Matrix-Analytic Methods in Stochastic Models

S. Chakravarthy, Attahiru S. Alfa

• 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.