The Squared Coefficient of Variation for MMPP is Greater than Unity

TL;DR

This paper proves that the squared coefficient of variation for Markov Modulated Poisson Processes exceeds one, confirming the folklore that these processes are bursty, and provides a stochastic order relation.

Contribution

It offers the first proof that the squared coefficient of variation for MMPP is greater than one, establishing a theoretical foundation for the burstiness characteristic.

Findings

Squared coefficient of variation for MMPP exceeds one

Provides a formal proof of burstiness property

Establishes a stochastic order relation for MMPP

Abstract

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.