In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such awaythat the discrete and continuous portions may a ect each other. Following this de nition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.

Modern production facilities (i.e., flexible manufacturing systems) exhibit a high degree of resource sharing, a situation in which deadlocks (circular waits) can arise. Using digraph theoretic concepts we derive necessary and sufficient conditions for a deadlock occurrence and rigorously characterize highly undesirable situations (second level deadlocks), which inevitably evolve to circular waits in the next future. We assume that the system dynamics is described by a discrete event dynamical model, whose state provides the information on the current interactions job-resources. This theoretic material allows us to introduce some control laws (named restriction policies) which use the state knowledge to avoid deadlocks by inhibiting or by enabling some transitions. The restriction policies involve small on-line computation costs, so they are suitable for realtime implementation. For a meaningful class of systems one of these policies is the least restrictive deadlock-free policy one ca...

The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, simulative solution also poses some interesting challenges, which are addressed in the paper. 1

) Vineet Gupta Radha Jagadeesan Prakash Panangaden y vgupta@mail.arc.nasa.gov radha@cs.luc.edu prakash@cs.mcgill.ca Caelum Research Corporation Dept. of Math. and Computer Sciences School of Computer Science NASA Ames Research Center Loyola University--Lake Shore Campus McGill University Moffett Field CA 94035, USA Chicago IL 60626, USA Montreal, Quebec, Canada Abstract This paper describes a stochastic concurrent constraint language for the description and programming of concurrent probabilistic systems. The language can be viewed both as a calculus for describing and reasoning about stochastic processes and as an executable language for simulating stochastic processes. In this language programs encode probability distributions over (potentially infinite) sets of objects. We illustrate the subtleties that arise from the interaction of constraints, random choice and recursion. We describe operational semantics of these programs (programs are run by sampling random choices), deno...

. We extend cc to allow the specification of a discrete probability distribution for random variables. We demonstrate the expressiveness of pcc by synthesizing combinators for default reasoning. We extend pcc uniformly over time, to get a synchronous reactive probabilistic programming language, Timed pcc. We describe operational and denotational models for pcc (and Timed pcc). The key feature of the denotational model(s) is that parallel composition is essentially set intersection. We show that the denotational model of pcc (resp. Timed pcc) is conservative over cc (resp. tcc). We also show that the denotational models are fully abstract for an operational semantics that records probability information. 1 Introduction Concurrent constraint programming(CCP, [Sar93]) is an approach to computation which uses constraints for the compositional specification of concurrent systems. It replaces the traditional notion of a store as a valuation of variables with the notion of a store as a cons...

: Recently, many companies have realized that their organization needs to be improved in order to enhance flexibility, efficiency, and effectiveness. Business Process Re-engineering has become the new organization paradigm to reconstitute profitability and competitiveness. Additionally, workflow management systems promise to provide a conceptual framework to describe and automate workflow. Analysts are asking for methods to evaluate alternative process designs for performance objectives, such as cycle time and throughput. These measures are dependent on the dynamic behavior of a process and can hardly be derived by traditional methods. In this paper we will outline an approach to model the dynamic behavior of business processes by Stochastic Petri nets. Our aim is to provide workflow management systems with an analytical evaluation component. We will summarize the problems we encountered following our approach to give directions for further research. Keywords: Business process re-en...

Numerous algorithms and tools have been deployed in supply chain modeling and problem solving. These are based on stochastic models, mathematical programming models, heuristic techniques, and simulation. Since different decision problems in supply chains entail different approaches to be used for modeling and problem solving, there is a need for a unified approach to modeling supply chains so that any required representation can be created in a rapid and flexible way. In this paper, we develop a decision support system DESSCOM (Decision Support for Supply Chains through Object Modeling) which enables strategic, tactical, and operational decision making in supply chains. DESSCOM has two major components: (1) DESSCOM-MODEL, a modeling infrastructure comprising a library of carefully designed generic objects for modeling supply chain elements and dynamic interactions among these elements, and (2) DESSCOM-WORKBENCH, a decision workbench that can potentially include powerful algorithmic and simulation-based solution methods for supply chain decision-making. Through DESSCOM-MODEL, faithful models of any given supply chain can be created rapidly at any desired level of abstraction. Given a supply chain decision problem to be solved, the object oriented models created at the right level of detail can be transformed into problem formulations that can then be solved using an appropriate strategy from DESSCOM-WORKBENCH. We have designed and implemented a prototype of DESSCOM. We provide a realworld case study of a liquid petroleum gas supply chain to demonstrate the use of DESSCOM to model supply chains and enable decision-making at various levels.

In this paper, we consider mixed systems containing both stochastic and non-stochastic 1 components. To compose such systems, we introduce a general combinator which allows the specification of an arbitrary mixed system in terms of elementary components of only two types. Thus, systems are obtained hierarchically, by composing subsystems, where each subsystem can be viewed as an "increment" in the decomposition of the full system. The resulting mixed stochastic system specifications are generally not "executable", since they do not necessarily permit the incremental simulation of the system variables. Such a simulation requires compiling the dependency relations existing between the system variables. Another issue involves finding the most likely internal states of a stochastic system from a set of observations. We provide a small set of primitives for transforming mixed systems, which allows the solution of the two problems of incremental simulation and estimation of stocha...

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