Matrix-Analytic Methods in Stochastic Models

Abstract

The Marcovian arrival process: some future directions an algorithm for the P(n,t) matrices of a continuous BMAP a pre-emptive priority Queue with non-renewal inputs analysis of a multiserver delay-loss system with a general Markovian arrival process analysis of a finite capacity multi-server Queue with non-preemptive priorities and non-renewal input matrix-multiplicative approach to quasi-birth-and-death processes a level crossing analysis in the MAP/G/1 Queue performance analysis and optimal threshold policies for Queueing systems with several heterogeneous servers and Markov modulated arrivals phase type distributions and related point processes fitting and recent advances parameter approximation for phase type distributions SPH-distributions and the rectangle-iterative algorithm execution time on unreliable server with latent breakdowns asymptotic analysis of switching Queueing systems in conditions of small and heavy loading matrix analytic methods: a tutorial overview with some extensions and new results matrix-analytic methods for Markov chains on a tree structure renewal theory and Queueing algorithms for matrix-exponential distributions determination of explicit solutions to a general class of Markov processes equilibrium distributions for level-dependent quasi-birth-and-death processes.