu while reading. However, when many users are simulaneously reading he same movie each user will cause all of he arms o move. The number of surfaces make i appear o be a very large disk surface under one arm. The following discussions will make use of some symbols and erminology: M S a b c he number of movies o be sored. he number of sreams o suppor. he number of movies ha can be sored on one disk he number of sreams ha can be read from each disk he cos per arm. There exiss a cross over poin a which he number of sreams and he library require he same number of disk arms. This is an imporan server sue. The prior discussion jusified he following equaion: Number o f Di sks=max(m/a,s/b) The cross over poin is when M/a equals S/b. S-Crossover= (M*b)/a Once he disk characerisics (a and b) are known i is possible o compue S-crossover based on he size of he video library. f a sysem is consruced o suppor fewer sreams han S-crossover hen he sorage cos is nonlinear, and expensive. This is because he number of arms is based on he library size ye he cos is spread across a relaively small number of users. Above he crossover poin he cos of sorage is minimized per user. n his range he number of arms becomes a linear funcion of he number of sreams. Servers should no be spli or disribued unil he resuling servers are approximaely of size S-Crossover. Arms Needed. Library size Crossover poin Throughpu 5 reams suppored Figure 1. Disk Arm Requiremens

3 cos Per Sream S-Crossover. n his example a library size of 100 movies and a hroughpu of 100 sreams is assumed. + Crossover poin Sreams suppored Movies per arm Sreams per arm Cos per arm Movie library Sreams per server a= 1 b = 10 c = 2000 M = 100 s = 100 one movie per arm O sreams per arm $2000 per arm 100 movies 100 sreams Arms Max(M/a,S/b) = Max( 100/1, OO/lO) = 100 Sorage cos per sream = (Arms*c)/S = 2000 Table 2. Sorage cos below crossover. Figure 2. Cos of sorage vs sreams Figure 1 makes i clear ha larger libraries will cause he crossover poin o move o he righ oward larger servers. also shows ha disks wih greaer hroughpu will lower he slope of he hroughpu line and lead o a higher crossover poin. Figure 2 shows he cos per sream as a funcion of seams suppored. Curren Technology wih MPEG-1 n he examples a daa rae of 1.5 Million Bis Per Second is assumed, which corresponds o MPEG- 1. The following parameers (Table 1) are mean o be illusraive of curren echnology bu no of a paricular device. Small diameer disks wih abou one gigabye capaciy are assumed. 1 Sorage Characerisics Assumpions 1 Movies per arm Sreams per arm a=1 b=10 arm one movie per 10 sreams per 1 Cos per arm 1 c=2000 $2000 per arm 100 movies Arms = Max( M/a,S/b) = Max( 1 OO/ 1, 000 /lo) = 100 Sorage cos per sream = (Arms*c)/S = 200 Table 1. Crossover wih sandard assumpions. For servers of 1000 sreams or greaer he sorage cos per sream is a very reasonable $200. Nex (Table 2) we will consider he economics of a server wih sream houghpu ha is below l For servers of 100 he sorage cos per sream is a very unreasonable $2000. Nex (Table 3) we will consider he oher side of he crossover poin, a server for 2000 sreams and 100 movies. rsorage Characerisics Assumpions Movies per arm Sreams per arm Sreams per server a= one movie per arm b= O 10 sreams per arm Cos per arm c=2000 $2000 per arm Movie library M= movies s sreams Table 3. Sorage cos above crossover. This confirms ha for servers of greaer han 1000 sreams he cos remains a very reasonable $200. Going o MPEG-2 MPEG-2 involves a daa rae and sorage size ha is wice ha of MPEG-1. This difference causes boh a and b o be cu in half. Since one is in he numeraor and he oher is in he denominaor he same number of sreams is served a he crossover poin. Despie he fac ha he number of sreams remains he same, going from MPEG- o MPEG-2 means mos resources of an MPEG-2 server will be wice ha of an MPEG-1 server. Since he crossover poin is no affeced by wheher he maerial is 432

4 MPEG-1 or MPEG-2 he examples will coninue o assume MPEG- 1. Effec of Disk rends. The bi densiy on he surface is improving regularly and a grea speed. The cos of a disk drive is decreasing moderaely each year. Finally he laency (seek ime plus roaion ime) is decreasing quie slowly. The nex example (Table 4) is a reasonable exrapolaion of Disk rends. Movies per arm a= % improvemen in surface densiy 20% improvemen due o daa rae and laency price Movie library M= mvvies S-Crossover = (M*b)/a=857 Sorage cos per sream = (Arms*c)/S = 134 Table 4. mproved Disk echnology. The changes in a and c resul in a 57 Percen reducion in he cos per bye. This is abou wha happens every wo years. This lowers he crossover poin moderaely from 1000 sreams o 857 sreams and a cos per sream of $134. Naurally i would be expeced ha library sizes would increase over ime. f half of he price per bye decrease is used o increase he size of he library o 130 movies, hen he crossover poin moves up from 1000 sreams o 1114 sreams (Table 5). Sorage Characerisics Assumpions Cos per arm 40% improvemen in surface densiv 20% improvemen due o daa rae and!aency 20% decrease in Movie library M= movies S-Crossover = (M*b)/a = Table 5. mproved echnology and more movies. The conclusion is ha Disk rends, and he need o sore more movies, will gradually increase he size of he crossover server. The crossover server size is independen of server organizaion, sofware, operaing sysem, RSC/CCS ec. also means ha a server ha is consruced as a collecion of microprocessors mus be able o show sream raes above he crossover poin. n fac, servers should no be spli unil he wo remaining pars are boh above he crossover poin. Thus any movie server should really be able o suppor a leas 2000 sreams if i is soring 100 MPEG-1 movies. Very High Throughpu Disk Devices The nex area o be invesigaed is he effec of a very large change in he performance of disk devices. This is a change beyond he hisorical rends and one ha does no scale wih oher aspecs of he sysem. This is he sor of change ha normally opens up new design radeoffs. n his case we will assume ha he capaciy remains he same bu ha he hroughpu riples. Sorage Characerisics Assumpions Movies per arm a=1 Sreams per 1 arm b = 30 Base assumpion Very high hroughpu device 1 Movie library M= movies S-Crossover = (M* b)/a = (100*30)/1 = 3000 Table 6. Very High Throughpu Disks. Table 6 shows ha an ou of proporion increase in disk hroughpu causes a ye larger crossover server size. The ripling of he disk hroughpu ripled he crossover poin from 1000 sreams o 3000 sreams. RAD3 Disk Drives RAD3 disk drive organizaions inerleave he daa blocks across a se of disks ha operae in parallel. The logical blocks are reassembled, on he fly, by a conrol uni funcion. The andem operaion means ha all disk arms mus move o he same poin a he same ime. Since disk arm moion is a key componen of disk hroughpu some of he hroughpu will be los. This can be compensaed for by increasing he amoun of daa ransferred on each read.

5 7 n his example (Table 7) he daa is assumed o be inerleaved across eigh disk arms. n order o mainain good hroughpu i will be necessary o increase he number of byes read per operaion by eigh imes, in order o mainain he same number of seeks per arm. n he firs analysis we wili rea a group of eigh arms as one logical disk and assume ha here is no problem in scaling. Sorage Characerisics Assumpions ~ Capaciy of 8 arms Sreams per arm b = 80 Throughpu of 8 arms Movies per arm a=8 Movie library M = 100 S-Crossover = (M*b)/a= (100*80)/8 = movies Table 7. Crossover wih RAD echnology. f he hroughpu does no acually scale by a facor of eigh hen a slighly differen resul is achieved (Table 8). Soraee Characerisics Assumpions Movies per arm a=8 arms Sreams per arm b = 70 scaling Capaciy of 8 Nonlinear Movie library M= movies S-Crossover =(M*b)/a=(100*70)/8=875 Table 8. Nonlinear RAD echnology. This shows ha RAD3 can lead o slighly smaller crossover servers. Anoher imporan consideraion is he cos of RAD sorage. The addiional conrol complexiy will increase he cos. The addiional pariy disk, which was no par of he above analysis, also adds o he cos. RAD3 only slighly changes he crossover server size. The conclusion is ha RAD will improve he reliabiliy of a server, bu will also add o he cos. Low cos per bye devices Opical sorage is characerized by a low cos per bye bu only modes daa rae and laency. The performance of opical drives is in an inermediae range where i could be used for eiher direc playou o a user or he maerial could be saged o an inermediae medium. For his analysis i is assumed ha here would be direc playou from he opical device. The imporan hing abou his analysis is no ha he device is opical..the imporan hing is ha i represens a device wih lower cos per bye of sorage wih lower performance. Any device like his would have he same impac on a sysem. ~~ 6 a g e Characerisics A&moions Movies per arm Sreams per arm Cos per arm a=4 * base b = 4 c = % reducion from base one fourh he cos Der bve Movie library M = movies Table 9. Low cos per bye devices. This is he firs example (Table 9) in which he crossover poin has gone down sigllfcanly. However, i is also necessary o consider he cos per video sream. This poins o an ineresing place for high densiy low performance sorage echnology. The cos of $500 per sream is above he cos of $200 per sream for a larger server of 1000 sreams. However, if i is no possible, or necessary, o serve a large number of sreams low performance disks may be more appropriae. An earlier example showed ha a sysem using convenional disks would cos $2000 per sream if only 100 sreams were needed. Library Devices Library devices creae a very low cos per bye by using some form of removable media. A roboic sysem is used o move he media from a shelf o a readlwrie saion. The cos per bye of sorage can be driven o a very small number by making he shelf very large. This is possible because making a large shelf is no a big problem. This example (Table 10) shows how he mehodology could be applied o a library device. The library device could be eiher playing direcly from a read saion or i could be saging o a roaing disk. Eiher sraegy can be used, depending upon he speed of he read saion. Technologies exis were he read saion operaes a jus above moion video speed, in which case direc playou is appropriae. Technologies ha are weny or more imes he speed of video exis, where saging makes more sense. n his example no assumpion is made abou which sraegy is used. Parameers are chosen ha 434

6 resul in a huge library, bu wih limied sream playou capabiliy. The playou capaciy could correspond o a sysem ha has 20 read saions ha are uilized half he ime. Simulaions have shown ha read saion use should be held o his range o keep queueing ime reasonable. Sorage Characerisics Assumpions Movies per a = library Sreams per library Huge b= 10 playou capaciy e Cos per library 1 c= Movie library M = OOOO movies S-Crossover= (M*b)/a=(10000*10)/10000= 10 Cos per movie /10000 = 50 Cos per sream /10 = Table O. Huge library device. n his example he crossover poin is less meaningful because i only represens he maximum sreams ha can be suppored. A library device would probably be used o hold a large number of infrequenly played movies. is imporan o consider boh he cos o sore a movie and he cos per sream o ge playou capaciy. Wih he parameers chosen for his library device he sorage cos is low bu he playou cos is very high. The cos per movie has dropped from $2000 per movie o $50 per movie, which is a facor of fory less expensive per movie. owever, he cos per sream of $50,000 is exremely high. The $50,000 cos is no fully comparable o he disk cos of $200 per sream bu he difference is cerainly imporan. Mid Sae Sorage The combinaion of servers ha can suppor large numbers of users, and he decreased cos of solid sae memory will evenually allow serving direcly from solid sae memory. A large number of users is needed o ge enough users waching hc same movie. Solid sae memory comes in o play when here are so many replicaions needed on disk ha he many copies exceed he cos of solid sae memory. This will become useful in large servers evenually. The analysis approach ha has been used on disks is also appropriae for solid sae memory. These parameers represen super high performance and high cos sorage. As in some of he oher examples he paricular hardware echnology is no he issue. Sorage Characerisics Assumpions 1 Movies per sore Sreams per sore Cos per library a= 1 One per devioe b= 1000 playou capaciy c = * base disk ~ ~~ Movie library M = movies S-Crossover =(M*b)/a=(100*1000)/1 = 100,000 Cos per sream= 100*100000/ = 100 Table 11. Crossover for all solid sae. n his case (Table 11) he crossover poin is no meaningful. akes a unreasonably large number of concurren sreams o ge o he linear par of he cos funcion. While he cos per sream is quie low he number of sreams remains unreasonably high. Thus a server ha sores everyhing in solid sae sorage does no seem reasonable. owever, as we will show laer, a hierarchical sysem in which one or several movies are in solid sae sorage is reasonable. Skew This analysis provides a floor on he number of disk arms needed. The acual number of disk arms is influenced by he skew of he workload. Skew is he endency of a few movies o have high aciviy and many o have low aciviy. f all movies had he same aciviy his analysis would be fully correc. f here is high skew oward one, or a few, movies hen acions mus be aken o provide he disk arm hroughpu o hose movies. One acion is o spread movies across several disk arms. This is usually referred o as sriping. f high aciviy movies are mixed wih low use movies hen accepable average arm use is achieved. The exreme case of sriping is o have some of every movie on every arm. This is unaccepable due o he fac ha a single arm failure makes all movies unavailable. is more likely ha sriping will divide he library ino 8 or 16 pars. f a single movie requires bandwidh beyond ha of one sriping group hen i mus be replicaed and placed in wo or more sriping groups. f he movie disribuion is skewed he replicaion wil be needed in sysems ha are smaller han he crossover poin. Even in he presence of skew he crossover poin should be considered he minimum size for a cos effecive server. sill represens he poin a which 435

7 ~~ he arm cos becomes linear wih he number of sreams suppored. The daa ha is available on movie viewing, and he consensus of mos people working on video on demand, is ha he disribuion will be very skewed. Some esimaes show as much as 25 percen of he viewers waching he mos popular movie. Mixed sysem of Disk and Solid sae for skew A mixed sysem could be creaed ha would sore he mos busy movie in solid sae memory and he oher movies on disk. will ake a very large server o spread he cos of he solid sae memory. n his example a sysem of 4000 sreams is analyzed. Sorage Characerisin Assumpions Movies per sore a-solid-sae = 1 Sreams per sore Cos per sore Movie library in solid sae Sreams per disk b-solid-sae = 1OO c= M = 1 One per device playou capaciy 50 * base disk 1 movies Movies per disk a-disk = 1 base assumpion b-disk = 10 base assumpion Cos per disk c = 2000 base assumpion c 1 99 movies disk Disks = S-disk/b-disk = 3000/10 = 300 Cos per disk sream= 300*2000/3000 = 200 Table 12. Solid sae and disk hierarchy. n his example (Table 12) he solid sae sorage for he single busies movie drops o $100 versus he cos of $200 for he remaining sreams. The break even for a movie of 25 percen usage would be a server wih 2000 sream capaciy. This clearly shows ha here can be a place for solid sae sorage a he op of he sorage hierarchy. However, he break even poin is quie dependen upon he skew in he viewing disribuion. Maximum Arm Requiremens The wors case for skew is ha all of he users wan o wach he same movie. Wihou sriping i would be necessary o have enough arms o hold he whole library for sorage purposes plus he number of arms needed for he hroughpu o he single movie. Maxi mum-d i s ks= ( (M- 1) /a) (S /b) Since M and M-1 are essenially he same we can use: Max! mum-d i sks= (M/a) +( S /b) is possible ha under very special circumsances a very large number of viewers, essenially all of hem, will wan o view he same maerial. A major, unexpeced even migh rigger large numbers of people o wach he same conen. For example individual abiliy o wach and replay he Superbowl fooball game would also creae huge numbers of sreams agains a small amoun of maerial. A precauion agains such aciviy would be he abiliy o sore one movie (or even) in solid sae memory wih nearly unlimied concurren viewing capabiliy. Wihou solid sae memory and wihou sriping here is an upper limi o he number of arms ha will be needed. The upper limi is he sum of he library size plus he number of arms needed o hold muliple copies of he single movie (Figure 3) ha everyone is viewing. Arms Needed Maximum Arms +. Minimum. Arms Crossover poin Sreams suppored Figure 3. Range of arms required vs sreams f all of he viewers wached one movie hen he disk requiremen is shown in Table

8 rsaiage Characerisics Assumpions Movies per arm a=1 arm Sreams per arm b=10 Movie library Sreams per server Movies per se one movie per 10 sreams per arm Cos per arm c=2000 $2000 per arm Sreams per se Cos per se M= movies s = sreams a crossover Maximum-disks = (M/a)+(S/b) = (100/1) + (looo/lo) = 200 Disk-cos = maximum-disks*c = 200*2000 = Table 13. Maximum disks a crossover. Sriping is poenially beneficial in managing exreme skew. A se of en disks ha are sriped give he appearance of a single disk wih beaer sorage and hroughpu capaciy. Movie library Sreams per server a= movies per se of 10 arms b = 100 c = M = 100 s = sreams per arm se $20000 per arm se 100 movies 1000 sreams a crossover Maximum-disks = (M/a)+ (S/b) = (100/10) + (1000/100) = 20 Disk-cos = maximumpdisks*c = 20*20000 = ~~~ ~~ ~~~ Table 14. Maximum disks a crossover. wih sriping While i appears ha he number of arms has been reduced he acual number of arms is really unchanged. This is because each sriped arm is really a collecion of en real arms. Thus sriping does no change he maximum number of arms in he wors case skew (Table 14). Reasonable Skew Curren workload esimaes show a mos 25 percen of he sreams applied o a single movie. From here he falloff is quie rapid. n he following examples he usual assumpions of a movie library of 100 movies and a 1000 sream server are assumed. Ten way sriping now has very real value because i increases he number of simulaneous viewers from 10 o 100 per movie. This means ha he hreshold a which a movie mus be replicaed has been grealy increased. Thus fewer movies will need o be replicaed. also means ha every replicaion suppors en imes he number of simulaneous users. n he nex example (Table 15) he mos popular movie is viewed by 30 percen of he viewers, 20 percen for he nex and 10 percen for he nex. This corresponds o 300, 200 and 100 sreams. Wih en way sriping, he busies movie would be sored wo redundan imes and he nex movie one redundan ime. This adds only 3 arms o he 100 needed a he crossover poin. However, since he sriping is in granulariy of en here would really be 110 arms. Wihou sriping he busies movie would need o be sored 29 redundan imes, hen nex one 19 redundan imes, and he hird 9 redundan imes. This comes o 57 addiional copies and 57 addiional disk arms. The oal arms on he sysem would become 157 a he crossover. Thus sriping allows for coping wih skew wih a 10 percen increase in he number of arms insead of he 57 percen ha would be needed wihou sriping. Sriping is clearly highly desirable. This also suggess ha real sysems wih reasonable skew will have disk requiremens ha are modesly above he minimum disks, and no approach he maximum line. Assumpions Top movie 30% of sreams Second movie 20% of sreams Third movie 10% of sreams Movies per se a=10 10 movies per se of 10 arms Sreams per se b= sreams per arm se Cos per se Arms = 110 Arms = 157 c = $20000 per arm se Movie library M = movies Sreams per 1000 sreams a server s=looo crossover Firs movie 2 redundan copies, second movie 1 redundan copy Firs movie 29 redundan copies, second movie 19, hird movie 9. Table 15. Max disks wih reasonable skew. 437

9 Decenralizaion and Neworking A above he crossover poin server cos becomes linear wih he number of sreams suppored. Thus any size server is economical wih respec o sorage. n his range i makes sense o spli ino local servers in order o reduce communicaions coss. As long as he spliing does no reduce he size of servers below he crossover poin, he cos of he sorage will remain consan. The cos of mos oher aspecs of he server will also be consan because hey are a linear funcion of he number of sreams suppored. Toally unbridled creaion of crossover sized servers hrough a deploymen has anoher se of undesirable characerisics. There are economies in having a modes number of video servers o operae and mainain. A some poin in he decenralizaion he savings due o lowered communicaions coss will be sligh and he operaional cos of addiional servers will exceed i. Hierarchical decenralized sysems Communicaions coss can be reduced if a sysem is decenralized ino smaller sysems ha ar-., nearer he clien. However, his may lead o servers ha are significanly below he crossover poin and hus have oo much sorage cos. Skew oward a few movies, which had been a bi of a problem o be solved, now can become a benefi. f a few movies represen he majoriy of he viewing hen hey migh be placed on servers nearer he viewer. Since hese movies would be replicaed o handle he load on a single server he addiional sorage for muliple servers migh no be grea. The smaller library on he inermediae servers would also cause hem o have smaller crossover poins. f five movies represened 80 percen of he viewing here could be muliple servers wih five movies and one server wih 95 movies. The crossover size for servers wih five movies is 50 sreams. Thus we would no wan o have inermediae servers wih less han 50 sreams. Naurally smaller numbers of larger servers could be creaed wihou any change in he oal number of arms The popular five movies would be served using 80 arms and disribued o 800 sreams. The remaining 200 sreams would be served from a more remoe server wih 95 arms. n oal 175 arms would be ;ised for his sysem. There is anoher consideraion ha should be aken ino accoun. While i is possible, from a hroughpu sandpoin, o make he servers as small as 50 sreams i may no be desirable. A 50 sream server is relaively small and will resul in oo much denial of service if i is highly uilized. This can be verified hrough sandard saisical calculaions used in elephony such as he Erlang-B formula. would be wiser o compose he sysem of inermediae servers on he order of 200 sreams. This would sill allow four 200 sream inermediae servers and one 200 sream large library server o serve 1000 sreams. This should have he poenial o save on communicaions coss. Naurally i mus be raded off agains he increase in arms from 110 o 175. f he skew is somewha less, and i akes 20 movies o serve 80 percen of he sreams hen he siuaion changes somewha. The crossover server sue for he inermediae servers wih 20 movies increases o 200 sreams. Four inermediae servers, each handling 200 sreams would require a oal of 80 arms. The large library server would require 80 arms for he library. This oals 160 arms for he enire sysem. This is slighly below he 175 arms when 5 movies oalled 80 percen. A furher savings could be had by coalescing one of he inermediae servers wih he large library server. This server would have a library of 100 movies and serve 400 sreams. This server would require 100 arms for he library, and wih sriping, should no need o replicae any movies. The oher hree inermediae servers would require 20 arms each. The oal number of arms becomes 160. The coalescing of one of he inermediae servers ino he large library server saves 15 arms and reduces he number of arms from 175 o 160. Large subscriber base f he subscriber base in an area became large enough o suppor 5000 sreams of service hen even he inermediae servers would be of crossover size. This subscribe base could be served eiher by one 5000 sream server or five 1000 sream servers. his sysem could be decenralized bu no hierarchical. Each sysem could have he full 100 movie library. 438

10 Large subscriber base and decreasing communicaions coss When he subscriber base becomes large i may acually pay o cenralize he mos wached several movies. This is because here will now be enough viewers o make he cos per sream be very low. migh also be accompanied by enough communicaions cos decline o make reducing communicaions coss less necessary. We again consider he case of five movies corresponding o 80 percen of he sreams. f 5000 sreams are o be shown hen 4000 come from he five movies and 1000 come from he oher 95 movies. Since 950 is he crossover poin for a 95 movie library he 1000 sreams will be handled by he 100 arms needed for hroughpu. The remaining five movies would be viewed on 4000 sreams from solid sae memory. The alernaive for serving he 4000 sreams of he five movies would be on eiher cenralized or decenralized servers. n eiher case he hroughpu would require 400 arms or 80 arms per movie. The 80 replicaions becomes an imporan relaionship beween disk and solid sae cos for a sysem of his size. Solid sae mus be no more han 80 imes as expensive as disk in order o be he less expensive. Solid sae sorage is considerably less han 80 imes as expensive so i seems a maer of ime unil servers become large enough for solid sae o be he preferred way o sore movies. However, he advanage in sorage cos mus sill overcome whaever increase in communicaions cos exiss. Conclusions Sriping is a necessary par of any video server. is needed o manage emporary changes in viewing, and o help reduce he replicaion needed of heavily viewed maerial. Replicaion is required. Even sriping will no eliminae he need o make exra copies of some heavily viewed maerial. A significan opimizaion funcion mus exis in a video server o adap o changing skew during he day and from day o day. This funcion will move fdes o place very unused movies wih busy movies o average he load on arms. will make replicaion copies when he number of sreams requires i. There is poenial o reduce overall coss by creaing a disribued hierarchical sysem. The key is knowing he communicaions coss ha are being offse by he somewha larger sorage coss. Solid sae sorage will evenually play a role. This simply depends upon subscriber bases geing large enough o spread he cos. The granulariy of servers should be a absolue minimum 50 sreams and 200 sreams would be much beer. This is due o having oo much denial of service due o small resource servers becoming overuilized. This is because larger servers can run a a higher percenage of heir maximum rae a he same denial of service rae. Skew cerainly exiss, bu he acual magniude is no ye known. will be wise o choose designs ha are graceful under unexpeced differences in skew. REFERENCES c11 c21 c31 c41 c51 Fox, E. A., The Coming Revoluion in neracive Digial Video, Communicaions of he ACM, vol. 32,7, Rangan, P. V., Kaeppner, T. and Vi, H. M., Techniques for Efficien Sorage of Digial Video and Audio, UCSD Technical Repor, vol. CS91-209, Rangan, P. V., Vin, 11. M. and Ramanahan, S., Designing a Muli-User Mulimedia-On-Demand Service, UCSD Technical Repor, vol. CS , Siaram, D., Design and Analysis of he WL,;S Mulimedia Server, Compuer Measuremen Group Transacions, vol. Winer, pp , Sincoskie, W. D., Sysem Archiecure for a Large Scale Video On Demand Service, Compuer Neworks and SDN Sysem, vol. 22,