TY - JOUR

T1 - Alternative fluid approximation approach for the steady-state distribution of the two-sided reflected Markov modulated Brownian motion and its computation

AU - Ahn, Soohan

N1 - Publisher Copyright:
© 2015 The Korean Statistical Society.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - The steady-state distribution of the two-sided reflected Markov Modulated Brownian motion is derived through an alternative fluid approximation approach. In this paper, we have shown that the distribution can be obtained by taking limit on the steady-state distribution of a weakly convergent Markov modulated fluid model. In addition, we present how the duality theorem developed by Ahn and Ramaswami is applied to get the limit result. For computation, we introduce a quadratically convergent algorithm and its related theories which rely on the fluid approximation approach. Through numerical examples, we finally illustrate behaviors of the steady-state distribution and also some performances of the algorithm.

AB - The steady-state distribution of the two-sided reflected Markov Modulated Brownian motion is derived through an alternative fluid approximation approach. In this paper, we have shown that the distribution can be obtained by taking limit on the steady-state distribution of a weakly convergent Markov modulated fluid model. In addition, we present how the duality theorem developed by Ahn and Ramaswami is applied to get the limit result. For computation, we introduce a quadratically convergent algorithm and its related theories which rely on the fluid approximation approach. Through numerical examples, we finally illustrate behaviors of the steady-state distribution and also some performances of the algorithm.

KW - Duality

KW - Markov modulated Brownian motion

KW - Quadratically convergent algorithm

KW - Steady-state distribution

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=84938210937&partnerID=8YFLogxK

U2 - 10.1016/j.jkss.2014.12.005

DO - 10.1016/j.jkss.2014.12.005

M3 - Article

AN - SCOPUS:84938210937

SN - 1226-3192

VL - 44

SP - 448

EP - 456

JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

IS - 3

ER -