Analyses of the Markov modulated fluid flow with one-sided ph-type jumps using coupled queues and the completed graphs

作者：Baek Jung Woo; Ahn Soohan^*

来源：Journal of the Korean Statistical Society, 2014, 43(3): 415-424.

DOI：10.1016/j.jkss.2013.12.004

• Markov modulated fluid flow model with jumps
• Riccati equation
• Duality
• ph-type distribution
• The completed graph

In this paper, we analyze Markov modulated fluid flow processes with one-sided ph-type jumps using the completed graph and also through the limits of coupled queueing processes to be constructed. For the models, we derive various results on time-dependent distributions and distributions of first passage times, and present the Riccati equations that transform matrices of the first return times to 0 satisfy. The Riccati equations enable us to compute the transform matrices using Newton%26apos;s method which is known very fast and stable. Finally, we present some duality results between the model with ph-type downward jumps and the model with ph-type upward jumps. This paper contains extended results of Ahn (2009) and probabilistic interpretations given by the completed graphs.

• 出版日期2014-9
• 单位南阳理工学院