Nonblocking Property Research Articles

Quantitatively nonblocking supervisory control of discrete-event systems

In this paper, we propose a new property of quantitative nonblockingness of an automaton with respect to a given cover on its set of marker states. This property quantifies the standard nonblocking property by capturing the practical requirement that every subset (i.e. cell) of marker states can be reached within a prescribed number of steps from any reachable state and following any trajectory of the system. Accordingly, we formulate a new problem of quantitatively nonblocking supervisory control, and characterize its solvability in terms of a new concept of quantitative language completability. It is proven that there exists the unique supremal quantitatively completable sublanguage of a given language, and we develop an effective algorithm to compute the supremal sublanguage. Finally, combining with the algorithm of computing the supremal controllable sublanguage, we design an algorithm to compute the maximally permissive solution to the formulated quantitatively nonblocking supervisory control problem.

Timed fault-tolerant supervisory control

In Mulahuwaish,1–4 we investigated the problem of fault tolerance in the framework of untimed discrete-event systems (DES). This approach is different from the typical fault-tolerant methodology as the approach does not rely on detecting faults and switching to a new supervisor; it requires a supervisor to work correctly under normal and fault conditions. This is a passive approach that relies upon inherent redundancy in the system being controlled. In this paper we extend the work of Mulahuwaish1–4 to the timed DES (TDES) setting. We introduce our setting, and then provide a set of timed fault tolerant definitions designed to capture different types of fault scenarios and to ensure that our system remains controllable in each scenario. As the nonblocking property is the same for timed and untimed DES, the untimed fault-tolerant nonblocking properties and algorithms from Mulahuwaish1–4 can also be used in the timed setting without any changes. We then present algorithms to verify these properties followed by complexity analyses and correctness proofs of the algorithms. An example is then provided to illustrate our approach.

Safe Performance of an Industrial Autonomous Ground Vehicle in the Supervisory Control Framework

A Cyberphysical system, being an autonomous guided vehicle (AGV) and having diverse applications such as thematic parks and product transfer in manufacturing units, is modeled and controlled. The models of all subsystems of the AGV are provided in discrete event systems (DES) form following the Ramadge–Wonham (R–W) framework. The safe performance of the AGV, being the desired behavior of the system, is presented in the form of desired rules and translated into a set of regular languages. Then, the regular languages are realized as supervisory automata in the framework of Supervisory Control Theory (SCT). To ease implementation and coordination of the control architecture, the supervisors are designed to be in two-state automata forms. The controllability of the regular languages, regarding the AGV, will be proved, using the physical realizability (PR) of the synchronous product of the automata of the system and the supervisors. Also, the nonblocking property of all the controlled automata will be proven to be satisfied. Simulation of the controlled AGV will validate the proposed method.

Modelling and modular supervisory control for the AODV routing protocol

The model of the Ad-hoc on Demand Distance Vector (AODV) routing protocol, being favorable in several wireless networks (Vehicular Ad-Hoc Networks (VANET), ZigBee etc.) is presented for a network with parametric number of nodes in the Ramadge Wonham (RW) framework of discrete event systems (DES). For a generic network, consisting of n nodes, the first goal is to introduce two specification rules, per node. The first rule guarantees the hierarchy of the requests of the nodes and the routing paths. The second rule offers a first level security regarding requests’ replies. The two rules are expressed as two regular languages. Each regular language is realized by a supervisor automaton. The two supervisor automata of each node compose the local controllers of a distributed supervisory control architecture controlling the total network. The physical realizability of the local controlled automaton is proved. Also, the nonblocking property and the satisfactory marked behavior of the total controlled automaton are proved. The complexity of the proposed distributed architecture is computed. To illustrate the effectiveness of the present control scheme, a four-node network simulation of the controlled automaton of the protocol is presented.

A Distributed Supervisor Architecture for a General Wafer Production System.

The current trend in the wafer production industry is to expand the production chain with more production stations, more buffers, and robots. The goal of the present paper is to develop a distributed control architecture to face this challenge by controlling wafer industrial units in a general production chain, with a parametric number of production stations, one robot per two stations where each robot serves its two adjacent production stations, and one additional robot serving a parametric number of stations. The control architecture is analyzed for individual control units, one per robot, monitoring appropriate event signals from the control units of the adjacent robots. Each control unit is further analyzed to individual supervisors. In the present paper, a modular parametric discrete event model with respect to the number of production stations, the number of buffers, and the number of robotic manipulators is developed. A set of specifications for the total system is proposed in the form of rules. The specifications are translated and decomposed to a set of local regular languages for each robotic manipulator. The distributed supervisory control architecture is developed based on the local regular languages, where a set of local supervisors are designed for each robotic manipulator. The desired performance of the total manufacturing system, the realizability, and the nonblocking property of the proposed architecture is guaranteed. Finally, implementation issues are tackled, and the complexity of the distributed architecture is determined in a parametric formula. Overall, the contribution of the present paper is the development of a parametric model of the wafer manufacturing systems and the development of a parametric distributed supervisory control architecture. The present results provide a ready-to-hand solution for the continuously expanding wafer production industry.

A model-based deep reinforcement learning approach to the nonblocking coordination of modular supervisors of discrete event systems

Modular supervisory control may lead to conflicts among the modular supervisors for large-scale discrete event systems. The existing methods for ensuring nonblocking control of modular supervisors either exploit favorable structures in the system model to guarantee the nonblocking property of modular supervisors or employ hierarchical model abstraction methods for reducing the computational complexity of designing a nonblocking coordinator. The nonblocking modular control problem is, in general, NP-hard. This study integrates supervisory control theory and a model-based deep reinforcement learning method to synthesize a nonblocking coordinator for the modular supervisors. The deep reinforcement learning method significantly reduces the computational complexity by avoiding the computation of synchronization of multiple modular supervisors and the plant models. The supervisory control function is approximated by the deep neural network instead of a large-sized finite automaton. Furthermore, the proposed model-based deep reinforcement learning method is more efficient than the standard deep Q network algorithm.

High-capacity strictly non-blocking optical switches based on new dual principle

In this paper the new dual principle of designing high-capacity strictly non-blocking optical switches is presented for the first time. The new type of switches with decentralized control based on the dual principle has been developed for the first time too. In accordance with the scheme topology this type of switching system was called as the quasi-complete dual switch. It also is analysed the optical signals minimal transmission time that provide the non-blocking property of the new schemes. For the circuit and link complexity calculations the accurate analytical expressions are obtained for the first time. The numerical investigation shows that the proposed schemes significantly benefit in comparison with the well-known switches, for example, the crossbar and Clos schemes. The results of comparing of the dual switch and other types of self-routing switches throughput show an obvious advantage of the proposed scheme. It also is shown that the offered switch type can be considered as a perspective for high-capacity strictly non-blocking optical systems. Indeed, the strictly non-blocking property, the scalability, high throughput, and the decentralized control are the main advantages of offered switches.

Integrated non-blocking optical router harnessing wavelength- and mode-selective property for photonic networks-on-chip.

In this paper, we propose and demonstrate a 4×4 non-blocking optical router utilizing 8 mode (de)multiplexers and a 4×4 microring-based grid network, which can passively assign signals carried by optical wavelength and mode channels from an arbitrary input port to corresponding output ports without additional switch time, realizing the non-blocking property. The proposed device is fabricated on a silicon-on-insulator platform using the standard Complementary Metal-Oxide-Semiconductor (CMOS) fabrication processes. The insertion loss is lower than 5.7 dB including the loss of the auxiliary mode (de)multiplexers (AMUXs), while the crosstalk is lower than -15.6 dB for all routing states. Moreover, the transmission spectra from the input ports to the next cascading device are also measured to demonstrate the feasibility of further expanding via cascading multiple blocks, with the insertion loss and crosstalk lower than 7.1 dB (including the mode coupling loss of AMUXs) and -16.4 dB, respectively. The 12 Gbps dynamic transmission experiment is demonstrated with clear and open eye diagrams, illustrating the utility of the device. The device has high geometrical symmetry and good scalability, we exhibit all solutions to expand the 4×4 optical router to 8×8 and 16×16 optical routers with the advantages and deficiencies of each solution discussed.

Quantitative Analysis of Multistage Switching Networks for Embedded Programmable Devices

This paper analyzes the properties of a class of congestion-free multistage switching networks (MSSNs) are butterfly-based and suitable for embedded programmable devices, which require sustaining static multicast connectivity. These MSSNs are fully synthesizable and enable the design of programmable IPs with typical size in the order of 1 KLUT, coupling flexibility with fast turn-around time. The non-blocking property for static connection of this class of MSSN is discussed. Our analysis shows pros and cons of adopting radix-2 or radix-4 MSSN structures, as well as the impact of bypass-paths to make the network fully hierarchical and locality-aware thanks also to a dedicated programming strategy. Implementation experiments carried out on STM CMOS 65 nm technology show the availability of various area-speed trade-offs, resulting in a range of ≃2× in frequency and a range of ≃ 4 × in area. Depending on the specific application-field, an optimal interconnect definition is thus achieved without compromising the routability properties. In this respect, the paper proposes a simplified application-driven model for evaluation of the best MSSN, including bypass-adoption and radix selection.

Reliable Restricted Process Theory

Malfunctions of a mobile ad hoc network (MANET) protocol caused by a conceptual mistake in the protocol design, rather than unreliable communication, can often be detected only by considering communication among the nodes in the network to be reliable. In Restricted Broadcast Process Theory, which was developed for the specification and verification of MANET protocols, the communication operator is lossy. Replacing unreliable with reliable communication invalidates existing results for this process theory. We examine the effects of this adaptation on the semantics of the framework with regard to the non-blocking property of communication in MANETs, the notion of behavioral equivalence relation and its axiomatization. To utilize our complete axiomatization for analyzing the correctness of protocols at the syntactic level, we introduce a precongruence relation which abstracts away from a sequence of multi-hop communications, leading to an application-level action preconditioned by a multi-hop constraint over the topology. We illustrate the applicability of our framework through a simple routing protocol. To prove its correctness, we introduce a novel proof process, based on our precongruence relation.

A Learning-Based Synthesis Approach to the Supremal Nonblocking Supervisor of Discrete-Event Systems

This paper presents a novel approach to synthesize supremal nonblocking supervisors of discrete-event systems (DES), when the automaton models of specifications are not available. Extending the L* learning algorithm, an S* algorithm is developed to infer a tentatively correct supervisor. If the tentatively correct supervisor is nonblocking, it is indeed the supremal nonblocking supervisor with respect to the plant and specifications. Otherwise, the blocking automaton is regarded as a new plant, and the specification is the nonblocking property. Then, the supremal nonblocking supervisor with respect to the new problem is computed using supervisory control theory of DES. Two simplification rules are introduced to the S* algorithm to decrease the computational cost. Finally, the S* algorithm is implemented based on the LearnLib framework, and experiments are performed to verify the proposed approach.

High-Radix Nonblocking Integrated Optical Switching Fabric for Data Center

To accomplish high-bandwidth and low-latency communications among tens or even hundreds of nodes with low power consumption, dual radial and angular grating optical network (DRAGON), a new integrated high-radix strictly nonblocking optical switching fabric, is proposed in this paper. The topology and routing algorithms of DRAGON are discussed, and a formal proof for the strictly nonblocking property is presented. With the loss model developed, we show DRAGON has significantly lower worst-case loss as well as average loss compared with other widely studied integrated nonblocking switching fabrics. In addition, our crosstalk analysis also suggests a lower crosstalk of DRAGON. For example, for 32 wavelength division multiplexing channels, both the worst-case loss and average loss of ${\text{180}}\times {\text{180}}$ DRAGON are around 20 dB lower than crossbar of the same size, and 28 dB lower than ${\text{128}}\times {\text{128}}$ Benes. Furthermore, due to the strictly nonblocking property, DRAGON has advantages of smaller communication latency and larger throughput compared with Benes switching fabric.

Performance Analysis of $f$ -Cast Crosstalk-Free Optical Banyan Networks

Banyan networks serve as a class of important switching network architecture, whose multicast capability is critical for future high-performance switches to support multicast-intensive applications. The available literature indicates that, in order to construct optical multicast banyan networks based on the directional coupler (DC) technology, a high-hardware cost is usually involved to ensure the nonblocking property. In this paper, we conduct blocking probability analysis for such networks to explore the inherent tradeoff between blocking probability and hardware cost. In particular, we focus on a class of DC-based optical networks built on the replicated banyan network (RBN) architecture, and develop a theoretical upper bound on blocking probability for such networks under the general $f$ -cast traffic, which covers the unicast and multicast as special cases. This bound captures the overall blocking behavior of $f$ -cast optical RBN networks and agrees with the conditions of strictly nonblocking $f$ -cast optical RBN networks. The proposed bound is significant because it provides a fundamental guideline to achieve the desirable tradeoff between blocking probability and hardware cost. This paper shows that the hardware cost of an $f$ -cast optical RBN network can be dramatically reduced if a small blocking probability is allowed.

N-port strictly non-blocking optical router based on Mach-Zehnder optical switch for photonic networks-on-chip

A universal method for constructing an N-port strictly non-blocking optical router based on 2×2 Mach-Zehnder optical switch for photonic networks-on-chip is proposed. By analyzing the routing table of the N-port optical router, the relationship between the optical links of port m→port n and port m→port n−1 is indicated, as well as the relationships between the block matrices of the N-port optical router. The strictly non-blocking property of the N-port optical router is proved by the contradiction method. The scale of the N-port optical router can be increased with the improvement of the performance of the Mach-Zehnder optical switch.

Performance evaluation of a large-scale optical switch based on an arrayed waveguide grating router and wavelength converter

A scheduling scheme for a large-scale optical switch is presented and its performance is evaluated. The optical switch is built on an arrayed waveguide grating router (AWGR) and space switching enabled tunable wavelength converter (SS-TWC) and in a Clos switch structure. The SS-TWC has more than one output and in the switch structure enables a multiple fold expansion of the switch port count while using the same dimension AWGR. The switch reconfiguration is triggered by an event, e.g., packet arriving or input port transmitter available for its waiting packets, and the scheduling scheme operates asynchronously. Simulation results demonstrate that the traffic scheduling scheme enables the delivery of high-transmission bandwidth and low packet delay performance, and verify the nonblocking property of the switch.

Nonblocking Clos networks of multiple ROADM rings for mega data centers.

Optical networks have been introduced to meet the bandwidth requirement of mega data centers (DC). Most existing approaches are neither scalable to face the massive growth of DCs, nor contention-free enough to provide full bisection bandwidth. To solve this problem, we propose two symmetric network structures: ring-MEMS-ring (RMR) network and MEMS-ring-MEMS (MRM) network based on classical Clos theory. New strategies are introduced to overcome the additional wavelength constraints that did not exist in the traditional Clos network. Two structures that followed the strategies can enable high scalability and nonblocking property simultaneously. The one-to-one correspondence of the RMR and MRM structures to a Clos is verified and the nonblocking conditions are given along with the routing algorithms. Compared to a typical folded-Clos network, both structures are more readily scalable to future mega data centers with 51200 racks while reducing number of long cables significantly. We show that the MRM network is more cost-effective than the RMR network, since the MRM network does not need tunable lasers to achieve nonblocking routing.

Progressive events in supervisory control and compositional verification

This paper investigates some limitations of the nonblocking property when used for supervisor synthesis in discrete event systems. It is shown that there are cases where synthesis with the nonblocking property gives undesired results. To address such cases, the paper introduces progressive events as a means to specify more precisely how a synthesised supervisor should complete its tasks. The nonblocking property is modified to take progressive events into account, and appropriate methods for verification and synthesis are proposed. Experiments show that progressive events can be used in the analysis of industrial-scale systems, and can expose issues that remain undetected by standard nonblocking verification.

COMPOSITIONAL VERIFICATION OF THE GENERALIZED NONBLOCKING PROPERTY USING ABSTRACTION AND CANONICAL AUTOMATA

This paper brings together two methods to compositionally verify the generalized non-blocking property, which is a weak liveness property to express the ability of concurrent systems to terminate under given preconditions. Appropriate notions of equivalence and refinement for the generalized nonblocking property are discussed, and abstraction rules to simplify finite-state automata accordingly are presented. The paper also presents a unique canonical automaton representation for all generalized nonblocking equivalent automata, which gives rise to more general means of abstraction and to effective decision procedures for generalized nonblocking equivalence. Experimental results demonstrate how abstraction rules and canonical automata can be combined to model-check large models of concurrent software.

Conflict-preserving abstraction of discrete event systems using annotated automata

This paper proposes to enhance compositional verification of the nonblocking property of discrete event systems by introducing annotated automata. Annotations store nondeterministic branching information, which would otherwise be stored in extra states and transitions. This succinct representation makes it easier to simplify automata and enables new efficient means of abstraction, reducing the size of automata to be composed and thus the size of the synchronous product state space encountered in verification. The abstractions proposed are of polynomial complexity, and they have been successfully applied to model check the nonblocking property of the same set of large-scale industrial examples as used in related work.

Supervisory control for dynamic monopoly

A monopoly firm maximises profit by producing the quantity at which marginal revenue equals marginal cost. In order for a monopoly firm in a disequilibrium (non-profit-maximising) state to reach an equilibrium (profit-maximising) state, it usually adopts the following conventional strategy: when marginal revenue exceeds marginal cost, the firm increases output (the quantity of production), and when marginal cost exceeds marginal revenue, the firm decreases output. In this study, using supervisory control theory of discrete event systems, the authors study the dynamic monopoly problem: Does the monopoly firm’s conventional strategy always assure that the firm in disequilibrium eventually reaches an equilibrium state? The author show that the non-blocking property and controllability (which are the major concepts in supervisory control theory) are the necessary and sufficient conditions for the existence of a solution to the dynamic monopoly problem.