" operations research "

Ex. 4 Consider the following queuing system with four servers. Suppose, currently, all four serves are busy and three customers are waiting (Customers 5, 6, 7). Suppose Customer 1, Customer 2, Customer 3, and Customer I started getting serviced 5, 4, 2 and 1 minutes ago, respectively. The service time of all four servers follows an exponential distribution with a mean of 1 minute. Assume the interarrival times of customers to the queuing system are exponentially distributed with rate of 2 customers per minute. First server Customer1 O + Second server Customer-2 Customer Customer-6 Customers + Thind server Customer-3 Fourth server Customer-4 (a) What is the probability that the next customer takes more than 4 minutes to arrive? (b) What is the probability that it takes the first server more than 2 more minutes (1.d., more than 7 minutes since Customer 1 started getting serviced) to complete Customer 1's service? (c) What is the probability that Customer 4 completes service before Customer 1? Why? (d) What is the probability that Customer 4 completes service before Customers 1 and 27 Why? (e) What is the probability that Customer 5 will be the last of the five customers (Customers 1. 2. 3, 4, and 5) to complete service if first come first serve policy is tused? Why