Showing papers in "Discrete Event Dynamic Systems in 2008"

Approximate Simulation Relations for Hybrid Systems

Abstract: Approximate simulation relations have recently been introduced as a powerful tool for the approximation of discrete and continuous systems. In this paper, we extend this abstraction framework to hybrid systems. Using the notion of simulation functions, we develop a characterization of approximate simulation relations which can be used for hybrid systems approximation. For several classes of hybrid systems, this characterization leads to effective algorithms for the computation of approximate simulation relations. An application in the context of reachability analysis is shown.

An Algorithmic Toolbox for Network Calculus

Abstract: Network calculus offers powerful tools to analyze the performances in communication networks, in particular to obtain deterministic bounds. This theory is based on a strong mathematical ground, notably by the use of (min,+) algebra. However, the algorithmic aspects of this theory have not been much addressed yet. This paper is an attempt to provide some efficient algorithms implementing network calculus operations for some classical functions. Some functions which are often used are the piecewise affine functions which ultimately have a constant growth. As a first step towards algorithmic design, we present a class containing these functions and closed under the main network calculus operations (min, max, +, -, convolution, subadditive closure, deconvolution): the piecewise affine functions which are ultimately pseudo-periodic. They can be finitely described, which enables us to propose some algorithms for each of the network calculus operations. We finally analyze their computational complexity.

Stability of Parallel Queueing Systems with Coupled Service Rates

Abstract: This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the system are derived, based on stochastic monotonicity and marginal drift properties of multiclass birth and death processes. These conditions yield a sharp characterization of stability for systems where the service rate of each queue is decreasing in the number of customers in other queues, and has uniform limits as the queue lengths tend to infinity. The results are illustrated with applications where the stability region may be nonconvex.

On-Line Monitoring of Large Petri Net Models Under Partial Observation

Abstract: We consider a Petri Net model of the plant. The observation is given by a subset of transitions whose occurrence is always and immediately sensed by a monitoring agent. Other transitions not in this subset are silent (unobservable). Classical on-line monitoring techniques, which are based on the estimation of the current state of the plant and the detection of the occurrence of undesirable events (faults), are not suitable for models of large systems due to high spatial complexity (exponential in the size of the entire model). In this paper we propose a method based on the explanation of plant observation. A legal trace minimally explains the observation if it includes all unobservable transitions whose firing is needed to enable the observed transitions. To do so, starting from an observable transition, using backward search techniques, a set of minimal explanations is derived, which are sufficient for detecting whether a fault event must have occurred for sure in the plant or not. The technique also allows production of a set of basis markings for the estimation of the current state of the plant. The set of all possible current markings can then be characterized as the unobservable reach of these basis markings. The computational complexity of the algorithm depends on the size of the largest connected subnet which includes only unobservable transitions. This allows monitoring of plants of any size in which there is no large unobservable subnet. We also illustrate the applicability of the method for the monitoring of a class of infinite state systems, unbounded Petri Nets with unobservable trap circuits, and we show how this can be useful for distributed implementations.

Analyzing Security Protocols Using Time-Bounded Task-PIOAs

Abstract: This paper presents the time-bounded task-PIOA modeling framework, an extension of the probabilistic input/output automata (PIOA) framework that can be used for modeling and verifying security protocols. Time-bounded task-PIOAs can describe probabilistic and nondeterministic behavior, as well as time-bounded computation. Together, these features support modeling of important aspects of security protocols, including secrecy requirements and limitations on the computational power of adversarial parties. They also support security protocol verification using methods that are compatible with less formal approaches used in the computational cryptography research community. We illustrate the use of our framework by outlining a proof of functional correctness and security properties for a well-known oblivious transfer protocol.

Fault Diagnosis of Discretely Controlled Continuous Systems by Means of Discrete-Event Models

Abstract: Discretely controlled continuous systems consist of continuous plants whose operation mode is switched by a feedback controller. Fault diagnosis has to use the measured switching sequence and the measured continuous movement to detect and identify faults. In order to get the diagnostic algorithm with the least possible complexity, the kind of measurement information and the granularity of the model have to be chosen in accordance with the faults to be detected. The paper presents five diagnostic methods in a uniform way, which differ with respect to the model and the measurement information used. From the hybrid model of discretely controlled continuous systems, four more abstract representations are derived, which have the form of embedded maps, semi-Markov processes, timed automata and nondeterministic automata. The validity of the diagnostic result is ensured by the claim that the models should be complete and, hence, consistent with all the input-output sequences of the discretely controlled system in the appropriate fault case. In this way a hierarchy of models and of diagnostic results is obtained. The methods are illustrated by an example.

On the Minimization of Communication in Networked Systems with a Central Station

Abstract: The problem of minimizing communication in a distributed networked system is considered in a discrete-event formalism where the system is modeled as a finite-state automaton. The system consists of a central station and a set of N local agents, each observing a set of local events. The central station needs to know exactly the state of the system, whereas local agents need to disambiguate certain pre-specified pairs of states for purposes of control or diagnosis. This requirement is achieved by communication, which occurs only between the central station and the local agents but not among the local agents. A communication policy is defined as a set of event occurrences to be communicated between the central station and the local agents. A communication policy is said to be minimal if any removal of communication of event occurrences will affect the correctness of the solution. Under an assumption on the absence of cycles (other than self-loops) in the system model, this paper presents an algorithm that computes a minimal communication policy in polynomial time in all parameters of the system. These results improve upon previous algorithms for solving minimum communication problems.

Diagnosability Analysis of a Class of Hierarchical State Machines

Abstract: This paper addresses the problem of fault detection and isolation for a particular class of discrete event dynamical systems called hierarchical finite state machines (HFSMs). A new version of the property of diagnosability for discrete event systems tailored to HFSMs is introduced. This notion, called L1-diagnosability, captures the possibility of detecting an unobservable fault event using only high level observations of the behavior of an HFSM. Algorithms for testing L1-diagnosability are presented. In addition, new methodologies are presented for studying the diagnosability properties of HFSMs that are not L1-diagnosable. These methodologies avoid the complete expansion of an HFSM into its corresponding flat automaton by focusing the expansion on problematic indeterminate cycles only in the associated extended diagnoser.

Compositionally Progressive Solutions of Synchronous FSM Equations

Abstract: The paper addresses the problem of designing a component that combined with a known part of a system, called the context FSM, is a reduction of a given specification FSM. We study compositionally progressive solutions of synchronous FSM equations. Such solutions, when combined with the context, do not block any input that may occur in the specification, so they are of practical use. We show that, if a synchronous FSM equation has a compositionally progressive solution, then there is a largest regular compositionally progressive solution including all of them. We provide two different algorithms to compute a largest regular compositionally progressive solution: one deletes all compositionally non-progressive strings from a largest solution, the other splits states of a largest solution and then removes those inducing a non-progressive composition.

Tail Asymptotics for Discrete Event Systems

Abstract: In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail asymptotics of the stationary response time for a class of networks that admit a representation as (max,plus)-linear systems in a random medium. We are able to derive analytic results when the distribution of the holding times are light-tailed. We show that the lack of independence may lead in dimension bigger than one to non-trivial effects in the asymptotics of the sojourn time. We also study in detail a simple queueing network with multipath routing.

Throughput-Optimal Sequences for Cyclically Operated Plants

Abstract: In this paper, we present a method to determine globally optimal schedules for cyclically operated plants where activities have to be scheduled on limited resources. In cyclic operation, a large number of entities is processed in an identical time scheme. For strictly cyclic operation, where the time offset between entities is also identical for all entities, the objective of maximizing throughput is equivalent to the minimization of the cycle time. The resulting scheduling problem is solved by deriving a mixed integer optimization problem from a discrete event model. The model includes timing constraints as well as open sequence decisions for the activities on the resources. In an extension, hierarchical nesting of cycles is considered, which often allows for schedules with improved throughput. The method is motivated by the application to high throughput screening plants, where a specific combination of requirements has to be obeyed (e.g. revisited resources, absence of buffers, or time window constraints).

Timed Discrete Event Control of Parallel Production Lines with Continuous Outputs

Abstract: In this contribution we present an approach to formulate and solve certain scheduling tasks for hybrid systems using timed discrete event control methods. To demonstrate our approach, we consider a cyclically operated plant with parallel reactors using common resources and a continuous output. For this class of systems, we show how to pose the control problem within a discrete event framework by modelling system components as multirate timed automata. We propose a supervisory control strategy incorporating off-line optimisation to assure safety and nonconflicting use of resources. These properties have to be achieved in the presence of a class of bounded errors/disturbances and can be verified by applying formal methods.

Tracking Control of Join-Free Timed Continuous Petri Net Systems under Infinite Servers Semantics

Abstract: A new low-and-high gain algorithm is presented for tracking control of a subclass of timed continuous Petri Net (contPN) systems working under infinite servers semantics. The inherent properties of timed contPN determine that the control signals must be non-negative and upper bounded by functions of system states. In the proposed control approach, LQ theory is first used to design a low-gain controller such that the control signals satisfy the input constraints. Based on the low-gain controller, a high-gain term is further added to fully employ available control energy, and control performance can be improved consequently. In order to guarantee global tracking convergence and smoothness on the tracking target, a mixed trajectory (state step and ramp) is used instead of a pure step reference signal. The new tracking target is designed to ensure the existence of the low-gain controller and possible fast system response concurrently. Rigorous proof based on Lyapunov function is provided to guarantee that for a conservative and strongly connected Join-Free (JF) timed contPN system, the proposed algorithm can ensure the global asymptotical convergence of both system states and control signals.

Backward Coupling in Bounded Free-Choice Nets Under Markovian and Non-Markovian Assumptions

Abstract: In this paper, we show how to design a perfect sampling algorithm for stochastic Free-Choice Petri nets by backward coupling. For Markovian event graphs, the simulation time can be greatly reduced by using extremal initial states, namely blocking marking, although such nets do not exhibit any natural monotonicity property. Another approach for perfect simulation of non-Markovian event graphs is based on a (max,plus) representation of the system and the theory of (max,plus) stochastic systems. We also show how to extend this approach to one-bounded free choice nets to the expense of keeping all states. Finally, experimental runs show that the (max,plus) approach needs a larger simulation time than the Markovian approach.

Minimizing Place Capacities of Weighted Event Graphs for Enforcing Liveness

Abstract: This paper addresses the problem of minimizing place capacities of weighted event graphs in order to enforce liveness. Necessary and sufficient conditions of the solution existence are derived. Lower bounds of place capacities while preserving liveness are established and a polynomial algorithm is proposed to determine an initial marking leading to these lower bounds while preserving the liveness.

Zero-Automatic Networks

Abstract: We continue the study of zero-automatic queues first introduced in Dao-Thi and Mairesse (Adv Appl Probab 39(2):429---461, 2007). These queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The simple M/M/1 queue and Gelenbe's G-queue with positive and negative customers are the two simplest 0-automatic queues. All stable 0-automatic queues have an explicit "multiplicative" stationary distribution and a Poisson departure process (Dao-Thi and Mairesse, Adv Appl Probab 39(2):429---461, 2007). In this paper, we introduce and study networks of 0-automatic queues. We consider two types of networks, with either a Jackson-like or a Kelly-like routing mechanism. In both cases, and under the stability condition, we prove that the stationary distribution of the buffer contents has a "product-form" and can be explicitly determined. Furthermore, the departure process out of the network is Poisson.

Perfect Simulation of a Class of Stochastic Hybrid Systems with an Application to Peer to Peer Systems

Abstract: In this paper we present a class of hybrid systems made of deterministic differential equations and random discrete jumps. We then show how to construct a simulation of such a stochastic hybrid system that provides perfect samples of its asymptotic behavior based on the extension to continuous state-space of coupling-from-the-past techniques introduced by Foss and Tweedie (Stoch Models 14:187---204, 1998) and using suitable envelope trajectories to tackle non-monotonicity. The applicability of the method is illustrated by showing how this framework can be used to model the Squirrel peer to peer system and by reporting a simulation study based on this approach. This paper provides both a framework on how to carry simulation based experimental studies of large and complex hybrid systems and its application in the Squirrel model demonstrating how versatile and powerful this approach can be over a typical example.

Performance of the MAP/G/1 Queue Under the Dyadic Control of Workload and Server Idleness

Abstract: This paper studies the steady-state queue length process of the MAP/G/1 queue under the dyadic control of the D-policy and multiple server vacations. We derive the probability generating function of the queue length and the mean queue length. We then present computational experiences and compare the MAP queue with the Poisson queue.

Lose Fat, Not Muscle: An Examination of Supervisor Reduction in Discrete-Event Systems

Abstract: This paper is concerned with the elimination of unnecessary states in discrete-event system control agents. Several approaches to supervisor reduction are studied and a new relation between agents, comparability, is defined to encapsulate most of the concepts found in the aforementioned methods. This relation is also proven to be preserved under conjunction, which is commonly employed to determine the centralized representation of two decentralized DES supervisors.