Process algebra, process scheduling, and mutual exclusion

In the case of multi-threading as found in contemporary programming languages, parallel processes are interleaved according to what is known as a process-scheduling policy in the field of operating systems. In a previous paper, we extend ACP with this form of interleaving. In the current paper, we do so with the variant of ACP known as ACP$_\epsilon$. The choice of ACP$_\epsilon$ stems from the need to cover more process-scheduling policies. We show that a process-scheduling policy supporting mutual exclusion of critical subprocesses is now covered.Comment: 15 pages, there is noticeable text overlap with earlier papers (arXiv:1912.10041, arXiv:1703.06822); 15 pages, Section 3.2 improved; 15 pages, minor improvements including replacement of reference at end Section 3.

Generating effective project scheduling heuristics by abstraction and reconstitution

A project scheduling problem consists of a finite set of jobs, each with fixed integer duration, requiring one or more resources such as personnel or equipment, and each subject to a set of precedence relations, which specify allowable job orderings, and a set of mutual exclusion relations, which specify jobs that cannot overlap. No job can be interrupted once started. The objective is to minimize project duration. This objective arises in nearly every large construction project--from software to hardware to buildings. Because such project scheduling problems are NP-hard, they are typically solved by branch-and-bound algorithms. In these algorithms, lower-bound duration estimates (admissible heuristics) are used to improve efficiency. One way to obtain an admissible heuristic is to remove (abstract) all resources and mutual exclusion constraints and then obtain the minimal project duration for the abstracted problem; this minimal duration is the admissible heuristic. Although such abstracted problems can be solved efficiently, they yield inaccurate admissible heuristics precisely because those constraints that are central to solving the original problem are abstracted. This paper describes a method to reconstitute the abstracted constraints back into the solution to the abstracted problem while maintaining efficiency, thereby generating better admissible heuristics. Our results suggest that reconstitution can make good admissible heuristics even better

The weakest failure detector for wait-free dining under eventual weak exclusion

Dining philosophers is a classic scheduling problem for local mutual exclusion on arbitrary conflict graphs. We establish necessary conditions to solve wait-free dining under eventual weak exclusion in message-passing systems with crash faults. Wait-free dining ensures that every correct hungry process eventually eats. Eventual weak exclusion permits finitely many scheduling mistakes, but eventually no live neighbors eat simultaneously; this exclusion criterion models scenarios where scheduling mistakes are recoverable or only affect per-formance. Previous work showed that the eventually perfect failure detector (3P) is sufficient to solve wait-free dining under eventual weak exclusion; we prove that 3P is also necessary, and thus 3P is the weakest oracle to solve this problem. Our reduction also establishes that any such din-ing solution can be made eventually fair. Finally, the reduc-tion itself may be of more general interest; when applied to wait-free perpetual weak exclusion, our reduction produces an alternative proof that the more powerful trusting oracle (T) is necessary (but not sufficient) to solve the problem o

Static Analysis of Run-Time Errors in Embedded Real-Time Parallel C Programs

We present a static analysis by Abstract Interpretation to check for run-time errors in parallel and multi-threaded C programs. Following our work on Astr\'ee, we focus on embedded critical programs without recursion nor dynamic memory allocation, but extend the analysis to a static set of threads communicating implicitly through a shared memory and explicitly using a finite set of mutual exclusion locks, and scheduled according to a real-time scheduling policy and fixed priorities. Our method is thread-modular. It is based on a slightly modified non-parallel analysis that, when analyzing a thread, applies and enriches an abstract set of thread interferences. An iterator then re-analyzes each thread in turn until interferences stabilize. We prove the soundness of our method with respect to the sequential consistency semantics, but also with respect to a reasonable weakly consistent memory semantics. We also show how to take into account mutual exclusion and thread priorities through a partitioning over an abstraction of the scheduler state. We present preliminary experimental results analyzing an industrial program with our prototype, Th\'es\'ee, and demonstrate the scalability of our approach

Optimal Multiprocessor Locking Protocols Under FIFO Scheduling

Real-time locking protocols are typically designed to reduce any priority-inversion blocking (pi-blocking) a task may incur while waiting to access a shared resource. For the multiprocessor case, a number of such protocols have been developed that ensure asymptotically optimal pi-blocking bounds under job-level fixed-priority scheduling. Unfortunately, no optimal multiprocessor real-time locking protocols are known that ensure tight pi-blocking bounds under any scheduler. This paper presents the first such protocols. Specifically, protocols are presented for mutual exclusion, reader-writer synchronization, and k-exclusion that are optimal under first-in-first-out (FIFO) scheduling when schedulability analysis treats suspension times as computation. Experiments are presented that demonstrate the effectiveness of these protocols

The weakest failure detector for wait-free dining under eventual weak exclusion

ABSTRACT Dining philosophers is a classic scheduling problem for local mutual exclusion on arbitrary conflict graphs. We establish necessary conditions to solve wait-free dining under eventual weak exclusion in message-passing systems with crash faults. Wait-free dining ensures that every correct hungry process eventually eats. Eventual weak exclusion permits finitely many scheduling mistakes, but eventually no live neighbors eat simultaneously; this exclusion criterion models scenarios where scheduling mistakes are recoverable or only affect performance. Previous work showed that the eventually perfect failure detector (3P) is sufficient to solve wait-free dining under eventual weak exclusion; we prove that 3P is also necessary, and thus 3P is the weakest oracle to solve this problem. Our reduction also establishes that any such dining solution can be made eventually fair. Finally, the reduction itself may be of more general interest; when applied to wait-free perpetual weak exclusion, our reduction produces an alternative proof that the more powerful trusting oracle (T ) is necessary (but not sufficient) to solve the problem of Fault-Tolerant Mutual Exclusion (FTME)

Design of a Mutual Exclusion and Deadlock Algorithm in PCBSD – FreeBSD

This paper shows the implementation of mutual exclusion in PCBSD-FreeBSD operating systems on SMPng environments, providing solutions to problems like investment priority, priority propagation, interlock, CPU downtime, deadlocks, between other. Mutex Control concept is introduced as a solution to these problems through the integration of the scheduling algorithm of multiple queues fed back and mutexes

Scheduling model for systems with complex alternative behaviour

In this paper we propose a flexible model for scheduling problems, which allows the modeling of systems with complex alternative behaviour. This model could for example facilitate the step from process planning model to optimization model. We show how automatic constraint generation can be performed for both Constraint Programming and Mixed Integer Linear Programming (MILP) models. Also, for the MILP case, a new formulation for mutual exclusion of resources is proposed. This new formulation works well for proving optimality in systems with multiple capacity resources. Some benchmarks for such job shop scheduling problems as well as systems with a large number of alternatives are also presented