Preemptive Priority Scheduling Research Articles

Oris: a tool for modeling, verification and evaluation of real-time systems

Oris is a tool for qualitative verification and quantitative evaluation of reactive timed systems, which supports modeling and analysis of various classes of timed extensions of Petri Nets. As most characterizing features, Oris implements symbolic state space analysis of preemptive Time Petri Nets, which enable schedulability analysis of real-time systems running under priority preemptive scheduling; and stochastic Time Petri Nets, which enable an integrated approach to qualitative verification and quantitative evaluation. In this paper, we present the current version of the tool and we illustrate its application to two different case studies in the areas of qualitative verification and quantitative evaluation, respectively.

Exact quantification of the sub-optimality of uniprocessor fixed priority pre-emptive scheduling

This paper examines the relative effectiveness of fixed priority pre-emptive scheduling in a uniprocessor system, compared to an optimal algorithm such as Earliest Deadline First (EDF).The quantitative metric used in this comparison is the processor speedup factor, equivalent to the factor by which processor speed needs to increase to ensure that any taskset that is schedulable according to an optimal scheduling algorithm can be scheduled using fixed priority pre-emptive scheduling, assuming an optimal priority assignment policy.For constrained-deadline tasksets where all task deadlines are less than or equal to their periods, the maximum value for the processor speedup factor is shown to be 1/Ω≈1.76322 (where Ω is the mathematical constant defined by the transcendental equation ln (1/Ω)=Ω, hence, Ω≈0.567143). Further, for implicit-deadline tasksets where all task deadlines are equal to their periods, the maximum value for the processor speedup factor is shown to be 1/ln (2)≈1.44270. The derivation of this latter result provides an alternative proof of the well-known Liu and Layland result.

Solving a real-time allocation problem with constraint programming

In this paper, we present an original approach (CPRTA for “Constraint Programming for solving Real-Time Allocation”) based on constraint programming to solve a static allocation problem of hard real-time tasks. This problem consists in assigning periodic tasks to distributed processors in the context of fixed priority preemptive scheduling. CPRTA is built on dynamic constraint programming together with a learning method to find a feasible processor allocation under constraints. Two efficient new approaches are proposed and validated with experimental results. Moreover, CPRTA exhibits very interesting properties. It is complete (if a problem has no solution, the algorithm is able to prove it); it is non-parametric (it does not require specific tuning) thus allowing a large diversity of models to be easily considered. Finally, thanks to its capacity to explain failures, it offers attractive perspectives for guiding the architectural design process.

Timing analysis of compound scheduling policies: application to posix1003.1b

The analysis of fixed priority preemptive scheduling has been extended in various ways to improve its usefulness for the design of real-time systems. In this paper, we define the layered preemptive priority scheduling policy which generalizes fixed preemptive priorities by combination with other policies in a layered structure. In particular, the combination with the Round Robin scheduling policy is studied. Its compliance with Posix 1003.1b requirements is shown and its timing analysis is provided. For this purpose and as a basis for the analysis of other policies, the concept of majorizing work arrival function, is introduced to synthesize essential ideas used in existing analysis of the fixed preemptive priority policy.If critical resources are protected by semaphores, the Priority Ceiling Protocol (PCP) can be used under fixed preemptive priorities to control resulting priority inversions. An extension of the PCP is proposed for Round Robin, to allow a global control of priority inversions under the layered priority policy and to prevent deadlocks. The initial timing analysis is extended to account for the effects of the protocol. The results are illustrated by a small test case.

Utilization Bounds for N-Processor Rate MonotoneScheduling with Static Processor Assignment

We consider the schedulability of a set of independent periodic tasks under fixed priority preemptive scheduling on homogeneous multiprocessor systems. Assuming there is no task migration between processors and each processor schedules tasks preemptively according to fixed priorities assigned by the Rate Monotonic policy, the scheduling problem reduces to assigning the set of tasks to disjoint processors in such a way that the Monotonic policy, the scheduling problem reduces to assigning the set of tasks to disjoint processors in such a way that the schedulability of the tasks on each processor can be guaranteed. In this paper we show that the worst case achievable utilization for such systems is between n(2^{1/2}-1) and (n+1)/(1+2^{1/(n+1)}), where n stands for the number of processors. The lower bound represents 41 percent of the total system capacity and the upper bound represents 50 to 66 percent depending on n. Practicality of the lower bound is demonstrated by proving it can be achieved using a First Fit scheduling algorithm.

Fixed priority pre-emptive scheduling: An historical perspective

From its roots in job-shop scheduling, research into fixed priority pre-emptive scheduling theory has progressed from the artificial constraints and simplistic assumptions used in early work to a sufficient level of maturity that it is being increasingly used in the implementation of real-time systems. It is therefore appropriate that within this special issue we provide an historical perspective on the development of fixed priority pre-emptive scheduling.

Integrating Best Effort and Fixed Priority Scheduling

Adaptive and dynamic behaviour is seen as one of the key characteristics of next generation hard real-time systems. Whilst fixed priority pre-emptive scheduling is becoming a de facto standard in real-time system implementation, it remains inflexible in its purest form. One approach to countering this criticism is to allow optional components, not guaranteed offline, to be executed at nm-time. Optional components may be guaranteed a minimum set of resources at nm-time, with competing resource requests scheduled according to the best-effort approach. This allows increased dynamic behaviour and improves the utility of the system. In this paper, we discuss this integration of fixed priority and best-effort scheduling.

Integrating best effort and fixed priority scheduling

Adaptive and dynamic behaviour is seen as one of the key characteristics of next generation hard real-time systems. Whilst fixed priority pre-emptive scheduling is becoming a de facto standard in real-time system implementation, it remains inflexible in its purest form. One approach to countering this criticism is to allow optional components, not guaranteed offline, to be executed at run-time. Optional components may be guaranteed a minimum set of resources at run-time, with competing resource requests scheduled according to the best-effort approach. This allows increased dynamic behaviour and improves the utility of the system. In this paper, we discuss this integration of fixed priority and best-effort scheduling.

Scheduling algorithms and operating systems support for real-time systems

This paper summarizes the state of the real-time field in the areas of scheduling and operating system kernels. Given the vast amount of work that has been done by both the operations research and computer science communities in the scheduling area, we discuss four paradigms underlying the scheduling approaches and present several exemplars of each. The four paradigms are: static table-driven scheduling, static priority preemptive scheduling, dynamic planning-based scheduling, and dynamic best effort scheduling. In the operating system context, we argue that most of the proprietary commercial kernels as well as real-time extensions to time-sharing operating system kernels do not fit the needs of predictable realtime systems. We discuss several research kernels that are currently being built to explicitly meet the needs of real-time applications.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Applying new scheduling theory to static priority pre-emptive scheduling

The paper presents exact schedulability analyses for real-time systems scheduled at runtime with a static priority pre-emptive dispatcher. The tasks to be scheduled are allowed to experience internal blocking (from other tasks with which they share resources) and (with certain restrictions) to release jitter, such as waiting for a message to arrive. The analysis presented is more general than that previously published and subsumes, for example, techniques based on the Rate Monotonic approach. In addition to presenting the relevant theory, an existing avionics case study is described and analysed. The predictions that follow from this analysis are seen to be in close agreement with the behaviour exhibited during simulation studies.

Stack-based scheduling of realtime processes

The Priority Ceiling Protocol (PCP) of Sha, Rajkumar and Lehoczky is a policy for locking binary semaphores that bounds priority inversion (i.e., the blocking of a job while a lower priority job executes), and thereby improves schedulability under fixed priority preemptive scheduling. We show how to extend the PCP to handle: multiunit resources, which subsume binary semaphores and reader-writer locks; dynamic priority schemes, such as earliest-deadline-first (EDF), that use static “preemption levels”; sharing of runtime stack space between jobs. These extensions can be applied independently, or together. The Stack Resource Policy (SRP) is a variant of the SRP that incorporates the three extensions mentioned above, plus the conservative assumption that each job may require the use of a shared stack. This avoids unnecessary context switches and allows the SRP to be implemented very simply using a stack. We prove a schedulability result for EDF scheduling with the SRP that is tighter than the one proved previously for EDF with a dynamic version of the PCP. The Minimal SRP (MSRP) is a slightly more complex variant of the SRP, which has similar properties, but imposes less blocking. The MSRP is optimal for stack sharing systems, in the sense that it is the least restrictive policy that strictly bounds priority inversion and prevents deadlock for rate monotone (RM) and earliest-deadline-first (EDF) scheduling.

Multiprocessor systems with preemptive priorities

A system with N processors and R job classes subject to a preemptive priority scheduling discipline is considered. Exact analysis is presented for the case R = 2, under Markovian assumptions. That analysis suggests a method for obtaining approximate solutions for arbitrary R. The implementation of the methods is discussed and numerical results for some special cases are given.

MERT - a multi-environment real-time operating system

MERT is a multi-environment real-time operating system for the Digital Equipment PDP-11/45 and 11/70 computers. It is a structured operating system built on top of a kernel which provides the basic services such as memory management, process scheduling, and trap handling needed to build various operating system environments. Real-time response to processes is achieved by means of preemptive priority scheduling. The file system structure is optimized for real-time response. Processes are built as modular entities with data structures that are independent of all other processes. Interprocess communication is achieved by means of messages, event flags, shared segments, and shared files. Process ports are used for communication between unrelated processes.