Unbounded Product-Form Petri Nets

Computing steady-state distributions in infinite-state stochastic systems is in general a very difficult task. Product-form Petri nets are those Petri nets for which the steady-state distribution can be described as a natural product corresponding, up to a normalising constant, to an exponentiation of the markings. However, even though some classes of nets are known to have a product-form distribution, computing the normalising constant can be hard. The class of (closed) Pi^3-nets has been proposed in an earlier work, for which it is shown that one can compute the steady-state distribution efficiently. However these nets are bounded. In this paper, we generalise queuing Markovian networks and closed Pi^3-nets to obtain the class of open Pi^3-nets, that generate infinite-state systems. We show interesting properties of these nets: (1) we prove that liveness can be decided in polynomial time, and that reachability in live Pi^3-nets can be decided in polynomial time; (2) we show that we can decide ergodicity of such nets in polynomial time as well; (3) we provide a pseudo-polynomial time algorithm to compute the normalising constant

Synthesis and Analysis of Product-form Petri Nets

For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here we address three relevant issues for product-form Petri nets which were left fully or partially open: (1) we provide a sound and complete set of rules for the synthesis; (2) we characterise the exact complexity of classical problems like reachability; (3) we introduce a new subclass for which the normalising constant (a crucial value for product-form expression) can be efficiently computed.Comment: This is a version including proofs of the conference paper: Haddad, Mairesse and Nguyen. Synthesis and Analysis of Product-form Petri Nets. Accepted at the conference Petri Nets 201

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure

Mathematics in Software Reliability and Quality Assurance

This monograph concerns the mathematical aspects of software reliability and quality assurance and consists of 11 technical papers in this emerging area. Included are the latest research results related to formal methods and design, automatic software testing, software verification and validation, coalgebra theory, automata theory, hybrid system and software reliability modeling and assessment

Studying the effects of adding spatiality to a process algebra model

We use NetLogo to create simulations of two models of disease transmission originally expressed in WSCCS. This allows us to introduce spatiality into the models and explore the consequences of having different contact structures among the agents. In previous work, mean field equations were derived from the WSCCS models, giving a description of the aggregate behaviour of the overall population of agents. These results turned out to differ from results obtained by another team using cellular automata models, which differ from process algebra by being inherently spatial. By using NetLogo we are able to explore whether spatiality, and resulting differences in the contact structures in the two kinds of models, are the reason for this different results. Our tentative conclusions, based at this point on informal observations of simulation results, are that space does indeed make a big difference. If space is ignored and individuals are allowed to mix randomly, then the simulations yield results that closely match the mean field equations, and consequently also match the associated global transmission terms (explained below). At the opposite extreme, if individuals can only contact their immediate neighbours, the simulation results are very different from the mean field equations (and also do not match the global transmission terms). These results are not surprising, and are consistent with other cellular automata-based approaches. We found that it was easy and convenient to implement and simulate the WSCCS models within NetLogo, and we recommend this approach to anyone wishing to explore the effects of introducing spatiality into a process algebra model

Safety‐oriented discrete event model for airport A‐SMGCS reliability assessment

A detailed analysis of State of the Art Technologies and Procedures into Airport Advanced-Surface Movement Guidance and Control Systems has been provided in this thesis, together with the review ofStatistical Monte Carlo Analysis, Reliability Assessment and Petri Nets theories. This practical and theoretical background has lead the author to the conclusion that there is a lack of linkage in between these fields. At the same of time the rapid increasing of Air Traffic all over the world, has brought in evidence the urgent need of practical instruments able to identify and quantify the risks connected with Aircraft operations on the ground, since the Airport has shown to be the actual ‘bottle neck’ of the entire Air Transport System. Therefore, the only winning approach to such a critical matter has to be multi-disciplinary, sewing together apparently different subjects, coming from the most disparate areas of interest and trying to fulfil the gap. The result of this thesis work has come to a start towards the end, when a Timed Coloured Petri Net (TCPN) model of a ‘sample’ Airport A-SMGCS has been developed, that is capable of taking into account different orders of questions arisen during these recent years and tries to give them some good answers. The A-SMGCS Airport model is, in the end, a parametric tool relying on Discrete Event System theory, able to perform a Reliability Analysis of the system itself, that: • uses a Monte Carlo Analysis applied to a Timed Coloured Petri Net, whose purpose is to evaluate the Safety Level of Surface Movements along an Airport • lets the user to analyse the impact of Procedures and Reliability Indexes of Systems such as Surface Movement Radars, Automatic Dependent Surveillance-Broadcast, Airport Lighting Systems, Microwave Sensors, and so on… onto the Safety Level of Airport Aircraft Transport System • not only is a valid instrument in the Design Phase, but it is useful also into the Certifying Activities an in monitoring the Safety Level of the above mentioned System with respect to changes to Technologies and different Procedures.This TCPN model has been verified against qualitative engineering expectations by using simulation experiments and occupancy time schedules generated a priori. Simulation times are good, and since the model has been written into Simulink/Stateflow programming language, it can be compiled to run real-time in C language (Real-time workshop and Stateflow Coder), thus relying on portable code, able to run virtually on any platform, giving even better performances in terms of execution time. One of the most interesting applications of this work is the estimate, for an Airport, of the kind of A-SMGCS level of implementation needed (Technical/Economical convenience evaluation). As a matter of fact, starting from the Traffic Volume and choosing the kind of Ground Equipment to be installed, one can make predictions about the Safety Level of the System: if the value is compliant with the TLS required by ICAO, the A-SMGCS level of Implementation is sufficiently adequate. Nevertheless, even if the Level of Safety has been satisfied, some delays due to reduced or simplified performances (even if Safety is compliant) of some of the equipment (e.g. with reference to False Alarm Rates) can lead to previously unexpected economical consequences, thus requiring more accurate systems to be installed, in order to meet also Airport economical constraints. Work in progress includes the analysis of the effect of weather conditions and re-sequencing of a given schedule. The effect of re-sequencing a given schedule is not yet enough realistic since the model does not apply inter arrival and departure separations. However, the model might show some effect on different sequences based on runway occupancy times. A further developed model containing wake turbulence separation conditions would be more sensitive for this case. Hence, further work will be directed towards: • The development of On-Line Re-Scheduling based on the available actual runway/taxiway configuration and weather conditions. • The Engineering Safety Assessment of some small Italian Airport A-SMGCSs (Model validation with real data). • The application of Stochastic Differential Equations systems in order to evaluate the collision risk on the ground inside the Place alone on the Petri Net, in the event of a Short Term Conflict Alert (STCA), by adopting Reich Collision Risk Model. • Optimal Air Traffic Control Algorithms Synthesis (Adaptive look-ahead Optimization), by Dynamically Timed Coloured Petri Nets, together with the implementation of Error-Recovery Strategies and Diagnosis Functions

Measurements, Models, Systems and Design

531 s.

Search-based system architecture development using a holistic modeling approach

This dissertation presents an innovative approach to system architecting where search algorithms are used to explore design trade space for good architecture alternatives. Such an approach is achieved by integrating certain model construction, alternative generation, simulation, and assessment processes into a coherent and automated framework. This framework is facilitated by a holistic modeling approach that combines the capabilities of Object Process Methodology (OPM), Colored Petri Net (CPN), and feature model. The resultant holistic model can not only capture the structural, behavioral, and dynamic aspects of a system, allowing simulation and strong analysis methods to be applied, it can also specify the architectural design space. Both object-oriented analysis and design (OOA/D) and domain engineering were exploited to capture design variables and their domains and define architecture generation operations. A fully realized framework (with genetic algorithms as the search algorithm) was developed. Both the proposed framework and its suggested implementation, including the proposed holistic modeling approach and architecture alternative generation operations, are generic. They are targeted at systems that can be specified using object-oriented or process-oriented paradigm. The broad applicability of the proposed approach is demonstrated on two examples. One is the configuration of reconfigurable manufacturing systems (RMSs) under multi-objective optimization and the other is the architecture design of a manned lunar landing system for the Apollo program. The test results show that the proposed approach can cover a huge number of architecture alternatives and support the assessment of several performance measures. A set of quality results was obtained after running the optimization algorithm following the proposed framework --Abstract, page iii

Discrete Event Systems: Models and Applications; Proceedings of an IIASA Conference, Sopron, Hungary, August 3-7, 1987

Work in discrete event systems has just begun. There is a great deal of activity now, and much enthusiasm. There is considerable diversity reflecting differences in the intellectual formation of workers in the field and in the applications that guide their effort. This diversity is manifested in a proliferation of DEM formalisms. Some of the formalisms are essentially different. Some of the "new" formalisms are reinventions of existing formalisms presented in new terms. These "duplications" reveal both the new domains of intended application as well as the difficulty in keeping up with work that is published in journals on computer science, communications, signal processing, automatic control, and mathematical systems theory - to name the main disciplines with active research programs in discrete event systems. The first eight papers deal with models at the logical level, the next four are at the temporal level and the last six are at the stochastic level. Of these eighteen papers, three focus on manufacturing, four on communication networks, one on digital signal processing, the remaining ten papers address methodological issues ranging from simulation to computational complexity of some synthesis problems. The authors have made good efforts to make their contributions self-contained and to provide a representative bibliography. The volume should therefore be both accessible and useful to those who are just getting interested in discrete event systems