Matrix-Exponential Distributions in Applied Probability Page 1 Probability Theory and
Stochastic Modelling 81 Mogens Bladt Bo Friis Nielsen Matrix-Exponential Distributions in …

This paper is concerned on an M/M/1 queue with correlated interarrival and service times. In
particular, we assume that the interarrival time and service time of a customer have a …

Motivated by large-scale service systems, we consider an infinite-server queue with batch
arrivals, where the service times are dependent within each batch. We allow the arrival rate …

For a rather general class of risk-reserve processes, we provide an exact method for
calculating different kinds of ruin probabilities, with particular emphasis on variations over …

We study the generalization of the G/G/1 queue obtained by relaxing the assumption of
independence between inter-arrival times and service requirements. The analysis is carried …

Understanding the origin, maintenance and distribution of nature's astonishing diversity of
reproductive systems is a major endeavour in evolutionary biology. One of the oldest …

This work is concerned with the statistical inference of phase-type distributions and the
analysis of distributions with rational Laplace transform, known as matrix-exponential …

Using the bivariate phase-type distribution and Markov modulated fluid flow (MMFF)
process, we introduce a framework to analyze queues with correlated interarrival and …

We extend the construction principle of multivariate phase-type distributions to establish an
analytically tractable class of heavy-tailed multivariate random variables whose marginal …

In this paper, we consider two main families of bivariate distributions with exponential
marginals for a couple of random variables (X 1, X 2). More specifically, we derive closed …