4 research outputs found
Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments
This paper considers the tail asymptotics for a cumulative process sampled at a heavy-tailed random time . The main contribution of
this paper is to establish several sufficient conditions for the asymptotic
equality as , where and is a certain
positive constant. The main results of this paper can be used to obtain the
subexponential asymptotics for various queueing models in Markovian
environments. As an example, using the main results, we derive subexponential
asymptotic formulas for the loss probability of a single-server finite-buffer
queue with an on/off arrival process in a Markovian environment
Markovian arrivals in stochastic modelling: a survey and some new results
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
starting point is the versatile process introduced by Neuts (1979) which, under some simplified
notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general
point process can be approximated by appropriate MAPs and, on the other hand, the MAPs
provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian
formalism. While a number of well-known arrival processes are subsumed under a BMAP as
special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous
settings or even spatial arrivals. We survey on the main aspects of the BMAP,
discuss on some of its variants and generalizations, and give a few new results in the context of a
recent state-dependent extension.Peer Reviewe
Markovian arrivals in stochastic modelling : a survey and some new results
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 starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension
An EM algorithm for platoon arrival processes in discrete time
The platoon arrival process (PAP), a special case of Markovian arrival process (MAP), occurs in several practical queueing systems. Developing procedures for estimating its parameters is essential in order to successfully use it for representing arrival processes in real systems. We present an EM-based procedure for estimating the parameters of a PA