Payload Size to Maximize Goodput for Noisy Low-Speed Wireless Networks During Message Segmentation: Case of Exponential Message Sizes

This paper derives the exact analytical form of payload size to maximize goodput for wireless networks where a) applications generate messages whose sizes are exponentially distributed, b) packets created from the message through a segmentation function are lost due to independent bit errors, and c) these lost packets are recovered by a stop-and-wait protocol. In previous work, message sizes are assumed to be constant. However, the analytical form under constant message sizes yields approximate solutions because the goodput curve is not differentiable with respect to the payload size. In this paper, we derive the exact analytical form under the exponential message sizes with the same mean, which yields the differentiable goodput curve. Numerical results for the scenario of IPv6 over a LoWPAN show that a) goodput curves of exponential and constant message sizes with the same mean are nearly identical, and b) the specified payload size, that is 105 bytes, is smaller than the optimal payload size when timeout value is 100 msec and bit error rate is 10–⁴, which is measured for actual industrial wireless link conditions.