Packet Travel Times in Wireless Relay Chains under Spatially and Temporally Dependent Interference

TL;DR

This paper analyzes the travel times of packets in wireless relay chains considering realistic spatiotemporal interference dependencies, revealing significant impacts on expected travel time, variance, and packet speed compared to independent interference models.

Contribution

It introduces a method to compute the distribution, expected value, and variance of packet travel times under a realistic interference model with dependencies.

Findings

Spatiotemporal dependence increases expected travel time and variance.

Packet speed decreases due to interference dependencies.

Results differ significantly from independent interference assumptions.

Abstract

We investigate the statistics of the number of time slots $T$ that it takes a packet to travel through a chain of wireless relays. Derivations are performed assuming an interference model for which interference possesses spatiotemporal dependency properties. When using this model, results are harder to arrive at analytically, but they are more realistic than the ones obtained in many related works that are based on independent interference models. First, we present a method for calculating the distribution of $T$. As the required computations are extensive, we also obtain simple expressions for the expected value $\mathrm{E} [T]$ and variance $\mathrm{var} [T]$. Finally, we calculate the asymptotic limit of the average speed of the packet. Our numerical results show that spatiotemporal dependence has a significant impact on the statistics of the travel time $T$. In particular, we show that, with respect to the independent interference case, $\mathrm{E} [T]$ and $\mathrm{var} [T]$ increase, whereas the packet speed decreases.