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 …

Queueing theory applications can be discovered in many walks of life including;
transportation, manufacturing, telecommunications, computer systems and more. However …

We consider the asymptotic behaviour of the stationary tail probabilities in the discrete-time
GI/G/1-type queue with countable background state space. These probabilities are …

GI/M/1-type processes are Markov chains with transition matrices having the same structure
as the imbedded Markov chain of a GI/M/1 queue, except that the entries are matrices rather …

In this paper we study the augmented truncation of discrete-time block-monotone Markov
chains under geometric drift conditions. We first present a bound for the total variation …

Markov chains with block-structured transition matrices find many applications in various
areas. Such Markov chains are characterized by partitioning the state space into subsets …

This paper discusses the error estimation of the last-column-block-augmented northwest-
corner truncation (LC-block-augmented truncation, for short) of block-structured Markov …

In this paper, we use the Markov chain censoring technique to study infinite state Markov
chains whose transition matrices possess block-repeating entries. We demonstrate that a …

In this paper, we consider the asymptotic behavior of stationary probability vectors of Markov
chains of GI/G/1 type. The generating function of the stationary probability vector is explicitly …

This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-
augmented truncation, for short) of discrete-time block-monotone Markov chains under …