Instruction memories have a large influence on the timing behavior of hard real-time systems. Thus, to obtain safe and tight WCET estimates the instruction memory has to be predictable. Instruction memories in embedded real-time systems range from scratchpads with fixed content to dynamically managed fine-grained caches. In this paper we focus on a function-based dynamic instruction memory (D-ISP) and examine different replacement policies. We show their influence on the timing behavior of a hard real-time system and the complexity of a hardware implementation. A timing analysis unveils that a stack-based replacement policy reaches similar WCET estimates as LRU, especially for small scratchpad sizes. But in contrast to the stack-based replacement policy, LRU cannot be implemented with a reasonable amount of resources. Whereas, an experimental implementation of the proposed stack-based replacement policy needs only up to 23% more resources than a FIFO implementation.
{"title":"Replacement Policies for a Function-Based Instruction Memory: A Quantification of the Impact on Hardware Complexity and WCET Estimates","authors":"Stefan Metzlaff, T. Ungerer","doi":"10.1109/ECRTS.2012.22","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.22","url":null,"abstract":"Instruction memories have a large influence on the timing behavior of hard real-time systems. Thus, to obtain safe and tight WCET estimates the instruction memory has to be predictable. Instruction memories in embedded real-time systems range from scratchpads with fixed content to dynamically managed fine-grained caches. In this paper we focus on a function-based dynamic instruction memory (D-ISP) and examine different replacement policies. We show their influence on the timing behavior of a hard real-time system and the complexity of a hardware implementation. A timing analysis unveils that a stack-based replacement policy reaches similar WCET estimates as LRU, especially for small scratchpad sizes. But in contrast to the stack-based replacement policy, LRU cannot be implemented with a reasonable amount of resources. Whereas, an experimental implementation of the proposed stack-based replacement policy needs only up to 23% more resources than a FIFO implementation.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"65 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130754908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Soheil Samii, Unmesh D. Bordoloi, P. Eles, Zebo Peng, A. Cervin
In this paper, we propose a design framework for distributed embedded control systems that ensures reliable execution and high quality of control even if some computation nodes fail. When a node fails, the configuration of the underlying distributed system changes and the system must adapt to this new situation by activating tasks at operational nodes. The task mapping as well as schedules and control laws that are customized for the new configuration influence the control quality and must, therefore, be optimized. The number of possible configurations due to faults is exponential in the number of nodes in the system. This design-space complexity leads to unaffordable design time and large memory requirements to store information related to mappings, schedules, and controllers. We demonstrate that it is sufficient to synthesize solutions for a small number of base and minimal configurations to achieve fault tolerance with an inherent minimum level of control quality. We also propose an algorithm to further improve control quality with a priority-based search of the set of configurations and trade-offs between task migration and replication.
{"title":"Control-Quality Optimization for Distributed Embedded Systems with Adaptive Fault Tolerance","authors":"Soheil Samii, Unmesh D. Bordoloi, P. Eles, Zebo Peng, A. Cervin","doi":"10.1109/ECRTS.2012.40","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.40","url":null,"abstract":"In this paper, we propose a design framework for distributed embedded control systems that ensures reliable execution and high quality of control even if some computation nodes fail. When a node fails, the configuration of the underlying distributed system changes and the system must adapt to this new situation by activating tasks at operational nodes. The task mapping as well as schedules and control laws that are customized for the new configuration influence the control quality and must, therefore, be optimized. The number of possible configurations due to faults is exponential in the number of nodes in the system. This design-space complexity leads to unaffordable design time and large memory requirements to store information related to mappings, schedules, and controllers. We demonstrate that it is sufficient to synthesize solutions for a small number of base and minimal configurations to achieve fault tolerance with an inherent minimum level of control quality. We also propose an algorithm to further improve control quality with a priority-based search of the set of configurations and trade-offs between task migration and replication.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"182 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133172311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Component-Based Development (CBD) reduces development time and effort by allowing systems to be built from pre-developed reusable components. Partitioning the behavior into a set of major operational modes is a classical approach to reduce complexity of embedded systems design and execution. In supporting system modes in CBD, a key issue is seamless composition of pre-developed multi-mode components into systems. We have previously developed a Mode Switch Logic (MSL) for component-based multi-mode systems implementing such seamless composition. In this paper we extend our MSL to cope with atomic transactions, i.e., to handle sets of components that must not be aborted in the middle of the processing of data. This is in contrast with our original MSL, in which components are immediately aborted to perform a mode switch. Based on our extended MSL, we provide analysis of the mode switch timing.
{"title":"Timing Analysis for Mode Switch in Component-Based Multi-mode Systems","authors":"Y. Hang, H. Hansson","doi":"10.1109/ECRTS.2012.23","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.23","url":null,"abstract":"Component-Based Development (CBD) reduces development time and effort by allowing systems to be built from pre-developed reusable components. Partitioning the behavior into a set of major operational modes is a classical approach to reduce complexity of embedded systems design and execution. In supporting system modes in CBD, a key issue is seamless composition of pre-developed multi-mode components into systems. We have previously developed a Mode Switch Logic (MSL) for component-based multi-mode systems implementing such seamless composition. In this paper we extend our MSL to cope with atomic transactions, i.e., to handle sets of components that must not be aborted in the middle of the processing of data. This is in contrast with our original MSL, in which components are immediately aborted to perform a mode switch. Based on our extended MSL, we provide analysis of the mode switch timing.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126045433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Geoffrey Nelissen, V. Berten, J. Goossens, D. Milojevic
These last years, we have witnessed a dramatic increase in the number of cores available in computational platforms. Concurrently, a new coding paradigm dividing tasks into smaller execution instances called threads, was developed to take advantage of the inherent parallelism of multiprocessor platforms. However, only few methods were proposed to efficiently schedule hard real-time multi-threaded tasks on multiprocessor. In this paper, we propose techniques optimizing the number of processors needed to schedule such sporadic parallel tasks with constrained deadlines. We first define an optimization problem determining, for each thread, an intermediate (artificial) deadline minimizing the number of processors needed to schedule the whole task set. The scheduling algorithm can then schedule threads as if they were independent sequential sporadic tasks. The second contribution is an efficient and nevertheless optimal algorithm that can be executed online to determine the thread's deadlines. Hence, it can be used in dynamic systems were all tasks and their characteristics are not known a priori. We finally prove that our techniques achieve a resource augmentation bound of 2 when the threads are scheduled with algorithms such as U-EDF, PD2, LLREF, DP-Wrap, etc.
{"title":"Techniques Optimizing the Number of Processors to Schedule Multi-threaded Tasks","authors":"Geoffrey Nelissen, V. Berten, J. Goossens, D. Milojevic","doi":"10.1109/ECRTS.2012.37","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.37","url":null,"abstract":"These last years, we have witnessed a dramatic increase in the number of cores available in computational platforms. Concurrently, a new coding paradigm dividing tasks into smaller execution instances called threads, was developed to take advantage of the inherent parallelism of multiprocessor platforms. However, only few methods were proposed to efficiently schedule hard real-time multi-threaded tasks on multiprocessor. In this paper, we propose techniques optimizing the number of processors needed to schedule such sporadic parallel tasks with constrained deadlines. We first define an optimization problem determining, for each thread, an intermediate (artificial) deadline minimizing the number of processors needed to schedule the whole task set. The scheduling algorithm can then schedule threads as if they were independent sequential sporadic tasks. The second contribution is an efficient and nevertheless optimal algorithm that can be executed online to determine the thread's deadlines. Hence, it can be used in dynamic systems were all tasks and their characteristics are not known a priori. We finally prove that our techniques achieve a resource augmentation bound of 2 when the threads are scheduled with algorithms such as U-EDF, PD2, LLREF, DP-Wrap, etc.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123263157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
François Santy, L. George, P. Thierry, J. Goossens
Current trends in the embedded systems field tend to collocate multiple functionalities upon a single computing platform, the aim being to reduce both the size and cost of embedded systems. Nevertheless, it is unlikely that all functionalities share the same level of criticality, and certification of the system has to be achieved using varying degrees of rigorousness. Typically, a task τi is guaranteed to meet its temporal constraints up to a criticality level that is equal to its own criticality. When those conditions are no longer met, i.e. when another higher priority task τj has its execution time that exceeds its Worst Case Execution Time (WCET) w.r.t. the criticality level of τi, a common approach is to suspend τi. However, in some cases, it may not be necessary to suspend tasks with a lower criticality immediately as they could still be executed without compromising the deadlines of high criticality tasks. As a step towards this aim, we propose a method, denoted Latest Completion Time (LCT), that allows lower criticality tasks to proceed with their execution as long as they do not prevent higher criticality tasks from meeting their deadlines. Furthermore, we show that tasks suspension can only be temporary, and prove that a particular definition of idle times can be used to reset the system's criticality level. Finally, we study the performances of our LCT mechanism w.r.t. the classical mechanism that suspends a task as soon as the system criticality level becomes higher than its own criticality.
{"title":"Relaxing Mixed-Criticality Scheduling Strictness for Task Sets Scheduled with FP","authors":"François Santy, L. George, P. Thierry, J. Goossens","doi":"10.1109/ECRTS.2012.39","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.39","url":null,"abstract":"Current trends in the embedded systems field tend to collocate multiple functionalities upon a single computing platform, the aim being to reduce both the size and cost of embedded systems. Nevertheless, it is unlikely that all functionalities share the same level of criticality, and certification of the system has to be achieved using varying degrees of rigorousness. Typically, a task τi is guaranteed to meet its temporal constraints up to a criticality level that is equal to its own criticality. When those conditions are no longer met, i.e. when another higher priority task τj has its execution time that exceeds its Worst Case Execution Time (WCET) w.r.t. the criticality level of τi, a common approach is to suspend τi. However, in some cases, it may not be necessary to suspend tasks with a lower criticality immediately as they could still be executed without compromising the deadlines of high criticality tasks. As a step towards this aim, we propose a method, denoted Latest Completion Time (LCT), that allows lower criticality tasks to proceed with their execution as long as they do not prevent higher criticality tasks from meeting their deadlines. Furthermore, we show that tasks suspension can only be temporary, and prove that a particular definition of idle times can be used to reset the system's criticality level. Finally, we study the performances of our LCT mechanism w.r.t. the classical mechanism that suspends a task as soon as the system criticality level becomes higher than its own criticality.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129420365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. J. Bril, M. V. D. Heuvel, U. Keskin, J. Lukkien
Fixed-priority scheduling with deferred preemption(FPDS) and fixed-priority scheduling with preemption thresholds(FPTS) have been proposed in the literature as viable alternatives to fixed-priority preemptive scheduling (FPPS), that reduce memory requirements, reduce the cost of arbitrary preemptions, and may improve the feasibility of a task set even when preemption overheads are neglected. This paper aims at advancing the relative strength of limited preemptive schedulers by combining FPDS and FPTS. In particular, we present a refinement of FPDS with preemption thresholds for both jobs and sub-jobs, termed FPGS. We provide an exact schedulability analysis for FPGS, and show how to maximize the feasibility of a set of sporadic tasks under FPGS for given priorities, computation times, periods, and deadlines of tasks. We evaluate the effectiveness of FPGS by comparing the feasibility of task sets under FPGS with other fixed-priority scheduling algorithms by means of a simulation. Our experiments show that FPGS allows an increase of the number of task sets that are schedulable under fixed-priority scheduling.
{"title":"Generalized Fixed-Priority Scheduling with Limited Preemptions","authors":"R. J. Bril, M. V. D. Heuvel, U. Keskin, J. Lukkien","doi":"10.1109/ECRTS.2012.34","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.34","url":null,"abstract":"Fixed-priority scheduling with deferred preemption(FPDS) and fixed-priority scheduling with preemption thresholds(FPTS) have been proposed in the literature as viable alternatives to fixed-priority preemptive scheduling (FPPS), that reduce memory requirements, reduce the cost of arbitrary preemptions, and may improve the feasibility of a task set even when preemption overheads are neglected. This paper aims at advancing the relative strength of limited preemptive schedulers by combining FPDS and FPTS. In particular, we present a refinement of FPDS with preemption thresholds for both jobs and sub-jobs, termed FPGS. We provide an exact schedulability analysis for FPGS, and show how to maximize the feasibility of a set of sporadic tasks under FPGS for given priorities, computation times, periods, and deadlines of tasks. We evaluate the effectiveness of FPGS by comparing the feasibility of task sets under FPGS with other fixed-priority scheduling algorithms by means of a simulation. Our experiments show that FPGS allows an increase of the number of task sets that are schedulable under fixed-priority scheduling.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128035675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive demand-bound functions for mixed-criticality sporadic tasks, and use these to determine EDF-schedulability. Tasks have different demand-bound functions for each criticality mode. We show how to shift execution demand from high-to low-criticality mode by tuning the relative deadlines. This allows us to shape the demand characteristics of each task. We propose an efficient algorithm for tuning all relative deadlines of a task set in order to shape the total demand to the available supply of the computing platform. Experiments indicate that this approach is significantly more powerful than previous approaches to mixed-criticality scheduling. This new approach has the added benefit of supporting hierarchical scheduling frameworks.
{"title":"Outstanding Paper Award: Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks","authors":"Pontus Ekberg, W. Yi","doi":"10.1109/ECRTS.2012.24","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.24","url":null,"abstract":"We derive demand-bound functions for mixed-criticality sporadic tasks, and use these to determine EDF-schedulability. Tasks have different demand-bound functions for each criticality mode. We show how to shift execution demand from high-to low-criticality mode by tuning the relative deadlines. This allows us to shape the demand characteristics of each task. We propose an efficient algorithm for tuning all relative deadlines of a task set in order to shape the total demand to the available supply of the computing platform. Experiments indicate that this approach is significantly more powerful than previous approaches to mixed-criticality scheduling. This new approach has the added benefit of supporting hierarchical scheduling frameworks.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132110948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Scratchpad memory (SPM) provides a predictable and energy efficient way to store program instructions and data. It would be ideal for embedded real-time systems if not for the practical difficulty that most programs have to be modified in source or binary form in order to use it effectively. This modification process is called partitioning, and it splits a large program into sub-units called regions that are small enough to be stored in SPM. Earlier papers on this subject have only considered regions formed around program structures, such as loops, methods and even entire tasks. Region formation and SPM allocation are performed in two separate steps. This is an approximation that does not make best use of SPM. In this paper, we propose a k-partitioning algorithm as a new way to solve the problem. This allows us to carry out region formation and SPM allocation simultaneously. We can generate optimal partitions for programs expressed either as call trees or by a restricted form of control-flow graph (CFG). We show that this approach obtains superior results to the previous two-step approach. We apply our algorithm to various programs and SPM sizes and show that it reduces the execution time cost for executing those programs relative to execution with cache.
{"title":"Optimal Program Partitioning for Predictable Performance","authors":"J. Whitham, N. Audsley","doi":"10.1109/ECRTS.2012.18","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.18","url":null,"abstract":"Scratchpad memory (SPM) provides a predictable and energy efficient way to store program instructions and data. It would be ideal for embedded real-time systems if not for the practical difficulty that most programs have to be modified in source or binary form in order to use it effectively. This modification process is called partitioning, and it splits a large program into sub-units called regions that are small enough to be stored in SPM. Earlier papers on this subject have only considered regions formed around program structures, such as loops, methods and even entire tasks. Region formation and SPM allocation are performed in two separate steps. This is an approximation that does not make best use of SPM. In this paper, we propose a k-partitioning algorithm as a new way to solve the problem. This allows us to carry out region formation and SPM allocation simultaneously. We can generate optimal partitions for programs expressed either as call trees or by a restricted form of control-flow graph (CFG). We show that this approach obtains superior results to the previous two-step approach. We apply our algorithm to various programs and SPM sizes and show that it reduces the execution time cost for executing those programs relative to execution with cache.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133970701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Runtime controllers can be used in distributed embedded systems to throttle or stop software components and thus to limit the timing effects that applications have on each other through scheduling dependencies. Such runtime controllers require bounds on the worst-case admissible resource utilization per task to estimate and to control the worst-case interference between applications. Multi-dimensional sensitivity analysis can be used to derive efficient local controller bounds from global system constraints. In this paper we present a novel distributed algorithm to determine a multi-dimensional sensitivity bound on activation jitter which serves that purpose. Distribution makes it suitable for in-field application in modular designs, a main requirement in many industrial applications. Its properties are formally derived. Extensive experiments evaluate the solution quality and computation time.
{"title":"Deriving Monitoring Bounds for Distributed Real-Time Systems","authors":"M. Neukirchner, S. Stein, R. Ernst","doi":"10.1109/ECRTS.2012.10","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.10","url":null,"abstract":"Runtime controllers can be used in distributed embedded systems to throttle or stop software components and thus to limit the timing effects that applications have on each other through scheduling dependencies. Such runtime controllers require bounds on the worst-case admissible resource utilization per task to estimate and to control the worst-case interference between applications. Multi-dimensional sensitivity analysis can be used to derive efficient local controller bounds from global system constraints. In this paper we present a novel distributed algorithm to determine a multi-dimensional sensitivity bound on activation jitter which serves that purpose. Distribution makes it suitable for in-field application in modular designs, a main requirement in many industrial applications. Its properties are formally derived. Extensive experiments evaluate the solution quality and computation time.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114467430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multiprocessor platforms have been widely adopted to accommodate the increasing computation requirement of modern applications. Partitioned scheduling (or packing) has been widely exploited by partitioning real-time tasks onto processors to meet the timing constraints, which has been shown to be NP-complete in the strong sense. This paper studies the approximation of partitioned scheduling by exploiting resource augmentation with (1) speeding up or (2) allocating more processors. When adopting speeding up to meet timing constraints, we provide a polynomial-time approximation scheme (PTAS) to derive near-optimal solutions only with the assumption that the ratio of the maximum relative deadline to the minimum relative deadline is a constant. The previously known PTAS for this problem imposes additional restrictions on the periods and the execution times of tasks. By removing these additional constraints, our scheme can be adopted for wider task sets. When considering the resource augmentation by allocating more processors, we show that there does not exist any asymptotic polynomial-time approximation scheme (APTAS) unless P=NP.
{"title":"Partitioned Packing and Scheduling for Sporadic Real-Time Tasks in Identical Multiprocessor Systems","authors":"Jian-Jia Chen, S. Chakraborty","doi":"10.1109/ECRTS.2012.43","DOIUrl":"https://doi.org/10.1109/ECRTS.2012.43","url":null,"abstract":"Multiprocessor platforms have been widely adopted to accommodate the increasing computation requirement of modern applications. Partitioned scheduling (or packing) has been widely exploited by partitioning real-time tasks onto processors to meet the timing constraints, which has been shown to be NP-complete in the strong sense. This paper studies the approximation of partitioned scheduling by exploiting resource augmentation with (1) speeding up or (2) allocating more processors. When adopting speeding up to meet timing constraints, we provide a polynomial-time approximation scheme (PTAS) to derive near-optimal solutions only with the assumption that the ratio of the maximum relative deadline to the minimum relative deadline is a constant. The previously known PTAS for this problem imposes additional restrictions on the periods and the execution times of tasks. By removing these additional constraints, our scheme can be adopted for wider task sets. When considering the resource augmentation by allocating more processors, we show that there does not exist any asymptotic polynomial-time approximation scheme (APTAS) unless P=NP.","PeriodicalId":425794,"journal":{"name":"2012 24th Euromicro Conference on Real-Time Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124809941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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