Marco Jan Gerrit Bekooij

Scheduling multiple independent hard-real-time jobs on a heterogeneous multiprocessor

This paper proposes a scheduling strategy and an automatic scheduling flow that enable the simultaneous execution of multiple hard-real-time dataflow jobs. Each job has its own execution rate and starts and stops independently from other jobs, at instants unknown at compile-time, on a multiprocessor system-on-chip. We show how a combination of Time-Division Multiplex (TDM) and static-order scheduling can be modeled as additional nodes and edges on top of the dataflow representation of the job using Single-Rate Dataflow semantics to enable tight worst-case temporal analysis. We also propose algorithms to find combined TDM/static order schedules for jobs that guarantee a requested minimum throughput and maximum latency, while minimizing the usage of processing resources. We illustrate the usage of these techniques for a combination of Wireless LAN and TD-SCDMA radio jobs running on a prototype Software-Defined Radio platform.

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.

Self-Timed Scheduling Analysis for Real-Time Applications

This paper deals with the scheduling analysis of hard real-time streaming applications. These applications are mapped onto a heterogeneous multiprocessor system-on-chip (MPSoC), where we must jointly meet the timing requirements of several jobs. Each job is independently activated and processes streams at its own rate. The dynamic starting and stopping of jobs necessitates the usage of self-timed schedules (STSs). By modeling job implementations using multirate data flow (MRDF) graph semantics, real-time analysis can be performed. Traditionally, temporal analysis of STSs for MRDF graphs only aims at evaluating the average throughput. It does not cope well with latency, and it does not take into account the temporal behavior during the initial transient phase. In this paper, we establish an important property of STSs: the initiation times of actors in an STS are bounded by the initiation times of the same actors in any static periodic schedule of the same job; based on this property, we show how to guarantee strictly periodic behavior of a task within a self-timed implementation; then, we provide useful bounds on maximum latency for jobs with periodic, sporadic, and bursty sources, as well as a technique to check latency requirements. We present two case studies that exemplify the application of these techniques: a simplified channel equalizer and a wireless LAN receiver.

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.n 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.

Online resource management in a multiprocessor with a network-on-chip

We propose an online resource allocation solution for multiprocessor systems-on-chip, that executes several real-time, streaming media jobs simultaneously. The system consists of up to 24 processors connected by an AEthereal [7] Network-on-Chip (NoC) of 4 to 12 routers. A job is a set of processing tasks connected by FIFO channels. Each job can be independently started or stopped by the user. Each job is annotated with resource budgets per computation task and communication channel which have been computed at compile-time. When a job is requested to start, resources that meet the required resource budgets have to be found. Because it is done online, allocation must be done with low-complexity algorithms. We do the allocation in two-steps. First, tasks are assigned to virtual tiles (VTs), while trying to minimise the total number of VTs and the total bandwidth used. In the second step, these VTs are mapped to real tiles, and network bandwidth allocation and routing are performed simultaneously. We show with simulations that introducing randomisation in the processing order yields a significant improvement in the percentage of mapping succdesses. In combination, these techniques allow 95% of the processor resources to be allocated while handling a large number of job arrivals and departures.

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.

Monotonicity and run-time scheduling

Modern embedded multi-processors can execute several stream-processing applications concurrently. Typically, these applications are partitioned into tasks that communicate over buffers together forming a task graph. The fact that these applications are started and stopped by the user combined with the knowledge that not all applications are necessarily completely characterised makes it attractive to use run-time scheduling. We define and characterise a class of budget schedulers that by construction bound the interference from other applications. Furthermore, we will show that the worst-case effects of these schedulers can be included in dataflow process networks. The execution of the resulting dataflow process network is shown to result in tight and conservative bounds on the end-to-end temporal behaviour of the execution of the task graph on a cycle-true simulator. Given that the inter-task synchronisation of the application allows for a dataflow model that is functionally deterministic, this enables exploration of various buffer capacities and scheduler settings at a high level of abstraction.

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.

Exploiting the Expressiveness of Cyclo-Static Dataflow to Model Multimedia Implementations

The design of increasingly complex and concurrent multimedia systems requires a description at a higher abstraction level. Using an appropriate model of computation helps to reason about the system and enables design time analysis methods. The nature of multimedia processing matches in many cases well with cyclo-static dataflow (CSDF), making it a suitable model. However, channels in an implementation often use for cost reasons a kind of shared buffer that cannot be directly described in CSDF. This paper shows how such implementation specific aspects can be expressed in CSDF without the need for extensions. Consequently, the CSDF graph remains completely analyzable and allows reasoning about its temporal behavior. The obtained relation between model and implementation enables a buffer capacity analysis on the model while assuring the throughput of the final implementation. The capabilities of the approach are demonstrated by analyzing the temporal behavior of an MPEG-4 video encoder with a CSDF graph.