Assigning real-time tasks on heterogeneous multiprocessors with two unrelated types of processors

A preliminary version of this paper appeared in Proceedings of the 31st IEEE Real-Time Systems Symposium, 2010, pp. 239–248.

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.

Scheduling sporadic tasks on multiprocessors with mutual exclusion constraints

Consider the problem of scheduling sporadic tasks on a multiprocessor platform under mutual exclusion constraints. We present an approach which appears promising for allowing large amounts of parallel task executions and still ensures low amounts of blocking.

Competitive analysis of partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. We propose an algorithm which can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are three times faster.

Competitive analysis of static-priority partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. On each processor, tasks are scheduled according to rate-monotonic. We propose an algorithm that can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are √2 / √2−1 ≈ 3.41 times faster. No such guarantees are previously known for partitioned static-priority scheduling on uniform multiprocessors.

Scheduling arbitrary-deadline sporadic task systems on multiprocessors

A new algorithm is proposed for scheduling preemptible arbitrary-deadline sporadic task systems upon multiprocessor platforms, with interprocessor migration permitted. This algorithm is based on a task-splitting approach - while most tasks are entirely assigned to specific processors, a few tasks (fewer than the number of processors) may be split across two processors. This algorithm can be used for two distinct purposes: for actually scheduling specific sporadic task systems, and for feasibility analysis. Simulation- based evaluation indicates that this algorithm offers a significant improvement on the ability to schedule arbitrary- deadline sporadic task systems as compared to the contemporary state-of-art. With regard to feasibility analysis, the new algorithm is proved to offer superior performance guarantees in comparison to prior feasibility tests.

Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning implicit-deadline sporadic 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 low degree polynomial time-complexity algorithms, SA and SA-P, each providing the following guarantee. For a given two-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then (i) using SA, it is guaranteed to find such an 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 a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which processors are 1+α times faster. The parameter 0<α≤1 is a property of the task set; it is the maximum of all the task utilizations that are no greater than 1. We evaluate average-case performance of both the algorithms by generating task sets randomly and measuring how much faster processors the algorithms need (which is upper bounded by 1+α/2 for SA and 1+α for SA-P) in order to output a feasible task assignment (intra-migrative for SA and non-migrative for SA-P). In our evaluations, for the vast majority of task sets, these algorithms require significantly smaller processor speedup than indicated by their theoretical bounds. Finally, we consider a special case where no task utilization in the given task set can exceed one and for this case, we (re-)prove the performance guarantees of SA and SA-P. We show, for both of the algorithms, that changing the adversary from intra-migrative to a more powerful one, namely fully-migrative, in which tasks can migrate between processors of any type, does not deteriorate the performance guarantees. For this special case, we compare the average-case performance of SA-P and a state-of-the-art algorithm by generating task sets randomly. In our evaluations, SA-P outperforms the state-of-the-art by requiring much smaller processor speedup and by running orders of magnitude faster.

Real-time scheduling with resource sharing on heterogeneous multiprocessors

Consider the problem of scheduling a task set τ of implicit-deadline sporadic tasks to meet all deadlines on a t-type heterogeneous multiprocessor platform where tasks may access multiple shared resources. The multiprocessor platform has m k processors of type-k, where k∈{1,2,…,t}. The execution time of a task depends on the type of processor on which it executes. The set of shared resources is denoted by R. For each task τ i , there is a resource set R i ⊆R such that for each job of τ i , during one phase of its execution, the job requests to hold the resource set R i exclusively with the interpretation that (i) the job makes a single request to hold all the resources in the resource set R i and (ii) at all times, when a job of τ i holds R i , no other job holds any resource in R i . Each job of task τ i may request the resource set R i at most once during its execution. A job is allowed to migrate when it requests a resource set and when it releases the resource set but a job is not allowed to migrate at other times. Our goal is to design a scheduling algorithm for this problem and prove its performance. We propose an algorithm, LP-EE-vpr, which offers the guarantee that if an implicit-deadline sporadic task set is schedulable on a t-type heterogeneous multiprocessor platform by an optimal scheduling algorithm that allows a job to migrate only when it requests or releases a resource set, then our algorithm also meets the deadlines with the same restriction on job migration, if given processors 4×(1+MAXP×⌈|P|×MAXPmin{m1,m2,…,mt}⌉) times as fast. (Here MAXP and |P| are computed based on the resource sets that tasks request.) For the special case that each task requests at most one resource, the bound of LP-EE-vpr collapses to 4×(1+⌈|R|min{m1,m2,…,mt}⌉). To the best of our knowledge, LP-EE-vpr is the first algorithm with proven performance guarantee for real-time scheduling of sporadic tasks with resource sharing on t-type heterogeneous multiprocessors.

Global-EDF scheduling of multimode real- time systems considering mode independent tasks

Embedded real-time systems often have to support the embedding system in very different and changing application scenarios. An aircraft taxiing, taking off and in cruise flight is one example. The different application scenarios are reflected in the software structure with a changing task set and thus different operational modes. At the same time there is a strong push for integrating previously isolated functionalities in single-chip multicore processors. On such multicores the behavior of the system during a mode change, when the systems transitions from one mode to another, is complex but crucial to get right. In the past we have investigated mode change in multiprocessor systems where a mode change requires a complete change of task set. Now, we present the first analysis which considers mode changes in multicore systems, which use global EDF to schedule a set of mode independent (MI) and mode specific (MS) tasks. In such systems, only the set of MS tasks has to be replaced during mode changes, without jeopardizing the schedulability of the MI tasks. Of prime concern is that the mode change is safe and efficient: i.e. the mode change needs to be performed in a predefined time window and no deadlines may be missed as a function of the mode change.

LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, its characteristics upon multiprocessor platforms have been little studied until now. Orthogonally, it has remained open how to efficiently schedule general task systems, including constrained deadline task systems, upon multiprocessors. Recent studies have introduced zero laxity (ZL) policy, which assigns a higher priority to a task with zero laxity, as a promising scheduling approach for such systems (e.g., EDZL). Towards understanding the importance of laxity in multiprocessor scheduling, this paper investigates the characteristics of ZL policy and presents the first ZL schedulability test for any work-conserving scheduling algorithm that employs this policy. It then investigates the characteristics of LLF scheduling, which also employs the ZL policy, and derives the first LLF-specific schedulability test on multiprocessors. It is shown that the proposed LLF test dominates the ZL test as well as the state-of-art EDZL test.

The utilization bound of static-priority preemptive partitioned multiprocessor scheduling is 50%

This paper studies static-priority preemptive scheduling on a multiprocessor using partitioned scheduling. We propose a new scheduling algorithm and prove that if the proposed algorithm is used and if less than 50% of the capacity is requested then all deadlines are met. It is known that for every static-priority multiprocessor scheduling algorithm, there is a task set that misses a deadline although the requested capacity is arbitrary close to 50%.

Compositional multiprocessor scheduling: the GMPR interface

Composition is a practice of key importance in software engineering. When real-time applications are composed, it is necessary that their timing properties (such as meeting the deadlines) are guaranteed. The composition is performed by establishing an interface between the application and the physical platform. Such an interface typically contains information about the amount of computing capacity needed by the application. For multiprocessor platforms, the interface should also present information about the degree of parallelism. Several interface proposals have recently been put forward in various research works. However, those interfaces are either too complex to be handled or too pessimistic. In this paper we propose the generalized multiprocessor periodic resource model (GMPR) that is strictly superior to the MPR model without requiring a too detailed description. We then derive a method to compute the interface from the application specification. This method has been implemented in Matlab routines that are publicly available.

Real-Time Application Mapping for Many-Cores Using a Limited Migrative Model

Many-core platforms are an emerging technology in the real-time embedded domain. These devices offer various options for power savings, cost reductions and contribute to the overall system flexibility, however, issues such as unpredictability, scalability and analysis pessimism are serious challenges to their integration into the aforementioned area. The focus of this work is on many-core platforms using a limited migrative model (LMM). LMM is an approach based on the fundamental concepts of the multi-kernel paradigm, which is a promising step towards scalable and predictable many-cores. In this work, we formulate the problem of real-time application mapping on a many-core platform using LMM, and propose a three-stage method to solve it. An extended version of the existing analysis is used to assure that derived mappings (i) guarantee the fulfilment of timing constraints posed on worst-case communication delays of individual applications, and (ii) provide an environment to perform load balancing for e.g. energy/thermal management, fault tolerance and/or performance reasons.