Mathematics · Probability and Queueing Theory
Consider a petrol pump with a single dispensing unit. Customers arrive according to a Poisson process with rate λ = 1 per minute. An arriving customer enters only if there are 2 or fewer customers in the pump, otherwise they leave (maximum capacity is 3 customers). Service times are independent exponential random variables with mean 1 2 minutes. If X denotes the number of customers in the long run, then the expected value E(X) is:
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