Variational problem in the non-negative orthant of R3: reflective faces and boundary influence cones

Authors:
Ahmed El Kharroubi;Abdelhak Yaacoubi;Abdelghani Ben Tahar;Kawtar Bichard
Affiliations:
Faculté des Sciences, Ain Chock, Universite Hassan II, Casablanca, Maroc;Faculté des Sciences, Ain Chock, Universite Hassan II, Casablanca, Maroc;Faculté des Sciences, Ain Chock, Universite Hassan II, Casablanca, Maroc;Faculté des Sciences, Ain Chock, Universite Hassan II, Casablanca, Maroc
Venue:
Queueing Systems: Theory and Applications
Year:
2012

Citing 4
Cited 0

Simple necessary and sufficient conditions for the stability of constrained processes

SIAM Journal on Applied Mathematics
Explicit Solutions for Variational Problems in the Quadrant

Queueing Systems: Theory and Applications
Large deviations of the steady-state distribution of reflected processes with applications to queueing systems

Queueing Systems: Theory and Applications
Reflected Brownian motion in the quadrant: tail behavior of the stationary distribution

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the variational problem in the non-negative orthant of 驴3. The solution of this problem gives the large deviation rate function for the stationary distribution of an SRBM (Semimartingal Reflecting Brownian Motion). Avram, Dai and Hasenbein (Queueing Syst. 37, 259---289, 2001) provided an explicit solution of this problem in the non-negative quadrant. Building on this work, we characterize reflective faces of the non-negative orthant of 驴 d , we construct boundary influence cones and we provide an explicit solution of several constrained variational problems in 驴3. Moreover, we give conditions under which certain spiraling paths to a point on an axis have a cost which is strictly less than the cost of every direct path and path with two pieces.