probability modeling M

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A self-serve srvice station has two pumps. Suppose cars enter the station at an exponential rate lamda. this means that the times between entries are i.i.d exponential random variable with common rate lamda > 0. people serve themselves independtly at an exponential rate u for each pump. We assume that the service times and the entry times are independent. (a) if both pumps are currently busy what is the probability that another car will enter the station before either of pumps become free? (b) If Customer A is at Pump 1, Customer B is at Pump 2, and customer C now enters (and there are no other customers in the station) then what is the probability that B leaves C?

Industrial Engineering

Mathematics

Statistics

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