A Hierarchy of Scheduler Classes for Stochastic Automata

Stochastic automata are a formal compositional model for concurrent stochastic timed systems, with general distributions and non-deterministic choices. Measures of interest are defined over schedulers that resolve the nondeterminism. In this paper we investigate the power of various theoretically and practically motivated classes of schedulers, considering the classic complete-information view and a restriction to non-prophetic schedulers. We prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic reachability. We find that, unlike Markovian formalisms, stochastic automata distinguish most classes even in this basic setting. Verification and strategy synthesis methods thus face a tradeoff between powerful and efficient classes. Using lightweight scheduler sampling, we explore this tradeoff and demonstrate the concept of a useful approximative verification technique for stochastic automata

Embedding real-time in stochastic process algebras

We present a stochastic process algebra including immediate actions, deadlock and termination, and explicit stochastic delays, in the setting of weak choice between immediate actions and passage of time. The operational semantics is a spent time semantics, avoiding explicit clocks. We discuss the embedding of weak-choice real-time process theories and analyze the behavior of parallel composition in the weak choice framework

Optimal infinite scheduling for multi-priced timed automata

This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far

Distribution-based bisimulation for labelled Markov processes

In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based bisimulations, our distribution bisimulation is weaker, but corresponds more closely to linear properties. We construct a logic and a metric to describe our distribution bisimulation and discuss linearity, continuity and compositional properties.Comment: Accepted by FORMATS 201

Bounded Model Checking of GSMP Models of Stochastic Real-Time Systems

Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic real-time systems modeled as generalized semi-Markov processes (GSMP). While GSMPs is a rich model for stochastic systems widely used in performance evaluation, existing model checking algorithms are applicable only to subclasses such as discrete-time or continuous-time Markov chains. The main contribution of the paper is an algorithm to compute the probability that a given GSMP satisfies a property of the form “can the system reach a target before time T within k discrete events, while staying within a set of safe states”. For this, we show that the probability density function for the remaining firing times of different events in a GSMP after k discrete events can be effectively partitioned into finitely many regions and represented by exponentials and polynomials. We report on illustrative examples and their analysis using our techniques

A Geological Itinerary Through the Southern Apennine Thrust-Belt (Basilicata—Southern Italy)

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Physiologically based modeling of lisofylline pharmacokinetics following intravenous administration in mice

Lisofylline (LSF), is the R-(−) enantiomer of the metabolite M1 of pentoxifylline, and is currently under development for the treatment of type 1 diabetes. The aim of the study was to develop a physiologically based pharmacokinetic (PBPK) model of LSF in mice and to perform simulations in order to predict LSF concentrations in human serum and tissues following intravenous and oral administration. The concentrations of LSF in serum, brain, liver, kidneys, lungs, muscle, and gut were determined at different time points over 60 min by a chiral HPLC method with UV detection following a single intravenous dose of LSF to male CD-1 mice. A PBPK model was developed to describe serum pharmacokinetics and tissue distribution of LSF using ADAPT II software. All pharmacokinetic profiles were fitted simultaneously to obtain model parameters. The developed model characterized well LSF disposition in mice. The estimated intrinsic hepatic clearance was 5.427 ml/min and hepatic clearance calculated using the well-stirred model was 1.22 ml/min. The renal clearance of LSF was equal to zero. On scaling the model to humans, a good agreement was found between the predicted by the model and presented in literature serum LSF concentration–time profiles following an intravenous dose of 3 mg/kg. The predicted LSF concentrations in human tissues following oral administration were considerably lower despite the twofold higher dose used and may not be sufficient to exert a pharmacological effect. In conclusion, the mouse is a good model to study LSF pharmacokinetics following intravenous administration. The developed PBPK model may be useful to design future preclinical and clinical studies of this compound