Dynamic Multiple Parity (DMP) Disk Array for Serial Transaction Processing

Transcription

1 IEEE TRANSACTIONS ON COMPUTERS, VOL. 50, NO. 9, SEPTEMBER Dynamic Multiple Paity (DMP) Disk Aay fo Seial Tansaction Pocessing K.H. Yeung, Membe, IEEE, and T.S. Yum, Senio Membe, IEEE AbstactÐThe pefomance of today's database systems is usually limited by the speed of thei I/O devices. Fast I/O systems can be built fom an aay of low cost disks woking in paallel. This kind of disk achitectue is called RAID (Redundant Aays of Inexpensive Disks). RAID pomises impovement ove SLED (Single Lage Expensive Disks) in pefomance, eliability, powe consumption, and scalability. Howeve, a geneal fact about RAID is that the ªwiteº opeation is difficult to speedup. In this pape, we popose a new RAID achitectue, called Dynamic Multiple Paity (DMP) Disk Aay, fo seial tansaction pocessing database systems. Seial tansaction pocessing database systems include engineeing database systems, fully eplicated database systems using a completely centalized algoithm and distibuted systems using the consevative timestamp odeing algoithm. DMP Disk Aay can significantly incease the I/O thoughput by incopoating multiple paity disks. Due to the inheent distibuted spaing popety, DMP Disk Aay can povide nomal sevice to the uses unde single disk failue condition. Delay and maximum thoughput analysis on DMP Disk Aay is pefomed. Results show that, fo a typical ªwiteº job popotion of 20 pecent, DMP Disk Aay can povide nealy 20 pecent impovement on I/O thoughput ove that of RAID level 5 when one exta paity disk is used. Index TemsÐRAID, disk aays, I/O systems, database systems, tansaction pocessing. æ INTRODUCTION IN the past decade, consideable attention has been dawn to the eseach and development of database computes. As Su [] has stated in his book, thee ae thee easons why database computes ae needed: ) the need fo efficient and effective data management, 2) the need fo moe poweful database management systems, and 3) high pefomance database computes become economically feasible because of the advancement in hadwae technology and the eduction in hadwae cost. The pefomance of a database system is usually limited by the speed of its stoage devices. One good example is the Datacycle2 poject at BellCoe stating in the late 980s [2]. BellCoe poposed an innovative database achitectue called the Datacycle2. In this achitectue, the entie database is peiodically pumped out fom the cental database to a numbe of seves in which the use equied data ae filteed out. Since the whole database is pumped out, Datacycle2 has an unlimited thoughput fo ead-only tansactions. Datacycle2 technique assumes that the database is ªmemoy esident,º i.e., the entie database has to eside in vey fast stoage. This assumption, howeve, limits its scope of applications. Redundant Aays of Inexpensive Disks (RAID) is an innovative concept in designing fast and eliable data stoage systems. The philosophy behind RAID is that,. In the pototype built by BellCoe, the whole database esides in RAM.. K.H. Yeung is with the Depatment of Electonic Engineeing, City Univesity of Hong Kong, Yau Yat Chuen, Hong Kong. eeayeung@cityu.edu.hk.. T.S. Yum is with the Depatment of Infomation Engineeing, Chinese Univesity of Hong Kong, Shatin, Hong Kong. yum@ie.cuhk.edu.hk. Manuscipt eceived 2 Aug. 994; accepted 26 Feb Fo infomation on obtaining epints of this aticle, please send to: tc@compute.og, and efeence IEEECS Log Numbe instead of using one single expensive disk to achieve the pefomance and eliability equied, an aay of low cost disks woking in paallel ae used. Five levels of RAID wee defined when RAID was fist intoduced 2 and RAID level 5 was found to be one of the best [3]. Fo all levels of RAID, the ªwiteº opeations ae much slowe than the ªeadº ones. This limitation is paticulaly sevee fo applications with fequent data updates. Thee ae two easons why a ªwiteº opeation takes moe time fo RAID. Fist, a ªwiteº opeation involves the additional step of eading back the old data fom one disk and paity fom anothe disk. Second, a ªwiteº opeation involves the waiting time fo two specific disks to be fee simultaneously befoe actual witing. This waiting time can be educed by using the technique pesented in this pape. In this pape, we popose a new RAID achitectue, called Dynamic Multiple Paity (DMP) Disk Aay, fo seial tansaction pocessing database systems. Many database systems pocess tansactions in this way. Examples ae engineeing database systems [4], [5], [6], fully eplicated database systems using the completely centalized algoithm, and distibuted systems using the consevative timestamp odeing algoithm [7], [8], [9]. When we discuss the opeation of DMP Disk Aays, we will see how this kind of database systems handles I/O equests in a way diffeent fom othe database systems. We will also show that DMP Disk Aay can significantly educe the waiting time of disk opeations and povide a highe I/O thoughput than RAID level 5. In the next section, we descibe DMP Disk Aay in detail. We then pesent an aveage delay analysis in Section 3 and a maximum thoughput analysis in Section 4. In Section 5, esults of simulation with a pecise disk model ae given. We then conclude the pape in Section Some disk manufactos intoduced thei own levels of RAID late /0/$0.00 ß 200 IEEE

2 950 IEEE TRANSACTIONS ON COMPUTERS, VOL. 50, NO. 9, SEPTEMBER 200 Fig.. The secto coodinate system showing level 5 RAID. Fig. 2. The placement of paity sectos fo DMP Disk Aay when R ˆ 2. 2 DMP DISK ARRAY 2. Secto Coodinate System The secto coodinate system can be used to descibe RAID opeations, including that of DMP Disk Aay. Conside a disk aay system with M disks, whee each disk consists of Z sectos and each secto can stoe K bits of infomation (Fig. ). Let S i; j ˆ b i;j ;bi;j 2 ;bi;j 3 ;...;bi;j K be the bit patten of secto j in disk i. It can be data o paity. As an example, a RAID level is descibed in this secto coodinate system as: S i; j ˆS i ;j j ˆ ; 2; 3;...;Z; iˆ ; 3; 5;...;M : Similaly, RAID level 4 and level 5 can be descibed as: X M iˆ S i; j ˆ ; ; ;...; fo all j fodd paityg 0; 0; 0;...; 0 fo all j feven paityg; whee is defined hee as the mod-2 sum of the sectos' contents: X M iˆ S ; j ˆ S i; j S 2; j... S M; j 2 ˆ b ;j ;b;j 2 ;...;b;j K b2;j ;b2;j 2 ;...;b2;j K... b M;j ;b M;j 2 ;...;b M;j K ˆ b ;j b 2;j ;b ;j 2 b 2;j 2 2 ;...; b ;j K b2;j K... bm;j K : 3 Let E j be the location of the paity secto at ow j. Fo RAID level 4 E j ˆM and fo RAID level 5 E j ˆ j mod MŠ. The placement of these paity sectos is shown in Fig.. A study of the vaious paity placement methods fo RAID level 5 can be found in [0]. 2.2 Secto Oganization The DMP Disk Aay poposed in this pape is a new RAID achitectue fo which RAID level 5 is a special case. RAID level 5 has only one paity secto in each secto ow and, theefoe, it is not possible to simultaneously update two o moe sectos on the same ow. DMP Disk Aay allows such updates by placing R paity sectos in each ow. Thei locations E j ;E 2 j ;...;E R j fo ow j ae E j ˆ j 2 mod MŠ ˆ ; 2;...;R: 4 Lee and Katz [0] showed that, fo elatively lage equest sizes of hundeds of kilobytes, the choice of paity placement can significantly affect the pefomance of disk aays, wheeas, fo small equest sizes, the choice of paity placement is insignificant to system pefomance. We theefoe abitaily choose the paity locations as stated in (4). Although thee ae R paity sectos in each ow, paity integity descibed in (2) is always maintained fo DMP Disk Aay. (An example on the secto oganization of DMP Disk Aay fo R ˆ 2 is shown in Fig. 2.) Thee ae two advantages to placing R paity sectos in each ow. Fist, fo each data secto modification, we can choose any one of the R paity sectos in the same ow fo simultaneous paity modification. Hence, blocking due to busy disks can be significantly educed. Second, up to R data sectos on the same ow can now be modified simultaneously. We now pove that DMP Disk Aay has these useful popeties. 2.3 Popeties of DMP Disk Aay Popety concens the simultaneous negation of two bits on the same ow. Popety. Fo any ow j, simultaneous negation of any two bits in the same bit positions of two diffeent sectos will not affect the paity sum of the ow. Poof. Conside the set of th bits of each secto in secto ow j, i.e., b ;j, b2;j,..., and bm;j. In ode to maintain paity integity, the sum of these bits should always be fo odd paity o 0 fo even paity. The paity sum afte the negation of any two bits b a;j and b b;j, whee a 6ˆ b is:

3 YEUNG AND YUM: DYNAMIC MULTIPLE PARITY (DMP) DISK ARRAY FOR SERIAL TRANSACTION PROCESSING 95 b ;j... b a;j... b b;j b b;j b ;j fcommutative lawg b b;j b ;j fassociative lawg b b;j b a;j b b;j b ;j fdefinition of exclusive-og bb;j b a;j b b;j b ;j flaw of double negationg b b;j b ;j fdefinition of exclusive-og b b;j b ;j fassociative lawg ˆ b ;j... b a;j fcommutative lawg:... b b;j 5 tu secto update equies the old contents of two sectos only. Theefoe, each update is actually caied out by two disks woking in coopeation and is independent of the opeations of the est of the disks. Theefoe, with R paity sectos, R simultaneous updates can be pefomed. tu Popety 5. Conside a DMP Disk Aay with M disks and R paity sectos in each ow (R >). When a disk fails, it is possible to econfigue the emaining M disks to a new aay with R paity sectos in each ow without data loss. Poof. Let (p, p,..., p) be the paity sum of all the sectos in a ow, say ow j, and let S b ;j ;S b 2 ;j ;...;S b R ;j be the paity sectos. Obviously, b ˆ E j ;b 2 ˆ E 2 j ;...;b R ˆ E R j : Suppose disk i fails. We conside two cases fo the ecovey of S i; j.. If S i; j is a data secto, it can be ecoveed fom S i; j ˆ p; p;...;p XM nˆ;n6ˆi S n; j : 8 The last esult is identical to the paity sum befoe the simultaneous negation. We can extend the agument on the modification of two bits to that of the modification of two sectos on the same ow. This is stated as Popety 2. Popety 2. Paity integity of a ow can be maintained by modifying any one of the paity sectos in the same ow. Popety 2 implies that thee can be R diffeent ways to update a data secto. Due to this flexibility, the pobability that a ªwiteº equest is blocked due to the busy disk can be educed. Popety 3. Conside the simultaneous modification of data in secto j of disk a and paity in secto j of disk b. We denote the old data secto, the new data secto, the old paity secto, and the new paity secto as S a; j j old, S a; j j new, S b; j j old, and S b; j j new, espectively. Fo maintaining data integity, the new paity secto should be: S b; j j new ˆ S a; j j old S a; j j new S b; j j old : Poof. In ode to maintain paity integity, the patial sum of the two sectos S a; j and S b; j must not be changed afte secto modification, i.e., S a; j j new S b; j j new ˆ S a; j j old S b; j j old : Solving fo S b; j j new, (6) is obtained. Popety 4. Fo DMP Disk Aay with R paity sectos in each ow, R data sectos located in the same ow can be simultaneously updated. Poof. Equation (7) shows that, fo any secto update on ow j, the patial sum of the data secto and the paity secto will always be the same. Thus, the paticula secto update will not affect the updating of the othe sectos in ow j. Fom Popety 3, we find that each 6 7 tu One of the paity sectos, say S b R ;j, can be used to stoe the ecoveed data S i; j. To maintain paity integity anothe paity secto, say S b ;j, is modified as: S b ;j ˆS b ;j S b R ;j : 9 The ecoveed DMP Disk Aay now has R paity sectos. 2. If S i; j is a paity secto, then no data is lost. The paity integity can be ecoveed by modifying anothe paity secto, say b, as follows: S b; j ˆ p; p;...;p XM nˆ;n6ˆi; n6ˆb S n; j : 0 Popety 5 tell us that DMP Disk Aay has the distibuted spaing popety discussed in []. It is shown in [] that distibuted spaing is the best spaing technique fo small disk aays. 2.4 Pinciple of Opeation Fig. 3 shows the oganization of DMP Disk Aay. Requests fom a host ae diectly sent to the disk contolle fo the I/O opeations. The disk contolle consists of fou pats: an FCFS queue, a local memoy, a scheduling pocesso, and a DMA contolle. The queue is used fo stoing I/O equests. Since we ae consideing systems which execute tansactions in a stict ode, a single global queue with FCFS sevice discipline is used. Note that this is diffeent fom othe systems epoted in the liteatue, which use sepaate disk queues [2], [3], [4], [5]. The data associated with each equest (i.e., the new data fo a secto) is stoed in the local memoy when the equest is placed on the queue. The local memoy is also used fo buffeing the data sent to/ead fom each of the disks tu

4 952 IEEE TRANSACTIONS ON COMPUTERS, VOL. 50, NO. 9, SEPTEMBER 200 Fig. 3. Oganization of DMP Disk Aay. Fig. 4. Queuing models of DMP Disk Aay. with the help of the DMA contolle. The DMA contolle functions basically as a multiplexe/demultiplexe and handles simultaneous data tansfes to vaious disks. The scheduling pocesso is esponsible fo distibuting I/O equests to the disks and pefoms all necessay pocessing. Specifically, its functions ae outlined as follows:. It eads a equest fom the FCFS queue when eady and detemines whethe the equest is a ªeadº o a ªwiteº type. 2. Fo a ªeadº equest, the pocesso will a. check the status of the disk involved with this equest; b. instuct the disk involved to ead the taget secto; c. load the secto to the local memoy; and d. signal the host fo data eady. 3. Fo a ªwiteº equest, the pocesso will a. check the status of the disks and select at andom the paity secto of a nonbusy disk; b. ead the old data secto and the selected paity secto; c. compute the new paity secto accoding to (7); d. wite the new data secto and the new paity secto to thei coesponding disks; e. ead back the paity and data sectos fo veification; and f. signal the host fo ªwiteº completion. 3 AVERAGE DELAY 3. Analysis Fig. 4a shows a queuing model fo DMP Disk Aay. Requests sent fom host become jobs to be seved in the seves. Job aivals ae assumed to be a Poisson pocess with ate. A job is of the ªwiteº type with pobability and of the ªeadº type with the emaining pobability. Jobs not yet seved by the disk aay ae queued in an FCFS

5 YEUNG AND YUM: DYNAMIC MULTIPLE PARITY (DMP) DISK ARRAY FOR SERIAL TRANSACTION PROCESSING 953 queue. We call the job which is at the top of the queue the Head Of Line (HOL) job. The pobability that the HOL job needs to access a paticula disk is assumed to be the same fo all disks. This assumption is usually not tue, but it can be made tue by distibuting the fequently accessed data unifomly acoss all the disks. Fo mathematical convenience, we assume that the sevice time fo a job is exponentially distibuted with the sevice ates fo a ªwiteº job and a ªeadº job denoting as w and, espectively. Let andom vaiables N w and N denote the numbe of ªwiteº jobs and ªeadº jobs in the disk aay and N q be the numbe of queuing jobs (including the HOL job) at any time. It is easy to see that the tiplet N w ;N ;N q completely specifies the state of the system. Let S w;;q denote the state of the system when N w ˆ w, N ˆ, and N q ˆ q. State tansition will take place when a new job aives o when a job in the system depats. Since the time spent in a state is exponentially distibuted, the evolution of N w ;N ;N q is a continuous time Makov pocess. We define the tansition pobabilities to be P S w 0 ; 0 ;q 0 j S w;;q ˆ P N w ;N ;N q ˆ w 0 ; 0 ;q 0 afte state tansition j N w ;N ;N q ˆ w; ; q befoe state tansition : Conside a paticula state tansition at time t. Define events E, E 2, and E 3 as: E : A new job aives at time t. E 2 : A ªeadº job depats at time t. E 3 : A ªwiteº job depats at time t. The event E is listed in the fist column of Table. A complete table listing the othe two events is given in [3]. The disk aay is at S w;;q immediately befoe t, i.e., at time t t (t! 0). The pobability that a new job will aive in the inteval t t; t is t if t! 0. Similaly, the pobabilities that the disk aay will finish seving a ªwiteº job and a ªeadº job in this small time inteval ae w t and t, espectively. Theefoe, P E Šˆ w w P E 2 Šˆ 2 w w w w P E 3 Šˆ : w w When a new job aives (i.e., E occus), the pobabilities that this HOL job is of the ªeadº type and of the ªwiteº type ae and, espectively. Howeve, a diffeent pobability fo each of the job types fo the HOL job is found when a job depats (i.e., eithe E 2 o E 3 occus). We denote the pobabilities that the HOL job is of the ªwiteº type and of the ªeadº type by h w and h w, espectively, fo system tansitions due to job depatues. Pobability h w can be deived as follows: At the pevious state change, the HOL job was blocked because it equies the access of one o moe busy disks. By that time thee wee 2w busy disks. If the HOL job is of the ªeadº type, the pobability of blocking k is: numbe of busy disks k ˆ total numbe of disks ˆ 2w M : 3 On the othe hand, if the HOL job is of the ªwiteº type, the pobability of blocking k w can be deived as follows: We shall call the disk which the HOL job tagets fo data modification the data disk and the R disks stoing the equied paity infomation the paity disks. Let events and 2 be: : The data disk to be accessed was fee at the pevious state change. 2 : At least one of the R paity disks was fee at the pevious state change. Then, k w ˆ P no blockingš ˆ P and 2 Š ˆ P ŠP 2 j Š: P 2 j Š is given by: 0 numbe of ways to B choose R paity disks A fom 2w busy disks P 2 j Šˆ 0 numbe of ways to B choose R paity disks A fom M disks 8 2w <R >< 2w ˆ R 2w R: M >: R 4 5 Substituting into (4) and solving fo k w we obtain 8 2w 2w <R M >< 2w k w ˆ 2w M 2w R 2w R: M M M >: R 6 Having obtained k and k w, h w is given by: h w ˆ kw k k w : 7 Conditioning on event E i and giving the type of the HOL job, the pobabilities of having diffeent numbes of jobs located in the queue and in the disk aay ae listed in the sixth column of Table. Fo example, the fist ow of Table coesponds to the case that a ªeadº job entes an empty queue is blocked o the numbe of ªeadº jobs and ªwiteº jobs in the disk aay emain the same and q 0 becomes. The pobability of having the new tiplet w 0 ; 0 ;q 0 ˆ w; ; afte t unde the two given conditions is denoted as a. Similaly the fifth ow of Table coesponds to the case that a ªwiteº job entes an empty queue and gets seved immediately. The pobability of having w 0 ; 0 ;q 0 ˆ w ;;0 afte t unde

6 954 IEEE TRANSACTIONS ON COMPUTERS, VOL. 50, NO. 9, SEPTEMBER 200 TABLE Tansition Pobabilities of Event E fo Aveage Delay Analysis A complete table showing the tansition pobabilities of all othe events can be found in [3]. the two given conditions is denoted by a 3, as shown. The deivation of all a i s is given in [3]. The seventh column of Table shows the type of the new HOL job and its coesponding pobability. A new HOL job is blocked at time t with pobabilities k 0 and k 0 w when it is of the ªeadº type and of the ªwiteº type, espectively. Similaly to the deivations on k and k w, k 0 and k 0 w can be obtained fom (3) and (6) by changing the numbe of busy disks fom 2w to 2w 0 0. The last column of Table shows P S w 0 ; 0 ;q 0jS w;;q;e i Š.By emoving the condition on E i, the tansition pobabilities ae thus obtained: P S w 0 ; 0 ;q 0 j S X 3 w;;q ˆ iˆ P S w 0 ; 0 ;q 0 j S w;;q;e i P Ei Š: 8 Having obtained the tansition pobabilities, the equilibium distibution of diffeent states can be computed in the usual way. The expected numbes of jobs in the queue ae given by: E N q Šˆ X bm=2c X M X wˆ0 ˆ0 qˆ0 qp S w;;q Š: 9 Finally, by Little's fomula, the job's sojoun time D is given by D ˆ E N qš : 20 w 3.2 Numeical Example As an example, conside a small DMP Disk Aay with data stoage capacity of fou disks. We assume in this example that w ˆ 30 jobs/sec and ˆ 50 jobs/sec. Figs. 5 and 6 show both the analytic and simulation esults fo this disk aay and we obseve that they match vey well with each othe. Note that, fo all simulation esults shown in this pape, we have extended the simulation time sufficiently long to make the 95 pecent confidence intevals smalle than the size of the simulation points shown. Fig. 5 shows the job delay against the aival ate when half of the jobs ae of the ªwiteº type. As indicated by the cuve, the maximum thoughput fo RAID level 5 is about 50 jobs/sec. When one paity disk is added to the disk aay (i.e., when M ˆ 6 and R ˆ 2), we find that the aveage job delay is educed unde all taffic conditions and the maximum thoughput is inceased by about 3 pecent when compaed to RAID level 5. If one moe paity disk is used (R ˆ 3), we find that the job delay is futhe educed unde all taffic conditions and 23 pecent incease in maximum thoughput is obseved. Fig. 6 shows the job delay against the aival ate when 20 pecent of the jobs ae of the ªwiteº type ( ˆ 0:2). We obseve fom the figue that DMP Disk Aay with R ˆ 2 and R ˆ 3 again pefoms significantly bette than RAID level 5 unde all taffic levels. 4 MAXIMUM THROUGHPUT 4. Analysis Although the analysis given in Section 3 povides an exact solution on aveage job delay, the computation is vey demanding when the disk aay is lage. In the following, we pesent a simplified analysis which gives the maximum thoughput fo DMP Disk Aay. A modified model, shown in Fig. 4b, is used in ou analysis. Compaed with the pevious model (Fig. 4a), the FCFS queue is emoved and

7 YEUNG AND YUM: DYNAMIC MULTIPLE PARITY (DMP) DISK ARRAY FOR SERIAL TRANSACTION PROCESSING 955 Fig. 5. Aveage job delay against the aival ate fo small DMP Disk Aays (data stoage capacity M-R is fou disks). Half the jobs ae of ªwiteº type ( ˆ 0:5). Fig. 6. Aveage job delay against the aival ate fo small DMP Disk Aays (data stoage capacity M-R is fou disks). Eighty pecent of the jobs ae of the ªeadº type ( ˆ 0:2). we assume that thee is always a new job available at the input of the disk aay. All othe peviously used assumptions ae used in this maximum thoughput analysis. Since the queue is emoved, the system's state can solely be specified by N w and N and is denoted by S w;. State tansition will take place when a job in the disk aay depats, i.e., eithe E 2 o E 3 occus. Since the time spent in a state is exponentially distibuted, the evolution of N w and N emains a continuous time Makov pocess. As befoe, we define the tansition pobabilities to be P S w; ;S w0 ; 0Šˆ P N w ˆ w 0 ;N ˆ 0 afte system tansition j N w ˆ w; N ˆ befoe system tansitionš: 2 Conside a paticula state tansition occus at time t. The pobability of occuence of E 2 and E 3 is given by P E 2 Šˆ w w w w P E 3 Šˆ : w w 22 Given that a specific event E i occus, the tansition pobabilities P S w; ;S w 0 ; 0jE iš ae listed in the last column of Table 2. 3 The deivations on pobabilities a i shown in the table ae given in [3]. Having obtained the tansition pobabilities, the equilibium distibution of diffeent states can be computed as befoe. The expected time between successive job depatues X is given by 3. Table 2 shows only the tansition pobabilities of event E. A complete table fo all events can be found in [6].

8 956 IEEE TRANSACTIONS ON COMPUTERS, VOL. 50, NO. 9, SEPTEMBER 200 TABLE 2 Tansition Pobabilities of Event E 2 fo Maximum Thoughput Analysis A complete table showing the tansition pobabilities of all othe events can be found in [3]. Fig. 7. Thoughput gain ove that of RAID level 5 as a function of R fo small DMP Disk Aays (data stoage capacity M-R is fou disks). bm=2c X ˆ X wˆ0 X M ˆ0 P S w; Š : w w 23 Finally, the maximum thoughput fo DMP Disk Aays T is T ˆ X : Numeical Examples Fig. 7 shows the thoughput gain ove that of RAID level 5 against R fo a small DMP Disk Aay with data stoage capacity of fou disks. We obseve fom the figue that inceasing the numbe of paity disks R will always incease the maximum thoughput fo DMP Disk Aay. When the popotion of ªwiteº jobs is highe, the incease in

9 YEUNG AND YUM: DYNAMIC MULTIPLE PARITY (DMP) DISK ARRAY FOR SERIAL TRANSACTION PROCESSING 957 Fig. 8. Thoughput gain ove that of RAID level 5 as a function of R fo lage DMP Disk Aays (data stoage capacity M-R is 3 disks). maximum thoughput is moe appaent because DMP Disk Aay will educe the queuing time of ªwiteº jobs. Consideing the case of all ªwiteº jobs ( ˆ ), DMP Disk Aay with R ˆ 2 povides 24 pecent incease in maximum thoughput when compaed to RAID level 5. Futhe inceasing R to thee povides an additional 7 pecent incease in maximum thoughput. These pefomance figues match well with the numeical examples given in the pevious section. When R is geate than thee, linea incease in maximum thoughput is obseved fo each paity disk added. Fom the figue, we also obseve that significant thoughput gain is obtained fo a typical 20 pecent popotion of ªwiteº jobs. Fig. 8 plots the thoughput gain ove that of RAID level 5 against R fo a lage DMP Disk Aay with data stoage capacity of 3 disks. When compaed with Fig. 7, we obseve that DMP Disk Aay with R ˆ 2 povides even moe notable incease in maximum thoughput than the pevious case. We can thus conclude that a DMP Disk Aay with R ˆ 2 povides the best cost/pefomance atio. 5 SIMULATION WITH PRECISE DISK MODEL In ou pevious analysis, disk sevice time is assumed to be exponentially distibuted. This is usually not tue fo pactical disk dives. To bette undestand the pefomance of DMP Disk Aay in pactice, we pefom simulation on DMP Disk Aay with a pecise disk model. In ou simulation, disks ae not assumed to be otationally synchonized and thei simulation paametes ae summaized in Table 3. Each disk access involves a seek time, a latency, and a data tansfe time [6]. We use the seek pofile in [7], which states that the seek time Tseek (in msec) is elated to seek distance x (in numbe of cylindes) by: T seek ˆ 0 p fo x ˆ 0 0:4623 x 0:0092 x 2 fo x>0: 25 Latency is assumed to be unifomly distibuted. Data tansfe time fo one secto is equal to the disk evolution time divided by the numbe of sectos pe tack, as given in Table 3. With that, the mean sevice time fo ªwiteº jobs is computed to be 33.3 ms and, fo ªeadº jobs, it is 20 ms. The coesponding sevice ates ae theefoe the same as those in the pevious examples. As stated in [8], this kind of disk modeling povides moe than 94 pecent accuacy when ignoing the disk caching effect. Since disk caching has little impact on ªwiteº pefomance (which we ae most TABLE 3 Disk Paametes Used in Simulation Fig. 9. Simulation esults on aveage job delay against aival ate fo small disk aays (data stoage capacity M-R is fou disks). Half the jobs ae ªwiteº ( ˆ 0:5).

10 958 IEEE TRANSACTIONS ON COMPUTERS, VOL. 50, NO. 9, SEPTEMBER 200 Fig. 0. Simulation esults on aveage job delay against aival ate fo small disk aays (data stoage capacity M-R is fou disks). Eighty pecent of the jobs ae of the ªeadº type ( ˆ 0:2). inteested in), we can thus assume that the system has no disk caching mechanism. Figs. 9, 0,, and 2 show the simulation esults with the pecise disk model. We fist conside a small disk aay with data stoage capacity of fou disks and half the jobs ae of the ªwiteº type. Fig. 9 shows that the maximum thoughput fo RAID level 5 is about 56 jobs/sec. If DMP Disk Aay with M ˆ 6 and R ˆ 2 is used, the aveage job delay is educed unde all taffic conditions and the maximum thoughput is inceased by 23 pecent as compaed to RAID level 5. The maximum thoughput is futhe inceasted by about 40 pecent when DMP Disk Aay with M ˆ 7 and R ˆ 3 is used. We also obseve that when the numbe of disks M is fixed, DMP Disk Aay with R ˆ 2 still povides pecent impovement in maximum thoughput. Fig. 0 shows the esults fo ˆ 0:2. We obseve that DMP Disk Aay with R ˆ 2 and R ˆ 3 povides 7 pecent and 29 pecent inceases in I/O thoughput, espectively. The incease in thoughput when M ˆ 5 and R ˆ 2 is about 7 pecent. Fig. 2. Simulation esults on aveage job delay against aival ate fo lage disk aays (data stoage capacity M-R is 3 disks). Eighty pecent of the jobs ae of the ªeadº type ( ˆ 0:2). Figs. and 2 show the delay thoughput chaacteistics of a typical lage disk aay with data stoage capacity of 3 disks. DMP Disk Aay again povides significant I/O thoughput incease. When half the jobs ae of the ªwiteº type (Fig. ), the incease on maximum thoughput fo DMP Disk Aay with R ˆ 2 is about 2 pecent, wheeas the coesponding incease in system cost is at most 7 pecent. Unde the condition of 20 pecent of the jobs ae of the ªwiteº type (Fig. 2), we find that the 7 pecent incease in system cost can still give 2 pecent highe thoughput. Figs. 3 and 4 show the case when the numbe of disks, M, is fixed at 4 disks. When half the jobs ae of the ªwiteº type (Fig. 3), the incease on maximum thoughput fo DMP Disk Aay with R ˆ 2 is about 7 pecent. Note that thee is no incease in system cost. Unde the condition of 20 pecent of the jobs ae of the ªwiteº type (Fig. 4), we find that DMP Disk Aay with R ˆ 2 still povides 8 pecent highe thoughput at no additional system cost. Fig.. Simulation esults on aveage job delay against aival ate fo lage disk aays (data stoage capacity M-R is 3 disks). Half the jobs ae of ªwiteº type ( ˆ 0:5). Fig. 3. Simulation esults on aveage job delay against aival ate fo lage disk aays (total numbe of disks, M, is 4). Half the jobs ae of ªwiteº type ( ˆ 0:5).

11 YEUNG AND YUM: DYNAMIC MULTIPLE PARITY (DMP) DISK ARRAY FOR SERIAL TRANSACTION PROCESSING 959 [5] A.L. Naasimha Reddy and P. Banejee, ªAn Evaluation of Multiple-Disk I/O Systems,º IEEE Tans. Computes, vol. 38, no. 2, Dec [6] S.W. Ng, ªAdvances in Disk Technology: Pefomance Issues,º Compute, vol. 3, no. 5, pp. 75-8, May 998. [7] E.K. Lee and R.H. Katz, ªThe Pefomance of Paity Placements in Disk Aays,º IEEE Tans. Computes, vol. 42, no. 6, pp , June 993. [8] C. Ruemmle and J. Wilkes, ªAn Intoduction to Disk Dive Modeling,º Compute, vol. 27, no. 3, pp. 7-28, Ma Fig. 4. Simulation esults on aveage job delay against aival ate fo lage disk aays (total numbe of disks, M, is 4). Eighty pecent of the jobs ae of ªeadº type ( ˆ 0:2). 6 CONCLUSIONS In this pape, we popose a new RAID achitectue, called Dynamic Multiple Paity (DMP) Disk Aay, fo fast database system applications. The DMP Disk Aay povides significant impovement on I/O thoughput ove the RAID level 5. The DMP Disk Aay also inheently has the spaing popety so that it has a highe suvivability unde disk failue conditions. Delay and maximum thoughput analysis on DMP Disk Aay is pefomed. Simulation with pecise disk model shows that, fo a typical ªwiteº job popotion of 20 pecent, DMP Disk Aay can povide nealy 20 pecent impovement on I/O pefomance ove that of RAID level 5 when one exta paity disk is used. REFERENCES [] S.Y.W. Su, Database Computes. McGaw-Hill, 988. [2] T. Bowen, G. Gopal, G. Heman, and W. Mansfield, ªA Scale Database Achitectue fo Netwok Sevices,º IEEE Comm. Magazine, vol. 29, no., Jan. 99. [3] K.H. Yeung, ªHigh Pefomance Disk Aay Achitectues,º PhD dissetation, The Chinese Univ. of Hong Kong, 995. [4] J.L. Encanacao and P.C. Lockemann, Engineeing Databases. Spinge-Velag, 990. [5] K.H. Yeung and T.S. Yum, ªDynamic Paity Logging Disk Aays fo Engineeing Database Systems,º IEE Poc.ÐComputes and Digital Techniques, vol. 44, no. 5, pp , Sept [6] R.H. Katz, Infomation Management fo Engineeing Design, Spinge-Velag, 985. [7] M. Singhal and N.G. Shivaati, Advanced Concepts in Opeating Systems, chapte 20. McGaw-Hill, 994. [8] F.R. McFadden, J.A. Hoffe, and M.B. Pescott, Moden Database Management, fifth ed. Addison-Wesley, 999. [9] S. Cei and G. Pelagatti, Distibuted Databases: Pinciples and Systems, chapte 8. McGaw-Hill, 984. [0] E.K. Lee and R.H. Katz, ªThe Pefomance of Paity Placements in Disk Aays,º IEEE Tans. Computes, vol. 42, no. 6, June 993. [] J. Menon and D. Mattson, ªCompaison of Spaing Altenatives fo Disk Aay,º Poc. 9th Int'l Symp. Compute Achitectue, pp , May 992. [2] M.Y. Kim, ªSynchonized Disk Inteleaving,º IEEE Tans. Computes, vol. 35, no., pp , Nov [3] N.C. Wilhelm, ªA Geneal Model fo the Pefomance of Disk Systems,º J. ACM, vol. 24, no., pp. 4-3, Jan [4] S.W. Ng, ªImpoving Disk Pefomance via Latency Reduction,º IEEE Tans. Computes, vol. 40, no., pp , Jan. 99. K.H. Yeung eceived the BSc degee fom the Chinese Univesity of Hong Kong in 984, the postgaduate diploma and MSc degee fom the City Univesity of Hong Kong in 989 and 99, espectively, and the PhD degee fom the Chinese Univesity of Hong Kong in 995. He was an R&D enginee with a PC manufactue fo one yea befoe joining the City Univesity of Hong Kong in 985. He was an analyst pogamme fo five yeas befoe tansfeing to the Depatment of Electonic Engineeing in 990, whee he is cuently an associate pofesso. His eseach inteests include Intenet system design, mobile communication, infomation delivey, and VoD achitectues. Besides eseach, he is also active in poviding consultancy sevices to local industy in the aeas of compute netwoking, communication systems, and Intenet systems. He is also a Cetified Cisco Academy Instucto. He is a membe of the IEEE. T.S. Yum is a gaduate of Columbia Univesity. He woked at Bell Telephone Laboatoies fo two and a half yeas and taught at National Chiao Tung Univesity, Taiwan, fo two yeas befoe joining The Chinese Univesity of Hong Kong in 982. He has published oiginal eseach on packet switched netwoks with contibutions in outing algoithms, buffe management, deadlock detection algoithms, message esequencing analysis, and multiaccess potocols. In ecent yeas, he banched out to wok on the design and analysis of cellula netwok, lightwave netwoks, and video distibution netwoks. He believes that the next challenge is designing an intelligent netwok that can accommodate the needs of individual customes. Pofesso Yum's eseach benefits a lot fom his gaduate students. Seven of them ae now pofessos at local and oveseas univesities. He is on the editoial boad of six jounals on communications and infomation science, including the ecently launched IEEE Tansactions on Multimedia. He is a senio membe of the IEEE.. Fo futhe infomation on this o any computing topic, please visit ou Digital Libay at