source managemen, naming, proecion, and service provisions. This paper concenraes on he basic processor scheduling aspecs of resource managemen. 2 The

Transcription

1 Virual Compuers A New Paradigm for Disribued Operaing Sysems Banu Ozden y Aaron J. Goldberg Avi Silberschaz z 600 Mounain Ave. AT&T Bell Laboraories Murray Hill, NJ Absrac The virual compuers (VC) paradigm enables he incorporaion of predicabiliy and choice ino he design of an operaing sysem. Predicabiliy refers o he abiliy of he sysem o provide each user wih a compuing environmen whose performance is independen of he behavior of oher users. Choice refers o he abiliy of a user o selec a compuer sysem ha mees ha user's specicaions, needs or budge. In his paper, we inroduce his new paradigm and show how he VC paradigm can be incorporaed ino he processor scheduling, and how he on-line schedulers can be eecively implemened. 1 Inroducion Personal compuers provide wo aracive feaures ha are negleced in oday's disribued operaing sysems predicabiliy and choice. Predicabiliy is he abiliy of he sysem o provide each user wih a compuing environmen whose performance is independen ofhebehavior of oher users. Choice refers o he abiliy of a user o selec a compuer sysem ha mees ha user's specicaions, needs or budge. We refer o he pair of feaures as ownership, since hese wo feaures ogeher represen he righs of he compuer owner. The research of Banu Ozden and Avi Silberschaz was suppored in par by he Texas Advanced Research Program under Gran No. ATP-209, he Naional Science Foundaion under Gran Nos. IRI and IRI , and grans from he IBM and Hewle-Packard corporaions. y A PhD candidae in he Deparmen of Compuer and Elecrical Engineering a he Universiy of Texas a Ausin where he work was done. z On leave from he Deparmen of Compuer Sciences, a he Universiy of Texas a Ausin, where he work was done. In order o incorporae he concep of ownership ino operaing sysems, we propose he virual compuers (VC) paradigm. In a sysem based on he VC paradigm, each user is promised a given qualiy of service, and he sysem seeks o provide each user wih a leas he level of service promised. One can view he service promised o a user as a virual compuer owned by ha user. Ulimaely, a user should receive he promised service independen ofhe number of users accessing he sysem, he locaion where he acual execuion akes place, and where he user accesses he sysem. The users may bepromised a dieren level of service of heir choice corresponding o a dieren \ype" of virual compuer, and each user may own more han one virual compuer. The VC paradigm enables coexisence of virual compuers wih dieren scheduling algorihms, which is imporan for he simulaneous handling of applicaions ha require dieren scheduling policies (e.g., mulimedia applicaions ha require real-ime scheduling can coexis wih convenional applicaions). The VC paradigm can be realized on disribued sysems based on various sysem models including he processor-pool model, he worksaion model, and he ime-shared compuers model. By providing he users of a disribued sysem wih he desirable properies of personal compuers predicabiliy and choice he VC paradigm encourages he users o use a disribued sysem as well as o share heir compuers wih ohers. Furhermore, applying he VC paradigm o a single-user sysem provides he user wih more han one virual compuer wih dieren specicaions, and applying i o ime-sharing sysems enables sharing resources predicably among users. A sysem based on he VC paradigm will be referred o as a VC sysem. In order o implemen avc sysem, some of he issues in he design of a disribued operaing sysem mus be reconsidered including re-

2 source managemen, naming, proecion, and service provisions. This paper concenraes on he basic processor scheduling aspecs of resource managemen. 2 The VC Paradigm In a VC sysem, each user owns one or more imaginary compuers virual compuers. The virual compuer is only a descripion of a compuer and may no correspond o any real compuer in he sysem. The descripion includes he CPU ype (CPU speed, ec.) and a local scheduling algorihm (e.g., rs come rs served, round robin, earlies deadline rs). The real compuers used in a VC sysem may beworksaions, muliprocessors or mainframes depending on he sysem model. For our purpose, he sysem simply consiss of a se P = fp 1 P 2 ::: Pmg of processors. Le V = fv 1 V 2 ::: Vng be he se of virual compuers. The virual compuers may dier in erms of heir specicaion. Assignmen of dieren virual compuers o users will usually depend on facors such as user's needs, senioriy, and budge. Suppose ha ask Ti submied o a virual compuer is execued on a compuer which isequivalen o he virual compuer. Such an execuion is referred o as he execuion on he virual compuer. The absrac execuion of a ask Ti on a virual compuer can be characerized by wo aribues: arrival ime ai and compleion ime ci on he virual compuer. The arrival ime is he ime when Ti is submied o he sysem. The compleion ime is he ime when Ti would have been compleed if i were execued on a real compuer equivalen o he virual compuer. Clearly, ci depends on he local scheduling algorihm of he virual compuer, he lengh of he ask Ti, and he load of he virual compuer. We denoe he acual compleion ime of Ti in he sysem by ci. We model periodic asks as a sequence of independen asks wih separae arrival imes and compleion imes. A VC sysem seeks o guaranee predicable performance o each user. We dene he predicable performance in erms of he performance which he user could have obained on he corresponding virual compuer. However, i is no sucien o guaranee predicable performance in erms of ypical performance measures, such asheaverage response ime and he average hroughpu 1. This is because individual asks 1 The average response ime a ime is he raio of he sum of response imes (c i ; a i ) of all he asks compleed before and a o he number of asks compleed. The hroughpu in a given ime inerval is he number of asks compleed in ha inerval. We divide he ime axis ino inervals of size and submied o a virual compuer can be delayed far beyond heir compleion imes on he virual compuer, even if he average performance on he sysem is beer han he average performance on he virual compuer. Since cumulaive performance measures do no adequaely address predicabiliy, he VC paradigm is based on sronger guaranees so ha he performance of each individual ask will be predicable. Such guaranees can be expressed in erms of deadlines. Hence, each ask Ti is assigned a deadline di which is he ime by which Ti mus complee. The assignmen of deadlines depends on he he level of service guaranees. Various ypes of VC sysems can be dened, each wih dieren levels of guaranees. The ypes of VC sysems and, hence, he assignmen of he deadlines is discussed in Secion 3. AVC sysem is a se of asks T = ft 1 T 2 ::: Tkg ha mus be acually scheduled on P under he consrains ai and di for each ask. In pracice, here may befurher consrains on asks. For example, a resource consrainmay be needed o specify on which processor(s) a ask can be execued (e.g., if he ask is a high bandwidh ineracive applicaion such asa 3D CAD ool), hen i may be consrained o execue on he processor ha is conneced o he graphical display). In his paper, we consider only he ime consrains. 3 VC Sysem Types AVC sysem seeks o provide each user wih a level of service which is proporional o he one ha could have been obained on he user's virual compuer. Each level of service denes a dieren ype of a VC sysem. The discussions in his paper are conned o he following sysem ypes: The sric VC sysem, he average VC sysem, and he bounded VC sysem. The se of schedules for a bounded VC sysem conains he se of schedules for he average VC sysem, and he se of schedules for he average VC sysem conains he se schedules for he sric VC sysem. 3.1 Sric VC Sysem AsricVC sysem provides each user wih a service which is a leas as good as he one on he virual compuer. For each ask, he consrain ha he compleion ime of he ask will be less han or equal o dene he average hroughpu a ime as he average over b c ime inervals.

3 average response ime average hroughpu average response ime average hroughpu on he virual compuer on he sysem on he sysem on he sysem on he virual compuer on he virual compuer on he sysem on he virual compuer Figure 1: The average response ime and hroughpu for he asks submied o a virual compuer in a sric VC sysem. he compleion ime of he ask on he virual compuer is imposed. This consrain can be expressed by selecing he deadline for each ask Ti as: di =ci AsricVC sysem schedules all he asks in T so ha hey mee heir ime consrains. We refer o schedules generaed by asricvc sysem as sricly feasible. The average response ime for each user will be less han or equal o he average response ime ha could have been obained on his virual compuer a any given ime (see Figure 1). Similarly, he average hroughpu for he user will be greaer han or equal o he average hroughpu on he virual compuer a any given ime. Obviously, he deadline of a ask depends on he lengh of he ask, CPU speed, he local scheduling algorihm, and he load of he virual compuer. Since he load changes dynamically, for some local scheduling algorihms, he deadline of a ask is no xed a he arrival ime, even if he lengh of he ask is known. 3.2 Average VC Sysem An average VC sysemprovides each userwihalevel of service which is, on average, a leas as good as ha on he virual compuer while mainaining he delayof each individual ask bounded. Specically, an average VC sysem assumes a ime inerval and requires ha: 1. The average hroughpu of asks submied o a virual compuer will be greaer han or equal o he average hroughpu on he virual compuer a he end of every ime inerval of lengh : 2. Each individual ask can be delayed a mos : This consrain can be expressed by di = d c i e [in seonds] Figure 2: The average response ime and hroughpu for he asks submied o a virual compuer in an average VC sysem. for each ask Ti: This consrain disallows inerchanging he compleion imes of any wo asks compleed on he virual compuer in dieren ime inervals. For example, suppose ha ask Ti is compleed on he virual compuer in ime inerval [k (k +1) ) and ask Tj compleed on he virual compuer in ime inerval [(k + l) (k + l +1) ) : The average hroughpu will be equal o he average hroughpu on he virual compuer, if Ti complees in ime inerval [(k + l) (k + l +1) ) and Tj in [k (k +1) ) : An average VC sysem disallows such cases. An average VC sysem schedules all he asks in T so ha hey mee heir ime consrains. We refer o schedules generaed by an average VC sysem as average feasible. If a schedule is sricly feasible, i is also average feasible. However, he converse is no rue. The average response ime for asks submied o a virual compuer will be eiher less han or equal he sum of and he average response ime on he virual compuer a any given ime, whereas he average hroughpu for he asks submied o a virual compuer will be always greaer han or equal o he one on he virual compuer a any muliples of seconds (see Figure 2). 3.3 Bounded VC Sysem In many circumsances, a user will olerae delay if his asks are delayed by a known bound. This delay can be imposed by he sysem o express he upper bound of he delay ha a ask can experience. In a bounded VC sysem, he deadlines are assigned as di =ci + bi where bi is eiher a consan or a funcion (of eiher ime, or response ime on he virual compuer or he

4 sricly feasible schedules average feasible schedules bounded feasible schedules Figure 3: The conainmen relaion beween sricly, average and bounded feasible schedules. load of he sysem) bounded by a consan from above (i.e., bi is less han or equal o a consan). A bounded VC sysem schedules all he asks in T so ha hey mee heir ime consrains. We refer o schedules generaed by a bounded VC sysem as bounded feasible. If a schedule is average feasible, i is also bounded feasible. However, he converse is no rue. Figure 3 illusraes he conainmen relaion beween sricly, average and bounded feasible schedules of a given ask se. Suppose ha he maximum bi for he asks submied o a virual compuer is bmax. A any given ime, he average response ime for hese asks will be eiher on or below he sum of bmax and he average response ime ha could have obained on he virual compuer. Suppose ha over k ime inervals he average hroughpu on he virual compuer is a k,henhe average hroughpu for he asks submied o virual compuer will be eiher less han or equal o a k+d bmax This ype of he VC sysem is called bounded, since he guaraneed performance o each user has a lower bound below he performance on he virual compuer o wihin a consan facor (see Figure 4). 4 Scheduling in VC Sysems The primary goal of scheduling in a VC sysemiso mee he VC consrains. In his secion, we presen on-line feasible scheduling algorihms for uniprocessor and muliprocessor VC sysems. In his paper, we make a number of simplifying assumpions. We assume ha he cos of saring, resaring and killing aaskonany processor is negligible. We assumeha asks are muually independen, preempable, and he cos of preempion is negligible. We assume ha e. average response ime bound on he virual compuer on he sysem average hroughpu on he sysem on he virual compuer bound Figure 4: The average response ime and hroughpu for he asks submied o a virual compuer in a bounded VC sysem. asks are compuaion inensive and only consider processing resources (CPUs). Tha is, we assume ha he sysem always has sucien amouns of oher resources such as memory, secondary sorage, and nework bandwidh. We assume ha he processors are idenical and ha he local scheduling algorihm of all virual compuers is FCFS. We are currenly exending our resuls o allow he virual compuers o employe dieren local scheduling algorihms (e.g., xed prioriy, deadline-based algorihms, and round-robin). 4.1 Feasible Scheduler for Uniprocessor VC Sysems We rs examine on-line feasible schedulers for uniprocessor VC sysems where he real processor is a leas n imes faser han he CPUs of he virual compuers 2. If he clock rae of he processor is c, hen he clock rae of he virual compuer will be b c nc. For example, consider a uniprocessor VC sysem where he clock rae of he processor is 100 MHz and he number of virual compuers is four. The clock rae of virual compuers will be 25 MHz. We know ha here is always a feasible schedule ha can be obained on-line wihou knowing any characerisics of he asks wih he following algorihm. The processor ime is divided ino ime slices of lengh n c which in urn is divided ino n subslices of lengh 1 c : One subslice of each ime slice is reserved for a virual compuer. A subslice of a ime slice is allocaed o any virual compuer which is busy during his or a previous subslice of he same ime slice, and which has no ye assigned o a subslice in his ime slice. We refer o his algorihm as reservaion wih smalles ime slice. This algorihm is sricly feasible, 2 This means ha he clock of he real processor icks a leas n imes in he ime when he imaginary clock of virual compuer icks once.

5 Virual Compuer Task ai li di V 1 T V 2 T Figure 5: Tasks characerisics in Proof of Theorem 2. if we assume ha a mos one ask will arrive inany given subslice. However, his algorihm is no pracical due o he frequency of decision poins and he cos of conex swiching. Therefore, we mus search for a more pracical algorihm ha has less frequen decision poins, and herefore yields less conex swiches. One such algorihm is he earlies deadline rs (EDF) algorihm, which a each decision poin execues he ask wih he earlies deadline, and breaks ies arbirarily. Theorem 1: Consider a uniprocessor VC sysem. If ask lenghs are known, hen he EDF algorihm is sricly feasible. Proof: Since he local scheduling algorihm is FCFS and lengh of asks are known, he compleion imes of he asks on he virual compuers, hence, he deadlines for a sric VC sysem are xed and known a he ask arrival ime. I was shown ha he EDF algorihm is opimal in he sense if here exiss a feasible schedule, hen he EDF algorihm generaes a feasible schedule [?]. Since on a uniprocessor VC sysem here exiss always a schedule, he EDF algorihm is feasible. 2 Theorem 2: Consider a uniprocessor VC sysem. If he lengh of asks are no known, hen he only sricly feasible scheduling algorihms are hose ha have a decision poin aevery clock ick. Proof: The proof relies on he fac ha for any scheduling algorihm ha sequences asks in agiven order wihou knowledge of ask lenghs, one can nd a ask se for which he algorihm fails. Consider a uniprocessor VC sysem wih wo virual compuers and assume he ask se depiced in Figure 5, where li denoes he lengh of ask Ti on he real processor. Noe ha he ype of he local scheduling algorihm of he virual compuers does no aec he example, since only one ask is submied o each virual compuer. There are hree possible ways of sequencing hese asks on he uniprocessor. The sequence depiced in Figure 6 is no a feasible schedule. Since he scheduler does no know he lengh of asks, all asks appear o be he same o he scheduler. Thus, if a scheduler algorihm execues asks of virual compuers in agiven order, one can always nd anoher se of asks for which he algorihm fails. 2 Theorem 2 demonsraes ha here can be no ef- cien sricly feasible scheduling algorihm if asks lenghs are no known. However, here exiss an average feasible scheduling algorihm for a uniprocessor VC sysem. One such algorihm is he reservaion wih axed ime slice (RFT) which wepresen below. AFIFO queue is mainained for each virual compuer. The lengh of ime slice is denoed by 0 : During each period of lengh 0, each virual compuer is reserved a mos 0 n ime unis on he processor. A color, which is whie iniially, is associaed wih each virual compuer o indicae wheher a virual compuer has uilized all he ime reserved for iself during a ime slice. If so, he color of he virual compuer becomes red, else i remains whie. During each period of lengh 0, he scheduler execues he rs available ask from a whie queue unil he remaining reserved cycles for his virual compuer are nished or he ask complees, which ever is rs. In he rs case, he color of he virual compuer is changed o red. If he ask is no compleed, hen i is placed a he head of he queue. A heendofeach period, all colors are se o whie. Theorem 3: For a uniprocessor VC sysem, he RFT wih a ime slice of lengh 0 is an average feasible scheduler over ime inervals of lengh 0 : Proof: The algorihm delays each ask a mos 0 unis of ime. However, he number of asks compleed in each period is he same as he one on he virual compuer Feasible Scheduler for Muliprocessor VC Sysems In his paper, we only consider muliprocessor VC sysems where he number of real processors is equal o or greaer han he number of virual compuers, and he real processors and virual compuers have idenical speed, whereas in [?] we cover heerogeneous virual compuers. In such a sysem, here exiss always a sricly feasible schedule which can be obained online wihou knowing he characerisics of he asks by assigning each virual compuer o a processor, and 0 T 2 Figure 6: A nonfeasible schedule used in Theorem 2. 2 T 1 3

6 Virual Compuer Task ai li di V 1 T V 1 T V 2 T Figure 7: Tasks characerisics in Example 1. execuing all asks of he virual compuer on he same processor. However, his scheduler wases idle cycles. Therefore, we search for on-line scheduling algorihms ha uilize he idle cycles and remains sill feasible. One such algorihm is he leas laxiy rs (LLF) algorihm which a each decision poin execues he ask wih he minimum laxiy. The laxiy of a ask a agiven ime is he dierence beween he elapsed ime o he deadline of he ask and he remaining lengh of he ask. Ties are broken arbirarily. The feasibiliy of his algorihm is based on he assumpions ha he cos of he migraion is negligible. Theorem 4: Consider a muliprocessor VC sysem. If he local scheduling algorihms of he virual compuers are FCFS and ask lenghs are known, hen he LLF algorihm is sricly feasible. Proof: A anygiven ime, here can be a mos n asks wih zero laxiy. Since here are a leas n processors, all asks wih zero laxiy will always be scheduled. Hence, each ask will complee by is deadline. 2 In he case where he cos of migraion is no negligible, hen he LLF algorihm can be modied as follows. A any decision poin, if selecion of he leas laxiy ask for execuion preemps a ask, ha ask is killed and requeued a he head of he queue of he corresponding virual compuer. We call his algorihm he leas laxiy rs wih resars (LLFR). Theorem 5: Consider a muliprocessor VC sysem where he cos of migraion is no negligible. If he local scheduling algorihms of he virual compuers are FCFS and ask lenghs are known, hen he LLRF algorihm is sricly feasible. Proof: Since here can be a mos n asks wih zero laxiy, aany given ime, he ask which is killed and will be resared a a fuure ime canno have zero laxiy a he ime i is killed. 2 If ask lenghs are no known, average or bounded feasible schedulers can be derived [?]. InaVC sysem, he primary goal of he scheduling is o mee he VC consrains. The secondary goal is o opimize a secondary performance meric subjec o meeing deadlines. A scheduling algorihm is said o be opimal if i opimizes he secondary performance crierion subjec o VC consrains. Hence, an opimal scheduler chooses he bes among he feasible schedules. Derivaion of opimal schedulers for a given secondary performance meric is beyond he scope of his paper. 5 Comparison o Disribued and Real Time Sysems In his secion, we highligh he main dierences beween scheduling in VC sysems and radiional scheduling in disribued and real ime sysems. In radiional general-purpose disribued operaing sysems, he common performance crieria are average hroughpu, average response ime, and idle processor cycles [?,?,?,?,?,?,?,?,?]. However, he noion of providing predicable performance o each user is no emphasized. Below, we presen examples o demonsrae ha algorihms which balance load, minimize average response ime, or minimize idle cycles do no simulaneously saisfy he ime consrains ha he VC paradigm imposes on asks (despie he fac ha here is a schedule ha mees hese consrains). In all he examples, a sric VC sysem wih wo virual compuers (V 1 and V 2 ) and wo processors (P 1 and P 2 ) is used. The processing speeds of he real processors and virual compuers are idenical. The deadlines of asks are assigned by he a sric VC sysem. Example 1: Consider he hree asks in Figure 7 where T 1 and T 2 are submied o V 1 and T 3 is submied o V 2. Figure 7 gives he ask arrival imes (ai), lenghs (li) and deadlines (di where di = ci). Suppose ha sysem balances load on he processors P 1 and P 2 : Figure 8 depics he schedule on processors P 1 and P 2 under load balancing. As illusraed in Figure 8, ask T 3 misses he deadline imposed by a sric VC sysem, compleing a = 600 raher han = 400, alhough he LLF algorihm would have generaed a sricly feasible schedule. 2 Example 2: Consider he four asks wih he characerisics described in Figure??. Assume ha P 1 P T 1 T 3 T Figure 8: Schedule on P 1 and P 2 in Example 1.