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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000200011 

CUBO A Mathematical Journal Vol.12, N° 02, (169–187). June 2010

 

A new solution algorithm for skip-free processes to the left

Claus Bauer

Dolby Laboratories, San Francisco, 94103, USA email: cb@dolby.com


ABSTRACT

This paper proposes a new solution algorithm for steady state models describing skip-free processes to the left where each level has one phase. The computational complexity of the algorithm is independent of the number of levels of the system. If the skip parameter of the skip-free process is significantly smaller than the number of levels of the system, our algorithm numerically outperforms existing algorithms for skip-free processes. The proposed algorithm is based on a novel method for applying generalized Fibonacci series to the solution of steady state models.

Key words and phrases: Skip-free processes, Markovian environment, stationary distribution


RESUMEN

Este artículo propone un nuevo algoritmo solución para modelos estado-steady describiendo procesos libres-salto para la izquierda donde todo nivel tiene una fase. La complejidad computacional del algoritmo es independiente del número de niveles del sistema. Si el parámetro de salto de los procesos libre-salto es significativamente pequeño respecto del número de niveles del sistema, nuestro algoritmo numérico supera algoritmos existentes para procesos libre-salto. El algoritmo propuesto se basa en un método reciente para aplicar series de Fibonacci generalizados para la solución de modelos-steady.

AMS 2000 Subj. Class.: 60J10, 60J99



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Received: July 2008.

Revised: April 2009.