  We characterize trade-offs between the end-to-end communication delay and the
energy in urban vehicular communications with infrastructure assistance. Our
study exploits the self-similarity of the location of communication entities in
cities by modeling them with an innovative model called "hyperfractal". We show
that the hyperfractal model can be extended to incorporate road-side
infrastructure and provide stochastic geometry tools to allow a rigorous
analysis. We compute theoretical bounds for the end-to-end communication hop
count considering two different energy-minimizing goals: either total
accumulated energy or maximum energy per node. We prove that the hop count for
an end-to-end transmission is bounded by $O(n^{1-\alpha/(d_F-1)})$ where
$\alpha<1$ and $d_F>2$ is the fractal dimension of the mobile nodes process.
This proves that for both constraints the energy decreases as we allow choosing
routing paths of higher length. 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. We show that our model fits real deployments where open data
sets are available. The results are confirmed through simulations using
different fractal dimensions in a Matlab simulator.
