This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NP-completeness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, cross-references will be given to that book and the list of problems (NP-complete and harder) presented there. Readers who have results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.) or open problems they would like publicized, should

This paper considers the deadlock avoidance problem for the class of conjunctive / disjunctive (sequential) resource allocation systems (C/D-RAS), which allows for multiple resource acquisitions and flexible routings. First, a new siphon-based characterization for the liveness of Petri nets (PN's) modeling C/D-RAS is developed, and subsequently, this characterization facilitates the development of a polynomial-complexity deadlock avoidance policy (DAP) that is appropriate for the considered RAS class. The resulting policy is characterized as C/D-RUN, since the starting point for the policy development was motivated by the RUN DAP, originally developed for sequential RAS with unit resource allocations and no routing flexibility. The last part of the paper exploits the aforementioned siphonbased characterization of C/D-RAS liveness, in order to develop a su#ciency condition for C/D-RAS liveness that takes the convenient form of a Mixed Integer Programming (MIP) formulation. The availabil...

Although the typical process-layout manufacturing environment is susceptible to deadlocks, the problem of deadlock resolution in this context has only lately been undertaken by the scientific community. Previous studies have found that deadlock avoidance methodologies seem to be the most appropriate for this particular context. Unfortunately, in the general case, these methods suffer from high computational complexity which results in heuristic solutions and/or reduced performance. Taking the position that any solution to the problem should be scalable and provably correct, this paper proposes an analytical framework for designing deadlock avoidance policies for a subclass of Resource Allocation Systems (RAS). Specifically, this subclass is characterized by the fact that jobs in the system are defined by deterministic job-step sequences with every step in the sequence requiring a single unit of the system resources. Job-step models are appropriate for the study of the deadlo...

Deadlock free operation is essential for operating highly automated manufacturing systems. The seminal deadlock avoidance procedure, Banker's Algorithm, was developed for computer operating systems, an environment where very little information regarding the future resource requirements of executing processes is known. Manufacturing researchers have tended to dismiss Banker’s as being too conservative in the manufacturing environment where future resource requirements are well defined by part routes. In this work, we investigate this issue by developing variants of Banker’s Algorithm that are applicable to buffer space allocation in flexible manufacturing. We show that these algorithms are not overly conservative, and that indeed, Banker’s approach can provide very good operational flexibility when properly applied to the manufacturing environment. keywords: Banker’s Algorithm, deadlock, flexible manufacturing, manufacturing system control 1 Table 1. Selected notation. b(x,n,p) binomial distribution with parameters n and p

Abstract. We study the problem of thread allocation in asynchronous distributed real-time and embedded systems. Each distributed node handles a limited set of resources, in particular a limited thread pool. Different methods can be invoked concurrently in each node, either by external agents or as a remote call during the execution of a method. In this paper we study thread allocation under a WaitOnConnection strategy, in which each nested upcall made while a thread is waiting must be made in a different thread. We study protocols that control the allocation of threads to guarantee the absence of deadlocks. First, we introduce a computational model in which we formally describe the different protocols and their desired properties. Then, we study two scenarios: a single agent performing sequential calls, and multiple agents with unrestricted concurrency. For each scenario we present (1) algorithms to compute the minimum amount of resources to avoid deadlocks, and (2) run-time protocols that control the allocation of these resources. 1

Currently, conflict-free routing in AGV systems is established by means of one of the following three approaches: (i) the problem elimination through the adoption of a segmented path flow or tandem queue configuration, (ii) the identification of imminent collisions through forward sensing and their aversion through vehicle backtracking and/or rerouting, or (iii) the imposition of zone control and extensive route pre-planning, typically based on deterministic timing of the vehicle traveling and docking stages. Among these three approaches, the segmented path flow-based approach presents the highest robustness to the system stochasticities/randomness, but at the cost of restricted vehicle routings and the need for complicated handling operations. This paper proposes an alternative conflict resolution strategy that will ensure robust AGV conflict resolution, while maintaining the operational flexibility provided by free vehicle travel on arbitrarily structured guidepath networks. Specific...

The development of efficient deadlock avoidance policies (DAP's) for sequential resource allocation systems (RAS) is a problem of increasing interest in the scientific community, largely because of its relevance to the design of large-scale flexibly automated manufacturing systems. Much of the work on this problem existing in the literature, is focused on the so called Single-Unit RAS model, which is the simplest model in the considered class of RAS. Furthermore, due to a well-established result stating that, even for single-unit RAS, the computation of the maximally permissive DAP is computationally intractable (NP-hard), many researchers (including our group) have focused on obtaining good suboptimal policies which are computationally tractable (scalable) and provably correct. In the first part of the paper, it is shown, however, that for a large subset (in fact, a majority) of single-unit RAS, the optimal DAP can be obtained in real-time with a computational cost which is ...

Petri net modeling has clearly illuminated the need for formal structural analysis of Flexible Manufacturing Systems. Petri nets are not, however, the only formal models capable of supporting such analysis. Indeed, it is our position that structural analysis of the FMS is a fundamental design activity which must be defined independently of any particular modeling paradigm. This paper attempts to define FMS structural analysis and provides guidelines for developing FMS Structural Control Policies, SCP's. The FMS is a discrete event system and as such is structurally characterized by its state space. This state space can be represented by a State Transition Diagram, i.e. a directed graph with FMS states being vertices and directed edges being state transition. The objective of structural analysis is to characterize regions of the state space that are structurally sound. Structural Control Policies, SCP's, then assure that the FMS operates within these structurally sound regions. Deadlock has emerged as the paramount structural property for FMS's, and therefore, structural analysis emphasizes characterization of those state space regions that are safe. SCP's must then assure that the FMS operates within its safe subspace.

Current strategic and technological trends in discrete-part manufacturing require extensive and #exible automation of the underlying production systems. However, even though a great deal of work has been done to facilitate manufacturing automation at the hardware component level, currently there is no adequately developed control methodology for these environments.

Abstract Thread allocation is an important problem in dis-tributed real-time and embedded (DRE) systems. A too liberal thread allocation policy may cause deadlock, atoo conservative policy limits potential parallelism, thus wasting resources. However, achieving (global) optimalthread utilization, while avoiding deadlock, has been proven impractical in distributed systems: it requirestoo much communication between components. In previous work we showed that efficient local threadallocation protocols are possible if the protocols are parameterized by global static data, in particular, an an-notation of the global call graph of all tasks to be performed by the system. We proved that absence of cyclicdependencies in this annotation guarantees absence of deadlock. In this paper we present an algorithm to computeoptimal annotations, that is annotations that maximize