Section E (Questions 15 ~ 18): A Ridepool driver has a car f…

Section E (Questions 15 ~ 18): A Ridepool driver has a car for a total capacity of 3 passengers and Ridepool customers send requests in a group of 1 or 2 passengers. Assume that this is the only Ridepool driver available in the area. To analyze the performance of her business, the driver models it as a CTMC with X(t) = (n1, n2) where n1 = the number of requests of a group size 1 that are accepted and currently being served and n2 =the number of requests of a group size 2 that are accepted and currently being served. Then its rate diagram is given below:    All rates in the diagram are hourly rates. The stationary distribution of the CTMC is given below: 

Now suppose that the arrival of Ride-X requests can be model…

Now suppose that the arrival of Ride-X requests can be modeled as a non-homogeneous Poisson process. The arrival rate from 8 am to 5 pm is studied for many days. The following graph shows hourly arrival rates from 8 am to 5 pm.     We want to find the probability that the company receives less than 5 Ride-X requests from 8 am to 5 pm and the probability is