Maarten H. Wiggers

Efficient computation of buffer capacities for cyclo-static dataflow graphs

A key step in the design of cyclo-static real-time systems is the determination of buffer capacities. In our multi-processor system, we apply back-pressure, which means that tasks wait for space in output buffers. Consequently buffer capacities affect the throughput. This requires the derivation of buffer capacities that both result in a satisfaction of the throughput constraint, and also satisfy the constraints on the maximum buffer capacities. Existing exact solutions suffer from the computational complexity that is associated with the required conversion from a cyclo-static dataflow graph to a single-rate dataflow graph. In this paper we present an algorithm, with polynomial computational complexity, that does not require this conversion and that obtains close to minimal buffer capacities. The algorithm is applied to an MP3 play-back application that is mapped on our multi-processor system. For this application, we see that a cyclo-static dataflow model can reduce the buffer capacities by 50% compared to a multi-rate dataflow model.

Efficient computation of buffer capacities for multi-rate real-time systems with back-pressure

A key step in the design of multi-rate real-time systems is the determination of buffer capacities. In our multi-processor system, we apply back-pressure as caused by bounded buffers in order to control jitter. This requires the derivation of buffer capacities that both satisfy the temporal constraints as well as constraints on the buffer capacity. Existing exact solutions suffer from the computational complexity associated with the required conversion from a multi-rate dataflow graph to a single-rate dataflow graph. In this paper we present an algorithm, with linear computational complexity, that does not require this conversion and that determines close to minimal buffer capacities. The algorithm is applied to an MP3 play-back application that is mapped on our network based multi-processor system.

Enabling application-level performance guarantees in network-based systems on chip by applying dataflow analysis

A growing number of applications, often with real-time requirements, are integrated on the same system on chip (SoC), in the form of hardware and software intellectual property (IP). To facilitate real-time applications, networks on chip (NoC) guarantee bounds on latency and throughput. These bounds, however, only extend to the network interfaces (NI), between the IP and the NoC. To give performance guarantees on the application level, the buffers in the NIs must be sufficiently large for the particular application. At the same time, it is imperative to minimise the size of the NI buffers, as they are major contributors to the area and power consumption of the NoC. Existing buffer-sizing methods use coarse-grained application models, based on linear traffic bounds or periodic producers and consumers, thus severely limiting their applicability. In this work, the authors propose to capture the behaviour of the NoC and the applications using a dataflow model. This enables one to verify the temporal behaviour and to compute buffer sizes using existing dataflow analysis techniques. The authors show what is required from the NoC architecture and demonstrate how to construct an NoC model, with multiple levels of detail. Using the proposed model, buffer sizes are determined for a range of SoC designs with a run time comparable to existing analytical methods, and results comparable to exhaustive simulation. For an application case study, where existing buffer-sizing methods are not applicable, the proposed model enables the verification of end-to-end temporal behaviour.

Modelling run-time arbitration by latency-rate servers in dataflow graphs

In order to obtain a cost-efficient solution, tasks share resources in a Multi-Processor System-on-Chip. In our architecture, shared resources are run-time scheduled. We show how the effects of Latency-Rate servers, which is a class of run-time schedulers, can be included in a dataflow model. The resulting dataflow model, which can have an arbitrary topology, enables us to provide guarantees on the temporal behaviour of the implementation. Traditionally, the end-to-end behaviour of multiple Latency-Rate servers has been analysed with Latency-Rate analysis, which is a Network Calculus. This paper bridges a gap between Network Calculi and dataflow analysis techniques, since we show that a class of run-time schedulers can now be included in dataflow models, or, from a Network Calculus perspective, that restrictions on the topology of graphs that include run-time scheduling can be removed.

Buffer Capacity Computation for Throughput Constrained Streaming Applications with Data-Dependent Inter-Task Communication

Streaming applications are often implemented as task graphs, in which data is communicated from task to task over buffers. Currently, techniques exist to compute buffer capacities that guarantee satisfaction of the throughput constraint if the amount of data produced and consumed by the tasks is known at design-time. However, applications such as audio and video decoders have tasks that produce and consume an amount of data that depends on the decoded stream. This paper introduces a dataflow model that allows for data-dependent communication, together with an algorithm that computes buffer capacities that guarantee satisfaction of a throughput constraint. The applicability of this algorithm is demonstrated by computing buffer capacities for an H.263 video decoder.

Efficient Computation of Buffer Capacities for Cyclo-Static Real-Time Systems with Back-Pressure

This paper describes a conservative approximation algorithm that derives close to minimal buffer capacities for an application described as a cyclo-static dataflow graph. The resulting buffer capacities satisfy constraints on the maximum buffer capacities and end-to-end throughput and latency constraints. Furthermore we show that the effects of run-time arbitration can be included in the response times of dataflow actors. We show that modelling an MP3 playback application as a cyclo-static dataflow graph instead of a multi-rate dataflow graph results in buffer capacities that are reduced up to 39%. Furthermore, the algorithm is applied to a real-life car-radio application, in which two independent streams are processed

A Priority-Based Budget Scheduler with Conservative Dataflow Model

Currently, the guaranteed throughput of a stream processing application, mapped on a multi-processor system, can be computed with a conservative dataflow model, if only time division multiplex (TDM) schedulers are applied. A TDM scheduler is a budget scheduler. Budget schedulers can be characterized by two parameters: budget and replenishment interval. This paper introduces a priority-based budget scheduler (PBS), which is a budget scheduler that additionally associates a priority with every task. PBS improves the guaranteed minimum throughput of a stream processing application compared to TDM, given the same amount of resources. We construct a conservative dataflow model for a task scheduled by PBS. This dataflow model generalizes previous work, because it is valid for a sequence of execution times instead of one execution time per task which results in an improved accuracy of the model. Given this dataflow model, we can compute the guaranteed minimum throughput of the task graph that implements the stream processing application. Experiments confirm that a significantly higher guaranteed minimum throughput of the task graph can be obtained with PBS instead of TDM schedulers and that a conservative bound on the guaranteed throughput of the task graph can be computed with a dataflow model. Furthermore, our bound on the guaranteed throughput of the task graph is accurate, if the buffer capacities in the task graph do not affect the guaranteed throughput.

Buffer capacity computation for throughput-constrained modal task graphs

Increasingly, stream-processing applications include complex control structures to better adapt to changing conditions in their environment. This adaptivity often results in task execution rates that are dependent on the processed stream. Current approaches to compute buffer capacities that are sufficient to satisfy a throughput constraint have limited applicability in case of data-dependent task execution rates. In this article, we present a dataflow model that allows tasks to have loops with an unbounded number of iterations. For instances of this dataflow model, we present efficient checks on their validity. Furthermore, we present an efficient algorithm to compute buffer capacities that are sufficient to satisfy a throughput constraint. This allows to guarantee satisfaction of a throughput constraint over different modes of a stream processing application, such as the synchronization and synchronized modes of a digital radio receiver.

Dataflow analysis for multiprocessor systems with non-starvation-free schedulers

Dataflow analysis techniques are suitable for the temporal analysis of real-time stream processing applications. However, the applicability of these models is currently limited to systems with starvation-free schedulers, such as Time-Division Multiplexing (TDM) schedulers. Removal of this limitation would broaden the application domain of dataflow analysis techniques significantly. In this paper we present a temporal analysis technique for Homogeneous Synchronous Dataflow (HSDF) graphs, that is also applicable for systems with non-starvation-free schedulers. Unlike existing dataflow analysis techniques, the proposed analysis technique makes use of an enabling-jitter characterization and iterative fixed-point computation. The presented approach is applicable for arbitrary (cyclic) graph topologies. Buffer capacity constraints are taken into account during the analysis and sufficient buffer capacities can be determined afterwards. The approach presented in this paper is the first approach that considers non-starvation-free schedulers in combination with arbitrary HSDF graphs The proposed dataflow analysis technique is implemented in a tool. This tool is used to evaluate the analysis technique using examples that illustrate some important differences with other temporal analysis methods. The case-study discusses how the method presented in this paper can be used to solve a problem with the inaccuracy of the temporal analysis results of a real-time stream processing system. This stream processing system consists of an FM receiver together with a DAB receiver application which both share a Digital Signal Processor (DSP).

Computation of buffer capacities for throughput constrained and data dependent inter-task communication

Streaming applications are often implemented as task graphs. Currently, techniques exist to derive buffer capacities that guarantee satisfaction of a throughput constraint for task graphs in which the inter-task communication is data-independent, i.e. the amount of data produced and consumed is independent of the data values in the processed stream. This paper presents a technique to compute buffer capacities that satisfy a throughput constraint for task graphs with data dependent inter-task communication, given that the task graph is a chain. We demonstrate the applicability of the approach by computing buffer capacities for an MP 3 playback application, of which the MP 3 decoder has a variable consumption rate. We are not aware of alternative approaches to compute buffer capacities that guarantee satisfaction of the throughput constraint for this application.