Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201

Human Performance Modelling for Accident Risk Assessment of Active Runway Crossing Operation

A human performance modelling approach is presented for risk assessment of operations with multiple, dynamically interacting agents. The approach is illustrated for a risk model of runway incursion on an active departure runway. This model-based approach can provide detailed, systematically derived results on risk contributions of human operators and technical systems in complex multi-agent environments

Applying complexity science to air traffic management

Complexity science is the multidisciplinary study of complex systems. Its marked network orientation lends itself well to transport contexts. Key features of complexity science are introduced and defined, with a specific focus on the application to air traffic management. An overview of complex network theory is presented, with examples of its corresponding metrics and multiple scales. Complexity science is starting to make important contributions to performance assessment and system design: selected, applied air traffic management case studies are explored. The important contexts of uncertainty, resilience and emergent behaviour are discussed, with future research priorities summarised

Human Performance Modelling for Accident Risk Assessment of Active Runway Crossing Operation

A human performance modelling approach is presented for risk assessment of operations with multiple, dynamically interacting agents. The approach is illustrated for a risk model of runway incursion on an active departure runway. This model-based approach can provide detailed, systematically derived results on risk contributions of human operators and technical systems in complex multi-agent environments

Functional Abstraction of Stochastic Hybrid Systems

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways to define abstractions for stochastic hybrid systems, which preserve the parameters of stochastic reach- ability. A new concept of stochastic bisimulation is introduced and its connection with equivalence of stochastic processes is established

Rare event estimation for a large-scale stochastic hybrid system with air traffic application

Embedding of rare event estimation theory within a stochastic analysis framework has recently led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This chapter presents this rare event estimation theory for diffusions to a Stochastic Hybrid System (SHS) and extends it in order to handle a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the rare event estimation. Essentially, the approach taken is to introduce a suitable aggregation of the discrete modes, and to develop importance sampling and Rao-Blackwellization relative to these aggregated modes. The practical use of this approach is demonstrated for the stimation of mid-air collision for an advanced air traffic control example

Rare event estimation for a large-scale stochastic hybrid system with air traffic application

Embedding of rare event estimation theory within a stochastic analysis framework has recently led to signi��?cant novel results in rare event estimation for a diffusion process using sequential MC simulation. This chapter presents this rare event estimation theory for diffusions to a Stochastic Hybrid System (SHS) and extends it in order to handle a large scale SHS where a very huge number of rare discrete modes may contribute signi��?cantly to the rare event estimation. Essentially, the approach taken is to introduce a suitable aggregation of the discrete modes, and to develop importance sampling and Rao-Blackwellization relative to these aggregated modes. The practical use of this approach is demonstrated for the stimation of mid-air collision for an advanced air traf��?c control example