Assuming that there is no request currently, what is the val…

Assuming that there is no request currently, what is the value of the expected time in minutes until the company receives at least one request of both Ride-X and Ride-Pool? Show your work.  (Hint: It would be the expected time until a request is received and then the expected time until a request of the different type from the first arrival is received.)

Section G (Questions 25 ~ 27): Taxis looking for customers a…

Section G (Questions 25 ~ 27): Taxis looking for customers arrive at a taxi station as a Poisson process with rate 1 per minute, while customers looking for taxis arrive as a Poisson process with rate 1.25 per minute. Suppose taxis will wait, no matter how many taxis are in line before them. However, customers who arrive to find 2 other customers in line go away immediately.  We will set up a Markov chain with states {2, 1, 0, -1, -2, ….} as states. State 2 means two customers waiting at the taxi station; state 1 means one customer waiting at the taxi station; state -1 means one taxi waiting at the taxi station; state -2 means two taxis waiting at the taxi station and so on.