Requests for service in a queuing model follow a Poisson distribution with a mean of five per unit time (a) What is the probability that the time until the first request is less than 4 minutes (b) What is the probability that the time between the second and third requests is greater than 7 5 time units (c) Determine the mean rate of requests such that the probability is 0 9 that there are no requests in 0 5 time units (d) If the service times are independent and exponentially distributed with a mean of 0 4 time units, what can you conclude about the long term response of this system to requests

Question: Requests for service in a queuing model follow a Poisson distribution with a mean of five per unit time. (a) What is the probability that

Requests for service in a queuing model follow a Poisson distribution with a mean of five per unit time.

(a) What is the probability that the time until the first request is less than 4 minutes?

(b) What is the probability that the time between the second and third requests is greater than 7.5 time units?

(d) If the service times are independent and exponentially distributed with a mean of 0.4 time units, what can you conclude about the long-term response of this system to requests?

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