REAL-TIME and embedded systems are applied in many

Transcription

1 95 IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 7, JULY 008 Deferrable Schedulng for Mantanng Real-Tme Data Freshness: Algorthms, Analyss, and Results Mng Xong, Member, IEEE, Song Han, Student Member, IEEE, Kam-Yu Lam, and Dej Chen, Member, IEEE Abstract The perodc update transacton model has been used to mantan the freshness (or temporal valdty) of real-tme data. Perod and deadlne assgnment has been the man focus of past studes, such as the More-Less scheme [5], n whch update transactons are guaranteed by the Deadlne Monotonc schedulng algorthm [16] to complete by ther deadlnes. In ths paper, we propose a deferrable schedulng algorthm for fxed-prorty transactons, a novel approach for mnmzng update workload whle mantanng the temporal valdty of real-tme data. In contrast to pror work on mantanng data freshness perodcally, update transactons follow an aperodc task model n the deferrable schedulng algorthm. The deferrable schedulng algorthm explots the semantcs of temporal valdty constrant of real-tme data by judcously deferrng the samplng tmes of update transacton jobs as late as possble. We present a theoretcal estmaton of ts processor utlzaton and a suffcent condton for ts schedulablty. Our expermental results verfy the theoretcal estmaton of the processor utlzaton. We demonstrate through the experments that the deferrable schedulng algorthm s an effectve approach and t sgnfcantly outperforms the More-Less scheme n terms of reducng processor workload. Index Terms Deferrable schedulng, real-tme databases, temporal valdty, fxed-prorty schedulng. Ç 1 INTRODUCTION REAL-TIME and embedded systems are appled n many applcaton domans that requre tmely processng of a massve amount of real-tme data. Examples of real-tme data nclude sensor data n sensor networks, postons of arcraft n ar traffc control systems [14], and vehcle velocty n adaptve cruse control applcatons [6]. Such real-tme data are typcally managed n a real-tme database system (RTDBS). Those data values are used to model the current status of enttes n a system envronment. However, real-tme data are dfferent from tradtonal data n that they have tme semantcs n whch sampled values are vald only for a certan tme nterval [19], [18], [3]. The concept of temporal valdty s used to defne the correctness of real-tme data [19]. A real-tme data object s fresh (or temporally vald) f ts value truly reflects the current status of the correspondng entty n the system envronment. Each real-tme data object s assocated wth a valdty nterval as the lfespan of the current data value defned. M. Xong s wth Bell Labs, Alcatel-Lucent, 600 Mountan Avenue, Room D-51, Murray Hll, NJ E-mal: xong@research.bell-labs.com.. S. Han s wth the Department of Computer Scences, Unversty of Texas at Austn, Austn, TX E-mal: shan@cs.utexas.edu.. K.-Y. Lam s wth the Department of Computer Scence, Cty Unversty of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong. E-mal: cskylan@ctyu.edu.hk.. D. Chen s wth Emerson Process Management, 1301 Research Blvd., Research Park Plaza, Bldg. III, Austn, TX E-mal: dej.chen@emerson.com. Manuscrpt receved 14 Nov. 006; revsed 1 Oct. 007; accepted 18 Dec. 007; publshed onlne 9 Jan Recommended for acceptance by A. Zomaya. For nformaton on obtanng reprnts of ths artcle, please send e-mal to: tc@computer.org, and reference IEEECS Log Number TC Dgtal Object Identfer no /TC based on the dynamc propertes of the data object. A new data value needs to be nstalled nto the database before the valdty nterval of the old value expres, that s, the old one becomes temporally nvald. Otherwse, the RTDBS cannot detect and respond to envronmental changes n a tmely manner. In recent years, there has been a tremendous amount of work devoted to ths area [5], [1], [1], [14], [30], [19], [0], [1], [], [6], [11], [5], [8]. To mantan temporal valdty, sensor update transactons, whch capture the latest status of the enttes n the system envronment, are generated to refresh the values of the realtme data perodcally [19], [14], [5]. A sensor update transacton has an nfnte number of perodc jobs, whch have fxed-length perods and relatve deadlnes. The update problem for perodc update transactons conssts of two parts [5]: 1) the determnaton of the samplng perods and deadlnes of update transactons and ) the schedulng of update transactons. Pror work has proposed two approaches for mnmzng the update workload whle mantanng real-tme data freshness. As explaned n [19], [14], a smple method for mantanng the temporal valdty of real-tme data s to use the Half-Half (HH) scheme n whch the update perod for a real-tme data object s set to be half the valdty nterval of the object. To further reduce the update workload, the More-Less (ML) scheme s proposed and studed n [], [5]. Ths paper presents Deferrable Schedulng for Fxed- Prorty transactons (DS-FP), a novel algorthm for mantanng real-tme data freshness, wth the objectve beng to mnmze the update workload [7], [8]. We study the problem of data freshness mantenance for frm real-tme update transactons n a sngle-processor RTDBS. Dstnct from the past work of HH and ML, whch have a fxed /08/$5.00 ß 008 IEEE Publshed by the IEEE Computer Socety

2 XIONG ET AL.: DEFERRABLE SCHEDULING FOR MAINTAINING REAL-TIME DATA FRESHNESS: ALGORITHMS, ANALYSIS, AND RESULTS 953 perod and relatve deadlne for each transacton, DS-FP adopts an aperodc task model. In contrast to ML, n whch a relatve deadlne s always equvalent to the worst-case response tme of a transacton, DS-FP dynamcally assgns relatve deadlnes to transacton jobs by deferrng the samplng tme of a transacton job as much as possble whle stll guaranteeng the temporal valdty of real-tme data. The deferral of a job s samplng tme results n a shorter relatve deadlne than ts worst-case response tme, whch, n turn, ncreases the separaton of two consecutve jobs. Thus, the deferral of samplng tme lends tself to a reduced processor workload produced by update transactons. We prove that DS-FP outperforms ML n terms of schedulablty and present a suffcent condton for the schedulablty of a set of transactons under DS-FP. We also analyze the average processor utlzaton under DS-FP. Our expermental study of DS-FP demonstrates that t s an effectve algorthm for reducng the workload of real-tme update transactons. It also verfes the accuracy of our theoretcal estmaton of average processor utlzaton under DS-FP and demonstrates the effectveness of the DS-FP algorthms. The rest of ths paper s organzed as follows: Secton revews the exstng approaches for real-tme data freshness mantenance. In Secton 3, we propose the DS-FP algorthm. Our detaled dscusson on DS-FP ncludes an analyss of ts schedulablty and nonoptmalty, as well as an estmaton of ts average processor utlzaton. Secton 4 presents the performance studes and Secton 5 brefly descrbes the related work. Fnally, we conclude our study n Secton 6 and present open questons for DS-FP. BACKGROUND: DATA FRESHNESS MAINTENANCE Real-tme data, whose state may become nvald wth the passage of tme, need to be refreshed by sensor update transactons generated by ntellgent sensors that sample the values of real-world enttes. To montor the states of enttes fathfully, real-tme data must be refreshed before they become nvald. The actual length of the temporal valdty nterval of a real-tme data object s applcaton dependent. For example, real-tme data wth valdty nterval requrements are dscussed n [19], [0], [18]. One of the mportant desgn goals of RTDBSs s to guarantee that real-tme data reman fresh, that s, they are always vald..1 Temporal Valdty for Data Freshness As real-tme data values change contnuously wth tme, the correctness of a real-tme data object X depends on the dfference between the real-tme status SðE Þ of the realworld entty E and the current samplng value ValðX Þ of X. Defnton.1. A real-tme data object X at tme t s temporally vald (or temporally consstent) f (for ts update job, J ;j, fnshed last before t) the samplng tme r ;j plus the valdty nterval length (or valdty length) V of the data object s not less than t, that s, r ;j þv t [1], [19], [1]. A data value for real-tme data object X sampled at any tme t wll be vald for V followng that t up to ðt þv Þ. Next, we revew exstng approaches that adopt a perodc task model for sensor update transactons. TABLE 1 Symbols and Defntons. Half-Half and More-Less In ths secton, tradtonal approaches for mantanng temporal valdty, namely, the Half-Half (HH) and More- Less (ML) approaches, are revewed. In ths paper, T ¼ f g m ¼1 refers to a set of perodc update transactons f 1 ; ;...; m g, and X¼fX g m ¼1 refers to a set of real-tme data objects. We assume that has a hgher prorty than j for <j, unless specfed otherwse. All real-tme data objects are assumed to be kept n the man memory. Assocated wth X ð1 mþ s a valdty nterval of length V : Transacton ð1 mþ updates the correspondng data object X. Because each update transacton updates a dfferent data object, no concurrency control s consdered for update transactons. We assume that a sensor always samples the value of a real-tme data object at the begnnng of ts perod and the system s synchronous (that s, all of the frst jobs of update transactons are ntated at the same tme), unless stated otherwse. For convenence, let d ;j, f ;j, and r ;j denote the absolute deadlne, completon (fnshng) tme, and samplng (release) tme of job J ;j of, respectvely. We also assume that jtter between the samplng tme and the release tme of a job s zero for convenence of presentaton (readers are referred to Secton 3.3 for how jtters can be handled). Formal defntons of the frequently used symbols are gven n Table 1. Deadlnes of update transactons are frm deadlnes. The goal of HH and ML, whch adopt a perodc task model, s to determne perod P and relatve deadlne D so that all of the update transactons are schedulable and the CPU workload resultng from perodc update transactons s mnmzed. Both HH and ML assume a smple executon semantcs for perodc transactons: A transacton must be executed once every perod. However, there s no guarantee as to when a job of a perodc transacton s actually executed wthn a perod. Throughout ths paper, we assume that the schedulng algorthms are preemptve and we gnore all

3 954 IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 7, JULY 008 Fg. 1. Extreme executon cases of J ;j and J ;jþ1. preempton overhead. For convenence, we use the terms transacton and task nterchangeably. Half-Half. In HH, the perod and relatve deadlne of an update transacton are each typcally set to be half the data valdty length [19], [14]. In Fg. 1, the farthest dstance of two consecutve jobs of (based on the samplng tme r ;j of job J ;j and the deadlne d ;jþ1 of ts next job) s P. If P V, then the valdty of real-tme object X s guaranteed as long as jobs of meet ther deadlnes. Unfortunately, ths approach ncurs an unnecessarly hgh CPU workload of update transactons n the RTDBSs compared to More-Less. More-Less. Consder the worst-case response tme for any job of a perodc transacton, where the response tme s the dfference between the transacton ntaton tme ði þ KP Þ and the transacton completon tme, where I s the offset wthn the perod and K s a natural number. Lemma.1. For a set of perodc transactons T ¼ f g m ¼1 ðd P Þ wth transacton ntaton tme ði þ KP Þ ðk ¼ 0; 1; ;...Þ, the worst-case response tme for any job of occurs for the frst job of when I 1 ¼ I ¼...¼ I m ¼ 0 [16]. For I ¼ 0 ð1 mþ, the transactons are synchronous. A tme nstant after whch a transacton has the worst-case response tme s called a crtcal nstant. For example, tme 0 s a crtcal nstant for all of the transactons f those transactons are synchronous. To mnmze the update workload and guarantee temporal valdty, ML uses Deadlne Monotonc (DM) [16] to schedule perodc update transactons [], [5]. There are three constrants to follow for ð1 mþ:. Valdty constrant. The sum of the perod and the relatve deadlne of transacton s always less than or equal to V, that s, P þ D V, as shown n Fg... Deadlne constrant. The perod of an update transacton s assgned to be more than half the valdty length of the object to be updated, whle ts correspondng relatve deadlne s less than half the valdty length of the same object. For to be schedulable, D must be greater than or equal to C, the worst-case executon tme of, that s, C D P.. Schedulablty constrant. For a gven set of update transactons, the DM schedulng algorthm [16] s used to schedule the transactons. Consequently, P j¼1 ðdd P j ec j ÞD ð1 mþ f j has a hgher prorty than for >j. ML assgns prortes to transactons based on Shortest Valdty Frst (SVF), that s, n the nverse order of valdty Fg.. Illustraton of the ML scheme. length, and tes are resolved n favor of transactons wth less slack (that s, V C for ). It assgns deadlnes and perods to as follows: D ¼ f;0 ml rml ;0 ; ð1þ P ¼V D ; where f;0 ml and rml ;0 are the fnshng and samplng tmes of the frst job of under ML, respectvely. Note that, n a synchronous system, r ml ;0 ¼ 0 and the frst job s response tme s the worst-case response tme n ML. In ths paper, superscrpt ml s used to dstngush the fnshng and samplng tmes n ML from those n DS-FP. 3 DEFERRABLE SCHEDULING All schedulers dscussed n ths paper are work-conservng for released jobs. In other words, the scheduler never dles the processor whle there s a job awatng executon (that s, after t s released). Next, we ntroduce the Deferrable Schedulng algorthm for Fxed Prorty transactons (DS-FP). Secton 3.1 presents the ntuton of the algorthm and Secton 3. descrbes the detals of the algorthm. Secton 3.3 compares t wth ML. Secton 3.4 provdes an estmaton of DS-FP s average processor utlzaton. Secton 3.5 dscusses whether the algorthm s optmal. 3.1 Intuton of DS-FP In ML, D s determned by the frst job s response tme, whch s the worst-case response tme of all of the jobs of. Thus, ML s pessmstc on the deadlne and perod assgnment n the sense that t uses a perodc task model that has a fxed perod and relatve deadlne for each task, and the relatve deadlne s equvalent to the worst-case response tme. It should be noted that the valdty constrant can always be satsfed as long as P þ D V. However, the processor workload s mnmzed only f P þ D ¼V. Otherwse, P can always be ncreased to reduce processor workload as long as P þ D < V. Gven the release tme r ;j of job J ;j and the deadlne d ;jþ1 of job J ;jþ1 ðj 0Þ, d ;jþ1 r ;j þv ð3þ guarantees that the valdty constrant can be satsfed, as depcted n Fg. 3. Correspondngly, the followng equaton follows drectly from (3): ðr ;jþ1 r ;j Þþðd ;jþ1 r ;jþ1 ÞV : If r ;jþ1 s shfted onward to r 0 ;jþ1 along the tme lne n Fg. 3, t does not volate (4) and J ;jþ1 can stll be completed by ts deadlne. Ths shft can be acheved, for example, n the ML schedule f preempton to J ;jþ1 from hgher prorty ðþ ð4þ

4 XIONG ET AL.: DEFERRABLE SCHEDULING FOR MAINTAINING REAL-TIME DATA FRESHNESS: ALGORITHMS, ANALYSIS, AND RESULTS 955 TABLE Parameters and Results for Example 3.1 Fg. 3. Illustraton of DS-FP schedulng (r ;jþ1 s shfted to r 0 ;jþ1 ). transactons n ½r ;jþ1 ;d ;jþ1 Š s less than the worst-case preempton to the frst job of. Thus, temporal valdty can stll be guaranteed as long as J ;jþ1 s completed by ts deadlne d ;jþ1. The ntenton of DS-FP s to defer the samplng tme r ;jþ1 of J ;j s subsequent job as late as possble whle stll guaranteeng the valdty constrant. Note that the samplng tme of a job s also ts release tme, that s, the tme that the job s ready to execute, as we assume zero cost for samplng and no arrval jtter for a job for convenence of presentaton. The deferral of job J ;jþ1 s release tme reduces the relatve deadlne of the job f ts absolute deadlne s fxed as n (3). For example, although r ;jþ1 s deferred to r 0 ;jþ1 n Fg. 3, t stll has to be completed by ts deadlne d ;jþ1 n order to satsfy the valdty constrant (3). Thus, ts relatve deadlne D ;jþ1 becomes d ;jþ1 r 0 ;jþ1, whch s less than d ;jþ1 r ;jþ1. The deadlne of J ;jþ1 s subsequent job J ;jþ can be further deferred to ðr 0 ;jþ1 þv Þ to satsfy the valdty constrant. Consequently, the processor utlzaton for the completon 3C of three jobs J ;j, J ;jþ1, and J ;jþ then becomes V ðd ;jþ1 r 0 ;jþ1 Þ. 3C It s less than the utlzaton V ðd ;jþ1 r ;jþ1þ requred for the completon of the same amount of work n ML. Defnton 3.1. Let ða; bþ denote the total cumulatve processor demands made by all jobs of a hgher prorty transacton j for 8j ð1 j 1Þ durng the tme nterval ½a; bþ from a schedule S produced by a fxed-prorty schedulng algorthm. Then, ða; bþ ¼ X 1 j ða; bþ; j¼1 where j ða; bþ s the total processor demands made by all jobs of a sngle transacton j durng ½a; bþ. Next, we dscuss how much a job s release tme can be deferred. We shall use r ;jþ1 nstead of r 0 ;jþ1 to denote the fnal deferred release tme. Accordng to the fxed-prorty schedulng theory, r ;jþ1 can be derved backward from ts deadlne d ;jþ1 as follows: r ;jþ1 ¼ d ;jþ1 R ;jþ1 ðr ;jþ1 ;d ;jþ1 Þ; R ;jþ1 ðr ;jþ1 ;d ;jþ1 Þ¼ ðr ;jþ1 ;d ;jþ1 ÞþC ; where R ;jþ1 ðr ;jþ1 ;d ;jþ1 Þ denotes the response tme of J ;jþ1 n the tme nterval ½r ;jþ1 ;d ;jþ1 Þ. Note that the schedule of all hgher prorty jobs that are released pror to d ;jþ1 needs ð5þ ð6þ to be computed before ðr ;jþ1 ;d ;jþ1 Þ s computed. Ths computaton can be nvoked usng a recursve process from jobs of lower prorty transactons to hgher prorty transactons. Nevertheless, t does not requre that a complete schedule of all jobs should be constructed offlne before the task set s executed. Indeed, the computaton of job deadlnes and ther correspondng release tmes s performed onlne whle the transactons are beng scheduled. We only need to compute the frst jobs response tmes when the system starts. Upon the completon of job J ;j, the deadlne of ts next job d ;jþ1 s frst derved from (3) and, then, the correspondng release tme r ;jþ1 s derved from (5). If ðr ;jþ1 ;d ;jþ1 Þ cannot be computed due to ncomplete schedule nformaton of release tmes and absolute deadlnes from hgher prorty transactons, DS-FP computes ther schedule nformaton onlne untl t can gather enough nformaton to derve r ;jþ1. Job J ;j s DS-FP schedulng nformaton (for example, release tme, deadlne, and bookkeepng nformaton) can be dscarded after t s completed and no lower prorty transactons need ts nformaton for dervng ther schedules. Ths process s called garbage collecton n DS-FP. Let S J ðtþ denote the set of jobs of all transactons whose deadlnes have been computed by tme t. Also, let LSD ðtþ denote the latest scheduled deadlne of at t, that s, the maxmum of all d ;j for jobs J ;j of whose deadlnes have been computed by t. Then, LSD ðtþ ¼ max J ;j S J ðtþ fd ;j gðj 0Þ: ð7þ Gven job J k;j, whose schedulng nformaton has been computed at tme t, and 8 ð >kþ, f LSD ðtþ d k;j ; then the nformaton of J k;j can be garbage collected. Example 3.1. Suppose that there are three update transactons whose parameters are shown n Table. The resultng perods and deadlnes n HH and ML are shown n the same table. The utlzatons of HH and ML are U ml 0:68 and U hh ¼ 1:00, respectvely. Fgs. 4a and 4b depct the schedules produced by ML and DS-FP, respectvely. It can be observed from both schedules that the release tmes of transacton jobs J 3;1, J ;3, J ;4 are shfted from tmes 14, 1, and 8 n ML to 18,, and 30 n DS-FP, respectvely. The DS-FP algorthm s descrbed n Secton 3.. ð8þ

5 956 IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 7, JULY 008 od 3 return; 4 5 case (upon the completon of J ;k ): 6 //Schedule release tme for J ;kþ1. 7 d ;kþ1 r ;k þv ; // get the next deadlne for J ;kþ1 8 // r ;kþ1 s also the samplng tme for J ;kþ1 9 r ;kþ1 ScheduleRTð; k þ 1;C ;d ;kþ1 Þ; 30 return; Fg. 4. Comparng ML and DS-FP schedules. (a) An ML schedule. (b) A DS-FP schedule. 3. Deferrable Schedulng Algorthm Ths secton presents DS-FP, a fxed-prorty schedulng algorthm. Transacton prorty assgnment polcy n DS-FP s the same as n ML, that s, SFV. Gven an update transacton set T, t s assumed that has a prorty hgher than j f <j, as we let V V j. Algorthm 3.1 presents the DS-FP algorthm. For convenence of presentaton, garbage collecton s omtted n the algorthm. There are two cases for the DS-FP algorthm: 1) At the system ntalzaton tme, lnes 13-0 teratvely calculate the frst job s response tme for and the frst job s deadlne s set as ts response tme (lne 1) and ) upon the completon of s job J ;k ð1 m; k 0Þ, the deadlne of ts next job J ;kþ1, d ;kþ1, s derved at lne 7 so that the farthest dstance of J ;k s samplng tme and J ;kþ1 s fnshng tme s bounded by the valdty length V (3). Fnally, the samplng tme of J ;kþ1, r ;kþ1, s derved backward from ts deadlne by accountng for the nterferences from hgher prorty transactons (lne 9). Algorthm 3.1: the DS-FP algorthm Input: a set of update transactons T ¼ f g m ¼1 ðm 1Þ wth known fc g m ¼1 and fv g m ¼1. Output: construct a partal schedule S f T s feasble; otherwse, reject. 1 case ( system ntalzaton tme ): t 0; // Intalzaton 3 // LSD Latest Scheduled Deadlne of s jobs. 4 LSD 0, 8 ð1 mþ; 5 0, 8 ð1 mþ; 6 // s the latest scheduled job of 7 for ¼ 1 to m do 8 // Schedule fnsh tme for ;0. 9 r ;0 0; 10 f ;0 C ; 11 // Calculate hgher prorty (HP) preemptons. 1 oldhp P reempt 0; // ntal HP preemptons 13 hppreempt CalcHP Preemptð; 0; 0;f ;0 Þ; 14 whle ðhppreempt > oldhp P reemptþ do 15 // Accountng for the nterferences of HP tasks 16 f ;0 r ;0 þ hpp reempt þ C ; 17 f ðf ;0 > V C Þ then abort f; 18 oldhp P reempt hpp reemptj; 19 hpp reempt CalcHP Preemptjð; 0; 0;f ;0 Þ; 0 od 1 d ;0 f ;0 ; Algorthm 3.: ScheduleRTð; k; C ; d ;k Þ Input: J ;k, wth C and d ;k. Output: r ;k. 1 oldhp P reempt 0; // ntal HP preemptons hpp reempt 0; 3 r ;k d ;k C ; 4 // Calculate HP preemptons backwards from d ;k. 5 hpp reempt CalcHP P reemptð; k; r ;k ;d ;k Þ; 6 whle ðhpp reempt > oldhppreemptþ do 7 // Accountng for the nterferences of HP tasks 8 r ;k d ;k hpp reempt C ; 9 f ðr ;k <d ;k 1 Þ then abort f; 10 oldhp P reempt hpp reempt; 11 hppreempt GetHPPreempt ð; k; r ;k ;d ;k Þ; 1 od 13 return r ;k ; Algorthm 3.3: CalcHPPreemptð; k; t 1 ;t Þ Input: J ;k, and a tme nterval ½t 1 ;t Þ. Output: total cumulatve processor demands from HP transactons j ð1 j 1Þ durng ½t 1 ;t Þ. 1 k; // Record the latest scheduled job of. d ;k t ; 3 LSD t ; 4 f ð ¼ 1Þ 5 then // No preemptons from HP tasks. 6 return 0; 7 elsf ðlsd 1 LSD Þ 8 then // Get preemptons from j ð8j; 1 j<þ 9 // because j s schedule s complete before t. 10 return GetHP Preemptð; k; t 1 ;LSD Þ; 11 f 1 //buld S up to or exceedng t for j ð1 j<þ. 13 for j ¼ 1 to 1 do 14 whle ðd j; j <LSD Þ do 15 d j; jþ1 r j; j þv j ; 16 r j; jþ1 ScheduleRTðj; j þ 1;C j ;d j; jþ1þ; 17 j j þ 1; 18 LSD j d j; j ; 19 od 0 end 1 return GetHP Preemptð; k; t 1 ;LSD Þ; Functon ScheduleRT ð; k; C ;d ;k Þ (Algorthm 3.) calculates the release tme r ;k wth known computaton tme C and deadlne d ;k. It starts wth release tme r ;k ¼ d ;k C, then teratvely calculates ðr ;k ;d ;k Þ, whch s the total cumulatve processor demands made by all hgher prorty jobs of J ;k durng the nterval ½r ;k ;d ;k Þ, and adjusts r ;k by

6 XIONG ET AL.: DEFERRABLE SCHEDULING FOR MAINTAINING REAL-TIME DATA FRESHNESS: ALGORITHMS, ANALYSIS, AND RESULTS 957 accountng for the nterferences from hgher prorty transactons (lnes 5 to 1). The computaton of r ;k contnues untl the nterferences from hgher prorty transactons do not change n an teraton. In partcular, lne 9 detects any nfeasble schedule. A schedule becomes nfeasble under DS-FP f r ;k <d ;k 1 ðk>0þ, that s, the release tme of J ;k becomes earler than the deadlne of ts precedng job J ;k 1. Functon GetHP P reemptð; k; t 1 ;t Þ scans the nterval ½t 1 ;t Þ, adds up the total preemptons from j ð8j; 1 j 1Þ, and returns ðt 1 ;t Þ, the cumulatve processor demands of j durng ½t 1 ;t Þ from schedule S that has been bult. Functon CalcHP P reemptð; k; t 1 ;t Þ (Algorthm 3.3) calculates ðt 1 ;t Þ, the total cumulatve processor demands made by all hgher prorty jobs of J ;k durng the nterval ½t 1 ;t Þ. Lne 7 ensures that ð8j; 1 j<þ j s schedule s completely bult before tme t. Ths s because s schedule cannot be completely bult before t unless the schedules of ts hgher prorty transactons are complete before t. In ths case, the functon smply returns an amount of hgher prorty preemptons for durng ½t 1 ;t Þ by nvokng GetHPPreemptð; k; t 1 ;t Þ, whch returns ðt 1 ;t Þ. If any hgher prorty transacton j ðj<þ does not have a complete schedule durng ½t 1 ;t Þ, ts schedule S up to or exceedng t s bult on the fly (lnes 14-19). Ths enables the computaton of ðt 1 ;t Þ. The latest scheduled deadlne of s job LSD ndcates the latest deadlne of s jobs that have been computed. The worst-case complexty of ScheduleRT s Oðm V m Þ, assumng that Vm V 1 s a constant. An mportant property of ScheduleRT ð; k; C ;d ;k Þ termnatng at tme t ¼ d ;k s that the latest scheduled deadlne of l ðlsd l ðtþþ s not larger than that of j ðlsd j ðtþþ f l does not have a prorty hgher than j ðl jþ. Ths s proven n the followng lemma. Lemma 3.1. Gven a synchronous update transacton set T and ScheduleRTð; k; C ;tþ ð1 m & k 0Þ, LSD l ðtþ LSD j ðtþ ð l jþ holds when ScheduleRTð; k; C ;tþ termnates at tme t. Proof. Ths can be proven by contradcton. Suppose that LSD l ðtþ >LSD j ðtþ ð l jþ when ScheduleRTð; k; C ;tþ termnates at t. If LSD l ðtþ <t, then CalcHP P reemptð; k; t 1 ;t Þ does not termnate accordng to lne 14 because d l; l <LSD ðtþ ¼t. Thus, LSD l ðtþ LSD ðtþ ¼t. Let LSD l ðtþ ¼t n CalcHP Preemptðl; k l ;t 1 ;t Þ, whch must be nvoked before ScheduleRT ð; k; C ;tþ termnates at t. As we assume that LSD j ðtþ <LSD l ðtþ ¼t, smlarly, CalcHP Preemptðl; k l ;t 1 ;t Þ has not reached the pont to termnate accordng to lne 14. Ths contradcts the assumpton. tu The next example llustrates how the DS-FP algorthm works wth the transacton set n Example 3.1. Example 3.. Table 3 presents the comparson of (release tme, deadlne) pars assgned by ML and DS-FP (Algorthm 3.1) for the jobs of 1,, and 3 n Example 3.1. Note that only release tmes and deadlnes before tme 40 are depcted n the table. Note also that 1 has the same release tmes and deadlnes for all jobs under ML and DS-FP. TABLE 3 Release Tme and Deadlne Comparson However, J ;3, J ;4, J ;5, J 3;1, and J 3; have dfferent release tmes and deadlnes under ML and DS-FP. Algorthm 3.1 starts at the system ntalzaton tme. It calculates deadlnes for J 1;0, J ;0, and J 3;0. Upon the completon of J 3;0 at tme 6, d 3;1 s set to r 3;0 þv 3 ¼ 0. Then, Algorthm 3.1 nvokes ScheduleRT ð3; 1; ; 0Þ at lne 9, whch derves r 3;1. At ths moment, Algorthm 3.1 has already calculated the complete schedule up to d 3;0 (tme 6), but the schedule n the nterval ð6; 0Š has only been partally derved. Specfcally, only the schedule nformaton of J 1;0, J 1;1, J 1;, J 1;3 J ;0, and J ;1 has been derved for 1 and. Algorthm 3. ðschedulertþ obtans r 3;1 ¼ 0 ¼ 18 at lne 3 and then nvokes CalcHPPreemptð3; 1; 18; 0Þ. Algorthm 3.3 ðcalchp P reemptþ fnds that LSD ¼ 10 <t ¼ 0 and, then, t jumps to the for loop startng at lne 13 to buld the complete schedule of 1 and n the nterval ð6; 0Š, where the release tmes and deadlnes for J 1;4, J 1;5, J ;, J 1;6, and J ;3 are derved. Thus, hgher prorty transactons 1 and have a complete schedule before tme 0. Note that r 1;6 and d 1;6 for J 1;6 are derved when we calculate r ;3 and d ;3 such that the complete schedule up to tme d ;3 s bult for transactons wth prortes hgher than.asr ; s set to 14 by earler calculaton, d ;3 s set to 4. It derves r ;3 backward from d ;3 and sets t to because ð; 4Þ ¼0. Smlarly, d 3;1 and r 3;1 are set to 0 and 18, respectvely. 3.3 Comparson of DS-FP and ML Note that ML s based on the perodc task model, whle DS- FP adopts the aperodc task model. The relatve deadlne of a transacton n DS-FP s not fxed. Theoretcally, the separaton of two consecutve jobs of n DS-FP r ;j r ;j 1 satsfes the followng condton: V C r ;j r ;j 1 V WCRT ðj 1Þ; ð9þ where WCRT s the worst-case response tme of the jobs of n DS-FP. Note that the maxmal separaton of J ;j and J ;j 1 ðj 1Þ, max j fr ;j r ;j 1 g, cannot exceed V C, whch can be obtaned when there are no hgher prorty preemptons n the executon of jobs J ;j s (for example, the hghest prorty transacton 1 always has separaton V 1 C 1 for J 1;j and J 1;j 1 ). Thus, the processor utlzaton for DS- FP should be greater than P m C ¼1 V C, whch s the CPU

7 958 IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 7, JULY 008 workload resultng from the maxmal separaton V C of each transacton. If f ml, where fml ;0 s the frst job s response tme (that ;0 V s, the worst-case response tme) of s job n ML, ML can be regarded as a specal case of DS-FP n whch the samplng (or release) tme r ml ;jþ1 and deadlne dml ;jþ1ðj 0Þ can be specfed as follows: d ml ;jþ1 ¼ rml ;j þv ; ð10þ r ml ;jþ1 ¼ dml ;jþ1 ð ðr ml ;0 ;fml ;0 ÞþC Þ: ð11þ It s clear that ðr ml ;0 ;fml ;0 ÞþC ¼ f;0 ml when rml ;0 ¼ 0 ð1 mþ n ML. Theorem 3.1. Gven a synchronous update transacton set T wth known C and V ð1 mþ, fð8þf;0 ml V n ML, then WCRT f;0 ml ; where WCRT and f;0 ml denote the worst-case response tmes of n DS-FP and ML, respectvely. Proof. Ths can be proven by contradcton. Suppose that k s the hghest prorty transacton such that WCRT k > fk;0 ml holds n DS-FP. Also, t s assumed that the response tme of J k;n ðn 0Þ, R k;n, s the worst for k n DS-FP. Note that schedules of 1 n ML and DS-FP are the same, as, n both cases, 1 jobs have the same relatve deadlne C 1 and separaton/perod V 1 C 1. Therefore, 1 <k m holds. As WCRT k >fk;0 ml, there must be a transacton l such that 1) l has a prorty hgher than k ð1 l<kþ, )at least two consecutve jobs of l, J l;j 1 and J l;j overlap wth J k;n, and 3) the separaton of J l;j 1 and J l;j satsfes the followng condton: r l;j r l;j 1 < V l fl;0 ml ðj>0þ; ð1þ where V l fl;0 ml s the perod (that s, separaton) of the jobs of l n ML. Clam 1 s true because k>1. It s straghtforward that f each hgher prorty transacton of k only has one job overlappng wth J k;n, then R k;n fk;0 ml. Ths mples that Clam s true. Fnally, for ð8l <kþ and J l;j 1 and J l;j overlappng wth J k;n,f r l;j r l;j 1 V l fl;0 ml ðj >0Þ; then R k;n >fk;0 ml cannot be true because the amount of preemptons from hgher prorty transactons receved by J k;n n DS-FP s not more than that receved by J k;0 n ML. Thus, Clam 3 s also true. We know that the release tme r l;j n DS-FP s derved as follows: r l;j ¼ d l;j R l;j ; ð13þ where R l;j s the calculated response tme of job J l;j, that s, l ðr l;j ;d l;j ÞþC l. Followng (1) and (13), d l;j R l;j ¼ r l;j fby ð13þg <r l;j 1 þv l fl;0 ml fby ð1þg ¼ d l;j fl;0 ml fby ð3þg: Fnally, R l;j >fl;0 ml : ð14þ Equaton (14) contradcts the assumpton that k s the hghest prorty transacton such that WCRT k >fk;0 ml holds. Therefore, the theorem s proven. tu The followng theorem gves a suffcent condton for the schedulablty of DS-FP. Theorem 3.. Gven a synchronous update transacton set T wth known C and V ð1 mþ, fð8þ f;0 ml V n ML, then T s schedulable wth DS-FP. Proof. If f;0 ml V, then the worst-case response tmes of ð1 mþ n DS-FP WCRT satsfy the followng condton (by Theorem 3.1): WCRT f ml ;0 V : That s, WCRT s not more than V. Because the followng equatons hold n DS-FP, accordng to (5) and (6): r ;j ¼ d ;j R ;j ; d ;jþ1 ¼ r ;j þv ; d ;jþ1 ¼ r ;jþ1 þ R ;jþ1 : ð15þ ð16þ ð17þ Replacng r ;j and d ;jþ1 n (16) wth (15) and (17), respectvely, t follows that That s, Because r ;jþ1 þ R ;jþ1 ¼ d ;j R ;j þv : r ;jþ1 d ;j þ R ;jþ1 þ R ;j ¼V : R ;jþ1 þ R ;j WCRT V ; ð18þ t follows from (18) that r ;jþ1 d ;j 0 holds. Ths ensures that t s schedulable to schedule two jobs of n one valdty nterval V under DS-FP. Thus, T s schedulable wth DS-FP. tu The followng corollary states the correctness of DS-FP. Corollary 3.1. Gven a synchronous update transacton set T wth known C and V ð1 mþ, fð8þ f;0 ml V n ML, then DS-FP correctly guarantees the temporal valdty of realtme data. Proof. As deadlne assgnment n DS-FP follows (3), the largest dstance of two consecutve jobs d ;jþ1 r ;j ðj 0Þ does not exceed V. The valdty constrant can be satsfed f all jobs meet ther deadlnes, whch s guaranteed by Theorem 3.. tu

8 XIONG ET AL.: DEFERRABLE SCHEDULING FOR MAINTAINING REAL-TIME DATA FRESHNESS: ALGORITHMS, ANALYSIS, AND RESULTS 959 Fg. 5. A transacton set schedulable by DS-FP but not by ML. (a) ML s unschedulable. (b) DS-FP s schedulable. If T can be scheduled by ML, then by ML defnton, ð8þ f;0 ml V. Thus, Corollary 3., whch states a suffcent schedulablty condton for DS-FP, drectly follows from Theorem 3.. Corollary 3.. Gven a synchronous update transacton set T wth known C and V ð1 mþ, ft can be scheduled by ML, then t can also be scheduled by DS-FP. However, the converse statement of Corollary 3. s not true. That s, f T can be scheduled by DS-FP, then t s not necessarly true that T can also be scheduled by ML. Ths s demonstrated n the followng example. Example 3.3. Consder a set of three transactons f 1 ; ; 3 g wth computaton tmes, 3, and 3 and valdty ntervals 6, 15, and 47, respectvely. Fg. 5a depcts a schedule of the transactons under ML. The frst job of 3, J 3;0, completes at tme 4, whch s greater than V 3 (that s, 3.5). Thus, the set of transactons s not schedulable by ML. Fg. 5b depcts a schedule of the transactons under DS-FP. The same transacton set s schedulable by DS-FP, because the schedule pattern between tmes 6 and 50 repeats tself forever. In summary, f a set of synchronous update transactons can be scheduled by ML to satsfy the valdty constrant, then t can also be scheduled by DS-FP. However, the converse statement s not true, whch mples that DS-FP outperforms ML n terms of schedulablty. Thus, the followng corollary drectly follows from both Corollary 3. and Example 3.3. Corollary 3.3. DS-FP outperforms ML n terms of schedulablty for satsfyng the valdty constrant. Dscusson of jtters. Our results can be easly extended to the case where jtter between the samplng tme and the release tme of a job s nonzero f the maxmum jtter of a transacton s known. In the presence of nonzero jtters, we can transform a transacton 0 (wth valdty length V0 and maxmum jtter ) to a transacton (wth valdty length Fg. 6. DS-FP schedules wth fxed patterns. (a) A DS-FP schedule for two transactons. (b) A DS-FP schedule for three transactons. V ¼V 0 and zero jtter). Such a transformaton guarantees that f can meet ts valdty constrant, then 0 can also meet ts valdty constrant. 3.4 Theoretcal Estmaton of Processor Utlzaton for DS-FP Ths secton presents means of estmatng the average CPU utlzaton. Note that DS-FP does not usually schedule transactons perodcally. Thus, t s hard to derve ts exact CPU utlzaton unless there s a fxed pattern that repeats tself n a DS-FP schedule. In what follows, we shall nvestgate two cases n order: 1) a DS-FP schedule that has a detected pattern repeatng tself from a certan pont n tme and ) a DS-FP schedule that has no detected pattern DS-FP wth a Detected Pattern We ntroduce a fxed pattern n a DS-FP schedule wth a smple example, whch s shown n the followng: Example 3.4. Consder a DS-FP schedule for two transactons 1 and n Fg. 6a. Note that transacton parameters (C s and V s) are gven n the fgure. We observe that there s a fxed pattern repeatng tself n the schedule every three tme unts, startng from tme 8. If tme goes to nfnty, we can estmate that the average CPU utlzaton of the DS-FP schedule s about 66.7 percent. Smlarly, gven the three transactons n Fg. 6b, we observe a fxed pattern repeatng tself n the schedule every four tme unts, startng from tme 13. Agan, we can easly estmate that ts CPU utlzaton s close to 100 percent. Needless to say, the average CPU utlzaton for a DS-FP schedule can be approxmated based on a fxed pattern f such a pattern exsts n the schedule. However, t s not true that we can always easly detect a fxed pattern n every DS- FP schedule. It becomes harder to detect a fxed pattern n a DS-FP schedule f the sze of the transacton set s larger. Ths s because the complexty of pattern detecton grows exponentally wth the sze of the transacton set. Indeed, t remans open whether there s always a fxed pattern n

9 960 IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 7, JULY 008 every DS-FP schedule or not. As many DS-FP schedules may not be detected to have such fxed patterns, t becomes more mportant to estmate the average CPU utlzaton for such DS-FP schedules DS-FP wthout a Detected Pattern We now present an approxmaton of the average processor utlzaton of DS-FP from a statstcal perspectve n the absence of detected patterns n DS-FP schedules. Note that our approxmaton only works provded that T can be scheduled by ML. Ths mples that the approxmaton s applcable to transacton sets where all deadlnes are not greater than ther correspondng perods n ML. Our approxmaton s qute close to the average CPU utlzaton obtaned n our experments. The CPU utlzaton approxmaton depends on the approxmate values of the average deadlne D and perod P of transactons, whch s descrbed as follows. Gven a set of transactons T ¼ f g m ¼1, let U DS denote the average processor utlzaton n DS-FP and let P j be the average perod for j. The average relatve deadlne of, namely, D, s approxmated as follows: "! # D ¼ C þ X 1 D C j ð1 mþ: ð19þ j¼1 P j Let P ;j and D ;jþ1 ð1 m ^ j 0Þ denote r ;jþ1 r ;j and d ;jþ1 r ;jþ1 n (4), respectvely. It follows that P ;j þ D ;jþ1 ¼V : ð0þ Thus, the followng equaton holds, gven an arbtrarly large n ðn!1þ, where n s the number of jobs n averagng: P þ D ¼V : ð1þ Followng (19) and (1), D and P ð1 mþ can be calculated (from the hghest prorty transacton 1 to the lowest prorty transacton m ), respectvely, as follows: D ¼ C 1 P 1 C j j¼1 P j ð1 mþ; ðþ P ¼V D ð1 mþ: ð3þ Fnally, U DS, whch s the average utlzaton of the transacton set T under DS-FP, can be approxmated as 0 1 U DS ¼ Xm C ¼ Xm C B C C V A : ð4þ ¼1 ¼1 P 1 C 1 j j¼1p j The followng example llustrates how the average utlzaton s estmated. Example 3.5. Gven the transacton set n Table, we calculate the average relatve deadlne and perod of ð ¼ 1; ; 3Þ as follows: D 1 ¼ C 1 ¼ 1; P 1 ¼V 1 D 1 ¼ 4; D ¼ C 1 C1 P 1 ¼ :7; P ¼V D ¼ 7:3; D 3 ¼ C 3 ¼ 4:; P 3 ¼V 3 D 3 ¼ 15:8: 1 C 1 þ C P 1 P The average processor utlzaton s U DS ¼ P m C ¼1 ¼ 0:65. P Gven the transacton set n Table, t can be verfed that the processor utlzaton for the frst 00 tme unts s 63 percent, whch s very close to our theoretcal estmaton and lower than the processor utlzaton from ML (68 percent). Dscusson of fxed patterns. A fxed pattern n a DS-FP schedule may be exponentally long (wth respect to the number of transactons). Thus, t can be very expensve to detect. Assume that the mnmal number of jobs per transacton n ths pattern s n. Ifn s large, then (4) can be used to estmate the average CPU utlzaton of the fxed pattern, whch, n turn, s the utlzaton estmaton of the schedule. In summary, the average CPU utlzaton of a DS-FP schedule can be approxmated based on a fxed pattern f such a pattern exsts n the schedule. Otherwse, the CPU utlzaton can be estmated by (4) f the transacton set s schedulable accordng to Corollary The Nonoptmalty of DS-FP We have proven n Secton 3.4 that DS-FP s close to optmal n terms of mnmzng the CPU workload from a statstcal perspectve. Intutvely, DS-FP should be very close to an optmal algorthm because t always defers the executon of a job as late as possble, hence reducng the workload as much as possble. We have also proven that DS-FP can schedule any transacton set that s schedulable by ML n Secton 3.3. Now, t s nterestng to know f DS-FP s an optmal algorthm n terms of schedulablty. That s, gven any transacton set, f t s schedulable by a fxed-prorty scheduler, can t be scheduled by DS-FP? Unfortunately, the answer to the aforementoned queston s negatve, whch can be demonstrated wth the followng example. Example 3.6. Consder a set of three transactons f 1 ; ; 3 g wth computaton tmes 4, 4, and 3 and valdty ntervals 1,, and 36, respectvely. Ths set s not schedulable by DS-FP as t fals at tme 36, as shown n Fg. 7a. In ths case, the second job of 3 cannot be completed by the end of ts frst valdty nterval. However, f J 1; s scheduled two tme unts earler, ths transacton set can be successfully scheduled because there s a fxed pattern repeatng tself every 3 tme unts startng from tme 7, as depcted n Fg. 7b. Note that such a schedule s also a fxed-prorty schedule because no lower prorty jobs may nterrupt a hgher prorty job once the hgher one s released. By dong so, the release tme of J ;1 s postponed to tme 18, as shown n Fg. 7b (from tme 14 n Fg. 7a). Hence, the deadlne of J ; s also postponed.

10 XIONG ET AL.: DEFERRABLE SCHEDULING FOR MAINTAINING REAL-TIME DATA FRESHNESS: ALGORITHMS, ANALYSIS, AND RESULTS 961 TABLE 4 Expermental Parameters and Settngs model and parameters. Secton 4. compares DS-FP wth the ML algorthm. ML s known to outperform Half-Half [5], whch s not compared here. The experments demonstrate that our proposed approaches reduce CPU utlzaton whle guaranteeng data valdty constrants. Fg. 7. DS-FP s not optmal. (a) An unsuccessful DS-FP schedule. (b) A successful schedule. (c) An asynchronous DS-FP schedule. Fg. 8. SVF s not optmal for DS-FP. DS-FP requres that every transacton should fnsh ts frst two jobs n ½0; V Þ. If the requrement s relaxed so that the frst two jobs are allowed to fnsh n ½r ;0 ;r ;0 þv Þ, where r ;0 denotes the tme at whch J ;0 actually starts, then DS-FP can schedule the set n Example 3.6. In ths case, the frst jobs of transactons start asynchronously. An asynchronous schedule for the same transacton set n Example 3.6 s depcted n Fg. 7c, n whch there s a fxed pattern between tmes 16 and 48 repeatng tself forever. In general, whether the asynchronous DS-FP algorthm s optmal n terms of schedulablty remans an open queston. Another nterestng observaton s that the transacton set n Example 3.6 s schedulable by DS-FP f a prorty order dfferent from SVF s used. For example, f we swap the prortes of 1 and, DS-FP can schedule the set, as depcted n Fg. 8. In ths case, there s a fxed pattern between tmes 7 and 07 repeatng tself forever. In summary, DS-FP s not optmal for a set of synchronous update transactons n terms of schedulablty, but t remans open f t s optmal for asynchronous transactons or transacton prortes assgned dfferently from SVF. 4 PERFORMANCE EVALUATION Ths secton presents the mportant results from our smulaton studes. Secton 4.1 descrbes our smulaton 4.1 Smulaton Model and Parameters Our experments compare the update transacton workloads produced by DS-FP and ML. It s demonstrated that DS-FP produces a lower CPU workload than ML. Also, the experments demonstrate that the ncrease n the average samplng perod from DS-FP s the man reason for ts lower workload. The prmary performance metrc used n the experments s the CPU workload. A summary of the parameters and default settngs used n the experments s presented n Table 4. The baselne values for the parameters follow those used n [5], whch are orgnally from ar traffc control applcatons. We consder a sngle CPU man memory-based RTDBS. The number of realtme data objects vares from 10 to 300 and the valdty nterval of each real-tme data object s unformly dstrbuted between 4,000 and 8,000 ms. Each transacton updates one real-tme data object and the CPU tme for each transacton s unformly dstrbuted between 5 and 15 ms. In the experments, 95 percent confdence ntervals have been obtaned, whose wdths are less than 5 percent of the pont estmate for the performance metrcs. 4. Expermental Results In our experments, the CPU workloads of update transactons produced by ML and DS-FP are quanttatvely compared. Update transactons are generated randomly accordng to the parameter settngs n Table 4. The resultng CPU workloads generated from ML and DS-FP are depcted n Fg. 9. From the results, we observe that the CPU workload produced by DS-FP s consstently lower than that of ML. In fact, the dfference wdens as the number of update transactons ncreases. The dfference reaches 18 percent when the number of transactons s 300. It s also observed that the CPU utlzaton of DS-FP measured n our experments (DS-FP(Expt.)) nearly matches the CPU workload estmaton U DS (4), shown as DS-FP(Est.) n the fgure. Moreover, the DS-FP CPU workload s only slghtly hgher than P m C ¼1 V C, whch s the CPU workload resultng from the maxmal separaton V C ð1 mþ of each transacton (see Secton 3.3). In fact, the dfference s nsgnfcant n Fg. 9. The mprovement n the CPU workload of DS-FP s due to the fact that DS-FP adaptvely samples real-tme data objects at a lower

11 96 IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 7, JULY 008 Fg. 9. CPU workload comparson. rate. Ths s verfed by the average samplng perods of update transactons obtaned from experments. Fg. 10 shows the average samplng perod for each transacton n DS-FP when the number of update transactons s 300. Gven a set of update transactons, the perod of transacton n ML P ml s a constant and t can be calculated offlne [5], whle the separaton of the samplng tmes of two consecutve jobs from the same transacton n DS-FP s dynamc and t s obtaned onlne n the experments. The mean value of the separatons, that s, the average samplng perod, P ds for transacton s calculated as follows, where n s the number of jobs generated by n the experments: P ds ¼ 1 n 1 X n 1 j¼1 In Fg. 10, t s observed that P ds, whle the dfference ðp ds P ml ðr ;j r ;j 1 Þ: ð5þ s consstently larger than P ml Þ ncreases wth the decrease n the transacton s prorty. DS-FP reduces the average samplng rate more for lower prorty transactons, thus reducng the workload of CPU. Fg. 10 also shows that the trend of ð P ds Þ ncreases smlarly to that of ðp ds P ml Þ, P ml although t fluctuates. Fg. 11 depcts how much the CPU workload estmaton DS-FP(Est.) dffers from the actual CPU utlzaton obtaned from the experments DS-FP(Expt.) n fner granularty. The x-axs depcts the sze of update transactons and the y-axs Fg. 11. CPU workload estmaton error. depcts the relatve dfference between DS-FP(Est.) and DS- FP(Expt.), whch s defned as jds-fpðexpt:þ DS-FPðEst:Þj 100%: DS-FPðExpt:Þ Both the maxmum and mean relatve dfferences are depcted n the fgure. In our experments, t s observed that DS-FP(Expt.) s consstently hgher than DS-FP(Est.). As observed n the fgure, our CPU workload estmaton nearly matches the measured CPU utlzaton n our experments as the maxmum relatve dfference never exceeds 0.6 percent. We also conducted a set of experments by varyng V C and fxng P m C ¼1 V of the update transacton set at 45 percent. The results are depcted n Fg. 1, whch compares ML, DS-FP, P m C ¼1 V, and P m C ¼1 V C. Smlarly to Fg. 9, the actual utlzaton for DS-FP s very close to the utlzaton estmaton U DS (shown as DS-FP(Est.)). Note that P m C ¼1 V C s the CPU workload resultng from the possble maxmum separaton V C satsfyng the valdty constrant for each transacton. It s a CPU lower bound gnorng transacton nterference. It s observed n Fg. 1 that a CPU workload of DS-FP s very close to that of P m C ¼1 V C. The larger V C s, the closer DS-FP and P m C ¼1 V C are. Ths s because the probablty of transacton nterference decreases for DS-FP when V C ncreases. We have conducted more experments to study the performance of DS-FP wth dfferent expermental settngs. Fg. 10. Average samplng perod comparson. Fg. 1. CPU workloads wth fxed P m C ¼1. V

12 XIONG ET AL.: DEFERRABLE SCHEDULING FOR MAINTAINING REAL-TIME DATA FRESHNESS: ALGORITHMS, ANALYSIS, AND RESULTS 963 The results are reported n [9] and they are omtted here due to space lmtatons. In summary, when a set of update transactons s scheduled by DS-FP to mantan the temporal valdty of real-tme data objects, t produces a schedule wth a much lower CPU workload than ML does. Thus, more CPU capacty s avalable for mprovng the performance of other workloads (for example, trggered transactons [7]) n the system. 5 RELATED WORK There has been a lot of work on RTDBSs n whch valdty ntervals are assocated wth real-tme data [1], [], [1], [1], [13], [14], [5], [6], [11], [30], [8], [7], [5], [10]. In [6], a safety-crtcal automotve applcaton, that s, adaptve cruse control, s studed. It deals wth crtcal data and nvolves deadlne-bound computatons on data gathered from the automobles envronment. These applcatons have strngent requrements on the freshness of data objects and completon tmes of the tasks. In [8], a vehcular applcaton wth embedded engne control systems s presented and an on-demand schedulng algorthm s proposed for enforcng base and derved data freshness. In [7], an algorthm (ODTB) s proposed for updatng data tems that can skp unnecessary updates, allowng for better utlzaton of the CPU n the vehcular applcaton. Such systems ntroduce the need to mantan data temporal consstency n addton to logcal consstency. In the model ntroduced n [], a real-tme system conssts of perodc tasks whch are ether read-only, wrteonly, or update (read/wrte) transactons. Data objects are temporally nconsstent when ther ages or dspersons are greater than the absolute or relatve thresholds allowed by the applcaton. Two-phase lockng and optmstc concurrency control algorthms, as well as rate-monotonc and earlest deadlne frst schedulng algorthms are studed n []. In [1], [13], real-tme data semantcs are nvestgated, and a class of real-tme data access protocols, called Smlarty Stack Protocols (SSP), s proposed. The correctness of SSP s based on the concept of smlarty, whch allows dfferent but suffcently tmely data to be used n a computaton wthout adversely affectng the outcome. In [14], smlarty-based prncples are coupled wth the Half-Half approach to adjust the real-tme transacton load by skppng the executon of task nstances. The concept of data deadlne s proposed n [6]. It also proposes datadeadlne-based schedulng, forced-wat, and smlartybased schedulng technques to mantan the temporal valdty of real-tme data and to meet transacton deadlnes n RTDBSs. In [10], Jha et al. study whether, gven an update transacton schedule, a perodc query would read mutually consstent data. They propose desgn approaches to decde the perod and relatve deadlne of a query so that t satsfes mutual consstency. They then suggest ways of reducng the complexty of the soluton approach by usng harmonc perods n general. Our work s related to the ML scheme n [], [5], [30]. ML guarantees a bound on the samplng tme of a perodc transacton job and the fnshng tme of ts next job, but, as we showed, the deadlne and the perod of a perodc transacton are derved from the worst-case response tme of the transacton. Ths s dfferent from the aperodc task model-based DS-FP algorthm n whch the deadlne of a transacton job s derved adaptvely and the separaton of two consecutve jobs s not a constant. DS-FP further reduces the CPU workload resultng from update transactons by adaptvely adjustng the separaton of two consecutve jobs whle satsfyng the valdty constrant. DS-FP s also dfferent from the dstance constraned schedulng, whch guarantees a bound of the fnshng tmes of two consecutve nstances of a task [9]. The EDL algorthm proposed n [4] processes tasks as late as possble based on the Earlest Deadlne schedulng algorthm [17]. However, EDL assumes that all deadlnes of tasks are gven, whereas DS-FP derves deadlnes dynamcally. Fnally, our DS-FP algorthm s applcable to the schedulng of age constrant tasks n real-tme systems [4]. 6 CONCLUSIONS AND FUTURE WORK Ths paper proposes a novel algorthm, namely, deferrable schedulng for fxed prorty transactons (DS-FP). Dstnct from past studes of mantanng the freshness (or temporal valdty) of real-tme data n whch the perodc task model s adopted, DS-FP adopts the aperodc task model. The deadlnes of jobs and the separaton of two consecutve jobs of an update transacton are adjusted judcously so that the farthest dstance of the samplng tme of a job s acheved and the completon tme of ts next job s bounded by the valdty length of the updated real-tme data. Ths paper presents a suffcent condton for ts schedulablty. It also proposes a theoretcal estmaton of the processor utlzaton of DS-FP, whch s verfed n our expermental studes. It s also demonstrated n our experments that DS-FP greatly reduces update workload compared to ML, whle guaranteeng the valdty constrant. However, there are stll many open questons to be answered for DS-FP. For example, t s not clear what a suffcent and necessary condton for the schedulablty of DS-FP s, f tme 0 s a crtcal nstant for a synchronous transacton set scheduled by DS-FP, and f there s a least upper bound of CPU utlzaton for DS-FP. Moreover, the concept of deferrable schedulng s only used to schedule update transactons wth fxed prorty n ths paper. It s possble for the same concept to be used n the schedulng of update transactons wth dynamc prorty, for example, n the Earlest Deadlne schedulng [17], [4] of update transactons. ACKNOWLEDGMENTS Prelmnary versons of ths paper appeared n [7], [8]. 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Database Management, vol. 7, no., pp. 4-10, Sprng [1] X. Song and J.W.S. Lu, How Well Can Data Temporal Consstency Be Mantaned? Proc. IEEE Symp. Computer-Aded Control Systems Desgn, 199. [] X. Song and J.W.S. Lu, Mantanng Temporal Consstency: Pessmstc versus Optmstc Concurrency Control, IEEE Trans. Knowledge and Data Eng., vol. 7, no. 5, pp , Oct [3] J.A. Stankovc, S. Son, and J. Hansson, Msconceptons about Real-Tme Databases, Computer, vol. 3, no. 6, pp. 9-36, June [4] S. Vestal, Real-Tme Sampled Sgnal Flows through Asynchronous Dstrbuted Systems, Proc. 11th IEEE Real-Tme and Embedded Technology and Applcatons Symp., pp , 005. [5] M. Xong and K. Ramamrtham, Dervng Deadlnes and Perods for Real-Tme Update Transactons, Proc. 0th IEEE Real-Tme Systems Symp., [6] M. Xong, K. Ramamrtham, J.A. Stankovc, D. Towsley, and R.M. Svasankaran, Schedulng Transactons wth Temporal Constrants: Explotng Data Semantcs, IEEE Trans. Knowledge and Data Eng., vol. 14, no. 5, pp , Sept./Oct. 00. [7] M. Xong, S. Han, and K.Y. Lam, A Deferrable Schedulng Algorthm for Real-Tme Transactons Mantanng Data Freshness, Proc. 6th IEEE Real-Tme Systems Symp., 005. [8] M. Xong, S. Han, and D. Chen, Deferrable Schedulng for Temporal Consstency: Schedulablty Analyss and Overhead Reducton, Proc. 1th IEEE Int l Conf. Embedded and Real-Tme Computng Systems and Applcatons, 006. [9] M. Xong, S. Han, D. Chen, and K.Y. Lam, Deferrable Schedulng for Mantanng Real-Tme Data Freshness: Algorthms, Analyss, and Results, Techncal Report TR-07-44, Dept. of Computer Scences, Unv. of Texas at Austn, Sept [30] M. Xong, B. Lang, K.Y. Lam, and Y. Guo, Qualty of Servce Guarantee for Temporal Consstency of Real-Tme Transactons, IEEE Trans. Knowledge and Data Eng., vol. 18, no. 8, pp , Aug Mng Xong receved the PhD degree n computer scence from the Unversty of Massachusetts, Amherst, n 000. He s currently a member of techncal staff at Bell Laboratores. Hs research nterests nclude database systems, real-tme systems, and moble computng. He s a member of the IEEE. Song Han receved the BS degree n computer scence from Nanjng Unversty, Nanjng, People s Republc of Chna, n 003 and the MPhl degreen computerscence from CtyUnverstyof HongKongn 006. He s currently workngtoward the PhD degree n the Department of Computer Scences at the Unversty of Texas at Austn. Hs research nterests nclude real-tme systems, database systems, wreless networks, and data mnng. He s a student member of the IEEE. Kam-Yu Lam receved the BSc (Hons; wth dstncton) degree n computer studes and the PhD degree from Cty Unversty of Hong Kong n 1990 and 1994, respectvely. He s currently an assocate professor n the Department of Computer Scence at Cty Unversty of Hong Kong. Hs research nterests nclude real-tme database systems, real-tme actve database systems, moble computng, and dstrbuted multmeda systems. Dej Chen receved the PhD degree n computer scence from the Unversty of Texas at Austn n He s currently a senor prncpal software engneer at Emerson Process Management. Hs research nterests nclude real-tme systems and wreless process control. He s a member of the IEEE and the IEEE Computer Socety.. For more nformaton on ths or any other computng topc, please vst our Dgtal Lbrary at