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.

Optimal virtual cluster-based multiprocessor scheduling

Scheduling of constrained deadline sporadic task systems on multiprocessor platforms is an area which has received much attention in the recent past. It is widely believed that finding an optimal scheduler is hard, and therefore most studies have focused on developing algorithms with good processor utilization bounds. These algorithms can be broadly classified into two categories: partitioned scheduling in which tasks are statically assigned to individual processors, and global scheduling in which each task is allowed to execute on any processor in the platform. In this paper we consider a third, more general, approach called cluster-based scheduling. In this approach each task is statically assigned to a processor cluster, tasks in each cluster are globally scheduled among themselves, and clusters in turn are scheduled on the multiprocessor platform. We develop techniques to support such cluster-based scheduling algorithms, and also consider properties that minimize total processor utilization of individual clusters. In the last part of this paper, we develop new virtual cluster-based scheduling algorithms. For implicit deadline sporadic task systems, we develop an optimal scheduling algorithm that is neither Pfair nor ERfair. We also show that the processor utilization bound of us-edf{m/(2m−1)} can be improved by using virtual clustering. Since neither partitioned nor global strategies dominate over the other, cluster-based scheduling is a natural direction for research towards achieving improved processor utilization bounds.

Provably good multiprocessor scheduling with resource sharing

We present a 12(1 + 3R/(4m)) competitive algorithm for scheduling implicit-deadline sporadic tasks on a platform comprising m processors, where a task may request one of R shared resources.

Multiprocessor real-time scheduling considering concurrency and urgency

It has been widely studied how to schedule real-time tasks on multiprocessor platforms. Several studies find optimal scheduling policies for implicit deadline task systems, but it is hard to understand how each policy utilizes the two important aspects of scheduling real-time tasks on multiprocessors:inter-job concurrency and job urgency. In this paper, we introduce a new scheduling policy that considers these two properties. We prove that the policy is optimal for the special case when the execution time of all tasks are equally one and deadlines are implicit, and observe that the policy is a new concept in that it is not an instance of Pfair or ERfair. It remains open to find a schedulability condition for general task systems under our scheduling policy.

Notional processors: an approach for multiprocessor scheduling

Consider the problem of designing an algorithm with a high utilisation bound for scheduling sporadic tasks with implicit deadlines on identical processors. A task is characterised by its minimum interarrival time and its execution time. Task preemption and migration is permitted. Still, low preemption and migration counts are desirable. We formulate an algorithm with a utilisation bound no less than 66.¯6%, characterised by worst-case preemption counts comparing favorably against the state-of-the-art.

A two-competitive approximate schedulability analysis of CAN

Consider the problem of deciding whether a set of n sporadic message streams meet deadlines on a Controller Area Network (CAN) bus for a specified priority assignment. It is assumed that message streams have implicit deadlines and no release jitter. An algorithm to solve this problem is well known but unfortunately it time complexity is non-polynomial. We present an algorithm with polynomial time-complexity for computing an upper bound on the response times. Clearly, if the upper bound on the response time does not exceed the deadline then all deadlines are met. The pessimism of our approach is proven: if the upper bound of the response time exceeds the deadline then the response time exceeds the deadline as well for a CAN network with half the speed.

Uniprocessor EDF scheduling with mode change

Consider the problem of scheduling sporadically-arriving tasks with implicit deadlines using Earliest-Deadline-First (EDF) on a single processor. The system may undergo changes in its operational modes and therefore the characteristics of the task set may change at run-time. We consider a well-established previously published mode-change protocol and we show that if every mode utilizes at most 50% of the processing capacity then all deadlines are met. We also show that there exists a task set that misses a deadline although the utilization exceeds 50% by just an arbitrarily small amount. Finally, we present, for a relevant special case, an exact schedulability test for EDF with mode change.

The utilization bound of uniprocessor preemptive slack-monotonic scheduling is 50%

Consider the problem of scheduling a set of sporadically arriving implicit-deadline tasks to meet deadlines on a uniprocessor. Static-priority scheduling is considered using the slack-monotonic priority-assignment scheme. We prove that its utilization bound is 50%.

Global static-priority preemptive multiprocessor scheduling with utilization bound 38%

Consider the problem of scheduling real-time tasks on a multiprocessor with the goal of meeting deadlines. Tasks arrive sporadically and have implicit deadlines, that is, the deadline of a task is equal to its minimum inter-arrival time. Consider this problem to be solved with global static-priority scheduling. We present a priority-assignment scheme with the property that if at most 38% of the processing capacity is requested then all deadlines are met.

Implementation of the i-GAME mechanism in IEEE 802.15.4 WPANs

This technical report describes the implementation details of the Implicit GTS Allocation Mechanism (i-GAME), for the IEEE 802.15.4 protocol. The i-GAME was implemented in nesC/TinyOS for the CrossBow MICAz mote, over our own implementation of the IEEE 802.15.4 protocol stack. This document provides the implementation details, including a description of the i-GAME software interfaces.

On the robustness of the slotine-Li and the FPT/SVD-based adaptive controllers

A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes.

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.

Task Assignment Algorithms for Heterogeneous Multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising a constant number (denoted by t) of distinct types of processors—such a platform is referred to as a t-type platform. We present two algorithms, LPGIM and LPGNM, each providing the following guarantee. For a given t-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet their deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then: (i) LPGIM succeeds in finding such an assignment where the same restriction on task migration applies (intra-migrative) but given a platform in which only one processor of each type is 1 + α × t-1/t times faster and (ii) LPGNM succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which every processor is 1 + α times faster. The parameter α is a property of the task set; it is the maximum of all the task utilizations that are no greater than one. To the best of our knowledge, for t-type heterogeneous multiprocessors: (i) for the problem of intra-migrative task assignment, no previous algorithm exists with a proven bound and hence our algorithm, LPGIM, is the first of its kind and (ii) for the problem of non-migrative task assignment, our algorithm, LPGNM, has superior performance compared to state-of-the-art.