Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.

Pre-run-time schedulability analysis of P-NET fieldbus networks

P-NET is a fieldbus industrial communication standard, which uses a Virtual Token Passing MAC mechanism. In this paper we establish pre-run-time schedulability conditions for supporting real-time traffic with P-NET. Essentially we provide formulae to evaluate the minimum message deadline, ensuring the transmission of real-time messages within a maximum time bound

Extending fixed task-priority schedulability by interference limitation

While the earliest deadline first algorithm is known to be optimal as a uniprocessor scheduling policy, the implementation comes at a cost in terms of complexity. Fixed taskpriority algorithms on the other hand have lower complexity but higher likelihood of task sets being declared unschedulable, when compared to earliest deadline first (EDF). Various attempts have been undertaken to increase the chances of proving a task set schedulable with similar low complexity. In some cases, this was achieved by modifying applications to limit preemptions, at the cost of flexibility. In this work, we explore several variants of a concept to limit interference by locking down the ready queue at certain instances. The aim is to increase the prospects of schedulability of a given task system, without compromising on complexity or flexibility, when compared to the regular fixed task-priority algorithm. As a final contribution, a new preemption threshold assignment algorithm is provided which is less complex and more straightforward than the previous method available in the literature.

Slotted wiDom: schedulability analysis and its experimental validation

WiDom is a wireless prioritized medium access control protocol which offers a very large number of priority levels. Hence, it brings the potential to employ non-preemptive static-priority scheduling and schedulability analysis for a wireless channel assuming that the overhead of WiDom is modeled properly. One schedulability analysis for WiDom has already been proposed but recent research has created a new version of WiDom (we call it: Slotted WiDom) with lower overhead and for this version of WiDom no schedulability analysis exists. In this paper we propose a new schedulability analysis for slotted WiDom and extend it to work also for message streams with release jitter. We have performed experiments with an implementation of slotted WiDom on a real-world platform (MicaZ). We find that for each message stream, the maximum observed response time never exceeds the calculated response time and hence this corroborates our belief that our new scheduling theory is applicable in practice.

Practical aspects of slot-based task- splitting dispatching in its schedulability analysis

Consider the problem of scheduling a set of sporadic tasks on a multiprocessor system to meet deadlines using a tasksplitting scheduling algorithm. Task-splitting (also called semipartitioning) scheduling algorithms assign most tasks to just one processor but a few tasks are assigned to two or more processors, and they are dispatched in a way that ensures that a task never executes on two or more processors simultaneously. A certain type of task-splitting algorithms, called slot-based task-splitting, is of particular interest because of its ability to schedule tasks at high processor utilizations. We present a new schedulability analysis for slot-based task-splitting scheduling algorithms that takes the overhead into account and also a new task assignment algorithm.

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.

New schedulability analysis for WiDom

WiDom is a wireless prioritized medium access control (MAC) protocol which offers a very large number of priority levels. Hence, it brings the potential for employing non-preemptive static-priority scheduling and schedulability analysis for a wireless channel assuming that the overhead of WiDom is modeled properly. One schedulability analysis for WiDom has already been proposed but recent research has created a new version of WiDom with lower overhead (we call it: WiDom with a master node) and for this version of WiDom no schedulability analysis exists. Also, common to the previously proposed schedulability analyses for WiDom is that they cannot analyze message streams with release jitter. Therefore, in this paper we propose a new schedulability analysis for WiDom (with a master node). We also extend the WiDom analyses (with and without master node) to work also for message streams with release jitter.

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.

Linearizability and schedulability

Consider the problem of scheduling a set of tasks on a single processor such that deadlines are met. Assume that tasks may share data and that linearizability, the most common correctness condition for data sharing, must be satisfied. We find that linearizability can severely penalize schedulability. We identify, however, two special cases where linearizability causes no or not too large penalty on schedulability.

Schedulability analysis of generalized multiframe traffic on multihop-networks comprising software-implemented ethernet switches

Consider a multihop network comprising Ethernet switches. The traffic is described with flows and each flow is characterized by its source node, its destination node, its route and parameters in the generalized multiframe model. Output queues on Ethernet switches are scheduled by static-priority scheduling and tasks executing on the processor in an Ethernet switch are scheduled by stride scheduling. We present schedulability analysis for this setting.

Unified overhead-aware schedulability analysis for slot-based task-splitting

Hard real- time multiprocessor scheduling has seen, in recent years, the flourishing of semi-partitioned scheduling algorithms. This category of scheduling schemes combines elements of partitioned and global scheduling for the purposes of achieving efficient utilization of the system’s processing resources with strong schedulability guarantees and with low dispatching overheads. The sub-class of slot-based “task-splitting” scheduling algorithms, in particular, offers very good trade-offs between schedulability guarantees (in the form of high utilization bounds) and the number of preemptions/migrations involved. However, so far there did not exist unified scheduling theory for such algorithms; each one was formulated in its own accompanying analysis. This article changes this fragmented landscape by formulating a more unified schedulability theory covering the two state-of-the-art slot-based semi-partitioned algorithms, S-EKG and NPS-F (both fixed job-priority based). This new theory is based on exact schedulability tests, thus also overcoming many sources of pessimism in existing analysis. In turn, since schedulability testing guides the task assignment under the schemes in consideration, we also formulate an improved task assignment procedure. As the other main contribution of this article, and as a response to the fact that many unrealistic assumptions, present in the original theory, tend to undermine the theoretical potential of such scheduling schemes, we identified and modelled into the new analysis all overheads incurred by the algorithms in consideration. The outcome is a new overhead-aware schedulability analysis that permits increased efficiency and reliability. The merits of this new theory are evaluated by an extensive set of experiments.

Efficient schedulability tests for real-time embedded systems with urgent routines

Task scheduling is one of the key mechanisms to ensure timeliness in embedded real-time systems. Such systems have often the need to execute not only application tasks but also some urgent routines (e.g. error-detection actions, consistency checkers, interrupt handlers) with minimum latency. Although fixed-priority schedulers such as Rate-Monotonic (RM) are in line with this need, they usually make a low processor utilization available to the system. Moreover, this availability usually decreases with the number of considered tasks. If dynamic-priority schedulers such as Earliest Deadline First (EDF) are applied instead, high system utilization can be guaranteed but the minimum latency for executing urgent routines may not be ensured. In this paper we describe a scheduling model according to which urgent routines are executed at the highest priority level and all other system tasks are scheduled by EDF. We show that the guaranteed processor utilization for the assumed scheduling model is at least as high as the one provided by RM for two tasks, namely 2(2√−1). Seven polynomial time tests for checking the system timeliness are derived and proved correct. The proposed tests are compared against each other and to an exact but exponential running time test.

Logic-based schedulability analysis for compositional hard real-time embedded systems

Over the past decades several approaches for schedulability analysis have been proposed for both uni-processor and multi-processor real-time systems. Although different techniques are employed, very little has been put forward in using formal specifications, with the consequent possibility for mis-interpretations or ambiguities in the problem statement. Using a logic based approach to schedulability analysis in the design of hard real-time systems eases the synthesis of correct-by-construction procedures for both static and dynamic verification processes. In this paper we propose a novel approach to schedulability analysis based on a timed temporal logic with time durations. Our approach subsumes classical methods for uni-processor scheduling analysis over compositional resource models by providing the developer with counter-examples, and by ruling out schedules that cause unsafe violations on the system. We also provide an example showing the effectiveness of our proposal.

Overhead-aware schedulability evaluation of semi-partitioned real-time schedulers

Presented at IEEE 21st International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA 2015). 19 to 21, Aug, 2015.

An Exact Schedulability Test for Global FP Using State Space Pruning

Presented at 23rd International Conference on Real-Time Networks and Systems (RTNS 2015). 4 to 6, Nov, 2015, Main Track. Lille, France.