Interactive appendix

The Channel Strategy Simulator

A public-facing version of the internal model for price, market capture, candidate site allocation, city potential, and operating cost. It is a directional pilot-economics tool, not a financial forecast.

Site profit

Πi=∑j∈Ji[g(p)Qij(1−e−βijnij)−Fij1nij>0−Mijnij]−(Slog⁡+yi)Ni1+αgNi\Pi_i=\sum_{j\in J_i}\left[g(p)Q_{ij}\left(1-e^{-\beta_{ij}n_{ij}}\right)-F_{ij}\mathbf{1}_{n_{ij}>0}-M_{ij}n_{ij}\right]-\frac{(S_{\log}+y_i)N_i}{1+\alpha_g N_i}

Site demand

Qij=wij[(Aia+Bib+Cic)⋅Si⋅ρ],∑jwij≤1Q_{ij}=w_{ij}\left[(A_i a+B_i b+C_i c)\cdot S_i\cdot \rho\right],\qquad \sum_j w_{ij}\le 1

Greedy allocation rule

Δπij(n)=Πi(…,nij+1,…)−Πi(…,nij,…),install if max⁡i,jΔπij>0\Delta\pi_{ij}(n)=\Pi_i(\ldots,n_{ij}+1,\ldots)-\Pi_i(\ldots,n_{ij},\ldots),\qquad \text{install if }\max_{i,j}\Delta\pi_{ij}>0

Selected city

New York

N*

263 machines

Total profit

$385,845

Total machines

608

Profitability Phase Diagram

Monthly contribution across greedy site allocation. Curves continue after each city's N* so the forced-overdeployment decline remains visible. City labels sit at the peak.

min -$36,521 / max $307,394

$307k$221k$135k$49k-$37k089178267356$0New YorkSan FranciscoBostonWashington D.C.ChicagoSeattleLos AngelesPortlandDenverAustinAllocated machines (N)Monthly profit

Top Profitable Cities

$273,552
$44,708
$37,350
$7,453
$6,480
$3,700
$3,599
$3,546
$3,137
$2,320

Live Table

New York$273,552N* 263 - 107/107 active sites
Los Angeles$44,708N* 102 - 31/87 active sites
Chicago$37,350N* 79 - 24/68 active sites
Austin$7,453N* 55 - 24/68 active sites
Portland$6,480N* 39 - 17/48 active sites
Seattle$3,700N* 8 - 4/44 active sites
Denver$3,599N* 10 - 5/51 active sites
Washington D.C.$3,546N* 8 - 4/43 active sites
Boston$3,137N* 34 - 15/44 active sites
San Francisco$2,320N* 10 - 5/48 active sites

Model Notes

Machines are allocated into synthetic high-demand micro-sites, not spread uniformly across a city.

Site-level demand saturates by tier, so each added machine must clear a positive marginal-profit threshold.

The model is most useful for deciding what must be validated in the first campus pilot before broader city expansion.