This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs),
which constitute a rich class of point processes used extensively in stochastic modelling. Our …

Through the analysis of a dataset of ultra high frequency order book updates, we introduce a
model which accommodates the empirical properties of the full order book together with the …

A double quasi-birth-and-death (QBD) process is the QBD process whose background
process is a homogeneous birth-and-death process, which is a synonym of a skip-free …

We are concerned with the stationary distributions of reflecting processes on
multidimensional nonnegative orthants and other related processes, provided they exist …

The performance analysis of multiserver systems is notoriously hard, especially when the
system involves resource sharing or prioritization. We provide two new analytical tools for …

The two-node tandem Jackson network serves as a convenient reference model for the
analysis and testing of different methodologies and techniques in rare event simulation. In …

Denote by $\mathcal {W} _1 $ the set of complex valued functions of the form $ a (z)=\sum _
{i=-\infty}^{+\infty} a_iz^ i $ such that $\sum _ {i=-\infty}^{+\infty}| ia_i|<\infty $. We call QT …

A geometric tail decay of the stationary distribution has been recently studied for the GI/G/1
type Markov chain with both countable level and background states. This method is …

We consider the class of level-independent quasi-birth-and-death (QBD) processes that
have countably many phases and generator matrices with tridiagonal blocks that are …

Over the years, traffic lights have been used to manage traffic at road intersections. Though
relatively effective, the vehicular queues that build up at each intersection being managed …