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 wit
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Consider a two-server parallel queueing system where customers arrive according to a Poisson process with rate λ, and where the service times are exponential with rate μ. Moreover, suppose that arrivals finding both servers busy immediately depart without receiving any service (such a customer is said to be lost), whereas those finding at least one free server immediately enter service and then depart when their service is completed. (a) If both servers are presently busy, find the expected time
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