A single machine is used between 8 A.M. and 4 p.M. to perform EKGs (electrocardiograms). There are 3 waiting spaces, and any arrival finding no available waiting space is lost to the system. The arrival rate per hour at time t = (t = 0 is 8 A.M., and t = 8 is 4 p.M.) is given by
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Assume that service times are exponential and an average of 7 EKGs can be completed per hour. Also assume that arrivals follow a nonhomogeneous Poisson process. Determine how the probability that an arriving patient is lost to the system varies during the day.