On Exponential Ergodicity of Multiclass Queueing Networks
One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have finite moments, then the queue lengths also have finite m...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer
2011
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| Online Access: | http://hdl.handle.net/1721.1/65922 https://orcid.org/0000-0001-8898-8778 |
| Summary: | One of the key performance measures in queueing systems is the exponential
decay rate of the steady-state tail probabilities of the queue lengths. It is known
that if a corresponding fluid model is stable and the stochastic primitives have
finite moments, then the queue lengths also have finite moments, so that the tail
probability P(· > s) decays faster than s−n [s superscript -n] for any n. It is natural to conjecture
that the decay rate is in fact exponential.
In this paper an example is constructed to demonstrate that this conjecture
is false. For a specific stationary policy applied to a network with exponentially
distributed interarrival and service times it is shown that the corresponding fluid
limit model is stable, but the tail probability for the buffer length decays slower
than s−log s [s superscript -log s]. |
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