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.

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.

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.

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.

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.

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.

Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

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

Consider the problem of scheduling a set of implicitdeadline sporadic tasks on a heterogeneous multiprocessor so as to meet all deadlines. Tasks cannot migrate and the platform is restricted in that each processor is either of type-1 or type-2 (with each task characterized by a different speed of execution upon each type of processor). We present an algorithm for this problem with a timecomplexity of O(n·m), where n is the number of tasks and m is the number of processors. It offers the guarantee that if a task set can be scheduled by any non-migrative algorithm to meet deadlines then our algorithm meets deadlines as well if given processors twice as fast. Although this result is proven for only a restricted heterogeneous multiprocessor, we consider it significant for being the first realtime scheduling algorithm to use a low-complexity binpacking approach to schedule tasks on a heterogeneous multiprocessor with provably good performance.

A pseudo-medium-wide 8-competitive interface for two-level compositional real-time scheduling of constrained- deadline sporadic tasks on a uniprocessor

Compositional real-time scheduling clearly requires that ”normal” real-time scheduling challenges are addressed but challenges intrinsic to compositionality must be addressed as well, in particular: (i) how should interfaces be described? and (ii) how should numerical values be assigned to parameters constituting the interfaces? The real-time systems community has traditionally used narrow interfaces for describing a component (for example, a utilization/bandwidthlike metric and the distribution of this bandwidth in time). In this paper, we introduce the concept of competitive ratio of an interface and show that typical narrow interfaces cause poor performance for scheduling constrained-deadline sporadic tasks (competitive ratio is infinite). Therefore, we explore more expressive interfaces; in particular a class called medium-wide interfaces. For this class, we propose an interface type and show how the parameters of the interface should be selected. We also prove that this interface is 8-competitive.

Two protocols without periodicity for the global and preemptive scheduling problem of multi-mode real-time systems upon multiprocessor Platforms

We consider the problem of scheduling a multi-mode real-time system upon identical multiprocessor platforms. Since it is a multi-mode system, the system can change from one mode to another such that the current task set is replaced with a new task set. Ensuring that deadlines are met requires not only that a schedulability test is performed on tasks in each mode but also that (i) a protocol for transitioning from one mode to another is specified and (ii) a schedulability test for each transition is performed. We propose two protocols which ensure that all the expected requirements are met during every transition between every pair of operating modes of the system. Moreover, we prove the correctness of our proposed algorithms by extending the theory about the makespan determination problem.

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.

Coordinated transportation of a large object by a team of two robots

In this paper dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for a team of two robots that must transport a large object and simultaneously avoid collisions with obstacles (either static or dynamic). This work extends the previous work with two robots (see [1] and [5]). However here we demonstrate that it’s possible to simplify the architecture presented in [1] and [5] and reach an equally stable global behavior. The robots have no prior knowledge of the environment. The dynamics of behavior is defined over a state space of behavior variables, heading direction and path velocity. Task constrains are modeled as attractors (i.e. asymptotic stable states) of a behavioral dynamics. For each robot, these attractors are combined into a vector field that governs the behavior. By design the parameters are tuned so that the behavioral variables are always very close to the corresponding attractors. Thus the behavior of each robot is controlled by a time series of asymptotic stable states. Computer simulations support the validity of the dynamical model architecture.

Using attractor dynamics to generate decentralized motion control of two mobile robots transporting a long object in coordination

Dynamical systems theory is used here as a theoretical language and tool to design a distributed control architecture for a team of two mobile robots that must transport a long object and simultaneously avoid obstacles. In this approach the level of modeling is at the level of behaviors. A “dynamics” of behavior is defined over a state space of behavioral variables (heading direction and path velocity). The environment is also modeled in these terms by representing task constraints as attractors (i.e. asymptotically stable states) or reppelers (i.e. unstable states) of behavioral dynamics. For each robot attractors and repellers are combined into a vector field that governs the behavior. The resulting dynamical systems that generate the behavior of the robots may be nonlinear. By design the systems are tuned so that the behavioral variables are always very close to one attractor. Thus the behavior of each robot is controled by a time series of asymptotically stable states. Computer simulations support the validity of our dynamic model architectures.

Direct search optimization application programming interface with remote access

Search Optimization methods are needed to solve optimization problems where the objective function and/or constraints functions might be non differentiable, non convex or might not be possible to determine its analytical expressions either due to its complexity or its cost (monetary, computational, time,...). Many optimization problems in engineering and other fields have these characteristics, because functions values can result from experimental or simulation processes, can be modelled by functions with complex expressions or by noise functions and it is impossible or very difficult to calculate their derivatives. Direct Search Optimization methods only use function values and do not need any derivatives or approximations of them. In this work we present a Java API that including several methods and algorithms, that do not use derivatives, to solve constrained and unconstrained optimization problems. Traditional API access, by installing it on the developer and/or user computer, and remote API access to it, using Web Services, are also presented. Remote access to the API has the advantage of always allow the access to the latest version of the API. For users that simply want to have a tool to solve Nonlinear Optimization Problems and do not want to integrate these methods in applications, also two applications were developed. One is a standalone Java application and the other a Web-based application, both using the developed API.