Efficient algorithms for schedulability analysis and priority assignment for fixed-priority preemptive scheduling with offsets

This paper addresses the problem of priority assignment in multiprocessor real-time systems using global fixed task-priority pre-emptive scheduling. In this paper, we prove that Audsley’s Optimal Priority Assignment (OPA) algorithm, originally devised for uniprocessor scheduling, is applicable to the multiprocessor case, provided that three conditions hold with respect to the schedulability tests used. Our empirical investigations show that the combination of optimal priority assignment policy and a simple compatible schedulability test is highly effective, in terms of the number of tasksets deemed to be schedulable. We also examine the performance of heuristic priority assignment policies such as Deadline Monotonic, and an extension of the TkC priority assignment policy called DkC that can be used with any schedulability test. Here we find that Deadline Monotonic priority assignment has relatively poor performance in the multiprocessor case, while DkC priority assignment is highly effective.

Fixed-priority preemption-threshold scheduling (FPTS) is a generalization of fixed-priority preemptive scheduling (FPPS) and fixed-priority non-preemptive scheduling (FPNS). Since FPPS and FPNS are incomparable in terms of potential schedulability, FPTS has the advantage that it can schedule any task set schedulable by FPPS or FPNS and some that are not schedulable by either. FPTS is based on the idea that each task is assigned a priority and a preemption threshold. While tasks are admitted into the system according to their priorities, they can only be preempted by tasks that have priority higher than the preemption threshold. This paper presents a new optimal priority and preemption threshold assignment (OPTA) algorithm for FPTS which in general outperforms the existing algorithms in terms of the size of the explored state-space and the total number of worst case response time calculations performed. The algorithm is based on back-tracking, i.e. it traverses the space of potential priorities and preemption thresholds, while pruning infeasible paths, and returns the first assignment deemed schedulable. We present the evaluation results where we compare the complexity of the new algorithm with the existing one. We show that the new algorithm significantly reduces the time needed to find a solution. Through a comparative evaluation, we show the improvements that can be achieved in terms of schedulability ratio by our OPTA compared to a deadline monotonic priority assignment.

Audsley's optimal priority assignment (OPA) algorithm can be applied to multiprocessor scheduling provided that three conditions hold with respect to the schedulability tests used. In this short paper, we prove that no exact test for global fixed priority pre-emptive scheduling of sporadic tasks can be compatible with Audsley's algorithm, and hence the OPA algorithm cannot be used to obtain an optimal priority assignment for such systems.

Task partitioning and priority assignment for distributed hard real-time systems

The number of bus transactions in System-on-Chip (SoC) grows significantly in recent years. Because of different timing constraints for different applications, how to find a proper priority assignment for processing elements (PEs) of SoC becomes very challenging. In this paper, we first show that the priority assignment problem with one unique priority for each PE is NP-complete. When each bus transaction can have one unique priority, we propose an optimal priority assignment algorithm for a given workload. We then propose a priority assignment strategy based on Simulated Annealing (SA) for PEs, where bus arbitration is done in a priority-driven fashion. The objective is to minimize the number of priorities needed for each PE and to satisfy the timing constraints of applications. The experimental results show some encouraging results in priority assignment.

We address the problem of optimally scheduling automated vehicles crossing an intelligent intersection by assigning vehicles with priorities and desired speed. An idealized intersection traffic model is established for the development and verification of the required algorithms. We formulate the intersection scheduling problem as a mixed integer programming (or MIP) problem which co-designs the priority and traveling speed for each vehicle. The co-design aims to minimize the vehicle waiting time at the intersection area, under a set of safety constraints. We derived a contention-resolving model predictive control (or MPC) algorithm to dynamically assign priorities and compute the vehicles’ traveling speeds. A branch cost formulation is proposed for the decision tree constructed by contention-resolving MPC based on time instants when collisions might occur among vehicles. Based on the priority assignments, a decentralized control law is designed to control each vehicle to travel with an optimal speed given a specific priority assignment. The optimal priority assignment can be determined by searching the lowest cost path in the decision tree. The solution computed by contention-resolving MPC is proved to be optimal given the condition of immediate access (or CIA) required in real-time scheduling. The effectiveness of the proposed method is verified through simulation and compared with the first-come-first-serve (or FCFS) and highest-speed-first (or HSF) scheduling strategies.

For real-time applications, task scheduling is a problem of paramount importance. Several scheduling algorithms were proposed in the literature, starting from static scheduling or cyclic executives which provide very deterministic yet inflexible behaviour, to the so called best-effort scheduling, which facilitates maximum run-time flexibility but allows only probabilistic predictions of run-time performance presenting a non-predictable and nondeterministic solution. Between these two extremes lies fixed priority scheduling algorithms, such as Rate Monotonic, that is not so efficient for real-time purposes but exhibits a predictable approach because scheduling is doing offline and guarantees regarding process deadlines could be obtained using appropriate analysis methods. This paper investigates the use of Rate Monotonic algorithm by making adjustments in order to make it more suitable for real-time applications. The factors that motivate the interest for fixed priority scheduling algorithms such Rate Monotonic when doing with real-time systems lies in its associated analysis that could be oriented in two directions: schedulability analysis and analysis of process interactions. The analyzing process is carried out using a previously implemented framework that allows modelling, simulation and schedulability analysis for a set of real-time system tasks, and some of the results obtained are presented.

Memory is a limited resource in cost-sensitive, resource-constrained embedded applications. Preemption Threshold Scheduling (PTS) is a well-known technique for reducing the system stack size requirement. We consider Global Fixed Priority Scheduling with Preemption Threshold (gFPPT), as integration of PTS with global Fixed-Priority scheduling on a homogeneous multiprocessor platform, and formulate the optimization problem of minimizing the system stack size requirement while guaranteeing schedulability. We present schedulability analysis, optimization algorithms for priority and preemption threshold assignment, and an ILP formulation for computing system stack size requirement. Performance evaluation shows that the system stack size requirement can be reduced significantly with gFPPT compared to preemptive scheduling.

In the design optimization of real-time systems scheduled with fixed priority, schedulability analysis is used to define the feasibility region within which tasks meet their deadlines, so that optimization algorithms can find the best solution within the region. However, the complexity of schedulability analysis techniques often makes it difficult to leverage existing optimization frameworks and scale to large designs. In this paper, we propose the concept of unschedulability core, a compact representation of the schedulability conditions, and develop efficient algorithms for its calculation. We present a new optimization framework that leverages such a concept. We show that this concept is applicable to a range of optimization problems, for example, when the decision variables include the task priority assignment and the selection of mechanisms protecting shared buffers. Experimental results on two case studies demonstrate that the new optimization procedure maintains the optimality of the solutions, but is a few orders of magnitude faster than other exact algorithms (branch-and-bound, integer linear programming).

ECTM: A network-on-chip communication model to combine task and message schedulability analysis

To enable the intelligent management of Smart City and improve overall social welfare, it is desirable for the status of infrastructures detected and reported by intelligent devices embedded in them to be forwarded to the data centers. Using “SCmules” such as taxis, to opportunistically communicate with intelligent devices and collect data from the sparse networks formed by them in the process of moving is an economical and effective way to achieve this goal. In this paper, the social welfare data collection paradigm SWDCP-SCmules data collection framework is proposed to collect data generated by intelligent devices and forward them to data centers, in which “SCmules” are data transmitters picking up data from nearby intelligent devices and then store-carry-forwarding them to nearby data centers via short-range wireless connections in the process of moving. Because of the storage limitations, “SCmules” need to weigh the value of data and select some less valuable data to discard when necessary. To quantify the value of data and find a well-performed selection strategy, the concept of priority is introduced to the SWDCP-SCmules scheme, and then, the simulated annealing for priority assignment SA-PA algorithm is proposed to guide the priority assignment. The SA-PA algorithm is a universal algorithm that can improve the performance of SWDCP-SCmules scheme by finding better priority assignment with respect to various optimization targets, such as maximizing collection rate or minimizing redundancy rate, in which priority assignment problem is converted into an optimization problem and simulated annealing is used to optimize the priority assignment. From the perspective of machine learning, the process of optimization is equal to automatically learn social-aware patterns from past GPS trajectory data. Experiments based on real GPS trajectory data of taxis in Beijing are conducted to show the effectiveness and efficiency of SWDCP-SCmules scheme and SA-PA algorithm.

In this paper, a task scheduling problem for a cloud computing environment is formulated by using the M/M/n queuing model. A priority assignment algorithm is designed to employ a new data structure named the waiting time matrix to assign priority to individual tasks upon arrival. In addition to this, the waiting queue implements a unique concept based on the principle of the Fibonacci heap for extracting the task with the highest priority. This work introduces a parallel algorithm for task scheduling in which the priority assignment to task and building of heap is executed in parallel with respect to the non-preemptive and preemptive nature of tasks. The proposed work is illustrated in a step-by-step manner with an appropriate number of tasks. The performance of the proposed model is compared in terms of overall waiting time and CPU time against some existing techniques like BATS, IDEA, and BATS+BAR to determine the efficacy of our proposed algorithms. Additionally, three distinct scenarios have been considered to demonstrate the competency of the task scheduling method in handling tasks with different priorities. Furthermore, the task scheduling algorithm is also applied in a dynamic cloud computing environment.

Pull versus push strategy for automated guided vehicle load movement in a batch manufacturing system

Real-time systems usually consist of a set of interdependent periodic and sporadic threads. Scheduling theory has modeled thus far this interdependency with semaphores with priority protocols (inheritance/ceiling). However, RTOS services are far more comprehensive, including message queues, sleeps, counting semaphores, etc. This letter presents a novel scheduling theory based on response time analysis (RTA) to determine the schedulability of periodic or sporadic threads that can be blocked/suspended for a specified maximum amount of time under a fixed-priority pre-emptive scheduler.

End-to-end flows, which have a set of chainlike subtasks, are widely used in distributed real-time systems. For instance, multimedia and automative applications require that subtasks finish executing on a chain of processors before their end-to-end deadlines. The scheduling of such chained subtasks decides the schedulability of a distributed realtime system. Since the subtask priority assignment problem is NP-hard in general, most heuristics are presented to schedule end-to-end flows in two separate steps. The first step calculates intermediate relative deadlines for frames, and the second step makes scheduling decisions under EDF scheduling. Because the quality of the priority assignment of subtasks will directly affect the schedulability of the distributed systems, the two separate steps may cause pessimism in schedulability analysis. To reduce potential pessimism, we combine the two steps in our novel dGMF-PA (distributed generalized multiframe tasks with parameter adaption) model. We present an algorithm based on mixed-integer linear programming for optimally selecting frame relative deadlines in the dGMF-PA model. An approximation algorithm is also proposed to reduce computational running time. Our approximation algorithm has a tunable speed-up factor of 1 + ϵ where ϵ can be arbitrarily small, with respect to the exact schedulability test of dGMF-PA tasks under EDF scheduling. Extensive experiments have shown that our approximation algorithm (which is a sufficient schedulability test) can schedule at most 44 % more than HOSPA, an existing state-of-the-art algorithm.