Ten phones are linked by only one line to the network. Each phone

In summary, the conversation discusses the probability of multiple phones needing to use a single line at the same time. The average time each phone needs to use the line is 12 minutes per hour and the calls made by different phones are independent of each other. The conversation also touches on whether this situation can be modeled as a binomial or Poisson distribution, with the suggestion that it may be a M/M/1 queue. The rate at which the phones request the line is unclear, with a suggestion that it may follow a Poisson distribution with a parameter of 5.
  • #1
forty
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Ten phones are linked by only one line to the network. Each phone needs to log on average 12mins an hour to the network. calls made by different phones are independent of each other. They can't simultaneously call.

What is the probability that k phones (k=0,1,2...10) simultaneously need the line? what is the most likely number of phones requiring the line at one time?

Is this a binomial distribution?

if so, does P(X=k) = (10 choose k)(.2^k)(.8^(10-k)) ??

and also would E[X] = 2?

OR is this a Poisson (or other :S) distribution?

Any help as always is greatly appreciated :)
 
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  • #2


Personally I would use Poisson, esspecialy as it involves time you may want to use a Poisson process. The nice thing about Poisson is independent Poisson processes do not jump at the same time and you can add Poisson processes very easily.

It looks like a M/M/1 queue.
 
  • #3


So if i was to use a Poisson distribution would my parameter be the average? which is 2?
 
  • #4


Is there not a rate of calls? The rate should be the rate of people calling in.
 
  • #5


So by rate you mean 12/60 (12 minutes an hour)?
 
  • #6


No I mean the rate of calls being made or the line requested.
 
  • #7


Focus said:
No I mean the rate of calls being made or the line requested.

I don't really know what you mean by this. On average the likely hood of anyone line being used is (12/60)? Hmmm now I'm really lost >.<
 
  • #8


forty said:
I don't really know what you mean by this. On average the likely hood of anyone line being used is (12/60)? Hmmm now I'm really lost >.<

Sorry I think I confused myself here. The callers need 12mins each per hour right? How is their requests distributed? Do they have Poisson arrival then get served for 12 mins or can they call in for 2 mins then hang up and phone again after a while and spend 10 mins?
 
  • #9


So... I think what you are getting at is that its a Binomial distribution with the probability being a poisson distribution? if not I'm completely lost :(
 
  • #10


Sorry what I am trying to get at is this; if you have one line and people calling in with Poisson with rate [itex]\lambda[/itex] and say they take an exponential time on the line with parameter [itex]\mu[/itex] then you have a M/M/1 queue. Your question looks very similar to this but it depends on the rate they request the line at. The exponential parameter looks like 5 as they need on average 12 mins on the network, but I don't understand what rate they are calling with.
 

1. How does a phone network work with only one line?

The network uses a technique called "multiplexing" to allow multiple phones to share one line. This means that the phones take turns sending and receiving data over the line, so it appears as if each phone has its own dedicated line.

2. Can all ten phones make calls at the same time?

No, since there is only one line, only one phone can make a call at a time. The other phones will have to wait until the line is available.

3. What happens if the line gets disconnected or damaged?

If the line is disconnected or damaged, all ten phones will lose their connection to the network. This can be a major inconvenience and can disrupt communication for all users. It is important to ensure the line is well-maintained and protected.

4. How is data transmitted over the single line?

The data is transmitted using a technique called "packet switching." This means that the data is divided into small packets and sent over the line, with each packet containing information about its destination. Once all the packets arrive at their destination, they are reassembled to form the original data.

5. Can the network support internet access for all ten phones?

It depends on the capacity of the line and the internet speed. If the line has a high bandwidth and the internet speed is fast enough, then it is possible for all ten phones to have internet access. However, this may result in slower internet speeds for each phone due to the shared nature of the line.

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