The Finite Element Method for Computing the Stationary Distribution of an SRBM in a Hypercube with Applications to Finite Buffer Queueing Networks

Authors:
Xinyang Shen;Hong Chen;J. G. Dai;Wanyang Dai
Affiliations:
Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, Canada;Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, Canada;School of Industrial and Systems Engineering and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;Department of Mathematics, Nanjing University, Nanjing, China
Venue:
Queueing Systems: Theory and Applications
Year:
2002

Citing 7
Cited 4

Conformal mapping solution of Laplace's equation on a polygon with oblique derivative boundary conditions

Journal of Computational and Applied Mathematics
Data networks

Data networks
A set of level 3 basic linear algebra subprograms

ACM Transactions on Mathematical Software (TOMS)
The QNET method for two-moment analysis of open queueing networks

Queueing Systems: Theory and Applications
Steady-state analysis of reflected Brownian motions: characterization, numerical methods and queueing applications

Steady-state analysis of reflected Brownian motions: characterization, numerical methods and queueing applications
Design of manufacturing systems using queueing models

Queueing Systems: Theory and Applications - Special issue on queueing models of manufacturing systems
A heavy traffic limit theorem for a class of open queueing networks with finite buffers

Queueing Systems: Theory and Applications

A Brownian model for multiclass queueing networks with finite buffers

Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Computing the Stationary Distribution of an SRBM in an Orthant with Applications to Queueing Networks

Queueing Systems: Theory and Applications
Heavy traffic steady state approximations in stochastic networks with Lévy inputs

Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Heavy traffic approximation for the stationary distribution of stochastic fluid networks

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper proposes an algorithm, referred to as BNAfm (Brownian network analyzer with finite element method), for computing the stationary distribution of a semimartingale reflecting Brownian motion (SRBM) in a hypercube. The SRBM serves as an approximate model of queueing networks with finite buffers. Our BNAfm algorithm is based on the finite element method and an extension of a generic algorithm developed by Dai and Harrison [14]. It uses piecewise polynomials to form an approximate subspace of an infinite-dimensional functional space. The BNAfm algorithm is shown to produce good estimates for stationary probabilities, in addition to stationary moments. This is in contrast to the BNAsm algorithm (Brownian network analyzer with spectral method) of Dai and Harrison [14], which uses global polynomials to form the approximate subspace and which sometimes fails to produce meaningful estimates of these stationary probabilities. Extensive computational experiences from our implementation are reported, which may be useful for future numerical research on SRBMs. A three-station tandem network with finite buffers is presented to illustrate the effectiveness of the Brownian approximation model and our BNAfm algorithm.