Integrating Multimedia Applications in Hard Real-Time Systems

Transcription

1 Integrating Multimedia Applications in Hard Real-Time Systems Luca Abeni and Giorgio Buttazzo Scuola Superiore S. Anna, Pisa Abstract Tis paper focuses on te problem of providing efficient run-time support to multimedia applications in a real-time system, were two types of tass can coexist simultaneously: multimedia soft real-time tass and ard real-time tass. Hard tass are guaranteed based on worst case execution times and minimum interarrival times, wereas multimedia and soft tass are served based on mean parameters. Te paper describes a server-based mecanism for sceduling soft and multimedia tass witout jeopardizing te a priori guarantee of ard real-time activities. Te performance of te proposed metod is compared wit tat of similar service mecanisms troug extensive simulation experiments and several multimedia applications ave been implemented on te HARTIK ernel. 1. Introduction Continuous Media (CM) activities, suc as audio and video streams, need real-time support because of teir sensitivity to delay and jitter. On te oter and, owever, te use of a ard real-time system for andling CM applications can be inappropriate for te following reasons: If a multimedia tas manages compressed frames, te time for coding/decoding eac frame can vary significantly, ence te worst case execution time (WCET) of te tas can be muc bigger tan its mean execution time. Since ard real-time tass are guaranteed based on teir WCET (and not based on mean execution times), CM applications can cause a waste of te CPU resource. Providing a precise estimation of WCETs is very difficult even for tose applications always running on te same ardware. Tis problem is even more critical for multimedia applications, wic in general can run on a large number of different macines (tin of a video conferencing system running on several different PC worstations). Wen data are received from an external device (for instance, a communication networ) te interarrival time of te tass tat process suc data may not be deterministic, so it may be impossible to determine a minimum interarrival time for suc tass. As a consequence, no a priori guarantee can be performed. Advanced multimedia systems tend to be more dynamic tan classical real-time systems, so all te sceduling metodologies devised for static real-time systems are not suited for CM applications. For te reasons mentioned above, a large part of te multimedia community continues to use classical operating systems, as Unix or Windows, to manage CM. Recently, some sceduling algoritms ave been proposed [16, 6] to mix some form of real-time support wit a notion of fairness, but tey do not mae use of conventional real-time teory. Since we are interested in systems based on a conventional RT sceduler (suc as EDF or RM), we do not consider tis ind of solutions. In [8], Jeffay presents a ard real-time system based on EDF sceduling to be used as a test bed for video conference applications; te system can guarantee eac tas at its creation time based on its WCET and its minimum interarrival time. Wile a bound for te WCET can be found, te interarrival time may not ave a lower bound, because of te unpredictability of te networ (wic may even reverse te order of messages at te reception site). For tis reason, Jeffay in [7] introduces te Rate-Based Execution (RBE) tas model, wic is independent from te minimum interarrival time. Altoug tis ind of tas cannot be guaranteed to complete witin a given deadline, it is possible to guarantee tat it will not jeopardize te scedulability of oter ard real-time tass present in te system. In [12], Mercer, Savage, and Touda propose a sceme based on CPU capacity reserves, were a fraction of te CPU bandwidt is reserved to eac tas. A reserve is a couple (C i ;T i ) indicating tat a tas i can execute for at most C i units of time in eac period T i. Tis approac removes te need of nowing te WCET of eac tas, because it fixes te maximum time tat eac tas can execute in its X/98 $1. (c) 1998 IEEE

2 period. Since te periodic sceduler is based on te Rate Monotonic algoritm, te classical scedulability analysis can be applied to guarantee ard tass, if tey are present. Te only problem wit tis metod is tat overload situations on multimedia tass are not andled efficiently. In fact, if a tas instance executes for more tan C i units of time, te remaining portion of te instance is sceduled in bacground, prolonging its completion of an unpredictable time. In [9], Kaneo et al. propose a sceme based on a periodic process (te multimedia server) dedicated to te service of all multimedia requests. Tis allows to nicely integrate multimedia tass togeter wit ard real-time tass; owever, being te server only one, it is not easy to control te QoS of eac tas. In [3], Liu and Deng describe a sceduling ierarcy wic allows ard real-time, soft real-time, and non realtime applications to coexist in te same system, and to be created dynamically. According to tis approac, wic uses te EDF sceduling algoritm as a low-level sceduler, eac application is andled by a dedicated server, wic can be a Constant Utilization Server [4] for tass tat do not use nonpreemptable sections or global resources, and a Total Bandwidt Server [13, 15] for te oter tass. Tis solution can be used to isolate te effects of overloads at te application level, rater tan at te tas level. Moreover, te metod requires te nowledge of te WCET even for soft and non real-time tass. In tis paper, we propose a sceduling metodology based on reserving a fraction of te processor bandwidt to eac tas (in a way similar to processor capacity reserves of Mercer et al.[12]). However, to efficiently andle te problem of tas overloads, eac tas is sceduled by a dedicated server, wic does not require te nowledge of te WCET and assigns a suitable deadline to te served tas wenever te reserved time is consumed. Te rest of te paper is organized as follows: Section 2 specifies our notation, definitions and basic assumptions; Section 3 describes our sceduling sceme in detail and its formal properties; Section 4 compares te proposed algoritm wit oter server mecanisms, and presents some simulation results; Section 5 describes an implementation of te proposed algoritm on te HARTIK ernel and sows some experimental results; and, finally, Section 6 presents our conclusions and future wor. 2. Terminology and assumptions We consider a system consisting of tree types of tass: ard, soft, and non real-time tass. Any tas i consists of a sequence of jobs J i;j,werer i;j denotes te arrival time (or request time) of te j t job of tas i. A ard real-time tas is caracterized by two additional parameters, (C i ;T i ),werec i is te WCET of eac job and T i is te minimum interarrival time between successive jobs, so tat r i;j+1 r i;j +T i. Te system must provide an a priori guarantee tat all jobs of a ard tas must complete before a given deadline d i;j. In our model, te absolute deadline of eac ard job J i;j is implicitly set at te value d i;j r i;j + T i. A soft real-time tas is also caracterized by te parameters (C i ;T i ), owever te timing constraints are more relaxed. In particular, for a soft tas, C i represents te mean execution time of eac job, wereas T i represents te desired activation period between successive jobs. For eac soft job J i;j, a soft deadline is set at time d i;j r i;j + T i. Since mean values are used for te computation time and minimum interarrival times are not nown, soft tass cannot be guaranteed a priori. In multimedia applications, soft deadline misses may decrease te QoS, but do not cause critical system faults. Te objective of te system is to minimize te mean tardiness of soft tass, witout jeopardizing te scedulability of te ard tass. Te tardiness E i;j of a job J i;j is defined as E i;j maxf; f i;j, d i;j g (1) were f i;j is te finising time of job J i;j. Finally, a periodic tas is a tas (ard or soft) in wic te interarrival time between successive jobs is exactly equal to T i for all jobs (r i;j+1 r i;j + T i ). Periodic tass do not ave special treatment in tis model. Tass tat manage CM can be modeled as soft real-time tass, because missing deadlines may decrease te QoS witout causing catastropic consequences. Moreover, CM activities are typically caracterized by igly variable execution times, causing te WCET to be muc greater tan te mean execution time. For te reasons mentioned above, treating CM tass as ard real-time tass is not appropriate, firstly because an underestimation of te WCET would compromise te guarantee done on te oter tass, and secondly because it would be very inefficient, since trying to guarantee a tas wit a WCET muc greater tan its mean execution time would cause a waste of te CPU resource. Tis problem can be solved by a bandwidt reservation strategy, wic assigns eac soft tas a maximum bandwidt, calculated using te mean execution time and te desired activation period, in order to increase CPU utilization. If a tas needs more tan its reserved bandwidt, it may slow down, but it will not jeopardize te scedulability of te ard real-time tass. By isolating te effects of tas overloads, ard tass can be guaranteed using classical scedulability analysis [11]. To integrate ard and soft tass in te same system, ard tass are sceduled by te EDF algoritm based on teir absolute deadlines, wereas eac soft tas is andled by a ded-

3 icated server, te Constant Bandwidt Server (), wose beavior and properties are described in te next section. 3. Te Constant Bandwidt Server Te service mecanisms tat ave inspired tis wor are te Dynamic Sporadic Server (DSS) [13, 5] and te Total Bandwidt Server (TBS) [13, 15]. As te DSS, te guarantees tat, if U s is te fraction of processor time assigned to a server (i.e., its bandwidt), its contribution to te total utilization factor is no greater tan U s,eveninte presence of overloads. Notice tat tis property is not valid for a TBS, nor for a Constant Utilization Server (CUS) [4], wose actual contributions are limited by U s only under te assumption tat all te served jobs execute no more tan te declared WCET. Wit respect to te DSS, owever, te sows a muc better performance, comparable wit te one acievable by a TBS Definition of Te can be defined as follows: A is caracterized by a budget c s and by a ordered pair (Q s ;T s ),wereq s is te maximum budget and T s is te period of te server. Te ratio U s Q s T s is denoted as te server bandwidt. At eac instant, a fixed deadline d s; is associated wit te server. At te beginning d s;. Eac served job J i;j is assigned a dynamic deadline d i;j equal to te current server deadline d s;. Wenever a served job executes, te budget c s is decreased by te same amount. Wen c s, te server budget is recarged to te maximum value Q s and a new server deadline is generated as d s;+1 d s; + T s. Notice tat tere are no finite intervals of time in wic te budget is equal to zero. A is said to be active at time t if tere are pending jobs (remember te budget c s is always greater tan ); tat is, if tere exists a served job J i;j suc tat r i;j t<f i;j. A is said to be idle at time t if it is not active. Wen a job J i;j arrives and te server is active te request is enqueued in a queue of pending jobs according to a given (arbitrary) non-preemptive discipline (e.g., FIFO). Wen a job J i;j arrives and te server is idle, if c s (d s;, r i;j )U s te server generates a new deadline d s;+1 r i;j + T s and c s is recarged to te maximum value Q s, oterwise te job is served wit te last server deadline d s; using te current budget. Wen a job finises, te next pending job, if any, is served using te current budget and deadline. If tere are no pending jobs, te server becomes idle. At any instant, a job is assigned te last deadline generated by te server. Figure 1 illustrates an example in wic a ard periodic tas, 1, is sceduled togeter wit a soft tas, 2, served by a aving a budget Q s 2and a period T s 7.Te first job of 2 arrives at time r 1 2, wen te server is idle. Being c s (d s;, r 1 )U s, te job is assigned te deadline d s;1 r 1 + T s 9and c s is recarged at Q s 2. At time t 1 6, te budget is exausted, so a new deadline d s;2 d s;1 + T s 16isgenerated and c s is replenised. At time r 2, te second job arrives wen te server is active, so te request is enqueued. Wen te first job finises, te second job is served wit te actual server deadline (d s;2 16). At time t 2 12, te server budget is exausted so a new server deadline d s;3 d s;2 + t s 23isgenerated and c s is replenised to Q s. Te tird job arrives at time r 3 17, wen te server is idle and c s 1 < (d s;3, r 3 )U s (23, 17) 2 1:71, so it is sceduled wit te actual server 7 deadline d s;3 witout canging te budget. It is wort to notice tat under a a job J j is assigned an absolute time-varying deadline d j wic can be postponed if te tas requires more tan te reserved bandwidt. Tus, eac job J j can be tougt as consisting of a number of cuns H j;, eac caracterized by a release time a j; and a fixed deadline d j;. An example of cuns produced by a is sown in Figure 2. To simplify te notation, we will indicate all te cuns generated by a server wit an increasing index (in te example of Figure 2, H 1;1 H 1 ; H 1;2 H 2, H 2;1 H 3 andsoon). In order to provide a formal definition of te, let a and d be te release time and te deadline of te t cun generated by te server, and let c and n be te actual server budget and te number of pending requests in te server queue (including te request currently being served). Tese variables are initialized as follows: d c n Using tis notation, te server beavior can be described by te algoritm sown in Figure properties Te proposed service mecanism presents some interesting properties tat mae it suitable for supporting CM applications. Te most important one, te isolation property, is formally expressed by te following teorem.

4 τ1 (2,3) τ2 HARD SOFT (2,7) c13 c22 d1 d2 c31 r1 r2 r3 t d3 t t1 t2 t3 t Figure 1. An example of sceduling. H 1,1 d1,1 d1,2 d 2,1 d2,2 H 1,2 H 2,1 H 2,2 a 1,1 a 1,2 a 2,1 a 2,2 J1 c4 J2 c4 Figure 2. Example of jobs divided to cuns. Teorem 1 Given a set of n periodic ard tass wit processor utilization U p and a wit processor utilization U s, te wole set is scedulable by EDF if and only if U p + U s 1: and it is sceduled wit a budget Q s C i. Moreover, since c i;j Q s, eac job finises no later tan te budget is exausted, ence te deadline assigned to a job does not cange and is exactly te same as te one used by EDF. 2 Proof. See [1]. 2 Te isolation property allows us to use a bandwidt reservation strategy to allocate a fraction of te CPU time to soft tass wose computation time cannot be easily bounded. Te most important consequence of tis result is tat suc tass can be sceduled togeter wit ard tass witout affecting te a priori guarantee, even in te case in wic soft requests exceed te expected load. In addition to te isolation property, te as te following caracteristics. Te beaves as a plain EDF if te served tas i as parameters (C i ;T i ) suc tat C i Q s and T i T s. Tis is formally stated by te following lemma. Lemma 1 A ard tas i wit parameters (C i ;T i )is scedulable by a wit parameters Q s C i and T s T i if and only if i is scedulable wit EDF. Proof. For any job of a ard tas we ave tat r i;j+1, r i;j T i and c i;j Q s. Hence, by definition of te, eac ard job is assigned a deadline d i;j r i;j + T i Te automatically reclaims any spare time caused by early completions. Tis is due to te fact tat wenever te budget is exausted, it is always immediately replenised at its full value and te server deadline is postponed. In tis way, te server remains eligible and te budget can be exploited by te pending requests wit te current deadline. Tis is te main difference wit respect to te processor capacity reserves proposed by Mercer et al. [12]. Knowing te statistical distribution of te computation time of a tas served by a, it is possible to perform a statistical guarantee, expressed in terms of probability for eac served job to meet its deadline Statistical guarantee To perform a statistical guarantee on soft tass served by, we can model a as a queue, were eac arriving job J i;j can be viewed as a request of c i;j time units. At any time, te request at te ead of te queue is served using te current server deadline, so tat it is guaranteed tat Q s units of time can be consumed witin tis deadline. We analyze te following cases: a) variable computation time and constant inter-arrival time; and b) constant computation time and variable inter-arrival time.

5 Wen job J j arrives at time r j enqueue te request in te server queue; n n + 1; if (n 1) /* (te server is idle) */ if (r j + (c / Qs) * Ts > d ) /* Rule */ + 1; a r j ; d a + Ts; c Qs; else /* Rule */ + 1; a r j ; d d,1; /* c remains uncanged */ Wen job J j terminates dequeue J j from te server queue; n n - 1; if (n! ) serve te next job in te queue wit deadline d ; Wen job J j served by Ss executes for a time unit c c - 1; Wen (c ) /* Rule */ + 1; a actual time(); d d,1 + Ts; c Qs; Figure 3. Te algoritm. Case a. If job interarrival times are constant and equal to T s,and job execution times are randomly distributed wit a given probability distribution function, te can be modeled wit a D G D1 queue: every T s units of time, a request of c j units arrives and at most Q s units can be served. We can define a random process v j as follows: v1 c 1 v j maxf;v j,1, Q s g + c i;j were v j indicates te lengt of te queue (in time units) at time (j, 1)T s, tat is te unit of times tat are still to be served wen job J i;j arrives. Hence, since Q s units of time are served every period T s, te job will finis no later tan d j max r i;j + vj Q s T s wic is also te latest deadline assigned by te server to job J i;j. If P fv j g is te state probability of process v j and C P fc j g is te probability tat an arriving job requires units of time (since c j is time invariant, C does not depend on j), te value of can be calculated as follows: P fv j g P fmaxfv j,1, Q; g + c j g,1 P fmaxfv j,1,q; g+c j ^v j,1 g: Being v j greater tan by definition, te sum can be calculated for going from to infinity: Hence QX P fmaxf, Q; g + c j gp fv j,1 g C (j,1) + QX QX Q+1 C (j,1) + C (j,1) + P fc j, + Qg (j,1) Q+1 Q+1 C,+Q (j,1) : C,+Q (j,1) : (2) Using a matrix notation, equation (2) can be written as M (j,1) (3) were M and are described in Figure 4

6 M z Q+1 } { C C : : : C C 1 C 1 : : : C 1 C 2 C 2 : : : C 2 : : : : : : C : : : C 1 C : : : : : 1 C A and 1 2 : 1 C A Figure 4. Matrix describing te Marov cain for case a) Case b. In te case in wic jobs execution times are constant and equal to Q s (8j; c i;j Q s ) and jobs interarrival times are distributed according to a given distribution function, eac job is assigned a deadline d i;j maxfr i;j ;d i;j,1 g + T s, identical to tat assigned by a TBS. In tis situation, te can be modeled by a GD1 queue: jobs arrive in te queue wit a randomly distributed arrival time and te server can process a request eac T s time units. If we define a random process w j as w j d i;j, r i;j, T s,te distribution of te relative deadlines d i;j, r i;j of job J i;j can be computed from te distribution of w j, because d i;j, r i;j w i;j + T s : Since d i;j maxfr i;j ;d i;j,1 g + T s,weave w j+1 d i;j+1, T s, r i;j+1 maxfr i;j+1 ;d i;j g + T s, T s, r i;j+1 maxf;d i;j, r i;j+1 g maxf;r i;j + w j + T s, r i;j+1 g maxf;w j, a j+1 + T g aving defined a j+1 r i;j+1, r i;j. Being a j a stocastic stationary and time invariant process and w j a Marov process, te matrix M describing te w j Marov cain can be found. By defining P fw j g and A P fa j g,weave,1,1 P fw j g P fmaxf;w j,1, a j + T s g g P fmaxf;w j,1, a j + T g ^ w j,1 g P fmaxf;, a j + T g gp fw j,1 g In order to simplify te calculus, we distinguis two cases: and >:,1 P f, a j + T gp fw j,1 g 8 >;,1 r+t P fa j + T gp fw j,1 g r+t,1,1 P fa j rg (j,1) A r (j,1) P f, a j + T gp fw j,1 g P fa j, + T g (j,1) A,+T (j,1) Tus, matrix M describing te Marov cain is sown in Figure 5. For a generic queue, it is nown tat te queue is stable (i.e., te number of elements in te queue do not diverge to infinity) if mean interarrival rate mean service rate < 1: Hence, te stability can be acieved under te following conditions: 8 < : In general, c i;j < Q s in case a) r i;j+1, r i;j > T s in case b) c i;j < Q s : r i;j+1, r i;j T s If tis condition is not satisfied te difference between te deadline d i;j assigned by te server to a job J i;j and te job release time r i;j will increase indefinitely. Tis means tat, for preserving te scedulability of te oter tass, i will slow down in an unpredictable manner. If a queue is stable, a stationary solution of te Marov cain describing te queue can be found; tat is, tere exists

7 M 1 2 : : : : : : : : A T +1 A T A T,1 : : A : : : A T +2 A T +1 A T A T,1 : A 1 A : : A T +3 A T +2 A T +1 A T : A 2 C 1 A : : : : : : : : : : : 1 C A wit i ri+t A r : Figure 5. Matrix describing te Marov cain for case b) a solution suc tat lim j!1,and M. Tis solution can be approximated by truncating matrix M (aving infinite dimension) to an N N matrix M and solving te eigenvector problem M wit some numerical calculus tecnique. Te nowledge of te probability distribution function of te relative deadlines before wic a multimedia tas job is guaranteed to finis is useful for guaranteeing a QoS to eac tas and for coosing te rigt server parameters (Q s ;T s ) for eac soft tas. 4. Simulation results In tis section we compare te wit oter similar service mecanisms, namely te Total Bandwidt Server (TBS) and te Dynamic Sporadic Server (DSS). Te Constant Utilization Server (CUS) is not considered in te graps because it is very similar to te TBS (indeed, sligtly worse in performance). Te main difference between DSS and is visible wen te budget is exausted. In fact, wile te DSS becomes idle until te next replenising time (tat occurs at te server s deadline), te remains eligible by increasing its deadline and replenising te budget immediately. Tis difference in te replenising time, causes a big difference in te performance offered by te two servers to soft real-time tass. Te TBS does not suffer from tis problem, owever its correct beavior relies on te exact nowledge of job s WCETs, so it cannot be used for supporting CM applications. Moreover, since te automatically reclaims any available idle time coming from early completions, a reclaiming mecanism as also been added in te simulation of te TBS, as described in [14]. All te simulations presented in tis section ave been conducted on a ybrid tas set consisting of 5 periodic ard tass wit fixed parameters and 5 soft tass wit variable execution times and interarrival times. Te periods and te execution times of te periodic ard tass are randomly generated in order to acieve a desired processor utilization factor U ard, wile teir relative deadlines are equal to te periods. Te execution and interarrival times of te soft tass are uniformly P distributed in order to obtain a mean ci;j soft load U sof t wit U i sof t going from ri;j+1,ri;j to 1, U ard. All te soft tass ave te same relative deadline. Te metric used to measure te performance of te service algoritms is te mean tardiness E i computed over all instances of eac soft tas. Te reason for coosing suc a metric is motivated by te fact tat, as already mentioned above, in multimedia applications meeting all soft deadlines could be impossible or very inefficient. Tus, a more realistic objective is to guarantee all te ard tass and minimize te mean time tat soft tass execute after teir deadlines. Notice tat, since all te soft tass ave te same relative deadline, te tardiness is not dependent on tas s deadline. In te first experiment, we compare te mean tardiness experienced by soft tass wen tey are served by a, a TBS and a DSS. In tis test, te utilization factor of periodic ard tass is U ard :5. Te simulation results are illustrated in Figure 6, wic sows tat te performance of te DSS is dramatically worse tan te one acieved by te and TBS. Tis result was expected for te reasons explained above. Figure 7 sows te same results, but witout te DSS: te only difference is in te scale of te y-axis. In tis figure, te TBS and curves can be better distinguised, so we can see tat te tardiness experienced by soft tass under a is sligtly iger tan tat experienced using a TBS. However, te difference is so small tat can be neglected for any practical purposes. Figures 8 and 9 illustrate te results of similar experiments repeated wit U ard :7 and U ard :9 respectively. As we can see, te major difference in te performance between and TBS appears only for eavy ard loads. Fortunately, tis situation is of little interest for most practical multimedia applications. Wen WCET i >> c i;j te TBS can cause an underutilization of te processor. Tis fact can be observed in Figure 1, wic sows te results of a fourt experiment, in wic U ard :6, U sof t :4, te interarrival times are fixed, and te execution times of te soft tass are uniformly distributed wit an increasing variance. As can be seen from te grap, performs better tan TBS wen c i varies a lot among te jobs.

8 9 Hard tas load.5 8 Hard tas load.7 8 DSS TBS 7 TBS 7 6 Average soft tardiness Average soft tardiness Average soft load Average soft load Figure 6. First experiment (TBS, and DSS). 3 Hard tas load TBS Figure 8. Second experiment. Hard tas load.9 Average soft tardiness TBS Average soft tardiness Average soft load Average soft load Figure 9. Tird experiment. Figure 7. First experiment (TBS and ). 5. Implementation and experimental results Te proposed mecanism as been implemented on te HARTIK ernel [2, 1], to support some sample multimedia applications (see [1] for implementation details). For example, an MPEG player as been executed using EDF, wit and witout. Te application consists of two periodic tass: tas 1 wit a period T 1 125ms, corresponding to 8 frames per second (Fps), and tas 2 wit a period T 2 3ms (33 Fps). Figure 11 reports te number of decoded frames as a function of time, wen te two periodic tass are sceduled by EDF, activating 2 at t 2. Since C 1 49ms, C 2 53ms and :158 > 1, wen 2 is activated te system becomes overloaded. In fact, wen 1 is te only tas in te system, it runs at te required frame rate (8 Fps), but wen at time t 2 2 is activated, 1 slows down to 4:4Fps, wile 2 begins to execute at 17:96Fps. Wen 2 terminates, 1 increases its frame rate to its maximum value (23; 8Fps, tat corresponds to a period of about 42ms, wic is te mean execution time for 1 ). After tis transient interval, 1 returns to execute at 8Fps. Figure 12 sows te number of decoded frames as a function of time, wen te same periodic tass are sceduled by two s wit parameters (Q 1 ;T 1 ) (42; 125) and (Q 2 ;T 2 ) (19; 3). Being :969 < 1, te two servers are scedulable, and being Q 1 42' c 1, 1 will execute at a frame rate near to te required one. From te figure we can see tat te frame rate of 1 is about constant except for two little variations corresponding to te activation and te termination of 2 (remember tat Q c is a limit condition). Tis is obtained by slowing down te frame rate of 2 to 14:2 Fps: tis tas is clearly overloaded (T 2 < c 2 ), so it is penalized by te. Notice tat te proposed mecanism automatically arrange te tas periods witout using a-priori nowledge about te tass execution times. Te only information used

9 16 Hard tas load.6 2 Sceduler 14 TBS 18 Tas 1 Tas Average soft tardiness frame number Fps Fps Computation times variance Time (ms) 2 Figure 1. Fourt experiment. EDF Sceduler Figure 12. Two MPEG players sceduled by. frame number Tas 1 Tas Fps 4.44 Fps 23.8 Fps 8 Fps 8 Fps Time (ms) Figure 11. Two MPEG players sceduled by EDF. by te is te couple (Q i ;T i ) and te estimation of tas execution time given by te budget. Figure 11 sows anoter undesirable effect: wen 2 terminates, te frame rate of 1 increases to its maximum value (more tan te required rate), in order to terminate in te same time instant in wic it would terminate if 2 was not activated. Tis penomenon causes an acceleration of te movie tat appears unnatural and unpleasant. Tis problem can be solved using a sip strategy to serve soft tass: wen a job finises after its absolute deadline, te next job is sipped. As sown in Figure 13, a sip strategy eliminates accelerations in te movie, but it introduces anoter problem, wic is presented in te next experiment, were te same movie is decoded by two identical tass, wit U sof t 1. From Figure 14 it is easy to see tat, altoug te two tass ave te same period, tey proceed wit different speed. Tis is due to te fact tat te system is overloaded. frame number Tas 1 Tas 2 15 Fps EDF wit sip 8 Fps 4.51 Fps 2 8 Fps Time (ms) Figure 13. Two MPEG players sceduled by EDF wit sip. In fact, if U sof t ten U sof t C1 T 1 c 1;j c 2;j + 1 r 1;j+1, r 1;j r 2;j+1, r 2;j + C2 T 2 > 1. Serving te two tass by two identical s wit parameters Q s c 1;j c 2;j and T s 2Q s, tey proceed at te same rate (tass parameters are equal because te two tass play te same video). 6. Conclusions In tis paper, we presented a novel service mecanism, te Constant Bandwidt Server, for integrating ard realtime and soft multimedia computing in a single system, under te EDF sceduling algoritm. Te server as been

10 Decoded frames Tas 1 Tas 2 EDF wit sip Time (ms) Figure 14. Two identical MPEG players sceduled by EDF wit sip. formally analyzed and compared wit oter nown servers, obtaining very interesting results. Te proposed model as also been implemented on te HARTIK ernel and used to support typical multimedia applications. As a future wor, in order to extend te proposed model to more general situations, te following issues need to be investigated. A concurrency control protocol needs to be integrated wit te metod to avoid priority inversion wen accessing sared resources. Te difference between te first and te current deadline can be used as a ind of feedbac for evaluating te request in excess and react accordingly adjusting te QoS in overload conditions. Te mecanism can be used to safely partition te CPU bandwidt among different applications tat could coexist in te same system, as sown in [4]. A tas can be used as a QoS manager to dynamically cange te bandwidt reserved to eac multimedia tas. Te strategies for canging te parameters of eac still ave to be investigated. [6] P. Goyal, X. Guo, and H. M. Vin. A ierarcical cpu sceduler for multimedia operating systems. In 2nd OSDI Symposium, October [7] K. Jeffay and D. Bennet. A rate-based execution abstraction for multimedia computing. In Networ and Operating System Support for Digital Audio and Video, [8] K. Jeffay, D. L. Stone, and F. D. Smit. Kernel support for live digital audio and video. Computer Communications, 15(6), [9] H. Kaneo, J. A. Stanovic, S. Sen, and K. Ramamritam. Integrated sceduling of multimedia and ard real-time tass. In IEEE Real Time System Symposium, December [1] G. Lamastra, G. Lipari, G. Buttazzo, A. Casile, and F. Conticelli. Harti 3.: A portable system for developing real-time applications. In Real-Time Computing Systems and Applications, October [11] C. L. Liu and J. Layland. Sceduling algoritms for multiprogramming in a ard real-time environment. Journal of te ACM, 2(1), [12] C. W. Mercer, S. Savage, and H. Touda. Processor capacity reserves for multimedia operating systems. Tecnical Report CMU-CS , Carnegie Mellon University, Pittsburg, May [13] M. Spuri and G. Buttazzo. Sceduling aperiodic tass in dynamic priority systems. Real-Time Systems, 1(2), [14] M. Spuri, G. Buttazzo, and F. Sensini. Robust aperiodic sceduling under dynamic priority systems. In IEEE Real- Time Systems Symposium, December [15] M. Spuri and G. C. Buttazzo. Efficient aperiodic service under te earliest deadline sceduling. In IEEE Real-Time Systems Symposium, December [16] I. Stoica, H. Abdel-Waab, K. Jeffay, S. K. Barua, J. E. Gere, and C. G. Plaxton. A proportional sare resource allocation algoritm for real-time, time-sared systems. In IEEE Real Time System Symposium, December References [1] L. Abeni. Server mecanisms for multimedia applications. Tecnical Report RETIS TR98-1, Scuola Superiore S. Anna, [2] G. C. Buttazzo. Harti: A real-time ernel for robotics applications. In IEEE Real-Time Systems Symposium, December [3] Z. Deng and J. W. S. Liu. Sceduling real-time applications in open envirovment. In IEEE Real-Time Systems Symposium, December [4] Z. Deng, J. W. S. Liu, and J. Sun. A sceme for sceduling ard real-time applications in open system environment. In Nint Euromicro Worsop on Real-Time Systems, [5] T. M. Gazalie and T. Baer. Aperiodic servers in a deadline sceduling environment. Real-Time Systems, 9, 1995.