Question: need help with problem below Consider a queuing system M /M / 00 with unlimited number of servers. Service requests form a Poisson process with

need help with problem below

need help with problem below Consider a queuing system M /M /

Consider a queuing system M /M / 00 with unlimited number of servers. Service requests form a Poisson process with rate A = 5 per hour and service times are independent exponentially distributed with common expectation ,u'1 = 8 minutes. Assume that the system is functioning under stationary distribution. 1. Find expected number L = E [X (t)] of customers in the system. 2. For a departure process, D = {D(t) : t Z 0}, assuming that the system functions under steady state distribution, determine covariance, Cov [D(3), (D(5) - D(1))] between the numbers D(3) of customers who depart by the end of third hour and D(5) D(1) of customers who depart within the interval (1

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