Energy trade-offs in millimeter wave vehicular networks by exploiting a hyperfractal model

We present results on the trade-offs between the end-to-end communication delay and the energy spent in millimeter wave vehicular communications in urban settings. This study exploits the self-similarities of the traffic and vehicle locations in cities captured in our innovative model called “hyperfractal”. We enrich the model by incorporating road-side infrastructure. We use analytical tools to derive theoretical bounds for the end-to-end communication hop count under two different energy constraints: either total accumulated energy, or maximum energy per node. More precisely, we prove that the hop count is bounded by O(n¹−α/(^dm−1⁾) where α < 1 and d_m > 2 is the precise hyperfractal dimension. This proves that for both constraints the energy decreases as we allow to chose among paths of larger length. In fact, the asymptotic limit of the energy becomes significantly small when the number of nodes becomes asymptotically large. A lower bound on the network throughput capacity with constraints on path energy is also given. The results are confirmed through simulations using different fractal dimensions and path loss coefficients.