Students arrive at the automated vending machine located in the basement of the H-building at a rate of 4.5 per minute, following a Poisson distribution. The coffee machine dispenses a cup of coffee in exactly 9 seconds.(a) Does this situation satisfy the steady state condition?(b) How long does a student have to wait in line, on average, before receiving the service at the automated vending machine? (c) Suppose the vending machine is replaced by a server whose service time is negative exponentially distributed with 6.6667 per minute service rate. How long will a student wait for the service under this scenario?(d) Suppose the server is no longer able to maintain negative exponentially distributed service times. However, the service rate is still the same at 6.6667 per minute. What characteristic/s of the service times would ensure that the average waiting time now is the same as that of the case in part (c)?
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