A Brownian model for multiclass queueing networks with finite buffers
Author: 
Wanyang DaiAuthors Info & Claims
Pages 145 - 160
Abstract
This paper is concerned with the heavy traffic behavior of a type of multiclass queueing networks with finite buffers. The network consists of d single server stations and is populated by K classes of customers. Each station has a finite capacity waiting buffer and operates under first-in first-out (FIFO) service discipline. The network is assumed to have a feedforward routing structure under a blocking scheme. A server stops working when the downstream buffer is full. The focus of this paper is on the Brownian model formulation. More specifically, the approximating Brownian model for the networks is proposed via the method of showing a pseudo-heavy-traffic limit theorem which states that the limit process is a reflecting Brownian motion (RBM) if the properly normalized d-dimensional workload process converges in distribution to a continuous process. Numerical algorithm with finite element method has been designed to effectively compute the solution of the Brownian model (W. Dai, Ph.D. thesis (1996); X. Shen et al. The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks, under revision for Queueing Systems).
References
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{4} W. Dai, Brownian approximations for queueing networks with finite buffers: modeling, heavy traffic analysis and numerical implementations, Ph.D. Thesis, School of Mathematics, Georgia Institute of Technology, 1996. Also published in UMI Dissertation Services, A Bell & Howell Company, 300 N.Zeeb Road, Ann Arbor, Michigan 48106, USA, 1997.
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{12} R.J. Williams, Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse, Queueing Systems 30 (1998) 27-88.
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{13} X. Shen, H. Chen, J.G. Dai, W. Dai, The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks (2000) under revision for Queueing Systems.
Index Terms
- A Brownian model for multiclass queueing networks with finite buffers
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Elsevier Science Publishers B. V.
Netherlands
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Published: 01 July 2002
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