Question: Customer arrivals at a single-server queue follow a Poisson distribution with a rate of 4 customers per minute. The service duration time follows an exponential

Customer arrivals at a single-server queue follow a Poisson distribution with a rate of 4 customers per minute. The service duration time follows an exponential distribution and lasts, on average, 12 seconds. a) Determine: Arrival rate (customers/minute),  = ____________________. Service rate (clients/minute),  = ____________________. b) Percentage of time (%, two decimals) that the server is offering service,  = _____________. c) Average number of customers in line (waiting), Lq = _______________________. d) Average time (in seconds) that a customer spends waiting to receive the service, Wq = _______________________. e) In the current space for the queue, six people can comfortably fit. The probability (%, two decimal places) that the space will be overflowed is: _____________.

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