Stochastic Population Models

The chapter “Stochastic Population Models” introduces the concept of stochasticity, why it is sometimes incorporated into models, the consequences of stochasticity for population models, and how these types of models are used to evaluate extinction risk. Ecological systems are (seemingly) governed by randomness, or “stochasticity.” A stochastic model is one that explicitly includes randomness in the prediction of state variable dynamics. Because these models have a random component, each model run will be unique and will rarely look like a deterministic simulation. In this chapter, simple unstructured and density-dependent models are presented to show core concepts, and extensions to structured and density-dependent models are given.

Uncertainty Simulation of Wood Chipping Operation for Bioenergy Based on Queuing Theory

Managing uncertainty is the way to secure stability of the supply chain. Uncertainty within chipping operation and chip transportation causes production loss. In the wood chip supply chain for bioenergy, operational uncertainty mainly appears in the moisture content of the material, chipping productivity, and the interval of truck arrival. This study theoretically quantified the loss in wood chip production by applying queuing theory and stochastic modelling. As well as the loss in production, the inefficiency was identified as the idling time of chipper and the queuing time of trucks. The aim of this study is to quantify the influence of three uncertainties on wood chip production. This study simulated the daily chip production using a mobile chipper by applying queuing theory and stochastic modelling of three uncertainties. The result was compared with the result of deterministic simulation which did not consider uncertainty. Uncertainty reduced the production by 14% to 27% compared to the production of deterministic simulation. There were trucks scheduled but not used. The cases using small trucks show the largest daily production amount, but their lead time was the longest. The large truck was sensitive to the moisture content of material because of the balance between payload and volumetric capacity. This simulation method can present a possible loss in production amount and enables to evaluate some ways for the loss compensation quantitatively such as outsourcing or storing buffer. For further development, the data about the interval of truck arrival should be collected from fields and analyzed. We must include the other uncertainties causing technical and operator delays.