Duality results for Markov-modulated fluid flow models

Soohan Ahn, V. Ramaswami

Type: Article

Publication Date: 2011-08-01

Citations: 5

DOI: https://doi.org/10.1239/jap/1318940473

Abstract

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

Locations

Journal of Applied Probability - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Duality results for Markov-modulated fluid flow models	2011	Soohan Ahn V. Ramaswami
+	Rescaled Markov Processes and Fluid Limits	2003	Philippe Robert
+ PDF Chat	Duality for Stochastic Models of Transport	2013	Gioia Carinci Cristian Giardinà Claudio Giberti Frank Redig
+ PDF Chat	Continuous flows with Markov families	1990	Kazumine Moriyasu
+	Markov-modulated and feedback fluid queues	1998	Werner Scheinhardt
+	Duality theory for Markov processes	1978	Svend Erik Graversen
+	Fluid Flow Models and Queues—A Connection by Stochastic Coupling	2003	Soohan Ahn V. Ramaswami
+ PDF Chat	Duality and intertwining for discrete Markov kernels: relations and examples	2011	Thierry Huillet Servet Martı́nez
+ PDF Chat	Duality and intertwining for discrete Markov kernels: relations and examples	2011	Thierry Huillet Servet Martı́nez
+	Siegmund Duality for Continuous Time Markov Chains on ℤ + d	2018	Pan Zhao
+	Phase Transitions in Stochastic Models of Flow	2007	M. R. Evans
+	Duality for a class of continuous-time reversible Markov models	2021	Freddy Palma Ramsés H. Mena
+ PDF Chat	A Skorokhod map on measure-valued paths with applications to priority queues	2018	Rami Atar Anup Biswas Haya Kaspi Kavita Ramanan
+ PDF Chat	Approximations for Time-Dependent Distributions in Markovian Fluid Models	2016	Sarah Dendievel Guy Latouche
+	Markov-renewal fluid queues	2004	Guy Latouche Tetsuya Takine
+	Markov-renewal fluid queues	2004	Guy Latouche Tetsuya Takine
+	Duality and Intertwining for discrete Markov kernels: a relation and examples	2009	Thierry Huillet Servet Martı́nez
+	On decompositions of non-reversible processes	2022	M. H. Duong J. Zimmer
+	Fluid approach to two-sided Markov-modulated Brownian motion	2014	Guy Latouche Giang T. Nguyen
+	Fluid approach to two-sided Markov-modulated Brownian motion	2014	Guy Latouche Giang T. Nguyen

Works That Cite This (4)

Action	Title	Year	Authors
+	Alternative fluid approximation approach for the steady-state distribution of the two-sided reflected Markov modulated Brownian motion and its computation	2015	Soohan Ahn
+	Total shift during the first passages of Markov-modulated Brownian motion with bilateral ph-type jumps: Formulas driven by the minimal solution matrix of a Riccati equation	2016	Soohan Ahn
+	A quadratically convergent algorithm for first passage time distributions in the Markov-modulated Brownian motion	2016	Soohan Ahn V. Ramaswami
+	Analyses of the Markov modulated fluid flow with one-sided ph-type jumps using coupled queues and the completed graphs	2014	Jung Woo Baek Soohan Ahn

Works Cited by This (8)

Action	Title	Year	Authors
+	Matrix analytic methods for stochastic fluid flows	1999	V. Ramaswami
+	Probabilistic interpretations of some duality results for the matrix paradigms in queueing theory	1990	Søren Asmussen V. Ramaswami
+	A duality theorem for the matrix paradigms in queueing theory	1990	V. Ramaswami
+ PDF Chat	On the Dual Relationship Between Markov Chains of GI/M/1 and M/G/1 Type	2010	Peter Taylor Benny Van Houdt
+	Stationary distributions for fluid flow models with or without brownian noise	1995	Søren Asmussen
+	Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier	2007	Soohan Ahn Andrei L. Badescu V. Ramaswami
+	Fluid Flow Models and Queues—A Connection by Stochastic Coupling	2003	Soohan Ahn V. Ramaswami
+ PDF Chat	On the Dual Relationship Between Markov Chains of GI/M/1 and M/G/1 Type	2010	Peter Taylor Benny Van Houdt