A process algebra of communicating shared resources with dense time and priorities

Abstract

The correctness of real-time distributed systems depends not only on the function they compute but also on their timing characteristics. Furthermore, these characteristics are strongly influenced by the delays due to synchronization and resource availability. Process algebras have been used successfully to define and prove correctness of distributed systems. More recently, there has been a lot of activity to extend their application to real-time systems. The problem with most current approaches is that they ignore resource constraints and assume either maximum parallelism (i.e., unlimited resources) or pure interleaving (i.e., single resource). Algebra of Communicating Shared Resources (ACSR) is a process algebra designed for the formal specification and manipulation of distributed systems with resources and real-time constraints. A dense time domain provides a more natural way of specifying systems compared to the usual discrete time. Priorities provide a measure of urgency for each action and can be used to ensure that deadlines are met. In ACSR, processes are specified using resource bound, timed actions and instantaneous synchronization events. Processes can be combined using traditional operators such as nondeterministic choice and parallel execution. Specialized operators allow the specification of real-time behavior and constraints. The semantics of ACSR is defined as a labeled transition system. Equivalence between processes is based on the notion of strong bisimulation. A sound and complete set of algebraic laws can be used to transform almost any ACSR process into a normal form.

A Calculus and logic of resources and processes

“…A similar point of view may be found in the work of Gastin and Mislove [GM04] in which, perhaps deriving from its denotational semantics motivations, the association of resources and processes uses a global construction in the style of Mazurkiewicz traces [Maz87]. Neither [BGL97] nor [GM04], however, provides a logical characterization of the interaction between resources and processes. In contrast, our analysis provides not only a logical characterization but one which captures the concurrent structure of the system.…”

“…For instance, a semaphore is represented as a two-state process, representing whether the token is currently available or not. There have been extensions [BGL97] that attempt to model resource explicitly but these approaches carry both the communication structures of the process algebras alongside the representation of resource. We take the view that resource is the fundamental organizing principle of the underlying calculus, an approach taken within process-oriented discrete event languages [Bir79,Bir81].…”

“…Another approach to resources, in a synchronous setting, is that of Brémond-Grégoire and Lee's ACSR [BGL97]. Our approach is more foundational, starting from a logically well-founded model of resource and developing a foundational, yet applicable, theory of the interaction between processes and resources.…”

Process-Algebraic Analysis of Timing and Schedulability Properties

“…Extensions and variations include GCSR [4] which allows the visual representation of ACSR processes, Dense-time ACSR [6] which includes a more general notion of time, ACSR-VP [10] which includes a value-passing capability, PACSR [19], a probabilistic formalism for quantitative reasoning about fault-tolerant properties of resource-bound systems and P 2 ACSR [24] which allows to specify power-constrained systems. The PARAGON toolset [22] provides tool support for system modeling and analysis using these formalisms.…”

PAMR: A Process Algebra for the Management of Resources in Concurrent Systems

“…There are models to specify systems sharing resources (e.g. [5]), but in this case resources are just accessed, not traded; this access induces some delays in the behavior of processes. If we consider the maximizing utility policy, our proposal is somehow related to the ODP trading function [9].…”