A PTAS for assigning sporadic tasks on two-type heterogeneous multiprocessors

Consider the problem of determining a task-toprocessor assignment for a given collection of implicit-deadline sporadic tasks upon a multiprocessor platform in which there are two distinct kinds of processors. We propose a polynomialtime approximation scheme (PTAS) for this problem. It offers the following guarantee: for a given task set and a given platform, if there exists a feasible task-to-processor assignment, then given an input parameter, ϵ, our PTAS succeeds, in polynomial time, in finding such a feasible task-to-processor assignment on a platform in which each processor is 1+3ϵ times faster. In the simulations, our PTAS outperforms the state-of-the-art PTAS [1] and also for the vast majority of task sets, it requires significantly smaller processor speedup than (its upper bound of) 1+3ϵ for successfully determining a feasible task-to-processor assignment

ILP-based approaches to partitioning recurrent workloads upon heterogeneous multiprocessors

The problem of partitioning systems of independent constrained-deadline sporadic tasks upon heterogeneous multiprocessor platforms is considered. Several different integer linear program (ILP) formulations of this problem, offering different tradeoffs between effectiveness (as quantified by speedup bound) and running time efficiency, are presented

Real-Time Scheduling on Heterogeneous Multiprocessors

Embedded computing is one of the most important areas in computer science today, witnessed by the fact that 98 % of all computers are embedded. Given that many embedded systems have to interact “promptly” with their physical environment, the scientific community has invested signifi-cant efforts in developing algorithms for scheduling the workload, which is generally implemented as a set of tasks, at the right time and in proving before run-time that all the timing requirements will be satisfied at run-time. This field of study is referred to as the real-time scheduling theory. The scheduling theory for a unicore processor is well-developed; the scientific results are taught at all major universities world-wide and the results are widely-used in industry. Scheduling theory for multicores is emerging but the focus so far has been for multicores with identical pro-cessing units. This is unfortunate because the computer industry is moving towards heterogeneous multicores with a constant number of distinct processor types — AMD Fusion, Intel Atom and NVIDIA Tegra are some of the examples of such multicores. This work deals with the problem of scheduling a set of tasks to meet their deadlines on het-erogeneous multiprocessors with a constant number of distinct processor types. On heterogeneou

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

Partitioned EDF scheduling on a few types of unrelated multiprocessors

A polynomial-time approximation scheme (PTAS) is derived for the partitioned EDF scheduling of implicit-deadline sporadic task systems upon unrelated multiprocessor platforms that are comprised of a constant number of distinct types of processors. This generalizes earlier results showing the existence of polynomialtime approximation schemes for the partitioned EDF scheduling of implicit-deadline sporadic task systems on (1) identical multiprocessor platforms, and (2) unrelated multiprocessor platforms containing a constant number of processors

An EPTAS for Scheduling on Unrelated Machines of Few Different Types

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than $1.5$ unless P$=$NP. We consider the case that there are only a constant number $K$ of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $K=1$. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $\varepsilon > 0$ an assignment with makespan of length at most $(1+\varepsilon)$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $1/\varepsilon$. In particular we achieve a running time of $2^{\mathcal{O}(K\log(K) \frac{1}{\varepsilon}\log^4 \frac{1}{\varepsilon})}+\mathrm{poly}(|I|)$, where $|I|$ denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques

Approximate feasibility in real-time scheduling: Speeding up in order to meet deadlines

Stougie, L. [Promotor]Marchetti-Spaccamela, A. [Promotor

The multiprocessor real-time scheduling of general task systems

The recent emergence of multicore and related technologies in many commercial systems has increased the prevalence of multiprocessor architectures. Contemporaneously, real-time applications have become more complex and sophisticated in their behavior and interaction. Inevitably, these complex real-time applications will be deployed upon these multiprocessor platforms and require temporal analysis techniques to verify their correctness. However, most prior research in multiprocessor real-time scheduling has addressed the temporal analysis only of Liu and Layland task systems. The goal of this dissertation is to extend real-time scheduling theory for multiprocessor systems by developing temporal analysis techniques for more general task models such as the sporadic task model, the generalized multiframe task model, and the recurring real-time task model. The thesis of this dissertation is: Optimal online multiprocessor real-time scheduling algorithms for sporadic and more general task systems are impossible; however, efficient, online scheduling algorithms and associated feasibility and schedulability tests, with provably bounded deviation from any optimal test, exist. To support our thesis, this dissertation develops feasibility and schedulability tests for various multiprocessor scheduling paradigms. We consider three classes of multiprocessor scheduling based on whether a real-time job may migrate between processors: full-migration, restricted-migration, and partitioned. For all general task systems, we obtain feasibility tests for arbitrary real-time instances under the full-and restricted-migration paradigms. Despite the existence of tests for feasibility, we show that optimal online scheduling of sporadic and more general systems is impossible. Therefore, we focus on scheduling algorithms that have constant-factor approximation ratios in terms of an analysis technique known as resource augmentation. We develop schedulability tests for scheduling algorithms, earliest-deadline-first (edf) and deadline-monotonic (dm), under full-migration and partitioned scheduling paradigms. Feasibility and schedulability tests presented in this dissertation use the workload metrics of demand-based load and maximum job density and have provably bounded deviation from optimal in terms of resource augmentation. We show the demand-based load and maximum job density metrics may be exactly computed in pseudo-polynomial time for general task systems and approximated in polynomial time for sporadic task systems