A New Scheduling Algorithm for Servers

Transcription

1 A New Schedulng Algorth for Servers Nann Yao, Wenbn Yao, Shaobn Ca, and Jun N College of Coputer Scence and Technology, Harbn Engneerng Unversty, Harbn, Chna {yaonann, yaowenbn, cashaobn, nun}@hrbeu.edu.cn Abstract Slowdown s used to easure the farness degree of a schedulng algorth n exstng work. However, the farness degree should be consdered wthn a schedulng algorth; rather than beng tred wth syste envronent. An nnovatve farness odel s proposed naed hereby to ntutvely easure the farness of a server wthn through a schedulng algorth. The new schedulng algorth s called MPQ-LP whch coproses both the farness of PS and the hghest perforance of SRPT. Naely, MPQ-LP can easly adust the perforance and farness degree of the schedulng algorth. In addton, MPQ-LP allows each ob have the fxed copleton te wth less coputatonal coplexty copared to SRPT when assgnng the obs to the queues. Sulaton tests have been conducted to support our odel verfcaton. 1. Introducton Schedulng theory focuses on the optal allocaton of scarce resources to actvtes over te [1]. Ths paper tres to analyze two popular schedulng algorths such as PS (Processor-Sharng) and SRPT (Shortest-Reanng- Processng-Te). Each of the has pros and cons. In order to depct ther characterstcs, we frst gve the followng defntons for use [1]. Defnton 1: A schedulng odel s defned by three eleents: the achne envronent, the optalty crteron, and a set of sde constrans and characterstcs. Defnton 2: All the obs n a schedulng odel for a set denoted by J. The obs n J set can be nubered by J 1 J 1,, J n. Defnton 3: If the tasks can be nterrupted and can be resued at soe te later, we say that t can be preepted, denotng ths characterstc by pn. Defnton 4: A schedule S for J specfes, for each ob (1 n), n whch p unts of te the achne uses to process ob. Gven a schedule S, we denote the S copleton te of ob as C. Defnton 5: The nuber or the state of the processors s called the achne envronent. If there s one processor, we call t one achne envronent. If there are processors, we call t achne envronents and the process s notated as P. A schedulng odel can be denoted by (the achne envronent) (sde constrants and characterstcs) (optalty crteron). For exaple, 1 r, p, tn C denotes that a schedulng odel whch has one processor. The obs release the requred te and can be preepted. The crteron s to nze the su of all the obs copleton te. The r denotes that each ob has ts own released te. Therefore, n ths odel, a ob can only be scheduled and processed after ts released te. Defnton 6: If we denote s release te by r, ts C copleton te by, expected process te by, then ( C r) / p s called ob s stretch or slowdown. Apparently, each ob s stretch can t be less than Related Works The followng theore s rected n [1]: p r, p, tn C Theore 1: SRPT s optal for 1. The SRPT s defned to, at each pont n te, schedule the ob wth shortest reanng processng te, preeptng when obs of shortest processng te are released. We can see that SRPT s very unfar to the obs wth long expected process te. If durng a whle, any short obs are ceaselessly released, then the long obs ay be delayed all the te. We call that the long obs are starved. Ths s why SRPT s not popular n practcal applcatons. For nstance, alost all the Web servers do not use SRPT to schedule the requests of the clents. A aorty of the are usng PS, for exaple, Apache [2]. In the PS algorth, each of the N tasks receves servce at a rate that s 1/N tes the rate when there s only one task n the syste. The PS s therefore an dealzaton of round-robn schedulng, n whch the schedulng quantu approaches zero, and there s no te lost swtchng between tasks. But n the real world, Proceedngs of the Frst Internatonal Mult-Syposus on Coputer and Coputatonal Scences (IMSCCS'06)

2 n fact, there exst ore or less costs n swtchng. So ts schedulng quantu can t be too lttle. Intutvely, the PS algorth does wth each task farly, so t has the ost farness. Many works use slowdown to wegh the farness of schedulng algorths [-4]. Many works try to schedule the clents requests n servers by SRPT algorth. For exaple, n [2], the authors desgned a new archtect to test the perforance of the SRPT. Ther results show that usng SRPT n Web servers can not only reduce the average response te, but also ake the long connectons suffer lttle. [3,4] got the sae results. They have done atheatcal analyss to prove that for clents whch have heavy-taled dstrbuton, SRPT both can decreases the average response te and has not great effects on the long te requests. [6] ndcates that standard strateges and the etrcs they optze whle producng a schedule, are unfar snce they ay delay soe ob to an unbounded extent. They proposed two new etrcs to optze, naely, ax-flow and ax-stretch. There are soe good, new works n schedulng area besdes those recounted above, for nstance, [7] proposed Deadlne Far Schedulng(DFS) and proportonate-far CPU whch can be used n ult-processor servers. In [8], the author suarzed the weghted round-robn algorth and pleented t to schedule the packets n an ATM swtch chp. We wll talk about ths work later. [9,10] present a new schedulng algorth naed GR3 whch can narrow down the tradtonal tradeoff between farness and coputatonal coplexty. Ths algorth s soethng lke the one presented n secton 4, but ours s ore sple to pleent so t s sutable to be used n servers whle the forer s ore sutable to be used n operatng systes. 3. Metrc of Farness Though any papers[2,3,4] use slowdown of obs as the etrc of farness of the schedulng algorths. But we don t thnk so. We beleve the slowdown can only be used as a etrc of the obs qualty of servce. The reason s that the farness should be each schedulng algorth s own character, and t shouldn t have drect relatonshp wth the obs count or released te. But fro the defnton 6, we can see that the slowdown ust has the drect relatonshp wth the obs characterstcs such as expected process te and released te. For exaple, f n a schedulng, every task has equal slowdown, we can t ensure that the schedulng algorth beng used s far, because usng SRPT can also ake ths happen when the obs released tes are controlled properly. And f one task slowdown s very large n a schedulng process, we can t say the schedulng algorth beng used s unfar to the tasks as well, because that algorth beng used ay be PS. When usng the PS algorth, f the requests of clents are cong contnuously, even a sall request can take very long te to be processed and has a bg slowdown snce processor needs to do wth a lot of requests concurrently. Fro the arguent above, we conclude that the slowdown sn t a good etrc of schedulng algorth s farness. We thnk that a sutable etrc of farness ust have the propertes below: Has not drect relatonshp wth the obs beng scheduled. Ths property ensures that the algorth has the sae farness degree n dfferent envronent. Regards the PS as the farest algorth. Because the PS does wth each ob equally, and ntutvely t has the hghest farness degree. For each algorth, t can gve a certan value and all the values are n a fxed range and by whch we can copare the farness of the schedulng algorths. Obvously, the slowdown does not accord wth the frst two propertes. So far we have not found a sutable etrc of farness n prevous works. In ths paper, we try to propose a new etrc of schedulng farness: Mnal-Prorty-Rato (MPR). Defnton 7: When all the obs can be scheduled, the probablty off s beng scheduled s called the s absolute prorty. We assue the absolute prorty can t be zero. Defnton 8: The rato of and prorty s called and s absolute relatve prorty rato. Defnton 9: A schedulng algorth s the sallest relatve prorty rato s called the algorth s Mnal- Prorty-Rato (MPR). Fro the defntons above, we can draw soe conclusons below: 1. SRPT s MPR s 0; 2. PS s relatve prorty rato and the sallest prorty all equal MPR s n [0,1]. (Though the relatve prorty can be a very large nteger, for exaple, let M denote a relatve prorty, and M>>1, fro defnton 8, we can get that N=1/M s also a relatve prorty rato, and N<<M and N [0,1].) 4. If a schedulng algorth s MPR s near to 0, then there s a whch has very sall prorty and can be starved. So we can say that ths algorth s very unfar. 5. If a schedulng algorth s MPR s near to 1, then all the tasks have nearly equal prorty. So we can say that ths algorth s very far. Fro the conclusons above, we can conclude that the MPR ay be a sutable etrc of farness. By t, we now can dfferentate schedulng algorths farness. For exaple, f one algorth s MPR s larger than the other s, then we can say the forer s farer. Obvously, Proceedngs of the Frst Internatonal Mult-Syposus on Coputer and Coputatonal Scences (IMSCCS'06)

3 usng MPR as the etrc to easure the farness of schedulng algorths s ore ntutve. We should pont out that ths etrc s not sutable for all algorths, because MPR ay not be got drectly for soe schedulng algorths. 4. MPQLP Schedulng Algorth SRPT s used n Web servers n [2-4] and they have gotten good results, but t s rare used n real servers because t s so unfar to long requests. In [3], the authors only proved that f the requests are heavy-taled dstrbuted, long requests have sall slowdown whle usng SRPT. But for other dstrbutons, SRPT can ake long requests have bg slowdown. More than that, any of the results n [3] are average values, so the SRPT can t ensure soe of the long requests servce qualty. We beleve that though SRPT can ncrease the perforance of Web servers, ts an deert s that short requests have absolute prorty to long requests. So we try to propose an practcal schedulng algorth whch can lt the prorty of short requests to long requests and ensure each long request s servce qualty. We nae t Mult- Prorty-Queue-and-Lted-Prorty (MPQ-LP) algorth. If the requests can be dvded nto prorty classes, we can buld prorty queues such as Q1Q2 Q and set each queue wth an nteger naed prorty level such as P1 P2 P. When scheduled, the contnuously cong requests are frst put nto the prorty queues they belong to by the order of FIFO (Frst n frst out). Then the processor selects a request fro a queue to process. The rule to select s that the processor frst selects P1 nuber of requests fro the Q1 to process and then P2 nuber of requests fro the Q2 and so on untl t returns to the Q1. In a turn lke ths, f current queue s epty, then the processor selects requests fro the next queue, and f a new request coes nto a queue whch has hgher prorty than current queue and whose due n ths turn s not fnshed, then the new coer can preept the current one and be processed. Fro the descrpton of MPQ-LP, we can get: Corollary 1: In MPQ-LP, f every queue s not epty, the possblty of the requests n Q beng selected s P / P 1 Fro the defnton 7, t s ust the requests absolute prortes n Q. Corollary 2: The relatve prorty rato of the requests n Q and Q s p / p. Corollary 3: If p 1 p 2... p... p and >1, then MPQ-LP s MPR s p / p 1. Fro these corollares, we can see that by tunng the queues prorty level we can adust MPQ-LP s farness degree and by changng, we can adust the granularty of the prorty dvson. More than that, we know that when usng SRPT, once a task coes, t needs to be put n a queue by the order of ts reanng processng te. The average coputatonal coplexty of ths process s O(log(n)). However, n MPQ-LP the process of puttng tasks nto the queues needs at ost log 2 (n) tes of coparng. Snce the s a constant, the average coputatonal coplexty of ths process s O(1). So we can get: Corollary 4: In the process of puttng tasks nto the queues, MPQ-LP s average coputatonal coplexty s O(1) whch s uch lower than SRPT. Corollary 5: In MPQ-LP, the processng te of an arbtrary task s less than a constant. Proof: We assue, for each queue, P s the longest expected process te of the tasks n Q, and an arbtrary task k s n Q and ts sequence n Q s k. Then f k P ( P s the prorty level of the Q), can be fnshed before the te Pp. If k P, t can be fnshed before the te 1 k Pp p. 1 Corollary 6: Usng MPQ-LP n Web servers when the nuber of the queues s 1, then t s approxately lke the PS; f s very large and the prorty levels of the queues are onotonously decreasng, then the algorth s approxately lke the SRPT. Proof: Let the nuber of queues be and =1, then all requests order of beng processed s the sae as the sequence of they coe, naely the sequence of beng processed when usng PS(n a real Web servers usng PS to schedule requests, the requests sequence of beng processed s the sae as the sequence of ther cong). If s very large, then all the queues can be connected by the order of ther prorty level to becoe one queue n whch the requests are ordered by the te they expected to be processed(in Web servers, the prorty level of requests usually s decded by ther expected te to be processed). So the sequence of beng processed s slar to the processng sequence of SRPT. We can also see that MPQ-LP algorth s work conservng. It s dfferent fro the schedulng algorths whch copletely select tasks by ther predefned probablty. These algorths ay keep soe tasks n starvng state durng soe te, so they can t ensure the result proved by corollary 5. We should pont out that the MPQ-LP s a lttle slar to the weghted round-robn algorth because they both try to lt the tasks prorty whch have hgh J k Proceedngs of the Frst Internatonal Mult-Syposus on Coputer and Coputatonal Scences (IMSCCS'06)

4 prorty. But the weghted round-robn s uch ore coplcated and often s pleented n hardware such as swtch to schedule packets. We haven t seen t was used n servers so far. Copared to t, the MPQ-LP algorth s so sple that t only needs a few sple steps of coputaton, so t s ore sutable n practcal applance especally for servers to schedule requests. 5 Sulaton Results In order to valdate the conclusons got n secton 4, we do the sulaton tests usng CSIM18 whch s a popular tool to sulate dscrete events. We buld a sulaton archtecture shown n fgure 5.1. effects of changng the MPR. The tests (n whch the MPQ-LP s the sallest prorty rato s 1/10) results are presented n table 5.1. In fgure 5.3, the results of MPQ- LP usng the varant MPRs are gven. Table 5.1 the results of the tests usng three algorths Average The longest Schedulng servce teservce te algorth (seconds) (seconds) PS Requests Generator Requests Queues Serve r SRPT MPQ-LP(the sallest prorty rato s 1/10) Fgure 1 Sulaton archtecture In fgure 5.1, n order to ake the sulaton envronent ore realstc, the requests generator produces requests n accordance wth the real Web server s access log whch ncludes NCSA s requests fro zero o clock July 1st, In fgure 5.2, we gve the dstrbuton of the fles szes of requests beng used, and we can see that t s typcal heavy-taled. By the way, n sulaton, we don t need to know the Web contents, only need to know the fle sze and ts released te. The paraeters of the sulaton are: the te unt s 1 second and the processor servces 1024 bytes per second. Fgure 2.Dstrbuton of the Web fle szes We frst sulate the Web server usng PS, SRPT and MPQ-LP respectvely. When usng MPQ-LP, we buld two queues Q1 and Q2. The requests whose fle sze s less than 5120 bytes are put nto Q1 and the others are put nto Q2. Q2 prorty level P2 s fxed as 1 n order to observe the In Table 5.1, we can see that the average and the longest servce te of MPQ-LP both are between the PS and SRPT s. Besdes, ts longest servce te s only larger than PS s by 3.8e-6, however, ts perforance s about a double of PS s. Though the perforance of SRPT s the best, ts longest servce te s uch longer than PS s whch ndcates that n SRPT, ther ust exsts the starvaton of soe long requests. Now, ost of the servers are usng PS algorth, so we beleve that applyng the MPQ-LP nto servers should be uch prosng. We should pont out that we haven t sulated the process of puttng the requests nto the queues and fro the corollary 4 we know that the MPQ- LP s uch better than SRPT at ths stage. Fgure 3 Test results of changng the sallest prorty rato n MPQ-LP Proceedngs of the Frst Internatonal Mult-Syposus on Coputer and Coputatonal Scences (IMSCCS'06)

5 References Fgure 4. test results of changng the nuber of the queues n MPQ-LP In Fgure 5.3, when we decrease the sallest prorty rato, the perforance s becong hgher. Then we try to observe the effects of changng the nuber of queues n MPQ-LP. We fx the relatve prorty rato of the adacent queues such as Q and Q +1 (1<) as 2 and the prorty level of Q as 1. The requests whose fle szes are ore than 5210 bytes are put nto Q and the others are evenly dvded nto groups by ther fle sze. For exaple, f dvded nto 3 prorty levels, the requests whose fle sze s n (0, 2560] are put nto Q 1 and whose fle sze s n (2560, 5120] are put nto Q 2, and so on. Then the requests whose fle sze are ore than 5120 bytes are put nto Q 3. We show the results of changng the nuber of queues n fgure 5.4. We can see that ncreasng the nuber of queues can boost the perforance. The above tests results prove that n MPQ-LP, we can easly adust the perforance and farness degree of the schedulng algorth, and ths ay be a very good property n real server s pleentaton. 6 Conclusons A new etrc of schedulng algorth s farness and a new schedulng algorth naed MPQ-LP whch can adust the farness and perforance are presented n ths paper. The sulaton tests prove that the MPQ-LP can adust the perforance by changng ts Mnal-Prorty-Rato or nuber of groups. So ts perforance can be between the PS and SRPT, and ore than that, the tests results prove that n a real Web envronent, ts longest-servce-te can be only a lttle ore than PS, and uch less than SRPT. D. Karger, C. Sten, and J. Wen: Schedulng Algorths. Algorths and Theory of Coputaton Handbook, CRC Press, M. Crovella, R. Frangoso, and M. Harchol-Balter: Connecton Schedulng n Web Servers. In USENIX Syposu on Internet Technologes and Systes, N. Bansal and M. Harchol-Balter: Analyss of srpt schedulng: Investgatng unfarness. In Sgetrcs, Mor Harchol-Balter, Nkhl Bansal, and Banca Schroeder: Ipleentaton of SRPT schedulng n web servers. Techncal Report CMU-CS , Carnege Mellon School of Coputer Scence, October C. A. Waldspurger. Lottery and Strde Schedulng: Flexble Proportonal-Share Resource Manageent. PhD thess, Massachusetts Insttute of Technology, Sept Mchael Bender, Souen Chakrabart, and S. Muthukrshnan: Flow and stretch etrcs for schedulng contnuous ob streas. In Proceedngs of the 9th Annual ACM-SIAM Syposu on Dscrete Algorths, A. Chandra, M. Adler, and P. Shenoy: Deadlne Far Schedulng: Brdgng the Theory and Practce of Proportonate Far Schedulng n Multprocessor Systes. Techncal Report TR00-38, Departent of Coputer Scence, Unversty of Massachusetts at Aherst, Deceber M. Katevens, S. Sdropoulos, C. Courcoubets: Weghted Round-Robn Cell Multplexng n a General- Purpose ATM Swtch Chp', IEEE Journal on Selected Areas n Councatons, vol. 9, no. 8, October 1991, pp Bogdan Caprta, Wong Chun Chan, Jason Neh, Clfford Sten, and Haoqang Zheng: Group Rato Round-Robn: O(1) Proportonal Share Schedulng for Unprocessor and Multprocessor Systes, Techncal Report CUCS , Departent of Coputer Scence, Coluba Unversty, July 2004 Wong Chun Chan: Group Rato Round-Robn: An O(1) Proportonal Share Scheduler, M.S. Thess, Departent of Coputer Scence, Coluba Unversty, June Acknowledgeent Ths work s supported by the Natonal Natural Scence Foundaton of Chna (No: and No: ) and the Basc Research Foundaton of Harbn Engneerng Unversty (No: HEUFT05011 and No: HEUFT05012). Proceedngs of the Frst Internatonal Mult-Syposus on Coputer and Coputatonal Scences (IMSCCS'06)