Modeling Technological Deployment and Renewal: Monotonic vs. Oscillating Industrial Dynamics

TL;DR

This paper develops a parsimonious framework that combines a logistic S-curve deployment with a renewal mechanism governed by end-of-life distributions to model long-run technology deployment and renewal. By analyzing P_{tot}(t) = P_{dep}(t) + \int_{0}^{\infty} P_{tot}(t-\theta) p_{EoL}(\theta) d\theta and decomposing into replacement waves via convolutions, the authors derive a Renewal Steady State and characterize transient dynamics using Laplace transforms, revealing an endogenous fast-versus-slow deployment dichotomy. A key finding is the overshoot criterion, with a critical ratio \tau_{dep}/\tau_{EoL} in roughly [0.27,0.34], predicting when production will oscillate versus converge monotonically, a result supported by case studies on nuclear power plants and smartphones. The work highlights important policy and industry implications, showing that long-life infrastructure deployment and renewal can generate endogenous business cycles that interact with macroeconomic conditions and inform strategies for capacity sizing, material planning, and second-hand markets in energy and digital infrastructure sectors.

Abstract

This study proposes a new model based on a classic S-curve that describes deployment and stabilization at maximum capacity. In addition, the model extends to the post-growth plateau, where technological capacity is renewed according to the distribution of equipment lifespans. We obtain two qualitatively different results. In the case of "fast" deployment, characterized by a short deployment time in relation to the average equipment lifetime, production is subject to significant oscillations. In the case of "slow" deployment, production increases monotonically until it reaches a renewal plateau. These results are counterintuitively validated by two case studies: nuclear power plants as a fast deployment and smartphones as a slow deployment. These results are important for long-term industrial planning, as they enable us to anticipate future business cycles. Our study demonstrates that business cycles can originate endogenously from industrial dynamics of installation and renewal, contrasting with traditional views attributing fluctuations to exogenous macroeconomic factors. These endogenous cycles interact with broader trends, potentially being modulated, amplified, or attenuated by macroeconomic conditions. This dynamic of deployment and renewal is relevant for long-life infrastructure technologies, such as those supporting the renewable energy sector and has major policy implications for industry players.

Figures (6)

• Figure 1: Comparison between Smartphones (left) and Nuclear Plants (right) deployment dynamics. Upper panels display the technology adoption or deployment, through number of active smartphone subscriptions and active nuclear capacity. Lower panels display the "equipment production" supporting the deployment, through annual smartphone sales and nuclear capacity novel connections to the grid.
• Figure 2: Fast deployment and Slow deployment behaviors. Model outputs simulates a discretized version of Eq. (\ref{['eq:model']}) with a $0.1$ year step and tools from $numpy$ package within the Python programming environment. All the curves are computed with $\tau_{EoL} = 30$ years and $CV_{EoL} = 0.2$, for the fast deployment$\tau_{dep} = 4$ years (\ref{['fig:FastProduction']}) and for slow deployment$\tau_{dep} = 12$ years (\ref{['fig:SlowProduction']}).
• Figure 3: Overshoot and roots of the characteristic equation for different distributions and values of $CV_{EoL}$
• Figure 4: Effectiveness of the analytical approximation (Eq. \ref{['eq:Ptotapprox']}) and corresponding transition time.
• Figure 5: The figure shows a comparison between historical data on global nuclear capacity and annual new plant connections (production) and the model output for production. The model output is generated using parameters from Table \ref{['tab:nuclear']}.