Variance-Time Curve for Packet Streams Generated by Exponentially Distributed ON/OFF Sources

In this letter we provide a solution to an open problem in network traffic characterization. Specifically we present a closed-form expression of the variance-time curve for a packet stream generated by exponentially distributed ON/OFF sources. So far, the variance-time curve for such processes was obtained by numerical analysis at the desired time scales. We also show that under low and medium loads, the variance-time curve obtained by approximating the ON/OFF/Exponential source as a stationary fluid source is over-estimated. Lastly, as a by-product of our analysis, we present a new mathematical identity based on the incomplete Gamma function.