Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The duration of a phone call is assumed to be distributed exponentially with mean 3 minutes. Find the following. (c) The telephone company will install a second booth when convinced that an arrival would expect to have to wait at least 3 minutes for the phone. By how much must the flow of arrivals be increased in order to justify a second booth?
Explanation
The utilization factor of the system is given by the formula λμ / (λ + μ), where λ is the arrival rate and μ is the service rate. In this case, λ = 1/10 and μ = 1/3. Therefore, the utilization factor is 0.5. The probability of waiting more than 3 minutes is given by the formula P(W > 3) = 1 - P(W ≤ 3), where P(W ≤ 3) is the probability of waiting less than or equal to 3 minutes. This can be calculated using the Erlang-C formula.
⬆ Related Topic
📘 Syllabus
View KERALA UNIVERSITY Class 5 Syllabus →
📝 Practice Questions
Practice Previous Year Questions →
🤖 Practice with AI
Generate Practice Question Paper →
📚 Related Concepts
- (b) If the customers arrive at a counter in accordance with Poisson Process with mean rate of 2 per minutes. Find the pr
- Arrivals at a telephone booth is a Poisson process with average lime of 12 minules belween one arrival and the next. The
- Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and th
- Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and th
- Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and th