Covariance Analysis for Packet Size Sequence with Message Segmentations

In many cases, each network imposes a maximum permitted packet size called payload size. Hence, some protocols such as TCP specify a message segmentation function allows a sender to divide a single message greater than the payload size into multiple packets. In this report, we derive an analytical form of a covariance of a packet size sequence for an environment where message segmentations happen. We show that when message sizes are exponentially distributed, the packet sizes are uncorrelated, that is, the covariance is always zero because of the memoryless property of an exponential distribution, even though the message segmentations happen. However, from numerical results where HTTP messages are lognormally distributed according to an actual traffic measurement, we demonstrate that TCP-packet sizes exhibit heavily-correlated property in cases of payload sizes used commonly for TCP.