On the Matrix Renewal Function for Markov Renewal Processes

A Diffusion Approximation for Markov Renewal Processes

For a Markov renewal process where the time parameter is discrete, we present a novel method for calculating the asymptotic variance. Our approach is based on the key renewal theorem and is applicable even when the state space of the Markov chain is countably infinite.

Limiting Covariance in Markov-renewal Processes

General additive functions called rewards are defined on a "regular" finite-state Markov-renewal process. The asymptotic form of the mean total reward in [0,t] has previously been obtained, and it is known that the total rewards are joint-normally distributed as t -► oo. This paper finds the dominant asymptotic term in the covariance of the total rewetrds as a simple function of the moments of ...

Statistical Inference : in Markov - Renewal Processes

The undesirable prospect of increasing congestion un the nation'sairways has caused attention to be focused more and more on terminalareas. Two distinct efforts to improve traffic flow have been studiedelsewhere. One, by means of careful control of aircraft separationalong flight paths leading to the terminal, runways attempts to reduceflow variability, while the other attem...

Renewal Theorems for Markov Chains

Markov Limid processes for representing and solving renewal problems

In this paper a new tool for simultaneous optimization of decisions on multiple time scales is discussed. It combines the dynamic properties of Markov decision processes with the flexible and compact state space representation of Limited Memory Influence Diagrams (LIMIDs).