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 …

Matrix analytic methods constitute a success story, illustrating the enrichment of a science,
applied probability, by a technology, that of digital computers. Marcel Neuts has played a …

Quasi-Birth-and-Death (QBD) processes have been analysed in detail by many authors.
This paper considers the calculation of equilibrium distributions in level dependent QBD …

A class of single server vacation queues which have single arrivals and non-batch service is
considered in discrete time. It is shown that provided the interarrival, service, vacation, and …

We develop a simple algorithm to compute the rate matrices of ergodic level-dependent
quasi-birth-and-death processes, based on a matrix continued fraction representation and a …

This paper analyzes the dynamics of a level-dependent quasi-birth–death process X={(I (t), J
(t)): t≥ 0}, ie, a bi-variate Markov chain defined on the countable state space∪ i= 0∞ l (i) …

Recently multiserver queues with setup times have been extensively studied because they
have applications in power-saving data centers. A challenging model is the M/M/c/Setup …

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 …

Abstract Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit
unusual and interesting behavior. One of the simplest examples of such a process is the two …

Note that the serial structure of blockchain has many essential pitfalls, thus a data network
structure and its DAG-based blockchain are introduced to resolve the blockchain pitfalls …