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Abstract:Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones. We establish a mathematical model to analyze the energy consequences of the cell phone revolution in terms of electricity use.
Key words:cell phone revolution;energy consequence;mathematical model
中圖分类号:TN916.1 文献标识码:A 文章编号:1009-8283(2009)09-0268-02
In the modern time, cell phone reduces the cost of important information, plays a crucial role in both facilitate international and domestic trades, as well as impacts the efficiency of medical service.
Consider a city and estimate from available data the number H of households, with m members each, that in the past were serviced by landlines. Now, suppose that some landlines are replaced by cell phones. We model the consequences of this change for electricity utilization in the city, during the transition steady state. The analysis takes into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones .
1 Definition
We define the variable following:
H is defined as the number of households.
m is defined as the number of the people per household.
A is defined as the number of cell phones being used.
M is defined as the number of landline phone being used.
p1 is defined as the energy cost per hour per landline phone.
p2 is defined as the energy cost per hour per cell phone.
p21 is defined as the energy cost per hour per cell phone which regularly works.
p22 is defined as the wasted energy cost per hour per cell phone which breaks or gets lost.
p23 is defined as the energy cost of wasteful practice per hour per cell phone.
Q is defined as the up level of the storage of energy per cell phone.
a is defined as the probability of the loss of cell phone per hour.
b is defined as the expected life span per cell phone.
c is defined as the proportion of the rechargers plugged in without recharging cell phones to all the recharges.
d is defined as the proportion of the cell phones charged every night to all the cell phones.
Pp is defined as the wasted power each recharger plugged in.
Qc is defined as the wasted electrical energy cost per night each cell phone charged every night.
P is defined as the sum of the cost of electrical energy per hour during cell phone revolution.
P0 is defined as the sum of the cost of electrical energy per hour before cell phone revolution.
△p is defined as the sum of the additional cost of electrical energy per hour because of cell phone revolution.
2 Assumption
To simplify the model, we make some assumption.
There is not any person who does not have any kind of communication equipment in this city.
There is not any person who has more than one cell phone in this city.
The left electrical energy z inside the battery of the lost or broken cell-phone obeys the mean distribution.
The life span of the cell-phone x obeys the exponential distribution.
All the landline phones are same. All the cell-phones are same.
When a person's cell-phone get lost or break, he (she) will begin to use a new one immediately and with no delay.
Both the cell-phone and the landline phone are being used always, unless they get lost or break.
Both the power of cell-phone and landline phone is two constant numbers(p1,p2).
The reasons that the cell-phone can not be used are only two: Get lost and break.
3 Modeling
3.1 measure p2
We know that there are many kinds of cost. But we simplify the kinds to three: the energy cost of the cell phones being used; the energy cost of the lost cell phones that break or get lost; the energy cost of wasteful practice.
(1)We can measure energy cost per hour per cell-phone being used by its normal rated power.
We consider it as a constant p21.
(2)We can know that the life span of the cell-phone x obey an exponential distribution:
The probability density of x is f(x)
The mathematical expectation of x is Ex
Ex=b
So the probability of break per cell phone per hour is 1/b.
And the probability of getting lost per cell phone per hour is a.
Thus the sum probability of break and getting lost per cell phone per hour is (a+1/b).
We also know that the energy left inside the lost cell phone obey a mean distribution, because the cell phone can be lost with any quantity of energy. It is random.
The probability density of z is f(z)
Q is the up-level of the energy inside the cell phone.
The mathematical expectation of z is Ez
Ez=Q/2
The excepted wasted energy cost because of break or getting lost per cell phone per hour is p22
p22=(a+1/b)*Ez=(a+1/b)*Q/2
(3)Cell phones periodically need to be recharged. However, many people always keep their recharger plugged in. The proportion of the rechargers plugged in without recharging cell phones to all the recharges is a constant c. The wasted power each recharger plugged in is Pp. The wasted power of all such behavior is c*Pp.
Additionally, many people charge their phones every night, whether they need to be recharged or not. The proportion of the cell phones charged every night to all the cell phones is d. The wasted electrical energy of each such person one night is Qc. The waster power of all such behavior is d*Qc/24.
Model the energy costs of this wasteful practice for this city.
p23= c*Pp+ d*Qc/24.
The energy cost per cell phone p2 is the sum of p21 , p22 and p23.
p2=p21+p22+p23
3.2 measure M and A.
Estimate from available data the number H of households, with m members each, that in the past were serviced by landlines,M=H, A=0.
Now some people have cell phones, if every member of a household owns cell-phone, they will not use landline phone any longer. M decrease and A increase.0 3.3 measure p,p0 and △p.
We assume that the power per cell phone is p1.
P0=H*p1.
We assume that there are M households using landlines in this city, that the number of landlines is M.And we assume that there are A people using landlines in this city, that the number of cell phones is A.So the power of all landlines and cell phones in this city is:
p=M*p1+A*p2.
Now we have got: p=M*p1+A*[p21+(a+1/b)*Q/2+ c*Pp+ d*Qc/24].
the sum of the additional cost of electrical energy per hour because of cell phone revolution:
△p=p-p0.
At last, we come up with a formula:
△p = M*p1+A*[p21+(a+1/b)*Q/2+ c*Pp+ d*Qc/24]- H*p1.
Key words:cell phone revolution;energy consequence;mathematical model
中圖分类号:TN916.1 文献标识码:A 文章编号:1009-8283(2009)09-0268-02
In the modern time, cell phone reduces the cost of important information, plays a crucial role in both facilitate international and domestic trades, as well as impacts the efficiency of medical service.
Consider a city and estimate from available data the number H of households, with m members each, that in the past were serviced by landlines. Now, suppose that some landlines are replaced by cell phones. We model the consequences of this change for electricity utilization in the city, during the transition steady state. The analysis takes into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones .
1 Definition
We define the variable following:
H is defined as the number of households.
m is defined as the number of the people per household.
A is defined as the number of cell phones being used.
M is defined as the number of landline phone being used.
p1 is defined as the energy cost per hour per landline phone.
p2 is defined as the energy cost per hour per cell phone.
p21 is defined as the energy cost per hour per cell phone which regularly works.
p22 is defined as the wasted energy cost per hour per cell phone which breaks or gets lost.
p23 is defined as the energy cost of wasteful practice per hour per cell phone.
Q is defined as the up level of the storage of energy per cell phone.
a is defined as the probability of the loss of cell phone per hour.
b is defined as the expected life span per cell phone.
c is defined as the proportion of the rechargers plugged in without recharging cell phones to all the recharges.
d is defined as the proportion of the cell phones charged every night to all the cell phones.
Pp is defined as the wasted power each recharger plugged in.
Qc is defined as the wasted electrical energy cost per night each cell phone charged every night.
P is defined as the sum of the cost of electrical energy per hour during cell phone revolution.
P0 is defined as the sum of the cost of electrical energy per hour before cell phone revolution.
△p is defined as the sum of the additional cost of electrical energy per hour because of cell phone revolution.
2 Assumption
To simplify the model, we make some assumption.
There is not any person who does not have any kind of communication equipment in this city.
There is not any person who has more than one cell phone in this city.
The left electrical energy z inside the battery of the lost or broken cell-phone obeys the mean distribution.
The life span of the cell-phone x obeys the exponential distribution.
All the landline phones are same. All the cell-phones are same.
When a person's cell-phone get lost or break, he (she) will begin to use a new one immediately and with no delay.
Both the cell-phone and the landline phone are being used always, unless they get lost or break.
Both the power of cell-phone and landline phone is two constant numbers(p1,p2).
The reasons that the cell-phone can not be used are only two: Get lost and break.
3 Modeling
3.1 measure p2
We know that there are many kinds of cost. But we simplify the kinds to three: the energy cost of the cell phones being used; the energy cost of the lost cell phones that break or get lost; the energy cost of wasteful practice.
(1)We can measure energy cost per hour per cell-phone being used by its normal rated power.
We consider it as a constant p21.
(2)We can know that the life span of the cell-phone x obey an exponential distribution:
The probability density of x is f(x)
The mathematical expectation of x is Ex
Ex=b
So the probability of break per cell phone per hour is 1/b.
And the probability of getting lost per cell phone per hour is a.
Thus the sum probability of break and getting lost per cell phone per hour is (a+1/b).
We also know that the energy left inside the lost cell phone obey a mean distribution, because the cell phone can be lost with any quantity of energy. It is random.
The probability density of z is f(z)
Q is the up-level of the energy inside the cell phone.
The mathematical expectation of z is Ez
Ez=Q/2
The excepted wasted energy cost because of break or getting lost per cell phone per hour is p22
p22=(a+1/b)*Ez=(a+1/b)*Q/2
(3)Cell phones periodically need to be recharged. However, many people always keep their recharger plugged in. The proportion of the rechargers plugged in without recharging cell phones to all the recharges is a constant c. The wasted power each recharger plugged in is Pp. The wasted power of all such behavior is c*Pp.
Additionally, many people charge their phones every night, whether they need to be recharged or not. The proportion of the cell phones charged every night to all the cell phones is d. The wasted electrical energy of each such person one night is Qc. The waster power of all such behavior is d*Qc/24.
Model the energy costs of this wasteful practice for this city.
p23= c*Pp+ d*Qc/24.
The energy cost per cell phone p2 is the sum of p21 , p22 and p23.
p2=p21+p22+p23
3.2 measure M and A.
Estimate from available data the number H of households, with m members each, that in the past were serviced by landlines,M=H, A=0.
Now some people have cell phones, if every member of a household owns cell-phone, they will not use landline phone any longer. M decrease and A increase.0
We assume that the power per cell phone is p1.
P0=H*p1.
We assume that there are M households using landlines in this city, that the number of landlines is M.And we assume that there are A people using landlines in this city, that the number of cell phones is A.So the power of all landlines and cell phones in this city is:
p=M*p1+A*p2.
Now we have got: p=M*p1+A*[p21+(a+1/b)*Q/2+ c*Pp+ d*Qc/24].
the sum of the additional cost of electrical energy per hour because of cell phone revolution:
△p=p-p0.
At last, we come up with a formula:
△p = M*p1+A*[p21+(a+1/b)*Q/2+ c*Pp+ d*Qc/24]- H*p1.