A fast food restraint manager is trying to determine how to have customers wait in line. There are two options under consideration: (i) a separate line for each of the three tellers, or (ii) a single line that will feed into the three tellers as they become available. Case (i) can be thought of as having three distinct single server queues, while case (ii) can be thought of as a single queue with three servers. Each waiter provides service times that follow an exponential distribution, with a mean service rate of 15 customers per hour. We assume that customer arrivals follow a Poisson distribution. In case (i) we assume that the average arrival rate to each queue is 10 customers per hour, and in case (ii) we assume that the average arrival rate is 30 customers per hour. If the manager’s only concern is the average time that each customer spends waiting in line, which option should be used?
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