STOCHASTIC PROCESS

QUESTION 1

Suppose that you arrive at a petrol station with only one pump to find that 10 cars are on the queue and one is being served. Assuming that you join the end of the queue and that the service time is exponentially distributed with mean three minutes. What is the expected time you will spend at the petrol station?

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THIS IS AN EXAMPLE WITH SOLUTIONS

QUESTION 1 Suppose that you arrive at a bank with 3 ATMs to nd 50 other customers, 3 being busy at the ATMS and the other 47 waiting. Assuming that you join the end of the queue and that the service time at each ATM is exponentially distributed with mean 2 minutes. What is the expected time you will spend in the system?