5 papers · 1 filter
Modeling random traffic accidents by conservation laws
Simone Göttlich, Stephan Knapp
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents a…
Piecewise deterministic Markov processes driven by scalar conservation laws
Stephan Knapp
We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized…
A Production Model with History Based Random Machine Failures
Stephan Knapp, Simone Göttlich
In this paper, we introduce a time-continuous production model that enables random machine failures, where the failure probability depends historically on the production itself. Th…
Continuous approximation of distributions with application to production
Dieter Armbruster, Simone Göttlich, Stephan Knapp
A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation ) is analyzed. Modeling the…
Load-dependent machine failures in production network models
Simone Göttlich, Stephan Knapp
In this paper, a production model based on (hyperbolic) differential equations with stochastic and load-dependent machine failures is introduced. We derive the model on the base of…