Question: Empty Taxis pass by a street corner at a Poisson
Empty Taxis pass by a street corner at a Poisson rate of two per minute and pick up passenger if one is waiting there. Passengers arrive at the street corner at a Poisson rate of one per minute and wait for a taxi only if there are less than four persons waiting; otherwise they leave and never return. Penelope arrives at the street corner at a given time. Find her expected waiting time, given that she joins the queue. Assume that the process is already in steady-state.
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