A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems

Central and Local Limit Theories in Markov Dependent Random Variables

Functional Limit Theorems for A New Class of Non-Stationary Shot Noise Processes

We study a class of non-stationary shot noise processes which have a general arrival process of noises with non-stationary arrival rate and a general shot shape function. Given the arrival times, the shot noises are conditionally independent and each shot noise has a general (multivariate) cumulative distribution function (c.d.f.) depending on its arrival time. We prove a functional weak law of...

Algorithms for Computing Limit distributions of Oscillating Systems with Finite Capacity

We address the batch arrival  systems with finite capacity under partial batch acceptance strategy where service times or rates oscillate between two forms according to the evolution of the number of customers in the system. Applying the theory of Markov regenerative processes and resorting to Markov chain embedding, we present a new algorithm for computing limit distributions of the number cus...

On Markov-Additive Jump Processes

In 1995, Pacheco and Prabhu introduced the class of so–called Markov–additive processes of arrivals in order to provide a general class of arrival processes for queueing theory. In this paper, the above class is generalized considerably, including time–inhomogeneous arrival rates, general phase spaces and the arrival space being a general vector space (instead of the finite–dimensional Euclidea...

Staffing a Service System with Non-poisson Nonstationary Arrivals

Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson nonstationary arrival process that includes as a special case the nonstationary Cox process (a modification of a Poisson proc...