### What would be average length of queue and waiting time

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At a parking lot, vehicles arrive according to a Poisson process and are processed (parking fee collected) at a uniform deterministic rate at a single station. The mean arrival rate is 4 veh/min and the processing rate is 5 veh/min. Determine the average length of queue, the average time spend in the system and the average waiting time in the queue. If the rate at which vehicles are processed became exponentially distributed (instead of deterministic) with a mean processing rate of 5 veh/min, what would be the average length of queue, the average time spent in the system, and the average waiting time in the queue?

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