Diffusion models are widely used in ecology, and in more general population biology contexts, for predicting population-size distributions and extinction times. They are often used because they areâ€¦ (More)

We propose a model for the presence/absence of a population in a collection of habitat patches. This model assumes that colonisation and extinction of the patches occur as distinct phases.â€¦ (More)

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide resultsâ€¦ (More)

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits aâ€¦ (More)

We construct a stochastic patch occupancy metapopulation model that incorporates variation in habitat quality and an Allee-like effect. Using some basic results from stochastic ordering, weâ€¦ (More)

Loss networks have long been used to model various types of telecommunication network , including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, toâ€¦ (More)

Admission controls, such as trunk reservation, are often used in loss networks to optimize their performance. Since the numerical evaluation of performance measures is complex, much attention hasâ€¦ (More)

For a random process (X(t), t â‰¥ 0), suppose that there is a cost fx associated with being in state x. This paper is concerned with evaluating the distribution and the expected value of the total costâ€¦ (More)