Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 1 (2013), 151-165.
Computing stationary expectations in level-dependent QBD processes
Stationary expectations corresponding to long-run averages of additive functionals on level-dependent quasi-birth-and-death processes are considered. Special cases include long-run average costs or rewards, moments and cumulants of steady-state queueing network performance measures, and many others. We provide a matrix-analytic scheme for numerically computing such stationary expectations without explicitly computing the stationary distribution of the process, which yields an algorithm that is as quick as its counterparts for stationary distributions but requires far less computer storage. Specific problems arising in the case of infinite state spaces are discussed and the application of the algorithm is demonstrated by a queueing network example.
J. Appl. Probab., Volume 50, Number 1 (2013), 151-165.
First available in Project Euclid: 20 March 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J28: Applications of continuous-time Markov processes on discrete state spaces
Baumann, Hendrik; Sandmann, Werner. Computing stationary expectations in level-dependent QBD processes. J. Appl. Probab. 50 (2013), no. 1, 151--165. doi:10.1239/jap/1363784430. https://projecteuclid.org/euclid.jap/1363784430