What is the PMF of the number of modems in use at the given time?

  • Thread starter wooya
  • Start date
  • Tags
    Time
In summary, an internet service provider has 50 modems for 1000 customers, with each customer having a 0.01 probability of needing a connection at a given time. To determine the PMF of the number of modems in use, we can use the Poisson PMF to approximate the number of customers needing a connection. The probability of there being more customers needing a connection than there are modems can be calculated using an exact formula or approximated using the Poisson approximation.
  • #1
wooya
1
0
An internet service provider uses 50 modems to serve the needs of 1000 customers. It is estimated that at a given time, each customer will need a connection with probability 0.01 independently of the other customers.
(a) What is the PMF of the number of modems in use at the given time?
(b) Repeat part (a) by approximating the PMF of the number of customers that need a connection with a Poisson PMF.
(c) What is the probability that there are more customers needing a connection than there
are modems? Provide an exact, as well as an approximate formula based on the Poisson
approximation of part (b).
 
Physics news on Phys.org
  • #2
What's the problem? The Poisson distribution is really easy to use: just find the expected number of people who will connect at a given point, then use the probability mass formula.
 

1. What is a PMF?

A PMF, or probability mass function, is a statistical function that describes the probability of a discrete random variable taking on a specific value. In other words, it maps out the probabilities of all possible outcomes of a random event.

2. How is the PMF calculated?

The PMF is calculated by dividing the number of times a specific value occurs by the total number of observations. This results in a probability for each possible value of the random variable.

3. What is the significance of the PMF for the number of modems in use at a given time?

The PMF for the number of modems in use at a given time provides valuable information about the distribution of modems in a specific area. It can help predict the likelihood of a certain number of modems being used at any given time, and can also be used to make decisions about network capacity and resources.

4. Can the PMF change over time?

Yes, the PMF can change over time as the number of modems in use at a given time can vary. Factors such as population growth, changes in technology, and network upgrades can all impact the PMF.

5. How can the PMF be used to improve network efficiency?

By analyzing the PMF, network engineers and planners can identify peak usage times and adjust resources accordingly. This can help prevent network congestion and improve overall efficiency and performance.

Similar threads

MHB Probability : minutes that customers get served
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
903
Landline Phone Q: Why is the phone line plugged into modem-not wall?
    • Computing and Technology
Replies
20
Views
5K
Using a modem in a LAN to access the Internet
    • Computing and Technology
Replies
27
Views
2K
MODEM Question -- Can a factory reset & re-register clear up intermittent drops?
    • Computing and Technology
Replies
8
Views
2K
MHB Linear Combination Poisson
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Who Limits My Internet Speed, and How Do They Do It?
    • Computing and Technology
Replies
15
Views
1K
Negative Poisson-Binomial Distribution
    • Set Theory, Logic, Probability, Statistics
Replies
14
Views
6K
Comp Sci Differences between tier-1, tier-2 and tier-3 ISPs-:
    • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
I Adding random numbers: Tolerance analysis
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
338
Cable modem+router recommendation needed
    • Computing and Technology
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top