Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning real-time tasks on a heterogeneous multiprocessor platform comprising two different types of processors — such a platform is referred to as two-type platform. We present two linearithmic timecomplexity algorithms, SA and SA-P, each providing the follow- ing guarantee. For a given two-type platform and a given task set, if there exists a feasible task-to-processor-type assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type, then (i) using SA, it is guaranteed to find such a feasible task-to- processor-type assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding 2 a feasible task-to-processor assignment where tasks are not allowed to migrate between processors but given a platform in which processors are 1+α/times faster, where 0<α≤1. The parameter α is a property of the task set — it is the maximum utilization of any task which is less than or equal to 1.

Makespan computation for GPU threads running on a single streaming multiprocessor

Graphics processors were originally developed for rendering graphics but have recently evolved towards being an architecture for general-purpose computations. They are also expected to become important parts of embedded systems hardware -- not just for graphics. However, this necessitates the development of appropriate timing analysis techniques which would be required because techniques developed for CPU scheduling are not applicable. The reason is that we are not interested in how long it takes for any given GPU thread to complete, but rather how long it takes for all of them to complete. We therefore develop a simple method for finding an upper bound on the makespan of a group of GPU threads executing the same program and competing for the resources of a single streaming multiprocessor (whose architecture is based on NVIDIA Fermi, with some simplifying assunptions). We then build upon this method to formulate the derivation of the exact worst-case makespan (and corresponding schedule) as an optimization problem. Addressing the issue of tractability, we also present a technique for efficiently computing a safe estimate of the worstcase makespan with minimal pessimism, which may be used when finding an exact value would take too long.

Using a prioritized medium access control protocol for incrementally obtaining an interpolation of sensor readings

This paper addresses sensor network applications which need to obtain an accurate image of physical phenomena and do so with a high sampling rate in both time and space. We present a fast and scalable approach for obtaining an approximate representation of all sensor readings at high sampling rate for quickly reacting to critical events in a physical environment. This approach is an improvement on previous work in that after the new approach has undergone a startup phase then the new approach can use a very small sampling period.

Preemption-light multiprocessor scheduling of sporadic tasks with high utilisation bound

Known algorithms capable of scheduling implicit-deadline sporadic tasks over identical processors at up to 100% utilisation invariably involve numerous preemptions and migrations. To the challenge of devising a scheduling scheme with as few preemptions and migrations as possible, for a given guaranteed utilisation bound, we respond with the algorithm NPS-F. It is configurable with a parameter, trading off guaranteed schedulable utilisation (up to 100%) vs preemptions. For any possible configuration, NPS-F introduces fewer preemptions than any other known algorithm matching its utilisation bound. A clustered variant of the algorithm, for systems made of multicore chips, eliminates (costly) off-chip task migrations, by dividing processors into disjoint clusters, formed by cores on the same chip (with the cluster size being a parameter). Clusters are independently scheduled (each, using non-clustered NPS-F). The utilisation bound is only moderately affected. We also formulate an important extension (applicable to both clustered and non-clustered NPS-F) which optimises the supply of processing time to executing tasks and makes it more granular. This reduces processing capacity requirements for schedulability without increasing preemptions.

Real-time scheduling with resource sharing on uniform multiprocessors

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a uniform multiprocessor platform where each task may access at most one of |R| shared resources and at most once by each job of that task. The resources have to be accessed in a mutually exclusive manner. We propose an algorithm, GIS-vpr, which offers the guarantee that if a task set is schedulable to meet deadlines by an optimal task assignment scheme that allows a task to migrate only when it accesses or releases a resource, then our algorithm also meets the deadlines with the same restriction on the task migration, if given processors 4 + 6|R| times as fast. The proposed algorithm, by design, limits the number of migrations per job to at most two. To the best of our knowledge, this is the first result for resource sharing on uniform multiprocessors with proven performance guarantee.

Scalable data acquisition for densely instrumented cyber-physical systems

Consider the problem of designing an algorithm for acquiring sensor readings. Consider specifically the problem of obtaining an approximate representation of sensor readings where (i) sensor readings originate from different sensor nodes, (ii) the number of sensor nodes is very large, (iii) all sensor nodes are deployed in a small area (dense network) and (iv) all sensor nodes communicate over a communication medium where at most one node can transmit at a time (a single broadcast domain). We present an efficient algorithm for this problem, and our novel algorithm has two desired properties: (i) it obtains an interpolation based on all sensor readings and (ii) it is scalable, that is, its time-complexity is independent of the number of sensor nodes. Achieving these two properties is possible thanks to the close interlinking of the information processing algorithm, the communication system and a model of the physical world.

A preliminary idea for an 8-competitive, log2 DMAX + log2 log2 1/U asymptotic-space, interface generation algorithm for two-level hierarchical scheduling of constrained-deadline sporadic tasks on a uniprocessor

Consider a single processor and a software system. The software system comprises components and interfaces where each component has an associated interface and each component comprises a set of constrained-deadline sporadic tasks. A scheduling algorithm (called global scheduler) determines at each instant which component is active. The active component uses another scheduling algorithm (called local scheduler) to determine which task is selected for execution on the processor. The interface of a component makes certain information about a component visible to other components; the interfaces of all components are used for schedulability analysis. We address the problem of generating an interface for a component based on the tasks inside the component. We desire to (i) incur only a small loss in schedulability analysis due to the interface and (ii) ensure that the amount of space (counted in bits) of the interface is small; this is because such an interface hides as much details of the component as possible. We present an algorithm for generating such an interface.

Provably good scheduling of sporadic tasks with resource sharing on a two-type heterogeneous multiprocessor platform

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform where a task may request at most one of |R| shared resources. There are m1 processors of type-1 and m2 processors of type-2. Tasks may migrate only when requesting or releasing resources. We present a new algorithm, FF-3C-vpr, which offers a guarantee that if a task set is schedulable to meet deadlines by an optimal task assignment scheme that only allows tasks to migrate when requesting or releasing a resource, then FF-3Cvpr also meets deadlines if given processors 4+6*ceil(|R|/min(m1,m2)) times as fast. As far as we know, it is the first result for resource sharing on heterogeneous platforms with provable performance.

WCET analysis considering contention on memory bus in COTS-based multicores

The usage of COTS-based multicores is becoming widespread in the field of embedded systems. Providing realtime guarantees at design-time is a pre-requisite to deploy real-time systems on these multicores. This necessitates the consideration of the impact of the contention due to shared low-level hardware resources on the Worst-Case Execution Time (WCET) of the tasks. As a step towards this aim, this paper first identifies the different factors that make the WCET analysis a challenging problem in a typical COTS-based multicore system. Then, we propose and prove, a mathematically correct method to determine tight upper bounds on the WCET of the tasks, when they are co-scheduled on different cores.

Response time analysis of COTS-Based multicores considering the contention on the shared memory bus

The current industry trend is towards using Commercially available Off-The-Shelf (COTS) based multicores for developing real time embedded systems, as opposed to the usage of custom-made hardware. In typical implementation of such COTS-based multicores, multiple cores access the main memory via a shared bus. This often leads to contention on this shared channel, which results in an increase of the response time of the tasks. Analyzing this increased response time, considering the contention on the shared bus, is challenging on COTS-based systems mainly because bus arbitration protocols are often undocumented and the exact instants at which the shared bus is accessed by tasks are not explicitly controlled by the operating system scheduler; they are instead a result of cache misses. This paper makes three contributions towards analyzing tasks scheduled on COTS-based multicores. Firstly, we describe a method to model the memory access patterns of a task. Secondly, we apply this model to analyze the worst case response time for a set of tasks. Although the required parameters to obtain the request profile can be obtained by static analysis, we provide an alternative method to experimentally obtain them by using performance monitoring counters (PMCs). We also compare our work against an existing approach and show that our approach outperforms it by providing tighter upper-bound on the number of bus requests generated by a task.

A conjecture about provably good task assignment on heterogeneous multiprocessor platforms but with a stronger adversary

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a heterogeneous multiprocessor platform. We use an algorithm proposed in [1] (we refer to it as LP-EE) from state-of-the-art for assigning tasks to heterogeneous multiprocessor platform and (re-)prove its performance guarantee but for a stronger adversary.We conjecture that if a task set can be scheduled to meet deadlines on a heterogeneous multiprocessor platform by an optimal task assignment scheme that allows task migrations then LP-EE meets deadlines as well with no migrations if given processors twice as fast. We illustrate this with an example.

Two-type heterogeneous multiprocessor scheduling: Is there a phase transition? (Extended Abstract)

Consider the problem of non-migratively scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform. We ask the following question: Does there exist a phase transition behavior for the two-type heterogeneous multiprocessor scheduling problem? We also provide some initial observations via simulations performed on randomly generated task sets.

Provably good task assignment on heterogeneous multiprocessor platforms for a restricted case but with a stronger adversary

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a heterogeneous multiprocessor platform. We consider a restricted case where the maximum utilization of any task on any processor in the system is no greater than one. We use an algorithm proposed in [1] (we refer to it as LP-EE) from state-of-the-art for assigning tasks to heterogeneous multiprocessor platform and (re-)prove its performance guarantee for this restricted case but for a stronger adversary. We show that if a task set can be scheduled to meet deadlines on a heterogeneous multiprocessor platform by an optimal task assignment scheme that allows task migrations then LP-EE meets deadlines as well with no migrations if given processors twice as fast.

Intra-type migrative scheduling of implicit-deadline sporadic tasks on two- type heterogeneous multiprocessor

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform. Each processor is either of type-1 or type-2 with each task having different execution time on each processor type. Jobs can migrate between processors of same type (referred to as intra-type migration) but cannot migrate between processors of different types. We present a new scheduling algorithm namely, LP-Relax(THR) which offers a guarantee that if a task set can be scheduled to meet deadlines by an optimal task assignment scheme that allows intra-type migration then LP-Relax(THR) meets deadlines as well with intra-type migration if given processors 1/THR as fast (referred to as speed competitive ratio) where THR <= 2/3.

Slotted wiDom: schedulability analysis and its experimental validation

WiDom is a wireless prioritized medium access control protocol which offers a very large number of priority levels. Hence, it brings the potential to employ non-preemptive static-priority scheduling and schedulability analysis for a wireless channel assuming that the overhead of WiDom is modeled properly. One schedulability analysis for WiDom has already been proposed but recent research has created a new version of WiDom (we call it: Slotted WiDom) with lower overhead and for this version of WiDom no schedulability analysis exists. In this paper we propose a new schedulability analysis for slotted WiDom and extend it to work also for message streams with release jitter. We have performed experiments with an implementation of slotted WiDom on a real-world platform (MicaZ). We find that for each message stream, the maximum observed response time never exceeds the calculated response time and hence this corroborates our belief that our new scheduling theory is applicable in practice.