Mean Delay in Poisson Wireless Networks with Optimal Packet Fragmentation

Abstract

We investigate simple packet fragmentation strategies to minimize the mean packet reception delay in a time-slotted wireless network where many static devices connect to their respective receivers, without prior knowledge of the effects of fading and interference on reception. When a packet of a given size is fragmented, and each slot is used to send one fragment, a smaller fragment size trades off an increase in the number of fragments for more robust reception of individual fragments (due to a lower per-slot transmission rate). Increasing fragment size has the opposite effect. We explicitly characterize this tradeoff in both noise-limited and interference-limited Poisson wireless networks, and derive bounds on the optimum number of fragments for a given packet size to minimize the mean packet delay. Beyond predicting the well-known threshold effect—i.e., packets smaller than the fragmentation threshold should not be fragmented to reduce mean packet delay—our model provides an analytical basis for deriving and applying such thresholds in practice. Interestingly, the fragmentation threshold depends on a parameter we term network conductance, which captures the average impact of the network’s geometry and fading. To the best of our knowledge, this is the first such analysis.