Wfj Wim Verhaegh

Worst-case response time analysis of real-time tasks under fixed-priority scheduling with deferred preemption

Fixed-priority scheduling with deferred preemption (FPDS) has been proposed in the literature as a viable alternative to fixed-priority pre-emptive scheduling (FPPS), that obviates the need for non-trivial resource access protocols and reduces the cost of arbitrary preemptions.This paper shows that existing worst-case response time analysis of hard real-time tasks under FPDS, arbitrary phasing and relative deadlines at most equal to periods is pessimistic and/or optimistic. The same problem also arises for fixed-priority non-pre-emptive scheduling (FPNS), being a special case of FPDS. This paper provides a revised analysis, resolving the problems with the existing approaches. The analysis is based on known concepts of critical instant and busy period for FPPS. To accommodate for our scheduling model for FPDS, we need to slightly modify existing definitions of these concepts. The analysis assumes a continuous scheduling model, which is based on a partitioning of the timeline in a set of non-empty, right semi-open intervals. It is shown that the critical instant, longest busy period, and worst-case response time for a task are suprema rather than maxima for all tasks, except for the lowest priority task. Hence, that instant, period, and response time cannot be assumed for any task, except for the lowest priority task. Moreover, it is shown that the analysis is not uniform for all tasks, i.e. the analysis for the lowest priority task differs from the analysis of the other tasks. These anomalies for the lowest priority task are an immediate consequence of the fact that only the lowest priority task cannot be blocked. To build on earlier work, the worst-case response time analysis for FPDS is expressed in terms of known worst-case analysis results for FPPS. The paper includes pessimistic variants of the analysis, which are uniform for all tasks, illustrates the revised analysis for an advanced model for FPDS, where tasks are structured as flow graphs of subjobs rather than sequences, and shows that our analysis is sustainable.

Worst-Case Response Time Analysis of Real-Time Tasks under Fixed-Priority Scheduling with Deferred Preemption Revisited

Fixed-priority scheduling with deferred preemption (FPDS) has been proposed in the literature as a viable alternative to fixed-priority pre-emptive scheduling (FPPS), that obviates the need for non-trivial resource access protocols and reduces the cost of arbitrary preemptions. This paper shows that existing worst-case response time analysis of hard real-time tasks under FPDS, arbitrary phasing and relative deadlines at most equal to periods is pessimistic and/or optimistic. The same problem also arises for fixedpriority non-pre-emptive scheduling (FPNS), being a special case of FPDS. This paper provides a revised analysis, resolving the problems with the existing approaches. The analysis is based on known concepts of critical instant and busy period for FPPS. To accommodate for our scheduling model for FPDS, we need to slightly modify existing definitions of these concepts. The analysis assumes a continuous scheduling model, which is based on a partitioning of the timeline in a set of non-empty, right semi-open intervals. It is shown that the critical instant, longest busy period, and worst-case response time for a task are suprema rather than maxima for all tasks, except for the lowest priority task, i.e. that instant, period, and response time cannot be assumed. Moreover, it is shown that the analysis is not uniform for all tasks, i.e. the analysis for the lowest priority task differs from the analysis of the other tasks. These anomalies for the lowest priority task are an immediate consequence of the fact that only the lowest priority task cannot be blocked. To build on earlier work, the worst-case response time analysis for FPDS is expressed in terms of known worst-case analysis results for FPPS. The paper includes pessimistic variants of the analysis, which are uniform for all tasks.

Improved force-directed scheduling in high-throughput digital signal processing

This paper discusses improved force-directed scheduling and its application in the design of high-throughput DSP systems, such as real-time video VLSL circuits. We present a mathematical justification of the technique of force-directed scheduling, introduced by Paulin and Knight (1989), and we show how the algorithm can be used to find cost-effective time assignments and resource allocations, allowing trade-offs between processing units and memories. Furthermore, we present modifications that improve the effectiveness and the efficiency of the algorithm. The significance of the improvements is illustrated by an empirical performance analysis based on a number of problem instances. >

Improved force-directed scheduling

Presents a mathematical justification of the technique of force-directed scheduling and propose two modifications of the basic algorithm introduced by Paulin and Knight. The newly presented modifications improve the effectiveness of force-directed scheduling without affecting its time complexity. This is illustrated by an empirical performance analysis based on a number of problem instances.<<ETX>>

A two-stage solution approach to multidimensional periodic scheduling

We present a two-stage solution approach to the multidimensional periodic scheduling (MPS) problem. This problem originates from the design of high-throughput digital-signal-processor systems, where highly parallel execution of loops is of utmost importance. We introduce the concept of multidimensional periodic operations in order to cope with problems originating from loop hierarchies and explicit timing requirements. In the first stage of the approach, we assign periods to the multidimensional periodic operations such that storage costs are minimized. This is done by means of branch-and-bound, based on a linear programming and constraint-generation technique. In the second stage, we assign start times to the operations and determine on which processing units (PUs) they are executed. This is done by means of an iterative approach. The two major subproblems of MPS concerning checking data dependency constraints and PU constraints are solved by means of an all-integer integer-linear-programming technique. This technique is used as a subroutine in the above two stages. The effectiveness and efficiency of the approach are good, which is illustrated by means of some practical examples.

Smoothing Streams in an In-Home Digital Network: Optimization of Bus and Buffer Usage

In an in-home digital network it may be expected that several data streams (audio, video) run simultaneously over a shared communication device, e.g., a bus. The burstiness of a data stream can be reduced by buffering data at the sending and receiving side, thereby allowing a lower bus share allocation for the stream. In this paper we present an algorithm that determines how much of the bus capacity and buffer space should be allocated to each stream, in order to have a feasible transmission schedule for each stream. Furthermore, the algorithm determines a transmission schedule for each stream, indicating how much data is transmitted over time. We show how this multiple-stream problem can be solved by repeatedly solving single-stream problems. We present efficient algorithms to solve these single-stream problems. Furthermore, we present some experimental results.

The complexity of generalized retiming problems

We discuss the complexity of a number of high-level synthesis problems that can be viewed as generalizations of the classical retiming problem introduced by Leiserson and Saxe. The generalizations are concerned with additional degrees of freedom resulting from timefolding and multiplexing. The central problem is the design of multicycle and multifunctional processing units. This problem consists of two subproblems known as operator assignment and retiming. In this paper, we are primarily concerned with the construction of appropriate models and their complexity analysis. We show that both operator assignment and retiming are NP-hard in the presence of multiplexing or timefolding. We present a novel proof of the result obtained by Leiserson and Saxe, which states that retiming without multiplexing or timefolding can be solved in polynomial time.

The complexity of multidimensional periodic scheduling

We discuss the computational complexity of the multidimensional periodic scheduling problem. This problem originates from the assignment of periodic tasks to processing units over time and it is related to the design of high-performance video signal processors. We present a model of multidimensional periodic operations and introduce the multidimensional periodic scheduling problem. Next, we show that this problem and two related sub-problems are NP-hard. Further-more, we identify several special cases induced by practical situations, of which some are proven to be polynomially solvable.

Random redundant storage in disk arrays: complexity of retrieval problems

Random redundant data storage strategies have proven to be a good choice for efficient data storage in multimedia servers. These strategies lead to a retrieval problem in which it is decided for each requested data block which disk to use for its retrieval. In this paper, we give a complexity classification of retrieval problems for random redundant storage.

Bus and Buffer Usage in In-Home Digital Networks: Applying the Dantzig–Wolfe Decomposition

In an in-home digital network several data streams (audio, video) may run simultaneously over a shared communication device, e.g. a bus. The burstiness of a data stream can be reduced by buffering data at the sending and receiving side, thereby allowing a lower bus share allocation for the stream. In this paper we present an algorithm that determines how much of the bus capacity and buffer space should be allocated to each stream, in order to have a feasible transmission schedule for each stream. Furthermore, the algorithm determines a transmission schedule for each stream, indicating how much data is transmitted over time. We model the problem as a linear program and apply a Dantzig–Wolfe decomposition such that the multiple-stream problem can be solved by repeatedly solving single-stream problems. For these single-stream problems we briefly describe efficient algorithms to solve them.