On the Convergence of Multiclass Queueing Networks in Heavy Traffic

Jim G. Dai · Viên Nguyen

25 citations0/0 files storedThe Annals of Applied Probability

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

The subject of this paper is the heavy traffic behavior of a general class of queueing networks with first-in-first-out (FIFO) service discipline. For special cases that require various assumptions on the network structure, several authors have proved heavy traffic limit theorems to justify the approximation of queueing networks by reflecting Brownian motions. Based on these theorems, some have conjectured that the Brownian approximation may in fact be valid for a more general class of queueing networks. In this paper, we prove that the Brownian approximation does not hold for such a general class of networks. Our findings suggest that it may be fruitful to consider a more general class of approximating processes.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 25 citations exist upstream.

References

1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1957Networks of Waiting Lines 1984Open Queueing Networks in Heavy Traffic 1970Multiple channel queues in heavy traffic. I 1981Reflected Brownian Motion on an Orthant 1988Brownian Models of Queueing Networks with Heterogeneous Customer Populations 1987Brownian models of open queueing networks with homogeneous customer populations ∗1970Multiple channel queues in heavy traffic. II: sequences, networks, and batches

Cited by

2002Stability of queueing networks and scheduling policies 2000A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines 1996Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline 2000Diffusion Approximations for Some Multiclass Queueing Networks with FIFO Service Disciplines 2001Existence Condition for the Diffusion Approximations of Multiclass Priority Queueing Networks

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.