Quasi-Birth-and-Death Processes with Rational Arrival Process Components

  title={Quasi-Birth-and-Death Processes with Rational Arrival Process Components},
  author={Bean and Bo Friis Nielsen},
In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We demonstrate the analysis by considering a queue where the arrival process and the sequence of service… CONTINUE READING

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Point processes with finite-dimensional conditional probabilities

  • S. Asmussen, M. Bladt
  • Stochastic Processes and their Applications, 82…
  • 1999
Highly Influential
10 Excerpts

Matrix-Exponential Distributions: Calculus and Interpretations via Flows

  • M. Bladt, M. F. Neuts
  • Stochastic Models, 19:113–124,
  • 2003
Highly Influential
4 Excerpts

Characterization of Matrix Exponential Distributions

  • M. Fackrell
  • Ph. D. Thesis, Department of Applied Mathematics…
  • 2003
3 Excerpts

A Tutorial Overview of Matrix Analytic Methods: with some Extensions & new Results In Matrix-Analytic Methods in Stochastic Models, Lecture Notes in Pure and Applied Mathematics, 183:261-296, eds

  • V. Ramaswami
  • S.R. Chakravarthy and A.S. Alfa, Marcel Dekker
  • 1996
2 Excerpts

Renewal Theory and Queueing Algorithms for Matrix- Exponential Distributions

  • S. Asmussen, M. Bladt
  • Matrix-Analytic Methods in Stochastic Models…
  • 1996
1 Excerpt

Queueing Theory: A Linear Algebra Approach

  • L. Lipsky
  • 1992
2 Excerpts

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