We derive a kinetic equation for flows on general,
unstructured networks with applications to
production, social and transportation networks.
This model allows for a
homogenization procedure, yielding a macroscopic
transport model for large networks on large time scales.
Continuum models of re-entrant production systems are developed that treat
the flow of products in analogy to traffic flow. Specifically, the dynamics of material flow through a re-entrant
factory via a parabolic conservation law is modeled describing the product density and flux in the factory. The basic
idea underlying the approach is to obtain transport coefficients for fluid dynamic models in a multi-scale setting
simultaneously from Monte Carlo simulations and actual observations of the physical system, i.e. the factory.
Since partial differential equation (PDE) conservation laws are successfully used for modeling the dynamical behavior of product flow in manufacturing systems, a re-entrant manufacturing system is modeled using a diffusive PDE. The specifics of the production process enter into the velocity and diffusion coefficients of the conservation law. The
resulting nonlinear parabolic conservation law model allows fast and accurate simulations. With the traffic flow-like
PDE model, the transient behavior of the discrete event simulation (DES) model according to the averaged influx, which
is obtained out of discrete event experiments, is predicted. The work brings out an almost universally applicable tool
to provide rough estimates of the behavior of complex production systems in non-equilibrium regimes.
A kinetic model for a specific agent based simulation to generate the sales curves of successive generations of high-end computer chips is developed.
The resulting continuum market model consists of transport equations in two variables, representing the availability of money and the desire to buy a new chip.
In lieu of typical collision terms in the kinetic equations that discontinuously change the attributes of an agent, discontinuous changes are initiated
via boundary conditions between sets of partial differential equations. A scaling analysis of the transport equations determines the different time scales that constitute
the market forces, characterizing different sales scenarios. It is argued that the resulting model can be adjusted to generic markets of multi-generational technology products
where the innovation time scale is an important driver of the market.
This paper presents a continuum - traffic flow like - model for the flow
of products through complex production networks, based on statistical
information obtained from extensive observations of the system.
The resulting model consists of a system of hyperbolic conservation laws,
which, in a relaxation limit, exhibit the correct diffusive properties
given by the variance of the observed data.
The dynamics of insurance plans have been under the microscope in recent years due to the controversy surrounding the implementation of the Affordable Care Act (Obamacare) in the United States. In this paper, we introduce a game between an insurance company and an ensemble of customers choosing between several insurance plans. We then derive a kinetic model for the strategies of the insurer and the decisions of the customers and establish the conditions for which a Nash equilibrium exists for some specific customer distributions. Finally, we give some agent-based numerical results for how the plan enrollment evolves over time which show qualitative agreement to "experimental" results in the literature from two plans in the state of Massachusetts.