America's New Calling Stephen R. Foster, J. Thomas Rogers, Robert S. Potter Southwestern University Georgetown, TX Adviser Rick denman The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
America’s New Calling by Stephen R. Foster, J. Thomas Rogers, Robert S. Potter Southwestern University Georgetown, TX Adviser: Rick Denman The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
Abstract The cell phone revolution warrants an examination of its energy impacts future. Thus, our model adheres to two requirements: it can evaluate e since 1990; and it is flexible enough to predict future energy needs. Mathematically speaking, our model treats households as state machines and uses actual demographic data to guide state transitions. We produce national projections by simu- ting multiple households. Our bottom-up approach remains flexible, allowing us to: 1 model energy consumption for the current United States, 2)determine efficient phone adoption schemes in emerging nations, 3) assess t t of wasteful practices, and 4) predict future energy needs. We show that the exclusive adoption of landlines by an emerging nation would be more than twice as efficient as the exclusive adoption of cell phones. However, we also show that the elemination of certain wasteful practices can make cell phone adoption 175% more efficient at the national level. Furthermore we give two forecasts of the current United States, revealing that a collaboration between cell phone users and manufacturers car result in savings of more than 3.9 billion Barrels of Oil Equivalent over the next 50 years Problem Back ckgroune In the year 1990, less than 3 percent of Americans owned cell phones ITU. Since then,a growing number of households have elected to ditch their landline in favor of acquiring cellular phones for each household member. Our task is to develop a model for analyzing how the cell hone revolution impacts electricity consumption at the national level Such a model ought be able to Assess the energy cost of the cell phone revolution in America Determine an efficient way of introducing phone service to an nation like America. Examine the effects of wasteful cell phone habits Predict future energy needs of a nation(based on multiple growth scenarios. Assumptions The population of the United States is increasing at a rate of roughly 3. 3 million people er year(according to the U.S. Census Bureau The relatively stable energy needs of business landlines, government landlines, payphones etc. have a negligible impact on energy consumption dynamics during the household transition from landlines to cell phones No household member old enough to need phone service is ever without phone service Citizens with more than one cell phone are rare enough to have a negligible energy The energy consumption of the average cell phone re The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
Abstract The ongoing cell phone revolution warrants an examination of its energy impacts – past, present, and future. Thus, our model adheres to two requirements: it can evaluate energy use since 1990; and it is flexible enough to predict future energy needs. Mathematically speaking, our model treats households as state machines and uses actual demographic data to guide state transitions. We produce national pro jections by simulating multiple households. Our bottom-up approach remains flexible, allowing us to: 1) model energy consumption for the current United States, 2) determine efficient phone adoption schemes in emerging nations, 3) assess the impact of wasteful practices, and 4) predict future energy needs. We show that the exclusive adoption of landlines by an emerging nation would be more than twice as efficient as the exclusive adoption of cell phones. However, we also show that the elemination of certain wasteful practices can make cell phone adoption 175% more efficient at the national level. Furthermore, we give two forecasts of the current United States, revealing that a collaboration between cell phone users and manufacturers can result in savings of more than 3.9 billion Barrels of Oil Equivalent over the next 50 years. Problem Background In the year 1990, less than 3 percent of Americans owned cell phones [ITU]. Since then, a growing number of households have elected to ditch their landline in favor of acquiring cellular phones for each household member. Our task is to develop a model for analyzing how the cell phone revolution impacts electricity consumption at the national level. Such a model ought be able to: • Assess the energy cost of the cell phone revolution in America. • Determine an efficient way of introducing phone service to an nation like America. • Examine the effects of wasteful cell phone habits. • Predict future energy needs of a nation (based on multiple growth scenarios.) Assumptions • The population of the United States is increasing at a rate of roughly 3.3 million people per year (according to the U.S. Census Bureau). • The relatively stable energy needs of business landlines, government landlines, payphones, etc. have a negligible impact on energy consumption dynamics during the household transition from landlines to cell phones. • No household member old enough to need phone service is ever without phone service. • Citizens with more than one cell phone are rare enough to have a negligible energy impact. • The energy consumption of the average cell phone remains constant. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
We justify the last assumption on the grounds that future changes in cell phone energy require- ments depend largely on changes in user habits and changes in manufacturing efficiency. Thus they are difficult to predict. However, we drop this assumption in our final sectio Energy Consumption Model Our approach involves three steps: We model households as state machines with various phones and appliances We use demographic data to determine the probability of households changing state. By simulating multiple households, we extrapolate national energy impacts Households The ributes: nt of our model is the household. each household has the follo attr m: A number of members old enough to need a telephone. t: A number of landline telephone c: A number of members with cellular phones The state of each household can be described in terms the above values. We will generate m from available demographic data and hold it constant A household can exist in one of four disjoint states at a time. Each state has two associated conditions Initial State-When a household only uses landline telephones 0 Acquisition State- After a household acquires its first cell phone 00 The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
We justify the last assumption on the grounds that future changes in cell phone energy requirements depend largely on changes in user habits and changes in manufacturing efficiency. Thus, they are difficult to predict. However, we drop this assumption in our final section. Energy Consumption Model Our approach involves three steps: • We model households as state machines with various phones and appliances. • We use demographic data to determine the probability of households changing state. • By simulating multiple households, we extrapolate national energy impacts. Households The basic component of our model is the household. Each household has the following attributes: • m : A number of members old enough to need a telephone. • t : A number of landline telephones. • c : A number of members with cellular phones. The state of each household can be described in terms the above values. We will generate m from available demographic data and hold it constant. A household can exist in one of four disjoint states at a time. Each state has two associated conditions. • Initial State - When a household only uses landline telephones. • t > 0 • c = 0 • Acquisition State - After a household acquires its first cell phone. • t > 0 • 0 0 • c = m The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
Final State- After the household abandons their landline telephones t=0 C= These states are disjoint, but we do not assume that all states must be reached during the time. line of a household. We do assume that cell phones, once acquired, are never lost; and we assume that landlines, once dropped, are never readopted. Thus, a household will never reenter a state that it has left. Thus. a household will reach one or more of the above states in the order listed Suppose a household with three members(m=3), one landline telephone (t= 1), and no cell phones yet(c=0). The graph below shows the complete timeline of a hypothetical household with each of the four phases labeled Landline Power Consumption =,-:= 6 °0gss9"s80oa2.4060811214-16-1820 Note that our model will generate household state transition probabilities from available demo- graphic data. However, this process is simulation dependent; and we discuss it later, in the con text of simulating the current United States Nations Households are only part of the story. We model the national timeline during the country-wide transition from landlines to cell phones as a composition of multiple overlapping household time lines. Furthermore, the decisions that households make regarding when to acquire cell phones and when to abandon their landlines are dependent on the larger national context. For example, a household would be much more likely to acquire its second or third cell phone in 2008 than it would have been in 1990 A hypothetical nation with only three households might have the following timeline composi- tion. The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
• Final State - After the household abandons their landline telephones. • t = 0 • c = m These states are disjoint, but we do not assume that all states must be reached during the timeline of a household. We do assume that cell phones, once acquired, are never lost; and we assume that landlines, once dropped, are never readopted. Thus, a household will never reenter a state that it has left. Thus, a household will reach one or more of the above states in the order listed. Suppose a household with three members (m = 3), one landline telephone (t = 1), and no cell phones yet (c = 0). The graph below shows the complete timeline of a hypothetical household with each of the four phases labeled. 0 2 4 6 8 10 12 14 16 18 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18 20 Power Consumption (watts) Total Power Landline Power Consumption Cell Phone Power Consumption Figure 1. Note that our model will generate household state transition probabilities from available demographic data. However, this process is simulation dependent; and we discuss it later, in the context of simulating the current United States. Nations Households are only part of the story. We model the national timeline during the country-wide transition from landlines to cell phones as a composition of multiple overlapping household timelines. Furthermore, the decisions that households make regarding when to acquire cell phones and when to abandon their landlines are dependent on the larger national context. For example, a household would be much more likely to acquire its second or third cell phone in 2008 than it would have been in 1990. A hypothetical nation with only three households might have the following timeline composition: The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
ouse 2 --a- =4==L= The fact that the three household power usages converge is a result of there being 3 memebers in each of the three randomly selected houses monitored here. For every day, we aggregate the total rate of energy consumption for each household, generating a national timeline like so 9092"9496980002"040608101214161820222426283032"343638‘40 Time We now proceed to construct such a timeline for the current United States. The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
0 5 10 15 20 25 ’90 ’92 ’94 ’96 ’98 ’00 ’02 ’04 ’06 ’08 ’10 ’12 ’14 ’16 ’18 ’20 ’22 ’24 ’26 ’28 ’30 ’32 ’34 ’36 ’38 ’40 Power Consumption (watts) Time House 1 House 2 House 3 Figure 2. The fact that the three household power usages converge is a result of there being 3 memebers in each of the three randomly selected houses monitored here. For every day, we aggregate the total rate of energy consumption for each household, generating a national timeline like so: 0 10 20 30 40 50 60 ’90 ’92 ’94 ’96 ’98 ’00 ’02 ’04 ’06 ’08 ’10 ’12 ’14 ’16 ’18 ’20 ’22 ’24 ’26 ’28 ’30 ’32 ’34 ’36 ’38 ’40 Power Consumption (watts) Time Total Figure 3. We now proceed to construct such a timeline for the current United States. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
The Current u.s Using Technological Data In order to use our model in conjunction with relevant data, we have to calculate the following Wattage: The average rate of energy consumption of a cell phone over its lifetime WAttage: The average rate of energy consumption of a landline phone over its lifetime Note that we only deal with cordless landline phones because corded phones use minimal levels of energy and are ignored in the literature we have reviewed(Frey, Rosen, and Watts) Ne derive Wattage as follows: Wattage= Chargerwattage front Joules) Lifetime(seconds) With this formula, we incorporate the upfront energy cost in joules of manufacturing a cell phone(Upfront)into the overall average wattage of a cell phone by dividing the upfront cost by the lifetime of a cell phone(Lifetime)in seconds. We add to this the wattage of the average cell phone charger which is what consumes energy during the use-phase of a cell phone's life cycle (Note: The vast majority of cell phone energy consumption occurs in the manufacturing-phas and the use-phase Frey, so we ignore the rest of a cell phone's life cycle Wattage=Cordlesswattage + Upfront (joules) The following table lists values obtained from research done by Frey et al Chargerwattage 1.835 watts Table 1 Though there exist many different kinds of cordless phones, we choose to use the values for cord less phones with integrated answering machines, as determined by rosen 167MJ =3 years Cordlesswattage 3.539 watts Thus, our simulation uses the following value Wattage =4.182 watts L 5.304 watts Using Demographic Data We need demographic data to help guide the transition of household states over the course of a simulation. We could allow houses to decide randomly when and whether to adopt new cell phones as well as when and whether to drop their landline. However, we prefer to use actual penetration data to probabilistically weight household decisions The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
The Current U.S. Using Technological Data In order to use our model in conjunction with relevant data, we have to calculate the following values: • Cwattage : The average rate of energy consumption of a cell phone over its lifetime. • LWattage : The average rate of energy consumption of a landline phone over its lifetime. Note that we only deal with cordless landline phones because corded phones use minimal levels of energy and are ignored in the literature we have reviewed (Frey, Rosen, and Watts). We derive Cwattage as follows: Cwattage = Chargerwattage + Cup front (joules) Clifetime (seconds) (1) With this formula, we incorporate the upfront energy cost in joules of manufacturing a cell phone (Cup front) into the overall average wattage of a cell phone by dividing the upfront cost by the lifetime of a cell phone (Clifetim e) in seconds. We add to this the wattage of the average cell phone charger – which is what consumes energy during the use-phase of a cell phone’s life cycle. (Note: The vast majority of cell phone energy consumption occurs in the manufacturing-phase and the use-phase [Frey], so we ignore the rest of a cell phone’s life cycle.) By analogy: Lwattage = Cordlesswattage + Lup front (joules) Llifetim e (seconds) (2) The following table lists values obtained from research done by Frey et al.. Cup front = 148 MJ Clifetim e = 2 years Chargerwattage = 1.835 watts Table 1. Though there exist many different kinds of cordless phones, we choose to use the values for cordless phones with integrated answering machines, as determined by Rosen. Lup front = 167 MJ Llifetim e = 3 years Cordlesswattage = 3.539 watts Table 2. Thus, our simulation uses the following values: • Cwattage = 4.182 watts • Lwattage = 5.304 watts Using Demographic Data We need demographic data to help guide the transition of household states over the course of a simulation. We could allow houses to decide randomly when and whether to adopt new cell phones as well as when and whether to drop their landline. However, we prefer to use actual penetration data to probabilistically weight household decisions. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
Consider the household decision of whether to purchase a cell phone in month M. We hree-step process to produce the cell phone acquisition probability function a(M) employed in our simulation: Find historic data about the number of of cell phone owners over time Interpolate between the data points Define a(M), the probability of a simulated household acquiring a cell phone in month M For step one, we used the following data obtained from the International Telecommunication Union. In step two, we use a linear interpolation between available data points to make a con tinuous function from 1990(the start of our simulation) to 2009 Cell Phone Penetration Demographics Then, we use a linear regression to extrapolate the function between 2009 and 2040. Call this function f. Then, for step three, C(H, M) a(M)=f(M) m(H, M H∈ Houses Where c(H, M) is the number of cell phones owned by members of simulated household H in month M; and m(H, M) is the number of members in simulated household H in month M and ' is the set of all households in the simulation. In essence, Equation 3 subtracts the current simulated cell phone penetration during month M from the approximated market pene- tration,f(M), which is derived from available data Using a(M), the households in our simulation make decisions that approximate historical data As the second term in Equation 3 approaches the historical value returned by f(M), the chances of a simulated household buying a cell phone decreases to zero The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
Consider the household decision of whether to purchase a cell phone in month M. We use a three-step process to produce the cell phone acquisition probability function a(M) employed in our simulation: • Find historic data about the number of of cell phone owners over time. • Interpolate between the data points. • Define a(M), the probability of a simulated household acquiring a cell phone in month M. For step one, we used the following data obtained from the International Telecommunication Union. In step two, we use a linear interpolation between available data points to make a continuous function from 1990 (the start of our simulation) to 2009. 0 0.2 0.4 0.6 0.8 1 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Percentage Year Cell Phone Penetration Demographics Figure 4. Then, we use a linear regression to extrapolate the function between 2009 and 2040. Call this function f. Then, for step three, a(M) = f(M) − X H∈H ouses c(H, M) X H∈Houses m(H, M) (3) Where c(H, M) is the number of cell phones owned by members of simulated household H in month M; and m(H, M) is the number of members in simulated household H in month M; and ‘Houses’ is the set of all households in the simulation. In essence, Equation 3 subtracts the current simulated cell phone penetration during month M from the approximated market penetration, f(M), which is derived from available data. Using a(M), the households in our simulation make decisions that approximate historical data. As the second term in Equation 3 approaches the historical value returned by f(M), the chances of a simulated household buying a cell phone decreases to zero. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
We perform an almost identical process with historic landline ownership data in order to deter mine the probability of a household dropping their landline in month M. Because the process is the same, we omit it. Mnemonically, however: a(M) shall be the probability of acquiring a cell phone; d(M)shall be the probability of dropping a landline Simulating the Current U. s The historical demographic data will help guide our simulation, and the technological data will help us calculate the rate of energy consumption at any point during the simulation. With that d, we algorithmically generate household timelines like While month m is before end date F H∈ Houses if h is in’ initial’or' acquisition’ state get a new cell phone with probability a(M) f h is in transition, state get rid of landline with probability d(m) End For alculate power consumption using Wattage, Wattage, and current ph +1 month Here is the national timeline detailing the rate of energy consumption for the current United States over the past nineteen years 2000 Landline power Cell Phone Power Consumption 1400 Time Interesting features of this graph are The steep energy consumption as Americans acquire cell phones yet retain their landlines. The drop after cell phone penetration slows and landlines are abandoned The slope after households dropped their landlines and the population grows The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
We perform an almost identical process with historic landline ownership data in order to determine the probability of a household dropping their landline in month M. Because the process is the same, we omit it. Mnemonically, however: a(M) shall be the probability of acquiring a cell phone; d(M) shall be the probability of dropping a landline. Simulating the Current U.S. The historical demographic data will help guide our simulation, and the technological data will help us calculate the rate of energy consumption at any point during the simulation. With that said, we algorithmically generate household timelines like so: While month M is before end date For every house H ∈ Houses do if H is in ’initial’ or ’acquisition’ state get a new cell phone with probability a(M) if H is in ’transition’ state get rid of landline with probability d(M) End For Calculate power consumption using Cwattage, Lwattage, and current phone ownership. Let M = M + 1 month end while Here is the national timeline detailing the rate of energy consumption for the current United States over the past nineteen years. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ’90 ’00 ’10 ’20 ’30 ’40 ’49 ’59 Power Consumption (Megawatts) Time Total Power Landline Power Consumption Cell Phone Power Consumption Figure 5. Interesting features of this graph are: • The steep energy consumption as Americans acquire cell phones yet retain their landlines. • The drop after cell phone penetration slows and landlines are abandoned. • The rising slope after households have dropped their landlines and the population grows. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
At first, most households tend to be in an Acquisition State, having both landlines and an increasing number of cell phones. Next, households begin to progress to a Transition State slowly dropping their landlines while retaining their cell phones - hence, the overall consump- tion drop. The final upward slope represents the steady state, in which population growth(and associated cell phone acquisition) is the only factor affecting energy consumption Optimal Telephone Adoption Imagine an emerging nation without phone service but with an economic status roughly similar to the current United States. We now examine two hypothetical scenarios for introducing phone service to this nation Cell phones Only · Landlines Only Because it took Russia roughly 6 years for cell phone penetration to go from 2 percent to 105 percent ITU, we assume a similar timescale for introducing cell phones to our hypothetical nation. Furthermore, a country with the same economic status as the U.s. should be capable of making a similarly quick adoption of either cell phones or landline phones, even though landline phone infrastructure involves the extra complexity of laying cables Cell Phones Only For our cell phone introduction plan, we assume that 0 percent of the population in 2009 has been given cell phones and that 100 percent of the population in 2015 has been given a cell phone. If we interpolate linearly between these two dates, we can derive the number of people that will be given a cell phone in any month during the 6 year period. If we assume that the rate at which cell phones consume energy remains roughly the same between 2009 and 2015 then we have all the information we need to run our simulation The only major change we make to our model is that the Initial State of a household now involves having no phones at all, and the Final State involves each household member owning a Cell Phone Nation=- 1200 The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
At first, most households tend to be in an Acquisition State, having both landlines and an increasing number of cell phones. Next, households begin to progress to a Transition State, slowly dropping their landlines while retaining their cell phones – hence, the overall consumption drop. The final upward slope represents the steady state, in which population growth (and associated cell phone acquisition) is the only factor affecting energy consumption. Optimal Telephone Adoption Imagine an emerging nation without phone service but with an economic status roughly similar to the current United States. We now examine two hypothetical scenarios for introducing phone service to this nation: • Cell phones Only • Landlines Only Because it took Russia roughly 6 years for cell phone penetration to go from 2 percent to 105 percent [ITU], we assume a similar timescale for introducing cell phones to our hypothetical nation. Furthermore, a country with the same economic status as the U.S. should be capable of making a similarly quick adoption of either cell phones or landline phones, even though landline phone infrastructure involves the extra complexity of laying cables. Cell Phones Only For our cell phone introduction plan, we assume that 0 percent of the population in 2009 has been given cell phones and that 100 percent of the population in 2015 has been given a cell phone. If we interpolate linearly between these two dates, we can derive the number of people that will be given a cell phone in any month during the 6 year period. If we assume that the rate at which cell phones consume energy remains roughly the same between 2009 and 2015, then we have all the information we need to run our simulation. The only major change we make to our model is that the Initial State of a household now involves having no phones at all, and the Final State involves each household member owning a cell phone. 0 200 400 600 800 1000 1200 1400 1600 ’10 ’12 ’14 ’16 ’18 ’20 ’22 ’24 ’26 ’28 ’30 Power Consumption (Megawatts) Time Cell Phone Nation Figure 6. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved
The steep slope levels off when cell phone market penetration reaches 100 percent, and the only relevant factor after that is the population growth Landlines Only Now we alter our model such that the Initial State of a household still involves having no hones, and the Final State involves having one landline. We take the previous graph and overlay a graph generated from a simulation that assumes the nation's households will adopt landlines instead of cell phone 1400 1200 ,-------:--- Based solely on this graph, the Landlines Only plan seems optimal, since it requires less than half the power of the Cell Phones Only plan. However, we prefer to delay our recommendation First, we examine a way to make cell phone adoption more energy efficient Wasteful Charging and "Vampire"Chargers Although the above comparative analysis of the two plans shows Landlines Only to be a clear winner,we should take into account that the rate at which cell phones consume energy varies depending on the practices of cell phone users. Until now, we have assumed that the energy consumption of a cell phone is equal to the consumption of its charger -even though many people do not use their charger as conservatively as they could. We now relax this assumption and assess the total cost of certain wasteful practices by supposing that our hypothetical mation's citizens never charge a cell phone after it is finished charging The UMAP Journal 30(3)(2009). @Copyright 2009 by COMAP, Inc. All rights reserved
The steep slope levels off when cell phone market penetration reaches 100 percent, and the only relevant factor after that is the population growth. Landlines Only Now we alter our model such that the Initial State of a household still involves having no phones, and the Final State involves having one landline. We take the previous graph and overlay a graph generated from a simulation that assumes the nation’s households will adopt landlines instead of cell phones. 0 200 400 600 800 1000 1200 1400 1600 ’10 ’12 ’14 ’16 ’18 ’20 ’22 ’24 ’26 ’28 ’30 Power Consumption (Megawatts) Time Cell Phone Nation Landline Nation Figure 7. Based solely on this graph, the Landlines Only plan seems optimal, since it requires less than half the power of the Cell Phones Only plan. However, we prefer to delay our recommendation. First, we examine a way to make cell phone adoption more energy efficient. Wasteful Charging and “Vampire” Chargers Although the above comparative analysis of the two plans shows Landlines Only to be a clear winner, we should take into account that the rate at which cell phones consume energy varies depending on the practices of cell phone users. Until now, we have assumed that the energy consumption of a cell phone is equal to the consumption of its charger – even though many people do not use their charger as conservatively as they could. We now relax this assumption and assess the total cost of certain wasteful practices by supposing that our hypothetical nation’s citizens never • charge a cell phone after it is finished charging. The UMAP Journal 30 (3) (2009). ©Copyright 2009 by COMAP, Inc. All rights reserved