## Section: New Results

### Energy Trade-offs for end-to-end Communications in Urban Vehicular Networks exploiting an Hyperfractal Model

In [33] presented this year at MSWIM DIVANet we show results on the trade-offs between the end-to-end communication delay and energy spent for completing a transmission in vehicular communications in urban settings. This study exploits our innovative model called " hyperfractal " that captures the self-similarity of the topology and vehicle locations in cities. We enrich the model by incorporating roadside 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 $O\left(n\right(1-\alpha )/(dm-1\left)\right)$ where $\alpha <1$ and $m>2$ 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 exhaustive simulations using different hyperfractal dimensions and path loss coefficients.