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