Data-unit-size distribution model when message segmentations occur

This paper proposes a data-unit-size distribution model to represent the message segmentation function implemented in many protocols, such as TCP and RLC, that allows a sender to divide a message larger than the payload size ℓ d into multiple packets. To develop a Markov chain for a segmented packet size sequence, we introduce an auxiliary random variable representing two packet types: body and edge packets. The body packet is defined as a segmented packet appearing between the head and penultimate packets in the original message. If a message is segmented, the edge packet is defined as the final segmented packet. If not, it is identified with the original message. The sizes of body packets are equal to ℓ d , whereas those of edge packets are variable, not to exceed ℓ d . Using the Markov chain, we derive analytical forms of the occurrence probability of edge packets, as well as the distribution, mean and variance of packet sizes in the steady state. The key findings from the numerical results based on traffic measurement examples include the following. (1) When Web objects embedded in static Web pages that have a long-tailed size property are transferred using TCP, the occurrence probability of edge packets is not negligible in the case of commonly used values of ℓ d , such as 1460 and 2272 bytes. (2) When IP messages are transferred using RLC protocol, the occurrence probability of edge packets is small because the payload size ℓ d is very small.