Energy/Reliability Trade-offs in Fault-Tolerant Event-Triggered Distributed Embedded Systems

Transcription

1 Energy/Reiabiity Trade-offs in Faut-Toerant Event-Triggered Distributed Embedded Systems Junhe Gan 1 Favius Gruian 2 1 Department of Informatics and Mathematica Modeing Technica University of Denmark, Denmark {juga, pop, jan}@imm.dtu.dk Pau Pop 1 Jan Madsen 1 2 Department of Computer Science Lund University, Sweden favius.gruian@cs.th.se Abstract This paper presents an approach to the synthesis of ow-power faut-toerant hard rea-time appications mapped on distributed heterogeneous embedded systems. Our synthesis approach decides the mapping of tasks to processing eements, as we as the votage and frequency eves for executing each task, such that transient fauts are toerated, the timing constraints of the appication are satisfied, and the energy consumed is minimized. Tasks are schedued using fixed-priority preemptive scheduing, whie repication is used for recovery from mutipe transient fauts. Addressing energy and reiabiity simutaneousy is especiay chaenging, since owering the votage to reduce the energy consumption has been shown to increase the transient faut rate. We presented a Tabu Search-based approach which uses an energy/reiabiity trade-off mode to find reiabe and scheduabe impementations with imited energy and hardware resources. We evauated the agorithm proposed using severa synthetic and reaife benchmarks. I. INTRODUCTION Safety-critica appications have to function correcty, meet their timing constraints and be energy-efficient even in the presence of fauts. Such fauts might be permanent (e.g., damaged microcontroers or communication inks), transient (e.g., caused by eectromagnetic interference), or intermittent (appear and disappear repeatedy). The transient fauts are the most common [1], and their number is increasing due to the rising eve of integration in semiconductors. Researchers have proposed severa hardware architecture soutions, such as TTA [2], that rey on hardware repication to toerate a singe permanent faut in any of the components of a faut-toerant unit. Such approaches can be used for toerating transient fauts as we, but they incur great hardware costs. Aternatives to such purey hardware-based soutions are approaches such as re-execution, repication, and checkpointing. Severa researchers have shown how the scheduabiity of an appication can aso be guaranteed with appropriate eves of faut-toerance [3 5]. With regard to energy minimization, the most common approach that aows energy/performance trade-offs during runtime of the appication is dynamic votage and frequency scaing (DVFS) [6]. DVFS aims at reducing the dynamic power consumption by scaing down operationa frequency and circuit suppy votage. A considerabe amount of work has been done on DVFS. See [6] for a survey. Incipient research has anayzed the interpay of energy/performance trade-offs and faut-toerance techniques [7 9]. Redundancy-based faut-toerance techniques (such as re-execution and repication) and DVFS-based ow-power techniques compete for the avaiabe sack. The interpay of power management and faut recovery has been addressed in [8], where checkpointing poicies were evauated with respect to energy. In [7], time redundancy was used in conjunction with information redundancy, which does not compete with DVFS for sack, to toerate transient fauts. In [9], faut toerance and dynamic power management were studied, and roback recovery with checkpointing was used to toerate mutipe transient fauts in distributed systems. Addressing energy and reiabiity simutaneousy is especiay chaenging because owering the votage to reduce energy consumption has been shown to increase the number of transient fauts exponentiay [10]. The main reason for such an increase is that, with ower votages, even very ow energy partices are ikey to create a critica charge that eads to a transient faut. However, this aspect has received very imited attention. Zhu [11] has proposed a reiabiity-aware DVFS heuristic for uni-processor systems, and a singe-task checkpointing scheme was evauated in [10]. Researchers have aso addressed reiabiity in the context of temperature-aware design. Their focus has been on imiting the operating temperature in order to increase the ife-time of the system [12]. Such a technique coud be used in conjunction with our approach. In [13], we show how re-execution and active repication can be combined in an optimized impementation that eads to a scheduabe faut-toerant appication without increasing the resources required. In [14], we consider the energy versus reiabiity trade-offs in the context of distributed time-triggered systems, where tasks and messages are schedued based on a static-cycic scheduing poicy, and transient fauts are toerated using task re-execution. In this paper, we consider heterogeneous distributed eventtriggered systems, where tasks are schedued using fixedpriority preemptive scheduing, and messages are schedued using fixed-priority non-preemptive scheduing. Transient fauts are toerated through task repication. In this context, we propose an optimization approach that decides offine the mapping of tasks to processing eements and the votage and frequency eves for executing each task, such that transient fauts are toerated, the timing constraints of the appication are satisfied, and the energy consumed is minimized. We have deveoped a nove Tabu Search-based approach for the synthesis of fauttoerant event-driven systems that takes into account the infuence of votage and frequency scaing on reiabiity. Our offine approach can be used in conjunction with existing onine DVFS /11/$ IEEE 731

2 techniques [15] to further reduce the energy consumption under reiabiity constraints. The next two sections present the system architecture and the appication mode, respectivey. The energy and reiabiity modes are presented in Section IV. Section V presents our probem formuation and a motivationa exampe. Section VI outines our proposed reiabiity-aware mapping, votage and frequency scaing approach (MVFS). An evauation of the proposed agorithm is presented in the ast section. II. SYSTEM MODEL We consider hardware architectures consisting of a set N of heterogeneous processing eements (PEs) and interconnected by a communication channe. Tasks are schedued using fixedpriority preemptive scheduing. We have shown [16] how reaistic protocos such as FexRay can be taken into account during the anaysis and synthesis. However, for simpicity, in this paper we use a simpe non-preemptive fixed-priority bus. We ignore the energy consumption of the bus, but we do take the bus timing into account during scheduabiity anaysis. In this paper we address the energy consumption in PE, which is a major component of the system-eve energy consumption, and use the system-eve power mode from [17]. Thus, a processing eement N i is characterized by a set of operating modes, where each operating mode, Λ N i j =(f N i j, v N i j, p N i j ), is described by three parameters: f N i j is the operating cock frequency of N i running in mode j, which is measured in Hz; v N i j is the suppy votage measured in Vots; p N i j is the power spent measured in Watts. We denote normaized frequency F and normaized votage V where F N i j = f N i j / f N i max and V N i j = v N i j /v N i max, respectivey. Switching between operating modes requires time and energy. We take this overhead into account through a matrix of time overheads X and a matrix of energy overheads Y. Each eement X j, j, is the time overhead required to mode-switch from j to. Simiary, each eement Y j, j, denotes the energy consumption when switching modes from j to. In this paper we are interested in toerating transient fauts, which are the most common fauts in today s embedded systems [1]. The faut rate λ has been reported [10] in the range fauts per second on each chip. We assume that fauts are detected at the competion of a task s execution, and the overhead of faut detection is incuded in the task s worstcase execution time (WCET). In [13] we have shown how reexecution, which provides time-redundancy, and active repication, which provides spatia-redundancy, can be combined in an optimized impementation that reduces the faut-toerance overheads. In this paper, we use active repication to toerate transient fauts. III. APPLICATION MODEL We mode an appication as a set Γ of periodic rea-time tasks. The mapping of a task τ i to N j is captured by the function M : Γ N, i.e., M (τ i )=N j. This mapping is not yet known and wi be decided by our approach presented in Section VI. For each task τ i we know the WCETs of C N j i (in the maximum 732 speed operating mode) with respect to each N j where it coud be mapped and executed, the period T i and deadine D i. We assume that the deadines are smaer or equa to the periods, i.e., D i T i. Each task τ i is assigned a unique priority. Tasks are divided into two categories: critica and noncritica. To prevent the appication faiure, critica tasks have to toerate transient fauts. We assume that for each critica task τ i, the designer wi specify a desired redundancy eve k i, i.e., how many repications of τ i have to be introduced. The desired redundancy eve depends on the functionaity and impementation of the task, and is captured by the function F : Γ, i.e., F (τ i ) = k i. If k i = 0, the task is non-critica. A critica task and its repicas coud be mapped on the same PE and run at different modes, or mapped on different PEs. Each execution of a periodic task is caed a job. The jth job of task τ i is referred to as J ij. In this paper, we assume that a the jobs J ij of task τ i are assigned offine to the same operating mode 1 (i.e., run in the same operating votage and frequency). The assigned mode of task τ i is captured by the function L: { Γ Λ M (τ i) }. For simpicity, we do not consider the situation when an intermediate mode can be obtained by using two modes appied to different execution segments of the same task, as in [17]. However, our approach can be extended to consider this aspect. Tasks communicate asynchronousy through buffers, i.e., a reader task wi bock if the buffer is empty and a writer task wi bock if the buffer is fu. We assume that the buffer size have been determined such that there is no overfow or underfow [18], and we know the size of each message. IV. ENERGY/RELIABILITY TRADE-OFF MODEL The reiabiity of executing a task, R i, is defined as the probabiity of its successfu execution, and it is captured by the exponentia faiure aw [19], R i = e λc (1) where λ is the average faut rate, and c is the execution time of the task. The reiabiity of a critica task, R rep i, is increased through introducing k i repicas. R rep i is expressed as the probabiity of not having a these tasks fai, R rep i k i +1 = 1 i=1 (1 R i ) (2) Note that when k i = 0 (i.e., the task is non-critica), R rep i = R i. Considering independent fauts, the reiabiity R s of the system is cacuated by, R s = Γ i=1 R rep i (3) where Γ denotes the number of tasks in Γ, the compete set of tasks, incuding the repicas. The assigned redundancy eves are ony vaid under the assumption that the system reiabiity R s does not fa beow a 1 Jobs might execute in different modes depending on the onine power management scheme.

3 specified reiabiity goa R g. If R s is beow R g, the faut rate might be higher and thus more redundancy might be necessary to toerate the increased number of fauts. For a task τ i mapped on N j and executed in mode, its WCET c i is cacuated by: c i = C N j i /F N j. The appication is executed periodicay with a hyperperiod 2 T Γ. The energy consumption E S of the task set Γ within T Γ is cacuated by: E S = τ i Γ TΓ T i p N j c i + O (4) where p N j c i is the energy consumed by each job of τ i mapped TΓ on N j and run in mode, T i is the number of τ i s jobs within T Γ, and O is the sum of mode switching overheads detected by the scheduabiity anaysis. However, the energy is aso inked to reiabiity, not ony performance. The faut rate is determined by the operating mode which the system runs in, i.e., the suppy votage v and the operating frequency f. In [10], it is assumed that when PE runs in the minimum votage and frequency eve, the faut rate increases 10 d times compared to that of PE running in the maximum votage and frequency eve. λ max = λ(λ N j min )=λ(λn j max) 10 d = λ min 10 d (5) where d (> 0) is an PE-specific constant. We derive Eq. 6 from [10] 3. Reca that normaized frequency F and normaized votage V are used. λ(λ N j )=λ 0 F α 10 βv (6) where λ 0 = λ min is the average faut rate of a system running on the maximum speed operating mode with the highest operating frequency and suppy votage, α and β coud be cacuated by Eq. 5 and Eq. 6. We can now update the Eq. 1. When a periodic task τ i is mapped on N j and executed in mode, its reiabiity R i is cacuated by: R i = e λ(λn j TΓ ) T c i i (7) Since the faut rate increases exponentiay when suppy votage and operating frequency decrease, switching the operating mode has an impact on the system reiabiity. within the imposed reiabiity goa, i.e., R s R g, and the energy consumption is minimized. Synthesizing an impementation S = (M, L) means deciding offine (1) the mapping M of tasks and repicas to the PEs and (2) the operating mode L for executing each task. A. Motivationa Exampe Let us consider the exampe in Fig.1 where we have a task set of six tasks (four tasks and two repicas) mapped on an architecture of two PEs. The WCETs, periods, deadines and priorities of a tasks are presented in Fig.1(a). τ 1 and τ 2 are critica tasks and they are repicated once. We denote the repicated task of τ i as τ i and its jobs as J ij. Reca that tasks are periodic and they are executed in accordance to fixed-priority preemptive scheduing (e.g. RM). The operating modes of two PEs are given in Fig.1(b), which aso contains λ 0, α, and β (we assume the same vaues for both PEs in this exampe, but they shoud be PE-specific). The hyperperiod of the appication is T Γ = 100. In Fig.1(c) and (d), the height of the rectange indicates the operating mode which the task is running in. The timeine on each PE considers the scenario when a tasks are reeased at t = 0 and executed up to their WCETs. However, tasks might be reeased at different times and coud be finished earier. In Section VI.A, we discuss the scheduabiity anaysis and the assumptions considered. For the discussion, we use a reference which runs a the tasks in the maximum speed operating mode and attempts to reduce the energy consumption by mapping the tasks on the ow energy consumed PEs, without missing the deadines. We present the referenced energy consumption E 0 and system reiabiity R 0 s after (a) and (b). The reiabiity goa R g is given as we. The typica approach for energy minimization is to decide the mapping and the operating mode for each task such that V. PROBLEM FORMULATION The probem we are addressing in this paper can be formuated as foows. Given (1) an appication modeed as a set Γ of tasks, with associated redundancy eves captured by function F, (2) an architecture consisting of a set N of heterogeneous PEs that work under different operating modes Λ, and (3) a reiabiity goa R g which bounds the system reiabiity R s, we are interested in synthesizing an impementation S, such that the deadines of a tasks are satisfied, the system reiabiity is 2 hyperperiod is equa to the east common mutipe of a tasks periods. 3 [10] provides the faut rate formua when a system runs in normaized frequency F and the corresponding normaized votage V = F V max = F. But we aso consider the case V F. 733 Fig. 1 Mapping and VFS Exampe

4 in a oca optimum by aowing seection of non-improving soutions. Our proposed cost funtion in Eq. 9 captures the energy minimization under timing and reiabiity constraints: cost(s)=e S +W R max(0,r g R s )+W r max(0,r S ) (9) Fig. 2 Runtime behavior for an arbitrary instance the energy consumed is minimized and the deadines are satisfied. Such an impementation, denoted with S c, is shown in Fig.1(c). S c meets a tasks deadines and reduces the energy by 42.58%, compared to E 0. However, S c does not meet the system reiabiity goa. Since 1 R s captures the probabiity of faiure, we use Eq. 8 to measure the degeneration of the system reiabiity: θ = 1 R s 1 R 0 s where R 0 s is the system reiabiity of initia soution. According to Eq. 8, the probabiity of faiure for S c is 160 times greater than that of the initia soution. By carefuy deciding the mapping M and operating modes L, it is possibe to reduce the negative impact on reiabiity without a significant oss of energy savings. Another impementation S d shown in Fig.1(d) fufis a timing and reiabiity requirements, with ony 0.45% oss in energy savings whie comparing the energy reduction resut between S c and S d. Additiona energy savings can be obtained at runtime by expoiting the avaiabe sack, because, for instance, a task may finish before its WCET. Severa such onine management schemes have been proposed, such as [15]. Our offine optimization can work in conjunction with any of them. The concern is whether we can obtain further gains without impacting the reiabiity goa. Any onine DVFS scheme woud have to use R g as a constraint. Fig.2 considers the case in Fig.1(d) where J 11 finished earier. An onine DVFS scheme can, in principe, avoid executing repicas if the current job of the origina task does not experience a faut, but such a discussion is beyond the scope of this paper. The shadow of the rectange shows the offine optimized soution of Fig.1(d). At runtime, the avaiabe sack wi be expoited by scaing votage and frequency to execute J 21, which further increases the energy savings to 50.66%. Athough the reiabiity is sighty decreased to , it is sti within R g. In genera, a task that finishes earier wi increase reiabiity (Eq. 7) and this can be transated into energy gains. VI. TABU SEARCH-BASED ALGORITHM The probem presented in the previous section is NP-hard. To sove it, we propose a Tabu Search-based approach, which decides offine the mapping M and operating mode L for executing each task. Tabu Search (TS) [20] is an optimization metaheuristic which iterativey expores the soutions in the vicinity (neighborhood) of the current soution, seecting the ones which optimize the cost funtion. TS woud avoid being stuck (8) where the first term is the energy consumption of running the impementation S within T Γ, the second term is the reiabiity constraint and the third term represents the timing constraint. Instead of considering soutions which do not meet timing and reiabiity constraints as infeasibe, we chose to penaize them heaviy in the cost function by giving arge vaues to W R and W r. This aows us to expore infeasibe regions of the search space and drive the search towards feasibe regions. r S is degree of scheduabiity which is presented in Section VI.A. Agorithm 1 presents our reiabiity-aware mapping, votage and frequency scaing optimization (MVFS). MVFS takes the compete the task set Γ and the architecture N as inputs, and returns the impementation S = (M, L) which minimizes the cost function. The search starts from an initia soution S 0 (ine 1) which is a mapping such that the utiization of the PEs is baanced and the communications are minimized. A tasks are assigned the maximum speed operating mode. The neighborhood of the current soution is generated using design transformations (moves) that change the current system impementation S now (ines 3 and 5). The neighborhood might be very arge, thus we consider a imited number of neighboring soutions caed a candidate set, denoted with C. We perform two types of design moves in MVFS: (1) mapping moves (M -moves) and (2) votage and frequency scaing moves (Lmoves). From a current soution, M -moves are performed by moving a task from one PE to another PE, or swapping two tasks between two PEs. Since evauating a neighboring mappings can be extremey expensive for arge task set, we use a probabiity of performing M -moves (P M ). Athough it is possibe to miss exceent soutions, the computationa overhead is significanty reduced and randomness is introduced which can act as an anti-cycing mechanism. An L-move is generated by randomy assigning operating mode for each task. For each neighboring mapping, a number of L-moves (nl) are added to the candidate set C. We evauate a candidates in C (ine 7). For seecting a new soution, we first attempt to seect an improved soution with Agorithm 1 MVFS 1: S 0 InitiaSoution(Γ, N ); S now S 0 2: whie max iterations is not exhausted do 3: C M -moves(s now, P M ) 4: for each soution Si new C do 5: C L-moves(Si new,nl) 6: for each soution S new j C do 7: Cacuate j = cost(s now ) cost(s new 8: end for 9: end for 10: S now SeectNewSoution( j, ength t) 11: S SaveBestSoution(S now ) 12: end whie 13: return S j ) 734

5 the argest improvement compared to current soution, as ong as it is not on the tabu ist or the tabu status can be aspirated 4. If no such improved soution exists, we randomy seect a nonimproved soution to be new soution as ong as it is on nontabu status. Randomy accepting non-improving moves introduces the diversification, which forces the search into previousy unexpored areas of the design space. We record the ast ength t design transformations (both M -moves and L-moves) to the tabu ist in order to prohibit reverse transformations. The seection of new soution and the maintenance of tabu ist are done inside the SeectNewSoution function (ine 10). Then, SaveBestSoution function (ine 11) saves the new soution if it is the best soution so far. After max iterations without an improvement, the agorithm stops and the best-found-soution S is reported. A. Scheduabiity Anaysis To determine the scheduabiity of an impementation we use response-time anaysis [21] to cacuate the worst-case response time r i of every task τ i, which is compared to the deadine D i. The basic anaysis presented in [21] has been extended over the years. For exampe, the state-of-the-art anaysis in [22] considers arbitrary arriva times and deadines, offsets and synchronous inter-task communication (where a receiving task has to wait for the input of the sender task), and the anaysis in [17] takes into account the time needed for the mode-switching overheads. Our focus in this paper is exporing the trade-off between energy and reiabiity. Hence, we decide to use the basic anaysis from [21]. We do, however, take communication into account to make sure that the mapping soutions do not create too much bus traffic. We consider a non-preemptive fixed-priority bus and during the design space exporation we mark as infeasibe soutions which resut in a bus utiization over 100%. The utiization is cacuated from the bus speed, the size of the messages exchanged over the bus and period of the sender tasks. The scheduabiity of an impementation S is captured using the degree of scheduabiity, r S over a tasks: { d 1 = r S = i max(0,r i D i ) if d 1 > 0 (10) d 2 = i (r i D i ) if d 1 = 0 If the appication is not scheduabe, there exists at east one r i greater than the deadine D i, therefore the term d 1 of the function wi be positive. In this case r S is equa to d 1. However, if the appication is scheduabe, then each r i is smaer than the corresponding deadine D i. In the case d 1 = 0 and we use d 2 as the r S, as it is abe to differentiate between two design aternatives, both eading to a scheduabe appication. VII. EXPERIMENTAL RESULTS For the evauation of our approach, we used ten synthetic benchmarks and five rea-ife case studies. In a benchmarks, a quarter of the tasks were considered critica and for each critica task we introduced one redundancy. We used three types 4 A tabu status can be aspirated when the soution has a better cost function than that of the current best-known soution, since it wi not produce any cycing in the exporation of the design space. TABLE 1 THREE TYPES OF PEs Fast PE Medium PE Sow PE Freq. Vot. Power Freq. Vot. Power Freq. Vot. Power [MHz] [V] [W] [MHz] [V] [W] [MHz] [V] [W] α = 6.5, β = α = 8.9, β = α = 6.5, β = of PEs described in Tabe 1. The minimum faiure rate (when system runs at the maximum speed operating mode) of a PEs was set to λ 0 = We used a reference for a experiments, the system energy consumption E 0 S and reiabiity R0 s obtained by our MVFS approach, but without performing L-moves (i.e., no mode changes that a tasks are run with the highest frequency and votage). The reiabiity goa R g is set such that we accept a probabiity of faiure which is ten times arger than R 0 s, i.e., R g = 1 10(1 R 0 s ). We tuned the MVFS parameters so that the resuts were as cose as possibe to optima (i.e., no improvements were seen with a onger run-time). In the first experiment we wanted to evauate the quaity of MVFS as the systems become arger. Tabe 2 presents the experimenta setup detais and the resuts. We used five synthetic benchmarks of 10 to 105 tasks (incuding repicated tasks) mapped on architectures with 2 to 6 different types of PEs. The resuts obtained with MVFS are presented in the ast two coumns. The increase in the faiure probabiity θ was cacuated using Eq. 8 and had to be smaer or equa to 10 in order to meet the reiabiity goa R g. Aongside the MVFS resuts, we aso present the resuts obtained with MVFS. This is an impementation which minimizes the energy, but without concern for reiabiity (the reiabiity constraint, the second term in Eq. 9, is removed). As we can see from Tabe 2, coumns 5 and 6, minimizing the energy without considering reiabiity eads to a dramatic increase in the probabiity of faiure, which increases more than 100 times in most cases. However, our MVFS approach is abe to keep the system reiabiity R s within the specified R g, without a significant oss in energy savings (ast coumn) compared to MVFS (coumn 6). In the second experiment we wanted to determine the abiity of MVFS to find good quaity soutions as the utiization of the system increases. The experimenta setup and the resuts obtained are presented in Tabe 3. We used a synthetic benchmark with 25 tasks (20 tasks and 5 repicated tasks) mapped on a heterogeneous architecture with 3 different types of PEs. We varied the execution times resuting in five cases corresponding to various initia utiization (coumn 5), from 27.21% to 71.98%. More energy can be saved in the ess utiized systems since more sack coud be used for owering operating votage TABLE 2 SYNTHETIC BENCHMARKS: DIFFERENT SYSTEM SIZES Numbers of MVFS MVFS Test PEs Orig. Rep. θ Saved θ Saved Set Tasks Tasks [times] E [%] [times] E [%]

6 TABLE 3 SYNTHETIC BENCHMARKS: VARYING INITIAL UTILIZATION Numbers of Initia MVFS MVFS Test PEs Orig. Rep. Uti. θ Saved θ Saved Set Tasks Tasks [%] [times] E [%] [times] E [%] TABLE 4 REAL-LIFE BENCHMARKS Numbers of MVFS MVFS Benchmarks PEs Orig. Rep. θ Saved θ Saved Tasks Tasks [times] E [%] [times] E [%] networking-cords auto-indust-cords teecom-cords Apps together Smart-phone and frequency without missing the deadines. As expected, using MVFS is especiay important where the energy saving potentia is greater, because reiabiity is significanty impaired without it. Finay, we evauated MVFS in rea-ife case studies. Five benchmarks were seected from the Embedded System Synthesis Benchmark Suite (E3S), version 0.9 [23], and Smart- Phone Benchmarks [6] 5. The experimenta setup detais and the resuts obtained are presented in Tabe 4. As can be seen, this evauation confirms the resuts obtained from the synthetic benchmarks. This means that by using MVFS we are abe to eiminate the negative impact of energy minimization on reiabiity with minima oss in energy savings. VIII. CONCLUSION In this paper we addressed the mapping, votage and frequency scaing for faut-toerant hard rea-time appications mapped on distributed embedded systems where tasks and messages are schedued using an event-driven scheduing poicy. We captured the effect of votage and frequency scaing on system reiabiity, and we showed that if the suppy votage and the operating frequency are owered to reduce energy consumption, reiabiity is significanty reduced. That is why we proposed a Tabu Search-based approach that takes reiabiity into account when performing task mapping and operating mode assignment. As the experimenta resuts show, our Tabu Search-based strategy is abe to produce energy-efficient impementations which are both scheduabe and faut-toerant. 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