On Numerical Solution of the Markov Renewal Equation: Tight Upper and Lower Kernel Bounds

D. A. Elkins () and M. A. Wortman ()
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D. A. Elkins: General Motors R&D Center
M. A. Wortman: Texas A&M University, College Station

Methodology and Computing in Applied Probability, 2001, vol. 3, issue 3, 239-253

Abstract: Abstract We develop tight bounds and a fast parallel algorithm to compute the Markov renewal kernel. Knowledge of the kernel allows us to solve Markov renewal equations numerically to study non-steady state behavior in a finite state Markov renewal process. Computational error and numerical stability for computing the bounds in parallel are discussed using well-known results from numerical analysis. We use our algorithm and computed bounds to study the expected number of departures as a function of time for a two node overflow queueing network.

Keywords: Markov renewal process; Markov renewal equation; Markov renewal kernel; Toeplitz matrix; convolution integral equation (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1013767704349

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