RAP-modulated Fluid Processes: First Passages and the Stationary Distribution

2021/01/08 by Bean, Nigel G., Nguyen, Giang T., Nielsen, Bo F. +1
#60G17 #60J25 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.03242

Abstract

We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (RAP), which we call the RAP-modulated fluid process. As opposed to the classic stochastic fluid process driven by a Markov jump process, the underlying PDMP of a RAP-modulated fluid process has a continuous state space and is driven by matrix parameters which may not be related to an intensity matrix. Through novel techniques we show how well-known formulae associated to the classic stochastic fluid process, such as first passage probabilities and the stationary distribution of its queue, translate to its RAP-modulated counterpart.

Related

• Weak convergence of quasi-birth-and-death processes with rational arrival process components to fluid queues
• The morphing of fluid queues into Markov-modulated Brownian motion
• Analysis of fluid flow models
• Doubling Algorithms for Stationary Distributions of Fluid Queues: A Probabilistic Interpretation
• Gaussian Fluid Queue with Autocorrelated Input