09年美国大学生数学建模大赛B题

Modeling Telephony Energy Consumption 353

Modeling Telephony Energy

Consumption

Amrish Deshmukh

Rudolf Nikolaus Stahl

Matthew Guay

Cornell University

Ithaca, NY

Advisor: Alexander Vladimirsky

have become a ubiquitous part of the modern world. Simultaneously, the

infrastructure for traditional telephones is well in place and the energy costs

of such phones may very well be less. As a superior technology, cellphones

have gradually begun to replace the landline but consumer habits and per-

ceptions have slowed this decline from being an outright abandonment.

To evaluate the energy consequences of continued growth in cellphone

use and a decline in landline use, we present a model that describes three

processes—landline consumption, cellphone consumption, and landline

abandonment—as economic diffusion processes. In addition, our model

describes the changing energy demands of the two technologies and con-

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354 The UMAP Journal 30.3 (2009)

Introduction

The telephone has become a fundamental part of our social fabric. In the

past couple of decades, we have seen a shift from fixed landline telephones,

generally one per household, to individual ownership of cellphones. We

attempt to determine the impact of this change on American energy con-

counterparts. Likewise, the total energy cost of cellphone usage is com-

plicated by such factors as recharging, replacement, and battery recycling.

Our model takes all of these factors into account, and additionally attempts

to use the limited real-world data available to chart the changes in each of

these factors over time.

Perhaps the most complex factor to model is adoption of technological

innovations in a population. This is relevant not only to landline adoption

and cellphone adoption, but additionally de-adoption of landline phones

in the face of cellphone usage can be considered an independent innovation

and modeled accordingly. Research into the phenomenon indicates that it

where P is the proportion of the population that has adopted the innova-

tion at time

t, r is the adoption rate, and K is the saturation point for the

innovation.

Using the descriptions of such a model, we arrive at an accurate fit to

available data and can predict future demand for cellphones and landlines.

Determining the cost for these respective technologies we arrive at the total

energy burden. Briefly, we explore how this question relates to the en-

ergy consumption of other household electronics, and how much waste is

generated therein. Additionally, we explore the caveat that technological

discover that a country, here a “Pseudo-U.S.,” which supports a cellphone-

only communicativeinfrastructure minimizesits total energy consumption,

and also does not violate social demand for novel technologies. Finally, we

Modeling Telephony Energy Consumption 355

estimate the total energy consumption by such a nation over the next 50

years.

Model Overview

We examine two approaches to modeling technology diffusion through

a population. The first attempts to gauge technology adoption at the house-

hold level and aggregate these results to model global trends. However,

this approach is unsuccessful, and we explain why. The second approach

Model Derivation

Our model describes U.S. usage rates for landlines and cellphones as

three diffusive innovation curves. Consider the adoption of an innova-

tion

Y . At small times after the development of this innovation, adoption

of

Y throughout a population is minimal. As the innovation spreads, de-

mand increases until a saturation point is reached. Thus, the spread of

Y

Of course, adoption is not uniform between different technologies, and

saturation rates likewise vary. By introducing constants

r for adoption rate

and

S for saturation rates, we can refine our model to

dY

= rY