How good is stationary analysis for the transient phenomena of connection admission in ATM?
How to decide about the admission of a new connection in ATM with exploiting statistical multiplexing is still an open question. Based on analytical queueing models describing the behaviour of a single line, the effective bandwidth of an individual source has been defined as the service rate necessary for guaranteeing a required loss probability (for a given buffer size) . By a stationary analysis, it was shown for some traffic sources that the effective bandwidth is additive, i.e. the sum of the effective bandwidths of two individual sources results in the effective bandwidth of their superposition . However, such results are only reasonable ”if sources come and go relatively slowly compared to the way congestion changes” . In the strict sense, they are only valid, if — after the admission of a new connection — the existing traffic does not change for a very long time. Such an assumption is obviously not realistic, since there will be considerable fluctuation within the existing traffic of a link. This paper applies the method of the unfinished work of [19, 10] for obtaining transient perstream Quality of Service (QOS) parameters for a (correlated) superposition of a new connection and the existing traffic of a given link. Numerical results show that transient loss probabilities can be significantly higher than the stationary ones. This illustrates that QOS will be — at least temporarily — worse than expected through the effective bandwidth estimate, which is based on stationary computations.
KeywordsDiscrete-time finite buffer queue per-stream loss probabilities deterministic service time transient analysis for CAC
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