Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes

We have recently defined a weak Markovian bisimulation equivalence in an integrated-time setting, which reduces sequences of exponentially timed internal actions to individual exponentially timed internal actions having the same average duration and execution probability as the corresponding sequences. This weak Markovian bisimulation equivalence is a congruence for sequential processes with abstraction and turns out to induce an exact CTMC-level aggregation at steady state for all the considered processes. However, it is not a congruence with respect to parallel composition. In this paper, we show how to generalize the equivalence in a way that a reasonable tradeoff among abstraction, compositionality, and exactness is achieved for concurrent processes. We will see that, by enhancing the abstraction capability in the presence of concurrent computations, it is possible to retrieve the congruence property with respect to parallel composition, with the resulting CTMC-level aggregation being exact at steady state only for a certain subset of the considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Markov chain models of instantaneously coupled intracellular calcium channels

Localized calcium elevations known as calcium puffs or sparks are cellular signals arising from cooperative activity of clusters of inositol 1,4,5-trisphosphate receptors (IP3Rs) or ryanodine receptors (RyRs) located at calcium release sites on the endoplasmic or sarcoplasmic reticulum membrane. When Markov chain models of these intracellular calcium-regulated calcium channels are coupled via a mathematical representation of the calcium microdomain, simulated calcium release sites may exhibit the phenomenon of stochastic calcium excitability where the IP3Rs or RyRs open and close in a concerted fashion. Although the biophysical theory relating the kinetics of single channels to the collective phenomena of puffs and sparks is only beginning to be developed, Markov chain models of coupled intracellular channels give insight into the dynamics of calcium puffs and sparks.;Interestingly, under some conditions simulated puffs and sparks can be observed even when the single channel model used does not include slow calcium inactivation or any long-lived closed state. In this case termination of the localized calcium elevation occurs when all of the intracellular channels at a release site simultaneously close through a process called stochastic attrition. This dissertation investigates the statistical properties of stochastic attrition viewed as an absorption time on a terminating Markov chain that represents a calcium release site composed of two-state channels that are activated by calcium. Assuming that the local calcium concentration experienced by a channel depends only on the number of open channels at the calcium release site, the probability distribution function for the time until stochastic attrition occurs is derived and an analytical formula for the expectation of this random variable is presented. Also explored is how the contribution of stochastic attrition to the termination of calcium puffs and sparks depends on the number of channels at a release site, the source amplitude of the channels, the background calcium concentration, channel kinetics, and the cooperativity of calcium binding.;This dissertation also studies whether single channel models with calcium inactivation are less sensitive to the details of release site ultrastructure than models that lack a slow calcium-inactivation process. Release site dynamics obtained from simulated calcium release sites composed of instantaneously coupled calcium-regulated calcium channels whose random spatial locations were chosen from a uniform distribution on a disc of specified radius are compared to simulations with channels arranged on hexagonal lattices. Analysis of puff/spark statistics confirms that puffs and sparks are less sensitive to the spatial organization of release sites when the single channel model includes a slow inactivation process. The validity of several different mean-field reductions that do not explicitly account for the details of release site ultrastructure is also investigated.;Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. A Kronecker structured representation for calcium release site models is presented and benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure are performed. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. When an exact solution is not feasible, iterative approximate methods based on the Power method may be used, with performance similar to Monte Carlo estimates

Fluid aggregations for Markovian process algebra

Quantitative analysis by means of discrete-state stochastic processes is hindered by the well-known phenomenon of state-space explosion, whereby the size of the state space may have an exponential growth with the number of objects in the model. When the stochastic process underlies a Markovian process algebra model, this problem may be alleviated by suitable notions of behavioural equivalence that induce lumping at the underlying continuous-time Markov chain, establishing an exact relation between a potentially much smaller aggregated chain and the original one. However, in the modelling of massively distributed computer systems, even aggregated chains may be still too large for efficient numerical analysis. Recently this problem has been addressed by fluid techniques, where the Markov chain is approximated by a system of ordinary differential equations (ODEs) whose size does not depend on the number of the objects in the model. The technique has been primarily applied in the case of massively replicated sequential processes with small local state space sizes. This thesis devises two different approaches that broaden the scope of applicability of efficient fluid approximations. Fluid lumpability applies in the case where objects are composites of simple objects, and aggregates the potentially massive, naively constructed ODE system into one whose size is independent from the number of composites in the model. Similarly to quasi and near lumpability, we introduce approximate fluid lumpability that covers ODE systems which can be aggregated after a small perturbation in the parameters. The technique of spatial aggregation, instead, applies to models whose objects perform a random walk on a two-dimensional lattice. Specifically, it is shown that the underlying ODE system, whose size is proportional to the number of the regions, converges to a system of partial differential equations of constant size as the number of regions goes to infinity. This allows for an efficient analysis of large-scale mobile models in continuous space like ad hoc networks and multi-agent systems

Design and Management of Manufacturing Systems

Although the design and management of manufacturing systems have been explored in the literature for many years now, they still remain topical problems in the current scientific research. The changing market trends, globalization, the constant pressure to reduce production costs, and technical and technological progress make it necessary to search for new manufacturing methods and ways of organizing them, and to modify manufacturing system design paradigms. This book presents current research in different areas connected with the design and management of manufacturing systems and covers such subject areas as: methods supporting the design of manufacturing systems, methods of improving maintenance processes in companies, the design and improvement of manufacturing processes, the control of production processes in modern manufacturing systems production methods and techniques used in modern manufacturing systems and environmental aspects of production and their impact on the design and management of manufacturing systems. The wide range of research findings reported in this book confirms that the design of manufacturing systems is a complex problem and that the achievement of goals set for modern manufacturing systems requires interdisciplinary knowledge and the simultaneous design of the product, process and system, as well as the knowledge of modern manufacturing and organizational methods and techniques

Fluid aggregations for Markovian process algebra

Quantitative analysis by means of discrete-state stochastic processes is hindered by the well-known phenomenon of state-space explosion, whereby the size of the state space may have an exponential growth with the number of objects in the model. When the stochastic process underlies a Markovian process algebra model, this problem may be alleviated by suitable notions of behavioural equivalence that induce lumping at the underlying continuous-time Markov chain, establishing an exact relation between a potentially much smaller aggregated chain and the original one. However, in the modelling of massively distributed computer systems, even aggregated chains may be still too large for efficient numerical analysis. Recently this problem has been addressed by fluid techniques, where the Markov chain is approximated by a system of ordinary differential equations (ODEs) whose size does not depend on the number of the objects in the model. The technique has been primarily applied in the case of massively replicated sequential processes with small local state space sizes. This thesis devises two different approaches that broaden the scope of applicability of efficient fluid approximations. Fluid lumpability applies in the case where objects are composites of simple objects, and aggregates the potentially massive, naively constructed ODE system into one whose size is independent from the number of composites in the model. Similarly to quasi and near lumpability, we introduce approximate fluid lumpability that covers ODE systems which can be aggregated after a small perturbation in the parameters. The technique of spatial aggregation, instead, applies to models whose objects perform a random walk on a two-dimensional lattice. Specifically, it is shown that the underlying ODE system, whose size is proportional to the number of the regions, converges to a system of partial differential equations of constant size as the number of regions goes to infinity. This allows for an efficient analysis of large-scale mobile models in continuous space like ad hoc networks and multi-agent systems

Rapid Mission Assurance Assessment via Sociotechnical Modeling and Simulation

How do organizations rapidly assess command-level effects of cyber attacks? Leaders need a way of assuring themselves that their organization, people, and information technology can continue their missions in a contested cyber environment. To do this, leaders should: 1) require assessments be more than analogical, anecdotal or simplistic snapshots in time; 2) demand the ability to rapidly model their organizations; 3) identify their organization’s structural vulnerabilities; and 4) have the ability to forecast mission assurance scenarios. Using text mining to build agent based dynamic network models of information processing organizations, I examine impacts of contested cyber environments on three common focus areas of information assurance—confidentiality, integrity, and availability. I find that assessing impacts of cyber attacks is a nuanced affair dependent on the nature of the attack, the nature of the organization and its missions, and the nature of the measurements. For well-manned information processing organizations, many attacks are in the nuisance range and that only multipronged or severe attacks cause meaningful failure. I also find that such organizations can design for resiliency and provide guidelines in how to do so

Stochastic abstraction of programs: towards performance-driven development

Distributed computer systems are becoming increasingly prevalent, thanks to modern technology, and this leads to significant challenges for the software developers of these systems. In particular, in order to provide a certain service level agreement with users, the performance characteristics of the system are critical. However, developers today typically consider performance only in the later stages of development, when it may be too late to make major changes to the design. In this thesis, we propose a performance driven approach to development — based around tool support that allows developers to use performance modelling techniques, while still working at the level of program code. There are two central themes to the thesis. The first is to automatically relate performance models to program code. We define the Simple Imperative Remote Invocation Language (SIRIL), and provide a probabilistic semantics that interprets a program as a Markov chain. To make such an interpretation both computable and efficient, we develop an abstract interpretation of the semantics, from which we can derive a Performance Evaluation Process Algebra (PEPA) model of the system. This is based around abstracting the domain of variables to truncated multivariate normal measures. The second theme of the thesis is to analyse large performance models by means of compositional abstraction. We use two abstraction techniques based on aggregation of states — abstract Markov chains, and stochastic bounds — and apply both of them compositionally to PEPA models. This allows us to model check properties in the three-valued Continuous Stochastic Logic (CSL), on abstracted models. We have implemented an extension to the Eclipse plug-in for PEPA, which provides a graphical interface for specifying which states in the model to aggregate, and for performing the model checking