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Folklore often treats the Markov Modulated Poisson Process as bursty becausethe variance divided by the expectation of counts is greater than unity. Whenviewed through the lens of the inter-event process, this ideally corresponds toa squared coefficient of variation greater than unity. As this has not beenproved to date, we provide a proof together with an associated stochastic orderrelation.

The Squared Coefficient of Variation for MMPP is Greater than Unity