Queueing Systems: Theory and Applications
Approximate analysis of the end-to-end delay in ATM networks
IEEE INFOCOM '92 Proceedings of the eleventh annual joint conference of the IEEE computer and communications societies on One world through communications (Vol. 2)
Queueing Systems: Theory and Applications
State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
A heavy traffic limit theorem for a class of open queueing networks with finite buffers
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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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).