The Squared Coefficient of Variation for MMPP is Greater than Unity

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