A mean field model for an optical switch with a large number of wavelengths and centralized partial conversion
Faculty of Sciences. Mathematics and Computer Science

article

2010
Amsterdam
, 2010

Computer. Automation

Performance evaluation. - Amsterdam

67(2010)
:11
, p. 1044-1058

0166-5316

000283808600006

E

English (eng)

University of Antwerp

This paper analyzes an optical switch with centralized partial wavelength conversion by means of a mean field model. The model can be used to approximate the behavior of a switch with a large number of output wavelengths, and it becomes more accurate as the number of wavelengths increases. At each wavelength, packets arrive according to a Markovian arrival process, and their size follows a general distribution with finite support. Moreover, these traffic characteristics may be different for each output port. The model provides insight into the effect of the traffic parameters on the packet loss probability, which is considered the main performance measure. In particular, we have found that, if the arrival process is Bernoulli, the loss probability is affected by the packet-size distribution only through its mean. This is no longer the case if the arrivals follow a more general Markovian process, although we have found that even in this case the loss probability is hardly sensitive to the packet-size distribution. Also, under Bernoulli arrivals we provide a closed expression for the minimum conversion ratio required to attain zero losses when the number of wavelengths tends to infinity. For Markovian arrivals we are able to compute this ratio with a single run of the mean field model.

https://repository.uantwerpen.be/docman/irua/2b7321/4446.pdf

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