The Annals of Applied Probability

A stable queueing network with unstable fluid model

Maury Bramson

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Fluid models have become a standard tool for demonstrating stability for queueing networks. It is presently not known, however, when the stability of a fluid model follows from that of the corresponding queueing network. We present an example of a queueing network where such stability does not, in fact, follow. This example also shows that the behavior of the fluid limits and the fluid model solutions for the same queueing network can differ considerably from one another.

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Ann. Appl. Probab. Volume 9, Number 3 (1999), 818-853.

First available in Project Euclid: 21 August 2002

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Queueing networks fluid limits fluid models


Bramson, Maury. A stable queueing network with unstable fluid model. Ann. Appl. Probab. 9 (1999), no. 3, 818--853. doi:10.1214/aoap/1029962815.

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