Abstract We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from quasi birth and death queue. This is accomplished through construction processes on common probability space demonstration distributional coupling relation between them. The results here provide an interpretation for quasi-birth-and-death matrix-geometric approach Ramaswami subsequent based them by Soares Latouche. Keywords: Fluid flowsQueuesStochastic...

We derive several algorithms for the busy period distribution of canonical Markovian fluid flow model. One them is similar to Latouche-Ramaswami algorithm quasi-birth-death models and shown be quadratically convergent. These significantly increase efficiency matrix-geometric procedures developed earlier by authors transient steady-state analyses models.

Abstract Markovian fluid flow models are used extensively in performance analysis of communication networks. They also instances Markov reward that find applications several areas like storage theory, insurance risk and financial models, inventory control. This paper deals with the transient (time dependent) such models. Given a flow, we construct on same probability space sequence queues stochastically coupled to sense at certain selected random epochs, distribution level phase (the state...

An analysis of the time-dependent evolution canonical Markov modulated fluid flow model is presented using elementary level-crossing arguments.

Abstract A new class of probability distributions called "bilateral phase type (BPH)" on (−∞, ∞) is defined as a generalization the versatile (PH) [0, introduced by Marcel F. Neuts. We derive basic descriptors such in an algorithmically tractable manner and show that this has many interesting closure properties dense all real line. Based established versatility tractability distributions, we believe high potential for general use statistics, particularly to cover non-normal also its inherent...

SUMMARY We consider a Markov‐modulated fluid flow queueing model under D ‐policy. As soon as the level reaches zero, server becomes idle. During idle period, arrives from outside according to an underlying continuous time Markov chain (UMC) and does not process fluid. two increase patterns of during period: vertical (Type‐V) linear (Type‐L). The is reactivated only when cumulative in system exceeds predetermined threshold value . derive distributions mean performance measures for both types....

A Markov-modulated Brownian motion (MMBM) is a substantial generalization of the classical Motion and obtained by allowing parameters to be modulated an underlying Markov chain environments. As with Motion, time-dependent analysis MMBM becomes easy once first passage times between levels are determined. However, in those distributions cannot explicitly, we need efficient algorithms compute them. In this article, provide powerful approach based on approximating sequence scaled fluid flows...

We derive several algorithms for the busy period distribution of canonical Markovian fluid flow model. One them is similar to Latouche-Ramaswami algorithm quasi-birth-death models and shown be quadratically convergent. These significantly increase efficiency matrix-geometric procedures developed earlier by authors transient steady-state analyses models.

This article describes our study of the total shift during first passages (one-sided and two-sided exit times) Markov-modulated Brownian motion with bilateral ph-type jumps, which is referred to as MMBM. The defined value a so-called process at passage epochs process, introduced by Bean O'Reilly, behaves like continuous Markovian fluid process; that is, it increases or decreases linearly slopes regulated underlying Markov determines path Hence, notion shift, includes times MMBM special...

We establish some interesting duality results for Markov-modulated fluid flow models. Though models are continuous-state analogues of quasi-birth-and-death processes, do differ by the inclusion a scaling factor.